id	sid	tid	token	lemma	pos
m-806	1	1	ijo	ijo	PROPN
m-806	1	2	international	international	PROPN
m-806	1	3	journal	journal	PROPN
m-806	1	4	of	of	ADP
m-806	1	5	mathematics	mathematics	PROPN
m-806	1	6	(	(	PUNCT
m-806	1	7	issn	issn	PROPN
m-806	1	8	:	:	PUNCT
m-806	1	9	2992	2992	NUM
m-806	1	10	-	-	SYM
m-806	1	11	4421	4421	NUM
m-806	1	12	)	)	PUNCT
m-806	2	1	i.u	i.u	PROPN
m-806	2	2	.	.	PROPN
m-806	2	3	udo	udo	PROPN
m-806	2	4	-	-	PROPN
m-806	2	5	akpan1	akpan1	ADJ
m-806	2	6	*	*	PUNCT
m-806	2	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	2	8	volume	volume	NOUN
m-806	2	9	07	07	NUM
m-806	2	10	issue	issue	NOUN
m-806	2	11	02	02	NUM
m-806	2	12	||	||	NUM
m-806	2	13	february	february	PROPN
m-806	2	14	,	,	PUNCT
m-806	2	15	2024	2024	NUM
m-806	2	16	||	||	NOUN
m-806	3	1	on	on	ADP
m-806	3	2	a	a	DET
m-806	3	3	-	-	PUNCT
m-806	3	4	two	two	NUM
m-806	3	5	-	-	PUNCT
m-806	3	6	parameter	parameter	NOUN
m-806	3	7	dynamic	dynamic	ADJ
m-806	3	8	buckling	buckling	NOUN
m-806	3	9	of	of	ADP
m-806	3	10	a	a	DET
m-806	3	11	viscously	viscously	ADV
m-806	3	12	damped	damp	VERB
m-806	3	13	but	but	CCONJ
m-806	3	14	clamped	clamp	VERB
m-806	3	15	column	column	NOUN
m-806	3	16	stressed	stress	VERB
m-806	3	17	by	by	ADP
m-806	3	18	a	a	DET
m-806	3	19	step	step	NOUN
m-806	3	20	load	load	NOUN
m-806	3	21	on	on	ADP
m-806	3	22	a	a	DET
m-806	3	23	-	-	PUNCT
m-806	3	24	two	two	NUM
m-806	3	25	-	-	PUNCT
m-806	3	26	parameter	parameter	NOUN
m-806	3	27	dynamic	dynamic	ADJ
m-806	3	28	buckling	buckling	NOUN
m-806	3	29	of	of	ADP
m-806	3	30	a	a	DET
m-806	3	31	viscously	viscously	ADV
m-806	3	32	damped	damp	VERB
m-806	3	33	but	but	CCONJ
m-806	3	34	clamped	clamp	VERB
m-806	3	35	column	column	NOUN
m-806	3	36	stressed	stress	VERB
m-806	3	37	by	by	ADP
m-806	3	38	a	a	DET
m-806	3	39	step	step	NOUN
m-806	3	40	load	load	NOUN
m-806	3	41	i.u	i.u	PROPN
m-806	3	42	.	.	PROPN
m-806	3	43	udo	udo	PROPN
m-806	3	44	-	-	PUNCT
m-806	3	45	akpan1	akpan1	PROPN
m-806	3	46	and	and	CCONJ
m-806	3	47	j.	j.	PROPN
m-806	3	48	u.	u.	PROPN
m-806	3	49	chukwuchekwa2	chukwuchekwa2	PROPN
m-806	3	50	1department	1department	NUM
m-806	3	51	of	of	ADP
m-806	3	52	mathematics	mathematic	NOUN
m-806	3	53	and	and	CCONJ
m-806	3	54	statistics	statistic	NOUN
m-806	3	55	,	,	PUNCT
m-806	3	56	university	university	NOUN
m-806	3	57	of	of	ADP
m-806	3	58	port	port	PROPN
m-806	3	59	harcourt	harcourt	PROPN
m-806	3	60	,	,	PUNCT
m-806	3	61	port	port	NOUN
m-806	3	62	harcourt	harcourt	PROPN
m-806	3	63	,	,	PUNCT
m-806	3	64	rivers	river	NOUN
m-806	3	65	state	state	PROPN
m-806	3	66	,	,	PUNCT
m-806	3	67	nigeria	nigeria	PROPN
m-806	3	68	.	.	PUNCT
m-806	4	1	2department	2department	NUM
m-806	4	2	of	of	ADP
m-806	4	3	mathematics	mathematic	NOUN
m-806	4	4	,	,	PUNCT
m-806	4	5	federal	federal	ADJ
m-806	4	6	university	university	PROPN
m-806	4	7	of	of	ADP
m-806	4	8	technology	technology	PROPN
m-806	4	9	,	,	PUNCT
m-806	4	10	owerri	owerri	PROPN
m-806	4	11	,	,	PUNCT
m-806	4	12	imo	imo	PROPN
m-806	4	13	state	state	PROPN
m-806	4	14	,	,	PUNCT
m-806	4	15	nigeria	nigeria	PROPN
m-806	4	16	.	.	PUNCT
m-806	5	1	abstract	abstract	ADJ
m-806	5	2	in	in	ADP
m-806	5	3	this	this	DET
m-806	5	4	investigation	investigation	NOUN
m-806	5	5	,	,	PUNCT
m-806	5	6	we	we	PRON
m-806	5	7	extend	extend	VERB
m-806	5	8	our	our	PRON
m-806	5	9	search	search	NOUN
m-806	5	10	on	on	ADP
m-806	5	11	the	the	DET
m-806	5	12	dynamic	dynamic	ADJ
m-806	5	13	buckling	buckling	NOUN
m-806	5	14	loads	load	NOUN
m-806	5	15	of	of	ADP
m-806	5	16	some	some	DET
m-806	5	17	elastic	elastic	ADJ
m-806	5	18	structures	structure	NOUN
m-806	5	19	to	to	ADP
m-806	5	20	that	that	PRON
m-806	5	21	of	of	ADP
m-806	5	22	a	a	DET
m-806	5	23	clamped	clamp	VERB
m-806	5	24	column	column	NOUN
m-806	5	25	lying	lie	VERB
m-806	5	26	on	on	ADP
m-806	5	27	a	a	DET
m-806	5	28	nonlinear	nonlinear	ADJ
m-806	5	29	(	(	PUNCT
m-806	5	30	cubic	cubic	ADJ
m-806	5	31	)	)	PUNCT
m-806	5	32	elastic	elastic	ADJ
m-806	5	33	foundation	foundation	NOUN
m-806	5	34	but	but	CCONJ
m-806	5	35	impacted	impact	VERB
m-806	5	36	upon	upon	SCONJ
m-806	5	37	axially	axially	ADV
m-806	5	38	by	by	ADP
m-806	5	39	a	a	DET
m-806	5	40	step	step	NOUN
m-806	5	41	load	load	NOUN
m-806	5	42	.	.	PUNCT
m-806	6	1	in	in	ADP
m-806	6	2	order	order	NOUN
m-806	6	3	to	to	PART
m-806	6	4	ensure	ensure	VERB
m-806	6	5	a	a	DET
m-806	6	6	uniformly	uniformly	ADV
m-806	6	7	valid	valid	ADJ
m-806	6	8	solution	solution	NOUN
m-806	6	9	,	,	PUNCT
m-806	6	10	we	we	PRON
m-806	6	11	employ	employ	VERB
m-806	6	12	multi	multi	ADJ
m-806	6	13	–	–	PUNCT
m-806	6	14	scaling	scale	VERB
m-806	6	15	two	two	NUM
m-806	6	16	–	–	PUNCT
m-806	6	17	timing	time	VERB
m-806	6	18	regular	regular	ADJ
m-806	6	19	perturbation	perturbation	NOUN
m-806	6	20	procedures	procedure	NOUN
m-806	6	21	in	in	ADP
m-806	6	22	asymptotic	asymptotic	ADJ
m-806	6	23	expansions	expansion	NOUN
m-806	6	24	of	of	ADP
m-806	6	25	the	the	DET
m-806	6	26	variables	variable	NOUN
m-806	6	27	.	.	PUNCT
m-806	7	1	it	it	PRON
m-806	7	2	is	be	AUX
m-806	7	3	shown	show	VERB
m-806	7	4	that	that	SCONJ
m-806	7	5	(	(	PUNCT
m-806	7	6	a	a	X
m-806	7	7	)	)	PUNCT
m-806	7	8	clamped	clamp	VERB
m-806	7	9	columns	column	NOUN
m-806	7	10	buckle	buckle	NOUN
m-806	7	11	at	at	ADP
m-806	7	12	higher	high	ADJ
m-806	7	13	buckling	buckling	NOUN
m-806	7	14	loads	load	NOUN
m-806	7	15	than	than	SCONJ
m-806	7	16	columns	column	NOUN
m-806	7	17	with	with	ADP
m-806	7	18	simply	simply	ADV
m-806	7	19	–	–	PUNCT
m-806	7	20	supported	support	VERB
m-806	7	21	ends	end	VERB
m-806	7	22	irrespective	irrespective	ADV
m-806	7	23	of	of	ADP
m-806	7	24	whether	whether	SCONJ
m-806	7	25	the	the	DET
m-806	7	26	columns	column	NOUN
m-806	7	27	are	be	AUX
m-806	7	28	loaded	load	VERB
m-806	7	29	statically	statically	ADV
m-806	7	30	or	or	CCONJ
m-806	7	31	dynamically	dynamically	ADV
m-806	7	32	and	and	CCONJ
m-806	7	33	whether	whether	SCONJ
m-806	7	34	damped	damp	VERB
m-806	7	35	or	or	CCONJ
m-806	7	36	undamped	undampe	VERB
m-806	7	37	,	,	PUNCT
m-806	7	38	(	(	PUNCT
m-806	7	39	b	b	NOUN
m-806	7	40	)	)	PUNCT
m-806	7	41	specifically	specifically	ADV
m-806	7	42	,	,	PUNCT
m-806	7	43	the	the	DET
m-806	7	44	inequalities	inequality	NOUN
m-806	7	45	satisfied	satisfy	VERB
m-806	7	46	by	by	ADP
m-806	7	47	the	the	DET
m-806	7	48	static	static	ADJ
m-806	7	49	buckling	buckling	NOUN
m-806	7	50	load	load	NOUN
m-806	7	51	�	�	PROPN
m-806	7	52	�	�	PROPN
m-806	7	53	and	and	CCONJ
m-806	7	54	dynamic	dynamic	ADJ
m-806	7	55	buckling	buckling	NOUN
m-806	7	56	load	load	NOUN
m-806	7	57	�	�	NOUN
m-806	7	58	�	�	PROPN
m-806	7	59	in	in	ADP
m-806	7	60	the	the	DET
m-806	7	61	clamped	clamp	VERB
m-806	7	62	case	case	NOUN
m-806	7	63	are	be	AUX
m-806	7	64	respectively	respectively	ADV
m-806	7	65	given	give	VERB
m-806	7	66	as	as	ADP
m-806	7	67	1	1	NUM
m-806	7	68	<	<	X
m-806	7	69	�	�	PROPN
m-806	7	70	�	�	PROPN
m-806	7	71	<	<	X
m-806	7	72	2.125	2.125	NUM
m-806	7	73	and	and	CCONJ
m-806	7	74	1	1	NUM
m-806	7	75	<	<	X
m-806	7	76	�	�	PROPN
m-806	7	77	�	�	PROPN
m-806	7	78	<	<	X
m-806	7	79	2.125	2.125	NUM
m-806	7	80	as	as	ADP
m-806	7	81	against	against	ADP
m-806	7	82	0	0	NUM
m-806	7	83	<	<	X
m-806	7	84	�	�	PROPN
m-806	7	85	�	�	PROPN
m-806	7	86	<	<	X
m-806	7	87	1	1	NUM
m-806	7	88	and	and	CCONJ
m-806	7	89	0	0	NUM
m-806	7	90	<	<	X
m-806	7	91	�	�	PROPN
m-806	7	92	�	�	PROPN
m-806	7	93	<	<	X
m-806	7	94	1	1	NUM
m-806	7	95	for	for	ADP
m-806	7	96	simply	simply	ADV
m-806	7	97	–	–	PUNCT
m-806	7	98	supported	support	VERB
m-806	7	99	end	end	NOUN
m-806	7	100	conditions	condition	NOUN
m-806	7	101	,	,	PUNCT
m-806	7	102	(	(	PUNCT
m-806	7	103	c	c	X
m-806	7	104	)	)	PUNCT
m-806	7	105	at	at	ADP
m-806	7	106	low	low	ADJ
m-806	7	107	values	value	NOUN
m-806	7	108	of	of	ADP
m-806	7	109	the	the	DET
m-806	7	110	static	static	ADJ
m-806	7	111	buckling	buckling	NOUN
m-806	7	112	load	load	NOUN
m-806	7	113	�	�	PROPN
m-806	7	114	�	�	PROPN
m-806	7	115	,	,	PUNCT
m-806	7	116	there	there	PRON
m-806	7	117	is	be	VERB
m-806	7	118	no	no	DET
m-806	7	119	appreciable	appreciable	ADJ
m-806	7	120	change	change	NOUN
m-806	7	121	in	in	ADP
m-806	7	122	the	the	DET
m-806	7	123	values	value	NOUN
m-806	7	124	of	of	ADP
m-806	7	125	the	the	DET
m-806	7	126	dynamic	dynamic	ADJ
m-806	7	127	buckling	buckling	NOUN
m-806	7	128	load	load	NOUN
m-806	7	129	�	�	NOUN
m-806	7	130	�	�	PROPN
m-806	7	131	but	but	CCONJ
m-806	7	132	at	at	ADP
m-806	7	133	higher	high	ADJ
m-806	7	134	values	value	NOUN
m-806	7	135	of	of	ADP
m-806	7	136	�	�	PROPN
m-806	7	137	�	�	PROPN
m-806	7	138	,	,	PUNCT
m-806	7	139	�	�	PROPN
m-806	7	140	�	�	PROPN
m-806	7	141	increases	increase	VERB
m-806	7	142	sharply	sharply	ADV
m-806	7	143	with	with	ADP
m-806	7	144	increased	increase	VERB
m-806	7	145	static	static	ADJ
m-806	7	146	buckling	buckling	NOUN
m-806	7	147	load	load	NOUN
m-806	7	148	�	�	PROPN
m-806	7	149	�	�	PROPN
m-806	7	150	.	.	PUNCT
m-806	8	1	however	however	ADV
m-806	8	2	,	,	PUNCT
m-806	8	3	the	the	DET
m-806	8	4	increase	increase	NOUN
m-806	8	5	seems	seem	VERB
m-806	8	6	to	to	PART
m-806	8	7	decrease	decrease	VERB
m-806	8	8	with	with	ADP
m-806	8	9	increased	increase	VERB
m-806	8	10	damping	damp	VERB
m-806	8	11	.	.	PUNCT
m-806	9	1	we	we	PRON
m-806	9	2	are	be	AUX
m-806	9	3	able	able	ADJ
m-806	9	4	to	to	PART
m-806	9	5	mathematically	mathematically	ADV
m-806	9	6	relate	relate	VERB
m-806	9	7	the	the	DET
m-806	9	8	dynamic	dynamic	ADJ
m-806	9	9	buckling	buckling	NOUN
m-806	9	10	load	load	NOUN
m-806	9	11	�	�	NOUN
m-806	9	12	�	�	PROPN
m-806	9	13	to	to	ADP
m-806	9	14	the	the	DET
m-806	9	15	static	static	ADJ
m-806	9	16	buckling	buckling	NOUN
m-806	9	17	load	load	NOUN
m-806	9	18	�	�	PROPN
m-806	9	19	�	�	PROPN
m-806	9	20	and	and	CCONJ
m-806	9	21	thereby	thereby	ADV
m-806	9	22	by	by	ADP
m-806	9	23	–	–	PUNCT
m-806	9	24	passing	pass	VERB
m-806	9	25	the	the	DET
m-806	9	26	labour	labour	NOUN
m-806	9	27	of	of	ADP
m-806	9	28	repeating	repeat	VERB
m-806	9	29	the	the	DET
m-806	9	30	entire	entire	ADJ
m-806	9	31	process	process	NOUN
m-806	9	32	for	for	ADP
m-806	9	33	different	different	ADJ
m-806	9	34	imperfection	imperfection	NOUN
m-806	9	35	parameters	parameter	NOUN
m-806	9	36	.	.	PUNCT
m-806	10	1	thus	thus	ADV
m-806	10	2	,	,	PUNCT
m-806	10	3	given	give	VERB
m-806	10	4	either	either	DET
m-806	10	5	�	�	PROPN
m-806	10	6	�	�	PROPN
m-806	10	7	or	or	CCONJ
m-806	10	8	�	�	PROPN
m-806	10	9	�	�	PROPN
m-806	10	10	,	,	PUNCT
m-806	10	11	we	we	PRON
m-806	10	12	can	can	AUX
m-806	10	13	predict	predict	VERB
m-806	10	14	either	either	DET
m-806	10	15	value	value	NOUN
m-806	10	16	without	without	ADP
m-806	10	17	the	the	DET
m-806	10	18	actual	actual	ADJ
m-806	10	19	knowledge	knowledge	NOUN
m-806	10	20	of	of	ADP
m-806	10	21	the	the	DET
m-806	10	22	size	size	NOUN
m-806	10	23	of	of	ADP
m-806	10	24	the	the	DET
m-806	10	25	small	small	ADJ
m-806	10	26	imperfection	imperfection	NOUN
m-806	10	27	parameter	parameter	NOUN
m-806	10	28	.	.	PUNCT
m-806	11	1	keywords	keyword	NOUN
m-806	11	2	:	:	PUNCT
m-806	11	3	dynamic	dynamic	ADJ
m-806	11	4	buckling	buckling	NOUN
m-806	11	5	,	,	PUNCT
m-806	11	6	viscously	viscously	ADV
m-806	11	7	damped	damp	VERB
m-806	11	8	clamped	clamp	VERB
m-806	11	9	column	column	NOUN
m-806	11	10	,	,	PUNCT
m-806	11	11	elastic	elastic	ADJ
m-806	11	12	structures	structure	NOUN
m-806	11	13	,	,	PUNCT
m-806	11	14	step	step	NOUN
m-806	11	15	load	load	NOUN
m-806	11	16	,	,	PUNCT
m-806	11	17	two	two	NUM
m-806	11	18	-	-	PUNCT
m-806	11	19	timing	timing	NOUN
m-806	11	20	perturbation	perturbation	NOUN
m-806	11	21	2010	2010	NUM
m-806	11	22	mathematical	mathematical	ADJ
m-806	11	23	subject	subject	ADJ
m-806	11	24	classification	classification	NOUN
m-806	11	25	:	:	PUNCT
m-806	11	26	74b20	74b20	NUM
m-806	11	27	,	,	PUNCT
m-806	11	28	74h10	74h10	NUM
m-806	11	29	,	,	PUNCT
m-806	11	30	34e10	34e10	NUM
m-806	11	31	1	1	NUM
m-806	11	32	.	.	PUNCT
m-806	12	1	introduction	introduction	NOUN
m-806	12	2	investigations	investigation	NOUN
m-806	12	3	into	into	ADP
m-806	12	4	the	the	DET
m-806	12	5	static	static	ADJ
m-806	12	6	or	or	CCONJ
m-806	12	7	dynamic	dynamic	ADJ
m-806	12	8	stability	stability	NOUN
m-806	12	9	(	(	PUNCT
m-806	12	10	or	or	CCONJ
m-806	12	11	otherwise	otherwise	ADV
m-806	12	12	)	)	PUNCT
m-806	12	13	of	of	ADP
m-806	12	14	columns	column	NOUN
m-806	12	15	(	(	PUNCT
m-806	12	16	finite	finite	NOUN
m-806	12	17	or	or	CCONJ
m-806	12	18	infinite	infinite	VERB
m-806	12	19	)	)	PUNCT
m-806	12	20	are	be	AUX
m-806	12	21	age	age	NOUN
m-806	12	22	old	old	ADJ
m-806	12	23	problems	problem	NOUN
m-806	12	24	that	that	PRON
m-806	12	25	have	have	AUX
m-806	12	26	been	be	AUX
m-806	12	27	embarked	embark	VERB
m-806	12	28	upon	upon	SCONJ
m-806	12	29	by	by	ADP
m-806	12	30	researchers	researcher	NOUN
m-806	12	31	for	for	ADP
m-806	12	32	some	some	DET
m-806	12	33	years	year	NOUN
m-806	12	34	now	now	ADV
m-806	12	35	.	.	PUNCT
m-806	13	1	as	as	SCONJ
m-806	13	2	observed	observe	VERB
m-806	13	3	by	by	ADP
m-806	13	4	[	[	X
m-806	13	5	1	1	NUM
m-806	13	6	]	]	PUNCT
m-806	13	7	and	and	CCONJ
m-806	13	8	[	[	X
m-806	13	9	2	2	NUM
m-806	13	10	]	]	PUNCT
m-806	13	11	,	,	PUNCT
m-806	13	12	buckling	buckling	NOUN
m-806	13	13	of	of	ADP
m-806	13	14	structures	structure	NOUN
m-806	13	15	is	be	AUX
m-806	13	16	one	one	NUM
m-806	13	17	of	of	ADP
m-806	13	18	the	the	DET
m-806	13	19	structural	structural	ADJ
m-806	13	20	instabilities	instability	NOUN
m-806	13	21	that	that	PRON
m-806	13	22	have	have	AUX
m-806	13	23	been	be	AUX
m-806	13	24	known	know	VERB
m-806	13	25	for	for	ADP
m-806	13	26	centuries	century	NOUN
m-806	13	27	ever	ever	ADV
m-806	13	28	since	since	SCONJ
m-806	13	29	the	the	DET
m-806	13	30	equation	equation	NOUN
m-806	13	31	to	to	PART
m-806	13	32	derive	derive	VERB
m-806	13	33	the	the	DET
m-806	13	34	critical	critical	ADJ
m-806	13	35	buckling	buckling	NOUN
m-806	13	36	of	of	ADP
m-806	13	37	a	a	DET
m-806	13	38	column	column	NOUN
m-806	13	39	was	be	AUX
m-806	13	40	derived	derive	VERB
m-806	13	41	by	by	ADP
m-806	13	42	leonhard	leonhard	PROPN
m-806	13	43	euler	euler	PROPN
m-806	14	1	[	[	X
m-806	14	2	3	3	NUM
m-806	14	3	]	]	PUNCT
m-806	14	4	.	.	PUNCT
m-806	15	1	as	as	ADP
m-806	15	2	a	a	DET
m-806	15	3	result	result	NOUN
m-806	15	4	of	of	ADP
m-806	15	5	this	this	PRON
m-806	15	6	,	,	PUNCT
m-806	15	7	previous	previous	ADJ
m-806	15	8	studies	study	NOUN
m-806	15	9	on	on	ADP
m-806	15	10	the	the	DET
m-806	15	11	subject	subject	NOUN
m-806	15	12	matter	matter	NOUN
m-806	15	13	are	be	AUX
m-806	15	14	indeed	indeed	ADV
m-806	15	15	enormous	enormous	ADJ
m-806	15	16	and	and	CCONJ
m-806	15	17	varied	varied	ADJ
m-806	15	18	,	,	PUNCT
m-806	15	19	and	and	CCONJ
m-806	15	20	include	include	VERB
m-806	15	21	investigations	investigation	NOUN
m-806	15	22	by	by	ADP
m-806	15	23	[	[	X
m-806	15	24	4]-[7	4]-[7	X
m-806	15	25	]	]	PUNCT
m-806	15	26	,	,	PUNCT
m-806	15	27	among	among	ADP
m-806	15	28	others	other	NOUN
m-806	15	29	.	.	PUNCT
m-806	16	1	we	we	PRON
m-806	16	2	must	must	AUX
m-806	16	3	stress	stress	VERB
m-806	16	4	that	that	SCONJ
m-806	16	5	columns	column	NOUN
m-806	16	6	,	,	PUNCT
m-806	16	7	are	be	AUX
m-806	16	8	in	in	ADP
m-806	16	9	themselves	themselves	PRON
m-806	16	10	,	,	PUNCT
m-806	16	11	indispensable	indispensable	ADJ
m-806	16	12	structural	structural	ADJ
m-806	16	13	materials	material	NOUN
m-806	16	14	and	and	CCONJ
m-806	16	15	their	their	PRON
m-806	16	16	utility	utility	NOUN
m-806	16	17	cuts	cut	VERB
m-806	16	18	across	across	ADP
m-806	16	19	all	all	DET
m-806	16	20	cultures	culture	NOUN
m-806	16	21	in	in	ADP
m-806	16	22	human	human	ADJ
m-806	16	23	history	history	NOUN
m-806	16	24	.	.	PUNCT
m-806	17	1	this	this	DET
m-806	17	2	investigation	investigation	NOUN
m-806	17	3	is	be	AUX
m-806	17	4	concerned	concern	VERB
m-806	17	5	with	with	ADP
m-806	17	6	analytical	analytical	ADJ
m-806	17	7	determination	determination	NOUN
m-806	17	8	of	of	ADP
m-806	17	9	the	the	DET
m-806	17	10	dynamic	dynamic	ADJ
m-806	17	11	buckling	buckling	NOUN
m-806	17	12	load	load	NOUN
m-806	17	13	of	of	ADP
m-806	17	14	a	a	DET
m-806	17	15	viscously	viscously	ADV
m-806	17	16	damped	damp	VERB
m-806	17	17	but	but	CCONJ
m-806	17	18	clamped	clamp	VERB
m-806	17	19	imperfect	imperfect	ADJ
m-806	17	20	column	column	NOUN
m-806	17	21	that	that	PRON
m-806	17	22	rests	rest	VERB
m-806	17	23	on	on	ADP
m-806	17	24	a	a	DET
m-806	17	25	nonlinear	nonlinear	ADJ
m-806	17	26	(	(	PUNCT
m-806	17	27	cubic	cubic	ADJ
m-806	17	28	)	)	PUNCT
m-806	17	29	elastic	elastic	ADJ
m-806	17	30	foundation	foundation	NOUN
m-806	17	31	,	,	PUNCT
m-806	17	32	where	where	SCONJ
m-806	17	33	the	the	DET
m-806	17	34	column	column	NOUN
m-806	17	35	is	be	AUX
m-806	17	36	struck	strike	VERB
m-806	17	37	by	by	ADP
m-806	17	38	a	a	DET
m-806	17	39	step	step	NOUN
m-806	17	40	load	load	NOUN
m-806	17	41	.	.	PUNCT
m-806	18	1	the	the	DET
m-806	18	2	viscous	viscous	ADJ
m-806	18	3	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	18	4	ijo	ijo	PROPN
m-806	18	5	journals	journal	NOUN
m-806	18	6	volume	volume	NOUN
m-806	18	7	07	07	NUM
m-806	18	8	|	|	ADV
m-806	18	9	issue	issue	NOUN
m-806	18	10	02	02	NUM
m-806	18	11	|	|	CCONJ
m-806	18	12	february	february	PROPN
m-806	18	13	2024	2024	NUM
m-806	18	14	|	|	ADV
m-806	18	15	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	18	16	1	1	NUM
m-806	18	17	ijo	ijo	PROPN
m-806	18	18	international	international	ADJ
m-806	18	19	journal	journal	PROPN
m-806	18	20	of	of	ADP
m-806	18	21	mathematics	mathematics	PROPN
m-806	18	22	(	(	PUNCT
m-806	18	23	issn	issn	PROPN
m-806	18	24	:	:	PUNCT
m-806	18	25	2992	2992	NUM
m-806	18	26	-	-	SYM
m-806	18	27	4421	4421	NUM
m-806	18	28	)	)	PUNCT
m-806	19	1	i.u	i.u	PROPN
m-806	19	2	.	.	PROPN
m-806	19	3	udo	udo	PROPN
m-806	19	4	-	-	PROPN
m-806	19	5	akpan1	akpan1	ADJ
m-806	19	6	*	*	PUNCT
m-806	19	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	19	8	volume	volume	NOUN
m-806	19	9	07	07	NUM
m-806	19	10	issue	issue	NOUN
m-806	19	11	02	02	NUM
m-806	19	12	||	||	NUM
m-806	19	13	february	february	PROPN
m-806	19	14	,	,	PUNCT
m-806	19	15	2024	2024	NUM
m-806	19	16	||	||	NOUN
m-806	20	1	on	on	ADP
m-806	20	2	a	a	DET
m-806	20	3	-	-	PUNCT
m-806	20	4	two	two	NUM
m-806	20	5	-	-	PUNCT
m-806	20	6	parameter	parameter	NOUN
m-806	20	7	dynamic	dynamic	ADJ
m-806	20	8	buckling	buckling	NOUN
m-806	20	9	of	of	ADP
m-806	20	10	a	a	DET
m-806	20	11	viscously	viscously	ADV
m-806	20	12	damped	damp	VERB
m-806	20	13	but	but	CCONJ
m-806	20	14	clamped	clamp	VERB
m-806	20	15	column	column	NOUN
m-806	20	16	stressed	stress	VERB
m-806	20	17	by	by	ADP
m-806	20	18	a	a	DET
m-806	20	19	step	step	NOUN
m-806	20	20	load	load	NOUN
m-806	20	21	damping	damp	VERB
m-806	20	22	,	,	PUNCT
m-806	20	23	though	though	SCONJ
m-806	20	24	small	small	ADJ
m-806	20	25	in	in	ADP
m-806	20	26	magnitude	magnitude	NOUN
m-806	20	27	,	,	PUNCT
m-806	20	28	is	be	AUX
m-806	20	29	not	not	PART
m-806	20	30	in	in	ADP
m-806	20	31	any	any	DET
m-806	20	32	way	way	NOUN
m-806	20	33	related	relate	VERB
m-806	20	34	either	either	CCONJ
m-806	20	35	physically	physically	ADV
m-806	20	36	or	or	CCONJ
m-806	20	37	mathematically	mathematically	ADV
m-806	20	38	,	,	PUNCT
m-806	20	39	to	to	ADP
m-806	20	40	an	an	DET
m-806	20	41	equally	equally	ADV
m-806	20	42	small	small	ADJ
m-806	20	43	imperfection	imperfection	NOUN
m-806	20	44	that	that	PRON
m-806	20	45	is	be	AUX
m-806	20	46	stress	stress	NOUN
m-806	20	47	-	-	PUNCT
m-806	20	48	free	free	ADJ
m-806	20	49	and	and	CCONJ
m-806	20	50	twicedifferentiable	twicedifferentiable	ADJ
m-806	20	51	.	.	PUNCT
m-806	21	1	the	the	DET
m-806	21	2	formulation	formulation	NOUN
m-806	21	3	therefore	therefore	ADV
m-806	21	4	contains	contain	VERB
m-806	21	5	two	two	NUM
m-806	21	6	small	small	ADJ
m-806	21	7	but	but	CCONJ
m-806	21	8	dimensionally	dimensionally	ADV
m-806	21	9	independent	independent	ADJ
m-806	21	10	parameters	parameter	NOUN
m-806	21	11	upon	upon	SCONJ
m-806	21	12	which	which	PRON
m-806	21	13	asymptotic	asymptotic	ADJ
m-806	21	14	expansions	expansion	NOUN
m-806	21	15	are	be	AUX
m-806	21	16	initiated	initiate	VERB
m-806	21	17	using	use	VERB
m-806	21	18	a	a	DET
m-806	21	19	twotiming	twotime	VERB
m-806	21	20	multi	multi	ADJ
m-806	21	21	-	-	ADJ
m-806	21	22	scaling	scaling	ADJ
m-806	21	23	perturbation	perturbation	NOUN
m-806	21	24	procedure	procedure	NOUN
m-806	21	25	.	.	PUNCT
m-806	22	1	the	the	DET
m-806	22	2	analysis	analysis	NOUN
m-806	22	3	contained	contain	VERB
m-806	22	4	here	here	ADV
m-806	22	5	is	be	AUX
m-806	22	6	an	an	DET
m-806	22	7	extension	extension	NOUN
m-806	22	8	of	of	ADP
m-806	22	9	a	a	DET
m-806	22	10	similar	similar	ADJ
m-806	22	11	study	study	NOUN
m-806	22	12	espoused	espouse	VERB
m-806	22	13	by	by	ADP
m-806	22	14	[	[	X
m-806	22	15	8	8	NUM
m-806	22	16	]	]	PUNCT
m-806	22	17	,	,	PUNCT
m-806	22	18	where	where	SCONJ
m-806	22	19	,	,	PUNCT
m-806	22	20	in	in	ADP
m-806	22	21	that	that	DET
m-806	22	22	study	study	NOUN
m-806	22	23	,	,	PUNCT
m-806	22	24	damping	damp	VERB
m-806	22	25	was	be	AUX
m-806	22	26	taken	take	VERB
m-806	22	27	to	to	PART
m-806	22	28	be	be	AUX
m-806	22	29	related	relate	VERB
m-806	22	30	in	in	ADP
m-806	22	31	some	some	DET
m-806	22	32	way	way	NOUN
m-806	22	33	,	,	PUNCT
m-806	22	34	to	to	ADP
m-806	22	35	the	the	DET
m-806	22	36	imperfection	imperfection	NOUN
m-806	22	37	�	�	PROPN
m-806	22	38	�	�	PROPN
m-806	22	39	(	(	PUNCT
m-806	22	40	�	�	PROPN
m-806	22	41	)	)	PUNCT
m-806	22	42	,	,	PUNCT
m-806	22	43	so	so	SCONJ
m-806	22	44	that	that	SCONJ
m-806	22	45	once	once	SCONJ
m-806	22	46	the	the	DET
m-806	22	47	imperfection	imperfection	NOUN
m-806	22	48	was	be	AUX
m-806	22	49	fixed	fix	VERB
m-806	22	50	,	,	PUNCT
m-806	22	51	the	the	DET
m-806	22	52	damping	damp	VERB
m-806	22	53	was	be	AUX
m-806	22	54	equally	equally	ADV
m-806	22	55	fixed	fix	VERB
m-806	22	56	.	.	PUNCT
m-806	23	1	however	however	ADV
m-806	23	2	,	,	PUNCT
m-806	23	3	we	we	PRON
m-806	23	4	note	note	VERB
m-806	23	5	,	,	PUNCT
m-806	23	6	from	from	ADP
m-806	23	7	physical	physical	ADJ
m-806	23	8	reasoning	reasoning	NOUN
m-806	23	9	,	,	PUNCT
m-806	23	10	that	that	SCONJ
m-806	23	11	damping	damp	VERB
m-806	23	12	need	need	VERB
m-806	23	13	not	not	PART
m-806	23	14	in	in	ADP
m-806	23	15	any	any	DET
m-806	23	16	way	way	NOUN
m-806	23	17	,	,	PUNCT
m-806	23	18	be	be	AUX
m-806	23	19	related	relate	VERB
m-806	23	20	to	to	ADP
m-806	23	21	the	the	DET
m-806	23	22	imperfection	imperfection	NOUN
m-806	23	23	in	in	ADP
m-806	23	24	all	all	DET
m-806	23	25	probabilities	probability	NOUN
m-806	23	26	.	.	PUNCT
m-806	24	1	similar	similar	ADJ
m-806	24	2	studies	study	NOUN
m-806	24	3	were	be	AUX
m-806	24	4	done	do	VERB
m-806	24	5	by	by	ADP
m-806	24	6	[	[	X
m-806	24	7	9]-[12	9]-[12	NOUN
m-806	24	8	]	]	PUNCT
m-806	24	9	,	,	PUNCT
m-806	24	10	among	among	ADP
m-806	24	11	others	other	NOUN
m-806	24	12	.	.	PUNCT
m-806	25	1	apart	apart	ADV
m-806	25	2	from	from	ADP
m-806	25	3	addressing	address	VERB
m-806	25	4	the	the	DET
m-806	25	5	phenomenon	phenomenon	NOUN
m-806	25	6	of	of	ADP
m-806	25	7	viscous	viscous	ADJ
m-806	25	8	damping	damping	NOUN
m-806	25	9	in	in	ADP
m-806	25	10	a	a	DET
m-806	25	11	special	special	ADJ
m-806	25	12	fashion	fashion	NOUN
m-806	25	13	,	,	PUNCT
m-806	25	14	this	this	DET
m-806	25	15	investigation	investigation	NOUN
m-806	25	16	is	be	AUX
m-806	25	17	related	relate	VERB
m-806	25	18	,	,	PUNCT
m-806	25	19	in	in	ADP
m-806	25	20	spirit	spirit	NOUN
m-806	25	21	,	,	PUNCT
m-806	25	22	to	to	ADP
m-806	25	23	similar	similar	ADJ
m-806	25	24	studies	study	NOUN
m-806	25	25	by	by	ADP
m-806	25	26	[	[	X
m-806	25	27	13]-[25	13]-[25	ADP
m-806	25	28	]	]	X
m-806	25	29	.	.	PUNCT
m-806	26	1	2	2	X
m-806	26	2	.	.	X
m-806	26	3	formulation	formulation	NOUN
m-806	26	4	of	of	ADP
m-806	26	5	the	the	DET
m-806	26	6	problem	problem	NOUN
m-806	26	7	as	as	ADP
m-806	26	8	in	in	ADP
m-806	26	9	[	[	X
m-806	26	10	6	6	NUM
m-806	26	11	]	]	PUNCT
m-806	26	12	,	,	PUNCT
m-806	26	13	the	the	DET
m-806	26	14	dimensional	dimensional	ADJ
m-806	26	15	differential	differential	ADJ
m-806	26	16	equation	equation	NOUN
m-806	26	17	satisfied	satisfy	VERB
m-806	26	18	by	by	ADP
m-806	26	19	the	the	DET
m-806	26	20	deflection	deflection	NOUN
m-806	26	21	�	�	PROPN
m-806	26	22	(	(	PUNCT
m-806	26	23	�	�	PROPN
m-806	26	24	,	,	PUNCT
m-806	26	25	�	�	PROPN
m-806	26	26	)	)	PUNCT
m-806	26	27	of	of	ADP
m-806	26	28	a	a	DET
m-806	26	29	finite	finite	NOUN
m-806	26	30	viscously	viscously	ADV
m-806	26	31	damped	damp	VERB
m-806	26	32	column	column	NOUN
m-806	26	33	lying	lie	VERB
m-806	26	34	on	on	ADP
m-806	26	35	a	a	DET
m-806	26	36	nonlinear	nonlinear	ADJ
m-806	26	37	(	(	PUNCT
m-806	26	38	cubic	cubic	ADJ
m-806	26	39	)	)	PUNCT
m-806	26	40	elastic	elastic	ADJ
m-806	26	41	foundation	foundation	NOUN
m-806	26	42	but	but	CCONJ
m-806	26	43	struck	strike	VERB
m-806	26	44	by	by	ADP
m-806	26	45	a	a	DET
m-806	26	46	load	load	NOUN
m-806	26	47	�	�	PROPN
m-806	26	48	(	(	PUNCT
m-806	26	49	�	�	PROPN
m-806	26	50	)	)	PUNCT
m-806	26	51	is	be	AUX
m-806	26	52	�	�	PROPN
m-806	26	53	�	�	PROPN
m-806	26	54	�	�	PROPN
m-806	26	55	,	,	PUNCT
m-806	26	56	�	�	PROPN
m-806	26	57	�	�	PROPN
m-806	26	58	+	+	SYM
m-806	26	59	�	�	PROPN
m-806	26	60	�	�	PROPN
m-806	26	61	,	,	PUNCT
m-806	26	62	�	�	PROPN
m-806	26	63	+	+	SYM
m-806	26	64	�	�	PROPN
m-806	26	65	�	�	PROPN
m-806	26	66	�	�	PROPN
m-806	26	67	,	,	PUNCT
m-806	26	68	�	�	PROPN
m-806	26	69	�	�	PROPN
m-806	26	70	�	�	PROPN
m-806	26	71	�	�	PROPN
m-806	26	72	+	+	CCONJ
m-806	26	73	2	2	NUM
m-806	26	74	�	�	PROPN
m-806	26	75	(	(	PUNCT
m-806	26	76	�	�	NOUN
m-806	26	77	)	)	PUNCT
m-806	26	78	�	�	PROPN
m-806	26	79	,	,	PUNCT
m-806	26	80	�	�	PROPN
m-806	26	81	�	�	PROPN
m-806	26	82	+	+	SYM
m-806	26	83	�	�	PROPN
m-806	26	84	�	�	PROPN
m-806	26	85	�	�	PROPN
m-806	26	86	−	−	PROPN
m-806	26	87	�	�	PROPN
m-806	26	88	�	�	PROPN
m-806	26	89	�	�	PROPN
m-806	26	90	�	�	PROPN
m-806	26	91	�	�	PROPN
m-806	26	92	=	=	PUNCT
m-806	26	93	−2	−2	PROPN
m-806	26	94	�	�	PROPN
m-806	26	95	(	(	PUNCT
m-806	26	96	�	�	PROPN
m-806	26	97	)	)	PUNCT
m-806	26	98	�	�	PROPN
m-806	26	99	�	�	PROPN
m-806	26	100	�	�	PROPN
m-806	26	101	�	�	PROPN
m-806	26	102	�	�	PROPN
m-806	26	103	�	�	PROPN
m-806	26	104	�	�	PROPN
m-806	26	105	,	,	PUNCT
m-806	26	106	�	�	PROPN
m-806	26	107	>	>	X
m-806	26	108	0	0	NUM
m-806	26	109	,	,	PUNCT
m-806	26	110	(	(	PUNCT
m-806	26	111	2.1a	2.1a	NOUN
m-806	26	112	)	)	PUNCT
m-806	26	113	�	�	PROPN
m-806	26	114	(	(	PUNCT
m-806	26	115	�	�	PROPN
m-806	26	116	,	,	PUNCT
m-806	26	117	0	0	NUM
m-806	26	118	)	)	PUNCT
m-806	26	119	=	=	SYM
m-806	26	120	�	�	PROPN
m-806	26	121	,	,	PUNCT
m-806	26	122	�	�	PROPN
m-806	26	123	(	(	PUNCT
m-806	26	124	�	�	PROPN
m-806	26	125	,	,	PUNCT
m-806	26	126	0	0	NUM
m-806	26	127	)	)	PUNCT
m-806	26	128	=	=	SYM
m-806	26	129	0	0	NUM
m-806	26	130	,	,	PUNCT
m-806	26	131	(	(	PUNCT
m-806	26	132	2.1b	2.1b	NUM
m-806	26	133	)	)	PUNCT
m-806	26	134	�	�	PROPN
m-806	26	135	=	=	SYM
m-806	26	136	�	�	PROPN
m-806	26	137	,	,	PUNCT
m-806	26	138	�	�	PROPN
m-806	26	139	=	=	SYM
m-806	26	140	0	0	NUM
m-806	26	141	,	,	PUNCT
m-806	26	142	�	�	PROPN
m-806	26	143	�	�	PROPN
m-806	26	144	�	�	PROPN
m-806	26	145	=	=	SYM
m-806	26	146	0	0	NUM
m-806	26	147	,	,	PUNCT
m-806	26	148	π	π	PROPN
m-806	26	149	,	,	PUNCT
m-806	26	150	�	�	PROPN
m-806	26	151	>	>	X
m-806	26	152	0	0	NUM
m-806	27	1	(	(	PUNCT
m-806	27	2	2.1c	2.1c	NUM
m-806	27	3	)	)	PUNCT
m-806	27	4	here	here	ADV
m-806	27	5	,	,	PUNCT
m-806	27	6	�	�	PROPN
m-806	27	7	�	�	PROPN
m-806	27	8	is	be	AUX
m-806	27	9	the	the	DET
m-806	27	10	mass	mass	NOUN
m-806	27	11	per	per	ADP
m-806	27	12	unit	unit	NOUN
m-806	27	13	length	length	NOUN
m-806	27	14	,	,	PUNCT
m-806	27	15	�	�	PROPN
m-806	27	16	is	be	AUX
m-806	27	17	the	the	DET
m-806	27	18	damping	damp	VERB
m-806	27	19	coefficient	coefficient	NOUN
m-806	27	20	,	,	PUNCT
m-806	27	21	ei	ei	X
m-806	27	22	is	be	AUX
m-806	27	23	the	the	DET
m-806	27	24	bending	bend	VERB
m-806	27	25	stiffness	stiffness	NOUN
m-806	27	26	,	,	PUNCT
m-806	27	27	where	where	SCONJ
m-806	27	28	e	e	NOUN
m-806	27	29	and	and	CCONJ
m-806	27	30	i	i	PRON
m-806	27	31	are	be	AUX
m-806	27	32	the	the	DET
m-806	27	33	young	young	ADJ
m-806	27	34	’s	’s	PART
m-806	27	35	modulus	modulus	NOUN
m-806	27	36	and	and	CCONJ
m-806	27	37	the	the	DET
m-806	27	38	moment	moment	NOUN
m-806	27	39	of	of	ADP
m-806	27	40	inertia	inertia	NOUN
m-806	27	41	respectively	respectively	ADV
m-806	27	42	.	.	PUNCT
m-806	28	1	the	the	DET
m-806	28	2	nonlinear	nonlinear	ADJ
m-806	28	3	elastic	elastic	ADJ
m-806	28	4	foundation	foundation	NOUN
m-806	28	5	exerts	exert	VERB
m-806	28	6	a	a	DET
m-806	28	7	force	force	NOUN
m-806	28	8	per	per	ADP
m-806	28	9	unit	unit	NOUN
m-806	28	10	length	length	NOUN
m-806	28	11	given	give	VERB
m-806	28	12	by	by	ADP
m-806	28	13	�	�	PROPN
m-806	28	14	�	�	PROPN
m-806	28	15	�	�	PROPN
m-806	28	16	−	−	PROPN
m-806	28	17	�	�	PROPN
m-806	28	18	�	�	PROPN
m-806	28	19	�	�	PROPN
m-806	28	20	�	�	PROPN
m-806	28	21	�	�	PROPN
m-806	28	22	on	on	ADP
m-806	28	23	the	the	DET
m-806	28	24	column	column	NOUN
m-806	28	25	,	,	PUNCT
m-806	28	26	where	where	SCONJ
m-806	28	27	�	�	PROPN
m-806	28	28	�	�	PROPN
m-806	28	29	and	and	CCONJ
m-806	28	30	�	�	PROPN
m-806	28	31	�	�	PROPN
m-806	28	32	are	be	AUX
m-806	28	33	constants	constant	NOUN
m-806	28	34	such	such	ADJ
m-806	28	35	that	that	PRON
m-806	28	36	�	�	PROPN
m-806	28	37	�	�	PROPN
m-806	28	38	>	>	NOUN
m-806	28	39	0	0	NUM
m-806	28	40	,	,	PUNCT
m-806	28	41	�	�	PROPN
m-806	28	42	�	�	PROPN
m-806	28	43	>	>	NOUN
m-806	28	44	0	0	NUM
m-806	28	45	,	,	PUNCT
m-806	28	46	and	and	CCONJ
m-806	28	47	�	�	PROPN
m-806	28	48	is	be	AUX
m-806	28	49	the	the	DET
m-806	28	50	imperfection	imperfection	NOUN
m-806	28	51	-	-	PUNCT
m-806	28	52	sensitivity	sensitivity	NOUN
m-806	28	53	parameter	parameter	NOUN
m-806	28	54	which	which	PRON
m-806	28	55	is	be	AUX
m-806	28	56	such	such	ADJ
m-806	28	57	that	that	PRON
m-806	28	58	for	for	ADP
m-806	28	59	�	�	PROPN
m-806	28	60	=	=	SYM
m-806	28	61	1	1	NUM
m-806	28	62	,	,	PUNCT
m-806	28	63	the	the	DET
m-806	28	64	nonlinear	nonlinear	ADJ
m-806	28	65	elastic	elastic	ADJ
m-806	28	66	foundation	foundation	NOUN
m-806	28	67	is	be	AUX
m-806	28	68	said	say	VERB
m-806	28	69	to	to	ADP
m-806	28	70	“	"	PUNCT
m-806	28	71	softening	soften	VERB
m-806	28	72	”	"	PUNCT
m-806	28	73	,	,	PUNCT
m-806	28	74	whereas	whereas	SCONJ
m-806	28	75	for	for	ADP
m-806	28	76	�	�	PROPN
m-806	28	77	=	=	SYM
m-806	28	78	-1	-1	PROPN
m-806	28	79	,	,	PUNCT
m-806	28	80	the	the	DET
m-806	28	81	foundation	foundation	NOUN
m-806	28	82	is	be	AUX
m-806	28	83	said	say	VERB
m-806	28	84	to	to	PART
m-806	28	85	be	be	AUX
m-806	28	86	“	"	PUNCT
m-806	28	87	hardening	harden	VERB
m-806	28	88	”	"	PUNCT
m-806	28	89	.	.	PUNCT
m-806	29	1	we	we	PRON
m-806	29	2	have	have	AUX
m-806	29	3	here	here	ADV
m-806	29	4	excluded	exclude	VERB
m-806	29	5	all	all	DET
m-806	29	6	nonlinearities	nonlinearitie	NOUN
m-806	29	7	of	of	ADP
m-806	29	8	�	�	PROPN
m-806	29	9	(	(	PUNCT
m-806	29	10	�	�	PROPN
m-806	29	11	,	,	PUNCT
m-806	29	12	�	�	PROPN
m-806	29	13	)	)	PUNCT
m-806	29	14	higher	high	ADJ
m-806	29	15	than	than	ADP
m-806	29	16	the	the	DET
m-806	29	17	cubic	cubic	ADJ
m-806	29	18	and	and	CCONJ
m-806	29	19	have	have	AUX
m-806	29	20	also	also	ADV
m-806	29	21	excluded	exclude	VERB
m-806	29	22	all	all	DET
m-806	29	23	nonlinear	nonlinear	ADJ
m-806	29	24	derivatives	derivative	NOUN
m-806	29	25	of	of	ADP
m-806	29	26	�	�	PROPN
m-806	29	27	(	(	PUNCT
m-806	29	28	�	�	PROPN
m-806	29	29	,	,	PUNCT
m-806	29	30	�	�	PROPN
m-806	29	31	)	)	PUNCT
m-806	29	32	.	.	PUNCT
m-806	30	1	3	3	X
m-806	30	2	.	.	X
m-806	30	3	non	non	ADJ
m-806	30	4	-	-	NOUN
m-806	30	5	dimensionalization	dimensionalization	NOUN
m-806	30	6	of	of	ADP
m-806	30	7	the	the	DET
m-806	30	8	governing	govern	VERB
m-806	30	9	equation	equation	NOUN
m-806	30	10	we	we	PRON
m-806	30	11	shall	shall	AUX
m-806	30	12	non	non	ADJ
m-806	30	13	-	-	VERB
m-806	30	14	dimensionalize	dimensionalize	VERB
m-806	30	15	the	the	DET
m-806	30	16	equations	equation	NOUN
m-806	30	17	(	(	PUNCT
m-806	30	18	2.1a	2.1a	NOUN
m-806	30	19	c	c	NOUN
m-806	30	20	)	)	PUNCT
m-806	30	21	by	by	ADP
m-806	30	22	using	use	VERB
m-806	30	23	the	the	DET
m-806	30	24	following	follow	VERB
m-806	30	25	nondimensional	nondimensional	ADJ
m-806	30	26	quantities	quantity	NOUN
m-806	30	27	�	�	PROPN
m-806	30	28	=	=	SYM
m-806	30	29	�	�	PROPN
m-806	30	30	�	�	PROPN
m-806	30	31	�	�	PROPN
m-806	30	32	�	�	PROPN
m-806	30	33	�	�	PROPN
m-806	30	34	�	�	PROPN
m-806	30	35	�	�	PROPN
m-806	30	36	�	�	PROPN
m-806	30	37	�	�	PROPN
m-806	30	38	,	,	PUNCT
m-806	30	39	�	�	PROPN
m-806	30	40	=	=	SYM
m-806	30	41	�	�	PROPN
m-806	30	42	�	�	PROPN
m-806	30	43	�	�	PROPN
m-806	30	44	�	�	PROPN
m-806	30	45	�	�	PROPN
m-806	30	46	�	�	PROPN
m-806	30	47	�	�	PROPN
m-806	30	48	�	�	PROPN
m-806	30	49	�	�	PROPN
m-806	30	50	,	,	PUNCT
m-806	30	51	�	�	PROPN
m-806	30	52	�	�	PROPN
m-806	30	53	(	(	PUNCT
m-806	30	54	�	�	PROPN
m-806	30	55	)	)	PUNCT
m-806	30	56	=	=	SYM
m-806	30	57	�	�	PROPN
m-806	30	58	(	(	PUNCT
m-806	30	59	�	�	PROPN
m-806	30	60	)	)	PUNCT
m-806	30	61	2	2	NUM
m-806	30	62	(	(	PUNCT
m-806	30	63	�	�	PROPN
m-806	30	64	�	�	PROPN
m-806	30	65	�	�	PROPN
m-806	30	66	�	�	PROPN
m-806	30	67	)	)	PUNCT
m-806	30	68	�	�	PROPN
m-806	30	69	�	�	PROPN
m-806	30	70	,	,	PUNCT
m-806	30	71	�	�	PROPN
m-806	30	72	�	�	PROPN
m-806	30	73	�	�	PROPN
m-806	30	74	=	=	SYM
m-806	30	75	�	�	PROPN
m-806	30	76	�	�	PROPN
m-806	30	77	�	�	PROPN
m-806	30	78	�	�	PROPN
m-806	30	79	�	�	PROPN
m-806	30	80	�	�	PROPN
m-806	30	81	�	�	PROPN
m-806	30	82	�	�	PROPN
m-806	30	83	�	�	PROPN
m-806	30	84	�	�	PROPN
m-806	30	85	,	,	PUNCT
m-806	30	86	2	2	NUM
m-806	30	87	�	�	PROPN
m-806	30	88	=	=	SYM
m-806	30	89	�	�	PROPN
m-806	30	90	(	(	PUNCT
m-806	30	91	�	�	PROPN
m-806	30	92	�	�	PROPN
m-806	30	93	�	�	PROPN
m-806	30	94	�	�	PROPN
m-806	30	95	)	)	PUNCT
m-806	30	96	�	�	PROPN
m-806	30	97	�	�	PROPN
m-806	30	98	,	,	PUNCT
m-806	30	99	�	�	PROPN
m-806	30	100	=	=	SYM
m-806	30	101	�	�	PROPN
m-806	30	102	�	�	PROPN
m-806	30	103	�	�	PROPN
m-806	30	104	�	�	PROPN
m-806	30	105	�	�	PROPN
m-806	30	106	�	�	PROPN
m-806	30	107	�	�	PROPN
m-806	30	108	�	�	PROPN
m-806	30	109	�	�	PROPN
m-806	30	110	,	,	PUNCT
m-806	30	111	0	0	NUM
m-806	30	112	<	<	X
m-806	30	113	�	�	PROPN
m-806	30	114	<	<	X
m-806	30	115	<	<	X
m-806	30	116	1	1	NUM
m-806	30	117	,	,	PUNCT
m-806	30	118	0	0	NUM
m-806	30	119	<	<	X
m-806	30	120	δ	δ	NOUN
m-806	30	121	≪	≪	ADJ
m-806	30	122	1	1	NUM
m-806	30	123	;	;	PUNCT
m-806	30	124	0	0	NUM
m-806	30	125	<	<	X
m-806	30	126	�	�	PROPN
m-806	30	127	<	<	X
m-806	30	128	2.125	2.125	NUM
m-806	30	129	;	;	PUNCT
m-806	30	130	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	30	131	ijo	ijo	PROPN
m-806	30	132	journals	journal	NOUN
m-806	30	133	volume	volume	NOUN
m-806	30	134	07	07	NUM
m-806	30	135	|	|	ADV
m-806	30	136	issue	issue	NOUN
m-806	30	137	02	02	NUM
m-806	30	138	|	|	CCONJ
m-806	30	139	february	february	PROPN
m-806	30	140	2024	2024	NUM
m-806	30	141	|	|	ADV
m-806	30	142	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	30	143	2	2	NUM
m-806	30	144	ijo	ijo	PROPN
m-806	30	145	international	international	ADJ
m-806	30	146	journal	journal	PROPN
m-806	30	147	of	of	ADP
m-806	30	148	mathematics	mathematics	PROPN
m-806	30	149	(	(	PUNCT
m-806	30	150	issn	issn	PROPN
m-806	30	151	:	:	PUNCT
m-806	30	152	2992	2992	NUM
m-806	30	153	-	-	SYM
m-806	30	154	4421	4421	NUM
m-806	30	155	)	)	PUNCT
m-806	31	1	i.u	i.u	PROPN
m-806	31	2	.	.	PROPN
m-806	31	3	udo	udo	PROPN
m-806	31	4	-	-	PROPN
m-806	31	5	akpan1	akpan1	ADJ
m-806	31	6	*	*	PUNCT
m-806	31	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	31	8	volume	volume	NOUN
m-806	31	9	07	07	NUM
m-806	31	10	issue	issue	NOUN
m-806	31	11	02	02	NUM
m-806	31	12	||	||	NUM
m-806	31	13	february	february	PROPN
m-806	31	14	,	,	PUNCT
m-806	31	15	2024	2024	NUM
m-806	31	16	||	||	NOUN
m-806	32	1	on	on	ADP
m-806	32	2	a	a	DET
m-806	32	3	-	-	PUNCT
m-806	32	4	two	two	NUM
m-806	32	5	-	-	PUNCT
m-806	32	6	parameter	parameter	NOUN
m-806	32	7	dynamic	dynamic	ADJ
m-806	32	8	buckling	buckling	NOUN
m-806	32	9	of	of	ADP
m-806	32	10	a	a	DET
m-806	32	11	viscously	viscously	ADV
m-806	32	12	damped	damp	VERB
m-806	32	13	but	but	CCONJ
m-806	32	14	clamped	clamp	VERB
m-806	32	15	column	column	NOUN
m-806	32	16	stressed	stress	VERB
m-806	32	17	by	by	ADP
m-806	32	18	a	a	DET
m-806	32	19	step	step	NOUN
m-806	32	20	load	load	NOUN
m-806	32	21	on	on	ADP
m-806	32	22	introducing	introduce	VERB
m-806	32	23	these	these	DET
m-806	32	24	non	non	ADJ
m-806	32	25	-	-	ADJ
m-806	32	26	dimensional	dimensional	ADJ
m-806	32	27	quantities	quantity	NOUN
m-806	32	28	into	into	ADP
m-806	32	29	(	(	PUNCT
m-806	32	30	2.1a	2.1a	NUM
m-806	32	31	-	-	PUNCT
m-806	32	32	c	c	NOUN
m-806	32	33	)	)	PUNCT
m-806	32	34	and	and	CCONJ
m-806	32	35	simplifying	simplify	VERB
m-806	32	36	,	,	PUNCT
m-806	32	37	we	we	PRON
m-806	32	38	get	get	VERB
m-806	32	39	�	�	PROPN
m-806	32	40	,	,	PUNCT
m-806	32	41	�	�	PROPN
m-806	32	42	�	�	PROPN
m-806	32	43	+	+	CCONJ
m-806	32	44	2	2	NUM
m-806	32	45	�	�	PROPN
m-806	32	46	�	�	PROPN
m-806	32	47	,	,	PUNCT
m-806	32	48	�	�	PROPN
m-806	32	49	+	+	SYM
m-806	32	50	�	�	PROPN
m-806	32	51	,	,	PUNCT
m-806	32	52	�	�	PROPN
m-806	32	53	�	�	PROPN
m-806	32	54	�	�	PROPN
m-806	32	55	�	�	PROPN
m-806	32	56	+	+	CCONJ
m-806	32	57	2	2	NUM
m-806	32	58	�	�	PROPN
m-806	32	59	�	�	PROPN
m-806	32	60	(	(	PUNCT
m-806	32	61	�	�	PROPN
m-806	32	62	)	)	PUNCT
m-806	32	63	�	�	PROPN
m-806	32	64	,	,	PUNCT
m-806	32	65	�	�	PROPN
m-806	32	66	�	�	PROPN
m-806	32	67	+	+	CCONJ
m-806	32	68	�	�	PROPN
m-806	32	69	−	−	PROPN
m-806	32	70	�	�	PROPN
m-806	32	71	�	�	PROPN
m-806	32	72	�	�	PROPN
m-806	32	73	=	=	PUNCT
m-806	32	74	−2	−2	PROPN
m-806	32	75	�	�	PROPN
m-806	32	76	�	�	PROPN
m-806	32	77	�	�	PROPN
m-806	32	78	(	(	PUNCT
m-806	32	79	�	�	PROPN
m-806	32	80	)	)	PUNCT
m-806	32	81	�	�	PROPN
m-806	32	82	�	�	PROPN
m-806	32	83	�	�	PROPN
m-806	32	84	�	�	PROPN
m-806	32	85	�	�	PROPN
m-806	32	86	�	�	PROPN
m-806	32	87	�	�	PROPN
m-806	32	88	,	,	PUNCT
m-806	32	89	�	�	PROPN
m-806	32	90	>	>	X
m-806	32	91	0	0	NUM
m-806	32	92	,	,	PUNCT
m-806	32	93	0	0	NUM
m-806	32	94	<	<	X
m-806	32	95	�	�	PROPN
m-806	32	96	<	<	X
m-806	32	97	π	π	PROPN
m-806	32	98	(	(	PUNCT
m-806	32	99	3.1a	3.1a	NUM
m-806	32	100	)	)	PUNCT
m-806	32	101	�	�	PROPN
m-806	32	102	(	(	PUNCT
m-806	32	103	�	�	PROPN
m-806	32	104	,	,	PUNCT
m-806	32	105	0	0	NUM
m-806	32	106	)	)	PUNCT
m-806	32	107	=	=	SYM
m-806	32	108	�	�	PROPN
m-806	32	109	,	,	PUNCT
m-806	32	110	�	�	PROPN
m-806	32	111	(	(	PUNCT
m-806	32	112	�	�	PROPN
m-806	32	113	,	,	PUNCT
m-806	32	114	0	0	NUM
m-806	32	115	)	)	PUNCT
m-806	32	116	=	=	SYM
m-806	32	117	0	0	NUM
m-806	32	118	,	,	PUNCT
m-806	32	119	0	0	NUM
m-806	32	120	<	<	X
m-806	32	121	�	�	PROPN
m-806	32	122	<	<	X
m-806	32	123	π	π	PROPN
m-806	32	124	(	(	PUNCT
m-806	32	125	3.1b	3.1b	PROPN
m-806	32	126	)	)	PUNCT
m-806	32	127	�	�	PROPN
m-806	32	128	=	=	SYM
m-806	32	129	�	�	PROPN
m-806	32	130	,	,	PUNCT
m-806	32	131	�	�	PROPN
m-806	32	132	=	=	SYM
m-806	32	133	0	0	NUM
m-806	32	134	,	,	PUNCT
m-806	32	135	�	�	PROPN
m-806	32	136	�	�	PROPN
m-806	32	137	�	�	PROPN
m-806	32	138	=	=	SYM
m-806	32	139	0	0	NUM
m-806	32	140	,	,	PUNCT
m-806	32	141	π	π	PROPN
m-806	32	142	,	,	PUNCT
m-806	32	143	�	�	PROPN
m-806	32	144	>	>	X
m-806	32	145	0	0	NUM
m-806	33	1	(	(	PUNCT
m-806	33	2	3.1c	3.1c	NUM
m-806	33	3	)	)	PUNCT
m-806	33	4	here	here	ADV
m-806	33	5	,	,	PUNCT
m-806	33	6	a	a	DET
m-806	33	7	subscript	subscript	NOUN
m-806	33	8	following	follow	VERB
m-806	33	9	a	a	DET
m-806	33	10	comma	comma	NOUN
m-806	33	11	indicates	indicate	VERB
m-806	33	12	partial	partial	ADJ
m-806	33	13	differentiation	differentiation	NOUN
m-806	33	14	and	and	CCONJ
m-806	33	15	�	�	PROPN
m-806	33	16	(	(	PUNCT
m-806	33	17	�	�	PROPN
m-806	33	18	)	)	PUNCT
m-806	33	19	indicates	indicate	VERB
m-806	33	20	the	the	DET
m-806	33	21	actual	actual	ADJ
m-806	33	22	time	time	NOUN
m-806	33	23	dependence	dependence	NOUN
m-806	33	24	of	of	ADP
m-806	33	25	the	the	DET
m-806	33	26	load	load	NOUN
m-806	33	27	having	have	VERB
m-806	33	28	its	its	PRON
m-806	33	29	magnitude	magnitude	NOUN
m-806	33	30	as	as	ADP
m-806	33	31	λ	λ	PROPN
m-806	33	32	.	.	PROPN
m-806	34	1	in	in	ADP
m-806	34	2	our	our	PRON
m-806	34	3	case	case	NOUN
m-806	34	4	,	,	PUNCT
m-806	34	5	�	�	PROPN
m-806	34	6	(	(	PUNCT
m-806	34	7	�	�	PROPN
m-806	34	8	)	)	PUNCT
m-806	34	9	is	be	AUX
m-806	34	10	a	a	DET
m-806	34	11	step	step	NOUN
m-806	34	12	load	load	NOUN
m-806	34	13	characterized	characterize	VERB
m-806	34	14	by	by	ADP
m-806	34	15	�	�	PROPN
m-806	34	16	(	(	PUNCT
m-806	34	17	�	�	PROPN
m-806	34	18	)	)	PUNCT
m-806	34	19	=	=	SYM
m-806	34	20	�	�	PROPN
m-806	34	21	1	1	NUM
m-806	34	22	,	,	PUNCT
m-806	34	23	�	�	X
m-806	34	24	>	>	X
m-806	34	25	0	0	NUM
m-806	34	26	0	0	NUM
m-806	34	27	,	,	PUNCT
m-806	34	28	�	�	X
m-806	34	29	<	<	X
m-806	34	30	0	0	NUM
m-806	34	31	�	�	PROPN
m-806	34	32	(	(	PUNCT
m-806	34	33	3.2	3.2	NUM
m-806	34	34	)	)	PUNCT
m-806	34	35	4	4	NUM
m-806	34	36	.	.	PUNCT
m-806	34	37	classical	classical	ADJ
m-806	34	38	buckling	buckling	NOUN
m-806	34	39	load	load	NOUN
m-806	34	40	,	,	PUNCT
m-806	34	41	�	�	PROPN
m-806	34	42	�	�	PROPN
m-806	34	43	the	the	DET
m-806	34	44	classical	classical	ADJ
m-806	34	45	buckling	buckling	NOUN
m-806	34	46	load	load	NOUN
m-806	34	47	�	�	PROPN
m-806	34	48	�	�	PROPN
m-806	34	49	is	be	AUX
m-806	34	50	the	the	DET
m-806	34	51	load	load	NOUN
m-806	34	52	that	that	PRON
m-806	34	53	the	the	DET
m-806	34	54	associated	associated	ADJ
m-806	34	55	linear	linear	PROPN
m-806	34	56	perfect	perfect	ADJ
m-806	34	57	column	column	NOUN
m-806	34	58	buckles	buckle	NOUN
m-806	34	59	statically	statically	ADV
m-806	34	60	.	.	PUNCT
m-806	35	1	the	the	DET
m-806	35	2	equations	equation	NOUN
m-806	35	3	required	require	VERB
m-806	35	4	are	be	AUX
m-806	35	5	obtained	obtain	VERB
m-806	35	6	from	from	ADP
m-806	35	7	(	(	PUNCT
m-806	35	8	3.1a	3.1a	NOUN
m-806	35	9	)	)	PUNCT
m-806	35	10	as	as	ADP
m-806	35	11	�	�	PROPN
m-806	35	12	,	,	PUNCT
m-806	35	13	�	�	PROPN
m-806	35	14	�	�	PROPN
m-806	35	15	�	�	PROPN
m-806	35	16	�	�	PROPN
m-806	35	17	+	+	CCONJ
m-806	35	18	2	2	NUM
m-806	35	19	�	�	PROPN
m-806	35	20	�	�	PROPN
m-806	35	21	,	,	PUNCT
m-806	35	22	�	�	PROPN
m-806	35	23	�	�	PROPN
m-806	35	24	+	+	CCONJ
m-806	35	25	�	�	PROPN
m-806	35	26	=	=	SYM
m-806	35	27	0	0	NUM
m-806	35	28	,	,	PUNCT
m-806	35	29	0	0	NUM
m-806	35	30	<	<	X
m-806	35	31	�	�	PROPN
m-806	35	32	<	<	X
m-806	35	33	�	�	PROPN
m-806	35	34	(	(	PUNCT
m-806	35	35	4.1a	4.1a	NOUN
m-806	35	36	)	)	PUNCT
m-806	35	37	�	�	PROPN
m-806	35	38	=	=	SYM
m-806	35	39	�	�	PROPN
m-806	35	40	,	,	PUNCT
m-806	35	41	�	�	PROPN
m-806	35	42	=	=	SYM
m-806	35	43	0	0	NUM
m-806	35	44	,	,	PUNCT
m-806	35	45	�	�	PROPN
m-806	35	46	�	�	PROPN
m-806	35	47	�	�	PROPN
m-806	35	48	=	=	SYM
m-806	35	49	0	0	NUM
m-806	35	50	,	,	PUNCT
m-806	35	51	π	π	X
m-806	35	52	.	.	PUNCT
m-806	36	1	(	(	PUNCT
m-806	36	2	4.1b	4.1b	NOUN
m-806	36	3	)	)	PUNCT
m-806	36	4	we	we	PRON
m-806	36	5	note	note	VERB
m-806	36	6	that	that	SCONJ
m-806	36	7	the	the	DET
m-806	36	8	deflection	deflection	NOUN
m-806	36	9	�	�	PROPN
m-806	36	10	at	at	ADP
m-806	36	11	this	this	DET
m-806	36	12	stage	stage	NOUN
m-806	36	13	depends	depend	VERB
m-806	36	14	only	only	ADV
m-806	36	15	on	on	ADP
m-806	36	16	�	�	PROPN
m-806	36	17	.	.	PUNCT
m-806	37	1	to	to	PART
m-806	37	2	solve	solve	VERB
m-806	37	3	(	(	PUNCT
m-806	37	4	4.1a	4.1a	NOUN
m-806	37	5	,	,	PUNCT
m-806	37	6	b	b	NOUN
m-806	37	7	)	)	PUNCT
m-806	37	8	,	,	PUNCT
m-806	37	9	we	we	PRON
m-806	37	10	let	let	VERB
m-806	37	11	�	�	PROPN
m-806	37	12	(	(	PUNCT
m-806	37	13	�	�	PROPN
m-806	37	14	)	)	PUNCT
m-806	37	15	=	=	PUNCT
m-806	38	1	∑	∑	PUNCT
m-806	38	2	(	(	PUNCT
m-806	38	3	1	1	NUM
m-806	38	4	−	−	PROPN
m-806	38	5	�	�	PROPN
m-806	38	6	�	�	PROPN
m-806	38	7	�	�	PROPN
m-806	38	8	2	2	NUM
m-806	38	9	�	�	PROPN
m-806	38	10	�	�	PROPN
m-806	38	11	)	)	PUNCT
m-806	38	12	�	�	PROPN
m-806	38	13	�	�	PROPN
m-806	38	14	�	�	PROPN
m-806	38	15	�	�	PROPN
m-806	38	16	�	�	PROPN
m-806	38	17	�	�	PROPN
m-806	38	18	(	(	PUNCT
m-806	38	19	4.2	4.2	NUM
m-806	38	20	)	)	PUNCT
m-806	38	21	on	on	ADP
m-806	38	22	substituting	substitute	VERB
m-806	38	23	(	(	PUNCT
m-806	38	24	4.2	4.2	NUM
m-806	38	25	)	)	PUNCT
m-806	38	26	into	into	ADP
m-806	38	27	(	(	PUNCT
m-806	38	28	4.1a),multiplying	4.1a),multiplye	VERB
m-806	38	29	by	by	ADP
m-806	38	30	�	�	PROPN
m-806	38	31	�	�	PROPN
m-806	38	32	�	�	PROPN
m-806	38	33	2	2	NUM
m-806	38	34	�	�	PROPN
m-806	38	35	�	�	PROPN
m-806	38	36	for	for	ADP
m-806	38	37	fixed	fix	VERB
m-806	38	38	�	�	PROPN
m-806	38	39	and	and	CCONJ
m-806	38	40	integrating	integrate	VERB
m-806	38	41	form	form	NOUN
m-806	38	42	0	0	NUM
m-806	38	43	to	to	ADP
m-806	38	44	�	�	PROPN
m-806	38	45	,	,	PUNCT
m-806	38	46	we	we	PRON
m-806	38	47	see	see	VERB
m-806	38	48	that	that	PRON
m-806	38	49	for	for	ADP
m-806	38	50	�	�	PROPN
m-806	38	51	=	=	SYM
m-806	38	52	�	�	PROPN
m-806	38	53	,	,	PUNCT
m-806	38	54	we	we	PRON
m-806	38	55	get	get	VERB
m-806	38	56	(	(	PUNCT
m-806	38	57	16	16	NUM
m-806	38	58	�	�	PROPN
m-806	38	59	�	�	PROPN
m-806	38	60	−	−	PROPN
m-806	38	61	8	8	NUM
m-806	38	62	�	�	PROPN
m-806	38	63	�	�	PROPN
m-806	38	64	�	�	PROPN
m-806	38	65	+	+	CCONJ
m-806	38	66	1	1	NUM
m-806	38	67	)	)	PUNCT
m-806	38	68	�	�	PROPN
m-806	38	69	�	�	PROPN
m-806	38	70	=	=	SYM
m-806	38	71	0	0	NUM
m-806	38	72	(	(	PUNCT
m-806	38	73	4.3	4.3	NUM
m-806	38	74	)	)	PUNCT
m-806	38	75	where	where	SCONJ
m-806	38	76	,	,	PUNCT
m-806	38	77	m	m	PROPN
m-806	38	78	is	be	AUX
m-806	38	79	a	a	DET
m-806	38	80	fixed	fix	VERB
m-806	38	81	value	value	NOUN
m-806	38	82	of	of	ADP
m-806	38	83	n.	n.	NOUN
m-806	38	84	according	accord	VERB
m-806	38	85	to	to	ADP
m-806	38	86	[	[	X
m-806	38	87	18	18	NUM
m-806	38	88	]	]	PUNCT
m-806	38	89	,	,	PUNCT
m-806	38	90	the	the	DET
m-806	38	91	condition	condition	NOUN
m-806	38	92	for	for	ADP
m-806	38	93	static	static	ADJ
m-806	38	94	buckling	buckling	NOUN
m-806	38	95	is	be	AUX
m-806	38	96	�	�	PROPN
m-806	38	97	�	�	PROPN
m-806	38	98	�	�	PROPN
m-806	38	99	�	�	PROPN
m-806	38	100	=	=	SYM
m-806	38	101	0	0	NUM
m-806	38	102	(	(	PUNCT
m-806	38	103	4.4	4.4	NUM
m-806	38	104	)	)	PUNCT
m-806	38	105	where	where	SCONJ
m-806	38	106	,	,	PUNCT
m-806	38	107	�	�	PROPN
m-806	38	108	is	be	AUX
m-806	38	109	the	the	DET
m-806	38	110	displacement	displacement	NOUN
m-806	38	111	(	(	PUNCT
m-806	38	112	or	or	CCONJ
m-806	38	113	deflection	deflection	NOUN
m-806	38	114	)	)	PUNCT
m-806	38	115	.	.	PUNCT
m-806	39	1	this	this	PRON
m-806	39	2	gives	give	VERB
m-806	39	3	the	the	DET
m-806	39	4	classical	classical	ADJ
m-806	39	5	buckling	buckling	NOUN
m-806	39	6	load	load	NOUN
m-806	39	7	�	�	NOUN
m-806	39	8	�	�	PROPN
m-806	39	9	as	as	ADP
m-806	39	10	λ	λ	PROPN
m-806	39	11	�	�	PROPN
m-806	39	12	=	=	SYM
m-806	39	13	�	�	PROPN
m-806	39	14	�	�	PROPN
m-806	39	15	�	�	PROPN
m-806	39	16	�	�	PROPN
m-806	39	17	�	�	PROPN
m-806	39	18	�	�	PROPN
m-806	39	19	�	�	PROPN
m-806	39	20	�	�	PROPN
m-806	39	21	�	�	PROPN
m-806	39	22	(	(	PUNCT
m-806	39	23	4.5a	4.5a	PROPN
m-806	39	24	)	)	PUNCT
m-806	39	25	the	the	DET
m-806	39	26	least	least	ADJ
m-806	39	27	value	value	NOUN
m-806	39	28	of	of	ADP
m-806	39	29	�	�	PROPN
m-806	39	30	�	�	PROPN
m-806	39	31	is	be	AUX
m-806	39	32	when	when	SCONJ
m-806	39	33	�	�	PROPN
m-806	39	34	=	=	PROPN
m-806	39	35	1	1	NUM
m-806	39	36	and	and	CCONJ
m-806	39	37	in	in	ADP
m-806	39	38	this	this	DET
m-806	39	39	case	case	NOUN
m-806	39	40	,	,	PUNCT
m-806	39	41	we	we	PRON
m-806	39	42	get	get	VERB
m-806	39	43	λ	λ	X
m-806	39	44	�	�	PROPN
m-806	39	45	=	=	SYM
m-806	39	46	�	�	PROPN
m-806	39	47	�	�	PROPN
m-806	39	48	�	�	PROPN
m-806	39	49	=	=	PROPN
m-806	39	50	2.125	2.125	NUM
m-806	39	51	(	(	PUNCT
m-806	39	52	4.5b	4.5b	NOUN
m-806	39	53	)	)	PUNCT
m-806	39	54	in	in	ADP
m-806	39	55	retrospect	retrospect	NOUN
m-806	39	56	,	,	PUNCT
m-806	39	57	a	a	DET
m-806	39	58	similar	similar	ADJ
m-806	39	59	column	column	NOUN
m-806	39	60	with	with	ADP
m-806	39	61	simply	simply	ADV
m-806	39	62	-	-	PUNCT
m-806	39	63	supported	support	VERB
m-806	39	64	end	end	NOUN
m-806	39	65	conditions	condition	NOUN
m-806	39	66	that	that	PRON
m-806	39	67	satisfy	satisfy	VERB
m-806	39	68	the	the	DET
m-806	39	69	same	same	ADJ
m-806	39	70	equation	equation	NOUN
m-806	39	71	as	as	ADP
m-806	39	72	(	(	PUNCT
m-806	39	73	4.1a	4.1a	NOUN
m-806	39	74	)	)	PUNCT
m-806	39	75	but	but	CCONJ
m-806	39	76	,	,	PUNCT
m-806	39	77	instead	instead	ADV
m-806	39	78	of	of	ADP
m-806	39	79	(	(	PUNCT
m-806	39	80	4.1b	4.1b	NOUN
m-806	39	81	)	)	PUNCT
m-806	39	82	,	,	PUNCT
m-806	39	83	it	it	PRON
m-806	39	84	would	would	AUX
m-806	39	85	satisfy	satisfy	VERB
m-806	39	86	the	the	DET
m-806	39	87	conditions	condition	NOUN
m-806	39	88	�	�	PROPN
m-806	39	89	=	=	SYM
m-806	39	90	�	�	PROPN
m-806	39	91	,	,	PUNCT
m-806	39	92	�	�	PROPN
m-806	39	93	�	�	PROPN
m-806	39	94	=	=	SYM
m-806	39	95	0	0	NUM
m-806	39	96	,	,	PUNCT
m-806	39	97	�	�	PROPN
m-806	39	98	�	�	PROPN
m-806	39	99	�	�	PROPN
m-806	39	100	=	=	SYM
m-806	39	101	0	0	PROPN
m-806	39	102	,	,	PUNCT
m-806	39	103	π	π	PROPN
m-806	39	104	(	(	PUNCT
m-806	39	105	4.5c	4.5c	NOUN
m-806	39	106	)	)	PUNCT
m-806	39	107	has	have	VERB
m-806	39	108	the	the	DET
m-806	39	109	classical	classical	ADJ
m-806	39	110	buckling	buckling	NOUN
m-806	39	111	load	load	NOUN
m-806	39	112	as	as	ADP
m-806	39	113	�	�	NOUN
m-806	39	114	�	�	PROPN
m-806	39	115	=	=	SYM
m-806	39	116	1	1	NUM
m-806	39	117	which	which	PRON
m-806	39	118	is	be	AUX
m-806	39	119	different	different	ADJ
m-806	39	120	from	from	ADP
m-806	39	121	(	(	PUNCT
m-806	39	122	4.5a	4.5a	NUM
m-806	39	123	,	,	PUNCT
m-806	39	124	b	b	NOUN
m-806	39	125	)	)	PUNCT
m-806	39	126	.	.	PUNCT
m-806	40	1	thus	thus	ADV
m-806	40	2	,	,	PUNCT
m-806	40	3	a	a	DET
m-806	40	4	clamped	clamp	VERB
m-806	40	5	column	column	NOUN
m-806	40	6	has	have	VERB
m-806	40	7	a	a	DET
m-806	40	8	higher	high	ADJ
m-806	40	9	classical	classical	ADJ
m-806	40	10	buckling	buckling	NOUN
m-806	40	11	load	load	NOUN
m-806	40	12	than	than	ADP
m-806	40	13	the	the	DET
m-806	40	14	same	same	ADJ
m-806	40	15	column	column	NOUN
m-806	40	16	with	with	ADP
m-806	40	17	simply	simply	ADV
m-806	40	18	–	–	PUNCT
m-806	40	19	supported	support	VERB
m-806	40	20	end	end	NOUN
m-806	40	21	conditions	condition	NOUN
m-806	40	22	.	.	PUNCT
m-806	41	1	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	41	2	ijo	ijo	PROPN
m-806	41	3	journals	journal	NOUN
m-806	41	4	volume	volume	NOUN
m-806	41	5	07	07	NUM
m-806	41	6	|	|	ADV
m-806	41	7	issue	issue	NOUN
m-806	41	8	02	02	NUM
m-806	41	9	|	|	CCONJ
m-806	41	10	february	february	PROPN
m-806	41	11	2024	2024	NUM
m-806	41	12	|	|	ADV
m-806	41	13	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	41	14	3	3	NUM
m-806	41	15	ijo	ijo	PROPN
m-806	41	16	international	international	PROPN
m-806	41	17	journal	journal	PROPN
m-806	41	18	of	of	ADP
m-806	41	19	mathematics	mathematics	PROPN
m-806	41	20	(	(	PUNCT
m-806	41	21	issn	issn	PROPN
m-806	41	22	:	:	PUNCT
m-806	41	23	2992	2992	NUM
m-806	41	24	-	-	SYM
m-806	41	25	4421	4421	NUM
m-806	41	26	)	)	PUNCT
m-806	42	1	i.u	i.u	PROPN
m-806	42	2	.	.	PROPN
m-806	42	3	udo	udo	PROPN
m-806	42	4	-	-	PROPN
m-806	42	5	akpan1	akpan1	ADJ
m-806	42	6	*	*	PUNCT
m-806	42	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	42	8	volume	volume	NOUN
m-806	42	9	07	07	NUM
m-806	42	10	issue	issue	NOUN
m-806	42	11	02	02	NUM
m-806	42	12	||	||	NUM
m-806	42	13	february	february	PROPN
m-806	42	14	,	,	PUNCT
m-806	42	15	2024	2024	NUM
m-806	42	16	||	||	NOUN
m-806	43	1	on	on	ADP
m-806	43	2	a	a	DET
m-806	43	3	-	-	PUNCT
m-806	43	4	two	two	NUM
m-806	43	5	-	-	PUNCT
m-806	43	6	parameter	parameter	NOUN
m-806	43	7	dynamic	dynamic	ADJ
m-806	43	8	buckling	buckling	NOUN
m-806	43	9	of	of	ADP
m-806	43	10	a	a	DET
m-806	43	11	viscously	viscously	ADV
m-806	43	12	damped	damp	VERB
m-806	43	13	but	but	CCONJ
m-806	43	14	clamped	clamp	VERB
m-806	43	15	column	column	NOUN
m-806	43	16	stressed	stress	VERB
m-806	43	17	by	by	ADP
m-806	43	18	a	a	DET
m-806	43	19	step	step	NOUN
m-806	43	20	load	load	NOUN
m-806	43	21	5	5	NUM
m-806	43	22	.	.	PUNCT
m-806	44	1	static	static	ADJ
m-806	44	2	buckling	buckling	NOUN
m-806	44	3	load	load	NOUN
m-806	44	4	,	,	PUNCT
m-806	44	5	�	�	PROPN
m-806	44	6	�	�	PROPN
m-806	44	7	this	this	PRON
m-806	44	8	is	be	AUX
m-806	44	9	the	the	DET
m-806	44	10	load	load	NOUN
m-806	44	11	that	that	PRON
m-806	44	12	the	the	DET
m-806	44	13	column	column	NOUN
m-806	44	14	would	would	AUX
m-806	44	15	require	require	VERB
m-806	44	16	to	to	PART
m-806	44	17	buckle	buckle	VERB
m-806	44	18	statically	statically	ADV
m-806	44	19	.	.	PUNCT
m-806	45	1	the	the	DET
m-806	45	2	required	require	VERB
m-806	45	3	differential	differential	NOUN
m-806	45	4	equation	equation	NOUN
m-806	45	5	is	be	AUX
m-806	45	6	�	�	PROPN
m-806	45	7	,	,	PUNCT
m-806	45	8	�	�	PROPN
m-806	45	9	�	�	PROPN
m-806	45	10	�	�	PROPN
m-806	45	11	�	�	PROPN
m-806	45	12	+	+	CCONJ
m-806	45	13	2	2	NUM
m-806	45	14	�	�	PROPN
m-806	45	15	�	�	PROPN
m-806	45	16	,	,	PUNCT
m-806	45	17	�	�	PROPN
m-806	45	18	�	�	PROPN
m-806	45	19	+	+	CCONJ
m-806	45	20	�	�	PROPN
m-806	45	21	−	−	PROPN
m-806	45	22	�	�	PROPN
m-806	45	23	�	�	PROPN
m-806	45	24	�	�	PROPN
m-806	45	25	=	=	PUNCT
m-806	45	26	−2	−2	PROPN
m-806	45	27	�	�	PROPN
m-806	45	28	�	�	PROPN
m-806	45	29	�	�	PROPN
m-806	45	30	�	�	PROPN
m-806	45	31	�	�	PROPN
m-806	45	32	�	�	PROPN
m-806	45	33	�	�	PROPN
m-806	45	34	�	�	PROPN
m-806	45	35	�	�	PROPN
m-806	45	36	,	,	PUNCT
m-806	45	37	0	0	NUM
m-806	45	38	<	<	X
m-806	45	39	�	�	PROPN
m-806	45	40	<	<	X
m-806	45	41	�	�	PROPN
m-806	45	42	(	(	PUNCT
m-806	45	43	5.1a	5.1a	NOUN
m-806	45	44	)	)	PUNCT
m-806	45	45	�	�	PROPN
m-806	45	46	=	=	SYM
m-806	45	47	�	�	PROPN
m-806	45	48	,	,	PUNCT
m-806	45	49	�	�	PROPN
m-806	45	50	=	=	SYM
m-806	45	51	0	0	NUM
m-806	45	52	,	,	PUNCT
m-806	45	53	�	�	PROPN
m-806	45	54	�	�	PROPN
m-806	45	55	�	�	PROPN
m-806	45	56	=	=	SYM
m-806	45	57	0	0	NUM
m-806	45	58	,	,	PUNCT
m-806	45	59	π	π	PROPN
m-806	45	60	,	,	PUNCT
m-806	45	61	(	(	PUNCT
m-806	45	62	5.1b	5.1b	PROPN
m-806	45	63	)	)	PUNCT
m-806	45	64	to	to	PART
m-806	45	65	determine	determine	VERB
m-806	45	66	the	the	DET
m-806	45	67	displacement	displacement	NOUN
m-806	45	68	(	(	PUNCT
m-806	45	69	or	or	CCONJ
m-806	45	70	deflection	deflection	NOUN
m-806	45	71	)	)	PUNCT
m-806	45	72	�	�	PROPN
m-806	45	73	(	(	PUNCT
m-806	45	74	�	�	PROPN
m-806	45	75	)	)	PUNCT
m-806	45	76	in	in	ADP
m-806	45	77	(	(	PUNCT
m-806	45	78	5.1a	5.1a	NOUN
m-806	45	79	,	,	PUNCT
m-806	45	80	b	b	NOUN
m-806	45	81	)	)	PUNCT
m-806	45	82	,	,	PUNCT
m-806	45	83	we	we	PRON
m-806	45	84	set	set	VERB
m-806	45	85	�	�	PROPN
m-806	45	86	(	(	PUNCT
m-806	45	87	�	�	PROPN
m-806	45	88	)	)	PUNCT
m-806	45	89	≡	≡	PROPN
m-806	45	90	1and	1and	PROPN
m-806	45	91	let	let	VERB
m-806	45	92	�	�	PRON
m-806	45	93	�	�	PROPN
m-806	45	94	=	=	SYM
m-806	45	95	�	�	PROPN
m-806	45	96	�	�	PROPN
m-806	45	97	�	�	PROPN
m-806	45	98	(	(	PUNCT
m-806	45	99	1	1	NUM
m-806	45	100	−	−	PROPN
m-806	45	101	�	�	PROPN
m-806	45	102	�	�	PROPN
m-806	45	103	�	�	PROPN
m-806	45	104	2	2	NUM
m-806	45	105	�	�	PROPN
m-806	45	106	�	�	PROPN
m-806	45	107	)	)	PUNCT
m-806	45	108	,	,	PUNCT
m-806	45	109	│	│	X
m-806	45	110	�	�	PROPN
m-806	45	111	�	�	PROPN
m-806	45	112	�	�	PROPN
m-806	45	113	│	│	PUNCT
m-806	45	114	≪	≪	VERB
m-806	45	115	1	1	NUM
m-806	45	116	next	next	ADJ
m-806	45	117	,	,	PUNCT
m-806	45	118	we	we	PRON
m-806	45	119	let	let	VERB
m-806	45	120	∑	∑	PROPN
m-806	45	121	�	�	PROPN
m-806	45	122	(	(	PUNCT
m-806	45	123	�	�	PROPN
m-806	45	124	)	)	PUNCT
m-806	45	125	�	�	PROPN
m-806	45	126	�	�	PROPN
m-806	45	127	�	�	PROPN
m-806	45	128	�	�	PROPN
m-806	45	129	�	�	PROPN
m-806	45	130	�	�	PROPN
m-806	45	131	;	;	PUNCT
m-806	45	132	�	�	PROPN
m-806	45	133	(	(	PUNCT
m-806	45	134	�	�	PROPN
m-806	45	135	)	)	PUNCT
m-806	45	136	=	=	SYM
m-806	45	137	�	�	PROPN
m-806	45	138	(	(	PUNCT
m-806	45	139	�	�	PROPN
m-806	45	140	)	)	PUNCT
m-806	45	141	(	(	PUNCT
m-806	45	142	�	�	PROPN
m-806	45	143	)	)	PUNCT
m-806	45	144	(	(	PUNCT
m-806	45	145	5.2	5.2	NUM
m-806	45	146	)	)	PUNCT
m-806	45	147	by	by	ADP
m-806	45	148	substituting	substitute	VERB
m-806	45	149	(	(	PUNCT
m-806	45	150	5.2	5.2	NUM
m-806	45	151	)	)	PUNCT
m-806	45	152	into	into	ADP
m-806	45	153	(	(	PUNCT
m-806	45	154	5.1a	5.1a	NOUN
m-806	45	155	)	)	PUNCT
m-806	45	156	and	and	CCONJ
m-806	45	157	equating	equate	VERB
m-806	45	158	the	the	DET
m-806	45	159	coefficients	coefficient	NOUN
m-806	45	160	of	of	ADP
m-806	45	161	powers	power	NOUN
m-806	45	162	of	of	ADP
m-806	45	163	�	�	PROPN
m-806	45	164	�	�	PROPN
m-806	45	165	,	,	PUNCT
m-806	45	166	�	�	PROPN
m-806	45	167	=	=	SYM
m-806	45	168	1	1	NUM
m-806	45	169	,	,	PUNCT
m-806	45	170	2	2	NUM
m-806	45	171	,	,	PUNCT
m-806	45	172	3	3	NUM
m-806	45	173	,	,	PUNCT
m-806	45	174	…	…	PUNCT
m-806	45	175	,	,	PUNCT
m-806	45	176	we	we	PRON
m-806	45	177	get	get	VERB
m-806	45	178	o(ϵ	o(ϵ	ADP
m-806	45	179	):	):	PUNCT
m-806	45	180	�	�	PROPN
m-806	45	181	�	�	PROPN
m-806	45	182	(	(	PUNCT
m-806	45	183	�	�	PROPN
m-806	45	184	)	)	PUNCT
m-806	45	185	≡	≡	PROPN
m-806	45	186	�	�	PROPN
m-806	45	187	,	,	PUNCT
m-806	45	188	�	�	PROPN
m-806	45	189	�	�	PROPN
m-806	45	190	�	�	PROPN
m-806	45	191	�	�	PROPN
m-806	45	192	(	(	PUNCT
m-806	45	193	�	�	PROPN
m-806	45	194	)	)	PUNCT
m-806	46	1	+	+	CCONJ
m-806	46	2	2	2	NUM
m-806	46	3	�	�	PROPN
m-806	46	4	�	�	PROPN
m-806	46	5	,	,	PUNCT
m-806	46	6	�	�	PROPN
m-806	46	7	�	�	PROPN
m-806	46	8	(	(	PUNCT
m-806	46	9	�	�	PROPN
m-806	46	10	)	)	PUNCT
m-806	46	11	+	+	SYM
m-806	46	12	�	�	PROPN
m-806	46	13	(	(	PUNCT
m-806	46	14	�	�	PROPN
m-806	46	15	)	)	PUNCT
m-806	46	16	=	=	SYM
m-806	46	17	−8	−8	SYM
m-806	46	18	�	�	PROPN
m-806	46	19	�	�	PROPN
m-806	46	20	�	�	PROPN
m-806	46	21	�	�	PROPN
m-806	46	22	�	�	PROPN
m-806	46	23	�	�	PROPN
m-806	46	24	�	�	PROPN
m-806	46	25	�	�	PROPN
m-806	46	26	�	�	PROPN
m-806	46	27	2	2	NUM
m-806	46	28	�	�	PROPN
m-806	46	29	�	�	PROPN
m-806	46	30	(	(	PUNCT
m-806	46	31	5.3	5.3	NUM
m-806	46	32	)	)	PUNCT
m-806	46	33	o	o	NOUN
m-806	46	34	(	(	PUNCT
m-806	46	35	�	�	PROPN
m-806	46	36	�	�	PROPN
m-806	46	37	):	):	SYM
m-806	46	38	�	�	PROPN
m-806	46	39	�	�	PROPN
m-806	46	40	(	(	PUNCT
m-806	46	41	�	�	PROPN
m-806	46	42	)	)	PUNCT
m-806	46	43	=	=	SYM
m-806	46	44	0	0	NUM
m-806	46	45	(	(	PUNCT
m-806	46	46	5.4	5.4	NUM
m-806	46	47	)	)	PUNCT
m-806	46	48	o	o	NOUN
m-806	46	49	(	(	PUNCT
m-806	46	50	�	�	PROPN
m-806	46	51	�	�	PROPN
m-806	46	52	):	):	PUNCT
m-806	46	53	�	�	PROPN
m-806	46	54	�	�	PROPN
m-806	46	55	(	(	PUNCT
m-806	46	56	�	�	PROPN
m-806	46	57	)	)	PUNCT
m-806	46	58	=	=	SYM
m-806	46	59	�	�	PROPN
m-806	46	60	�	�	PROPN
m-806	46	61	�	�	PROPN
m-806	46	62	(	(	PUNCT
m-806	46	63	�	�	PROPN
m-806	46	64	)	)	PUNCT
m-806	46	65	�	�	PROPN
m-806	46	66	�	�	PROPN
m-806	46	67	(	(	PUNCT
m-806	46	68	5.5	5.5	NUM
m-806	46	69	)	)	PUNCT
m-806	46	70	etc	etc	X
m-806	46	71	.	.	X
m-806	46	72	�	�	PROPN
m-806	46	73	(	(	PUNCT
m-806	46	74	�	�	PROPN
m-806	46	75	)	)	PUNCT
m-806	46	76	(	(	PUNCT
m-806	46	77	�	�	NOUN
m-806	46	78	)	)	PUNCT
m-806	46	79	=	=	SYM
m-806	46	80	�	�	PROPN
m-806	46	81	,	,	PUNCT
m-806	46	82	�	�	PROPN
m-806	46	83	(	(	PUNCT
m-806	46	84	�	�	PROPN
m-806	46	85	)	)	PUNCT
m-806	46	86	�	�	PROPN
m-806	46	87	�	�	PROPN
m-806	46	88	�	�	PROPN
m-806	46	89	=	=	SYM
m-806	46	90	0	0	PROPN
m-806	46	91	,	,	PUNCT
m-806	46	92	π	π	PROPN
m-806	46	93	(	(	PUNCT
m-806	46	94	5.6	5.6	NUM
m-806	46	95	)	)	PUNCT
m-806	46	96	we	we	PRON
m-806	46	97	seek	seek	VERB
m-806	46	98	for	for	ADP
m-806	46	99	the	the	DET
m-806	46	100	solutions	solution	NOUN
m-806	46	101	of	of	ADP
m-806	46	102	(	(	PUNCT
m-806	46	103	5.3	5.3	NUM
m-806	46	104	)	)	PUNCT
m-806	46	105	–	–	PUNCT
m-806	46	106	(	(	PUNCT
m-806	46	107	5.6	5.6	NUM
m-806	46	108	)	)	PUNCT
m-806	46	109	by	by	ADP
m-806	46	110	letting	let	VERB
m-806	46	111	�	�	PROPN
m-806	46	112	(	(	PUNCT
m-806	46	113	�	�	PROPN
m-806	46	114	)	)	PUNCT
m-806	46	115	(	(	PUNCT
m-806	46	116	�	�	PROPN
m-806	46	117	)	)	PUNCT
m-806	46	118	=	=	SYM
m-806	46	119	2	2	NUM
m-806	46	120	∑	∑	PUNCT
m-806	46	121	�	�	PROPN
m-806	46	122	�	�	PROPN
m-806	46	123	(	(	PUNCT
m-806	46	124	�	�	PROPN
m-806	46	125	)	)	PUNCT
m-806	46	126	�	�	PROPN
m-806	46	127	�	�	PROPN
m-806	46	128	�	�	PROPN
m-806	46	129	�	�	PROPN
m-806	46	130	sin	sin	PROPN
m-806	46	131	�	�	PROPN
m-806	46	132	�	�	PROPN
m-806	46	133	�	�	PROPN
m-806	46	134	=	=	SYM
m-806	46	135	∑	∑	PUNCT
m-806	46	136	(	(	PUNCT
m-806	46	137	1	1	NUM
m-806	46	138	−	−	PROPN
m-806	46	139	�	�	PROPN
m-806	46	140	�	�	PROPN
m-806	46	141	�	�	PROPN
m-806	46	142	2	2	NUM
m-806	46	143	�	�	PROPN
m-806	46	144	�	�	PROPN
m-806	46	145	)	)	PUNCT
m-806	46	146	�	�	PROPN
m-806	46	147	�	�	PROPN
m-806	46	148	(	(	PUNCT
m-806	46	149	�	�	PROPN
m-806	46	150	)	)	PUNCT
m-806	46	151	�	�	PROPN
m-806	46	152	�	�	PROPN
m-806	46	153	�	�	PROPN
m-806	46	154	�	�	PROPN
m-806	46	155	(	(	PUNCT
m-806	46	156	5.7	5.7	NUM
m-806	46	157	)	)	PUNCT
m-806	46	158	on	on	ADP
m-806	46	159	substituting	substitute	VERB
m-806	46	160	(	(	PUNCT
m-806	46	161	5.7	5.7	NUM
m-806	46	162	)	)	PUNCT
m-806	46	163	into	into	ADP
m-806	46	164	(	(	PUNCT
m-806	46	165	5.3	5.3	NUM
m-806	46	166	)	)	PUNCT
m-806	46	167	,	,	PUNCT
m-806	46	168	we	we	PRON
m-806	46	169	get	get	VERB
m-806	46	170	∑	∑	PROPN
m-806	46	171	�	�	PROPN
m-806	46	172	�	�	PROPN
m-806	46	173	�	�	PROPN
m-806	46	174	(	(	PUNCT
m-806	46	175	�	�	PROPN
m-806	46	176	)	)	PUNCT
m-806	46	177	(	(	PUNCT
m-806	46	178	8	8	NUM
m-806	46	179	�	�	PROPN
m-806	46	180	�	�	PROPN
m-806	46	181	�	�	PROPN
m-806	46	182	−	−	PROPN
m-806	46	183	16	16	NUM
m-806	46	184	�	�	PROPN
m-806	46	185	�	�	PROPN
m-806	46	186	)	)	PUNCT
m-806	46	187	�	�	PROPN
m-806	46	188	�	�	PROPN
m-806	46	189	�	�	PROPN
m-806	46	190	2	2	NUM
m-806	46	191	�	�	PROPN
m-806	46	192	�	�	PROPN
m-806	46	193	+	+	SYM
m-806	46	194	�	�	PROPN
m-806	46	195	�	�	PROPN
m-806	46	196	(	(	PUNCT
m-806	46	197	�	�	PROPN
m-806	46	198	)	)	PUNCT
m-806	46	199	(	(	PUNCT
m-806	46	200	1	1	NUM
m-806	46	201	−	−	PROPN
m-806	46	202	�	�	PROPN
m-806	46	203	�	�	PROPN
m-806	46	204	�	�	PROPN
m-806	46	205	2	2	NUM
m-806	46	206	�	�	PROPN
m-806	46	207	�	�	PROPN
m-806	46	208	)	)	PUNCT
m-806	46	209	�	�	PROPN
m-806	46	210	�	�	PROPN
m-806	46	211	�	�	PROPN
m-806	46	212	�	�	PROPN
m-806	46	213	�	�	PROPN
m-806	46	214	=	=	SYM
m-806	46	215	−8	−8	X
m-806	46	216	�	�	PROPN
m-806	46	217	�	�	PROPN
m-806	46	218	�	�	PROPN
m-806	46	219	�	�	PROPN
m-806	46	220	�	�	PROPN
m-806	46	221	�	�	PROPN
m-806	46	222	�	�	PROPN
m-806	46	223	�	�	PROPN
m-806	46	224	�	�	PROPN
m-806	46	225	2	2	NUM
m-806	46	226	�	�	PROPN
m-806	46	227	�	�	PROPN
m-806	46	228	(	(	PUNCT
m-806	46	229	5.8	5.8	NUM
m-806	46	230	)	)	PUNCT
m-806	46	231	on	on	ADP
m-806	46	232	multiplying	multiply	VERB
m-806	46	233	(	(	PUNCT
m-806	46	234	5.8	5.8	NUM
m-806	46	235	)	)	PUNCT
m-806	46	236	through	through	ADP
m-806	46	237	by	by	ADP
m-806	46	238	cos2mx	cos2mx	PROPN
m-806	46	239	and	and	CCONJ
m-806	46	240	integrating	integrate	VERB
m-806	46	241	from	from	ADP
m-806	46	242	0	0	NUM
m-806	46	243	to	to	ADP
m-806	46	244	π	π	PROPN
m-806	46	245	,	,	PUNCT
m-806	46	246	we	we	PRON
m-806	46	247	see	see	VERB
m-806	46	248	that	that	PRON
m-806	46	249	for	for	ADP
m-806	46	250	�	�	PROPN
m-806	46	251	=	=	SYM
m-806	46	252	�	�	PROPN
m-806	46	253	,	,	PUNCT
m-806	46	254	(	(	PUNCT
m-806	46	255	16	16	NUM
m-806	46	256	�	�	PROPN
m-806	46	257	�	�	PROPN
m-806	46	258	−	−	PROPN
m-806	46	259	8	8	NUM
m-806	46	260	�	�	PROPN
m-806	46	261	�	�	PROPN
m-806	46	262	�	�	PROPN
m-806	46	263	+	+	CCONJ
m-806	46	264	1	1	NUM
m-806	46	265	)	)	PUNCT
m-806	46	266	�	�	PROPN
m-806	46	267	�	�	PROPN
m-806	46	268	(	(	PUNCT
m-806	46	269	�	�	PROPN
m-806	46	270	)	)	PUNCT
m-806	46	271	=	=	SYM
m-806	46	272	8	8	NUM
m-806	46	273	�	�	PROPN
m-806	46	274	�	�	PROPN
m-806	46	275	�	�	PROPN
m-806	46	276	�	�	PROPN
m-806	46	277	�	�	PROPN
m-806	46	278	�	�	PROPN
m-806	46	279	this	this	PRON
m-806	46	280	gives	give	VERB
m-806	46	281	�	�	PROPN
m-806	46	282	�	�	PROPN
m-806	46	283	(	(	PUNCT
m-806	46	284	�	�	PROPN
m-806	46	285	)	)	PUNCT
m-806	46	286	=	=	SYM
m-806	46	287	�	�	PROPN
m-806	46	288	�	�	PROPN
m-806	46	289	�	�	PROPN
m-806	46	290	�	�	PROPN
m-806	46	291	�	�	PROPN
m-806	46	292	�	�	PROPN
m-806	46	293	�	�	PROPN
m-806	46	294	�	�	PROPN
m-806	46	295	�	�	PROPN
m-806	46	296	�	�	PROPN
m-806	46	297	�	�	PROPN
m-806	46	298	�	�	PROPN
m-806	46	299	�	�	PROPN
m-806	46	300	�	�	PROPN
m-806	46	301	�	�	PROPN
m-806	46	302	�	�	PROPN
m-806	46	303	�	�	PROPN
m-806	46	304	�	�	PROPN
m-806	46	305	=	=	SYM
m-806	46	306	�	�	PROPN
m-806	46	307	(	(	PUNCT
m-806	46	308	5.9a	5.9a	NUM
m-806	46	309	)	)	PUNCT
m-806	46	310	∴	∴	PROPN
m-806	46	311	�	�	PROPN
m-806	46	312	(	(	PUNCT
m-806	46	313	�	�	PROPN
m-806	46	314	)	)	PUNCT
m-806	46	315	=	=	SYM
m-806	46	316	�	�	PROPN
m-806	46	317	�	�	PROPN
m-806	46	318	(	(	PUNCT
m-806	46	319	�	�	PROPN
m-806	46	320	)	)	PUNCT
m-806	46	321	(	(	PUNCT
m-806	46	322	1	1	NUM
m-806	46	323	−	−	PROPN
m-806	46	324	�	�	PROPN
m-806	46	325	�	�	PROPN
m-806	46	326	�	�	PROPN
m-806	46	327	2	2	NUM
m-806	46	328	�	�	PROPN
m-806	46	329	�	�	PROPN
m-806	46	330	)	)	PUNCT
m-806	46	331	(	(	PUNCT
m-806	46	332	5.9b	5.9b	NUM
m-806	46	333	)	)	PUNCT
m-806	46	334	on	on	ADP
m-806	46	335	substituting	substitute	VERB
m-806	46	336	(	(	PUNCT
m-806	46	337	5.7	5.7	NUM
m-806	46	338	)	)	PUNCT
m-806	46	339	into	into	ADP
m-806	46	340	(	(	PUNCT
m-806	46	341	5.4	5.4	NUM
m-806	46	342	)	)	PUNCT
m-806	46	343	,	,	PUNCT
m-806	46	344	we	we	PRON
m-806	46	345	easily	easily	ADV
m-806	46	346	get	get	VERB
m-806	46	347	�	�	NOUN
m-806	46	348	�	�	PROPN
m-806	46	349	(	(	PUNCT
m-806	46	350	�	�	PROPN
m-806	46	351	)	)	PUNCT
m-806	46	352	=	=	SYM
m-806	46	353	0	0	NUM
m-806	46	354	(	(	PUNCT
m-806	46	355	5.10	5.10	NUM
m-806	46	356	)	)	PUNCT
m-806	46	357	next	next	ADV
m-806	46	358	,	,	PUNCT
m-806	46	359	we	we	PRON
m-806	46	360	substitute	substitute	VERB
m-806	46	361	(	(	PUNCT
m-806	46	362	5.7	5.7	NUM
m-806	46	363	)	)	PUNCT
m-806	46	364	in	in	ADP
m-806	46	365	(	(	PUNCT
m-806	46	366	5.5	5.5	NUM
m-806	46	367	)	)	PUNCT
m-806	46	368	and	and	CCONJ
m-806	46	369	use	use	NOUN
m-806	46	370	(	(	PUNCT
m-806	46	371	5.9a	5.9a	NUM
m-806	46	372	,	,	PUNCT
m-806	46	373	b	b	NOUN
m-806	46	374	)	)	PUNCT
m-806	46	375	to	to	PART
m-806	46	376	get	get	VERB
m-806	46	377	�	�	PROPN
m-806	46	378	�	�	PROPN
m-806	46	379	�	�	PROPN
m-806	46	380	�	�	PROPN
m-806	46	381	(	(	PUNCT
m-806	46	382	�	�	PROPN
m-806	46	383	)	)	PUNCT
m-806	46	384	(	(	PUNCT
m-806	46	385	8	8	NUM
m-806	46	386	�	�	PROPN
m-806	46	387	�	�	PROPN
m-806	46	388	�	�	PROPN
m-806	46	389	−	−	PROPN
m-806	46	390	16	16	NUM
m-806	46	391	�	�	PROPN
m-806	46	392	�	�	PROPN
m-806	46	393	)	)	PUNCT
m-806	46	394	�	�	PROPN
m-806	46	395	�	�	PROPN
m-806	46	396	�	�	PROPN
m-806	46	397	2	2	NUM
m-806	46	398	�	�	PROPN
m-806	46	399	�	�	PROPN
m-806	46	400	+	+	SYM
m-806	46	401	�	�	PROPN
m-806	46	402	�	�	PROPN
m-806	46	403	(	(	PUNCT
m-806	46	404	�	�	PROPN
m-806	46	405	)	)	PUNCT
m-806	46	406	(	(	PUNCT
m-806	46	407	1	1	NUM
m-806	46	408	−	−	PROPN
m-806	46	409	�	�	PROPN
m-806	46	410	�	�	PROPN
m-806	46	411	�	�	PROPN
m-806	46	412	2	2	NUM
m-806	46	413	�	�	PROPN
m-806	46	414	�	�	PROPN
m-806	46	415	)	)	PUNCT
m-806	46	416	�	�	PROPN
m-806	46	417	=	=	SYM
m-806	46	418	�	�	PROPN
m-806	46	419	�	�	PROPN
m-806	46	420	�	�	PROPN
m-806	46	421	(	(	PUNCT
m-806	46	422	�	�	PROPN
m-806	46	423	)	)	PUNCT
m-806	46	424	�	�	PROPN
m-806	46	425	�	�	PROPN
m-806	46	426	(	(	PUNCT
m-806	46	427	1	1	NUM
m-806	46	428	−	−	PROPN
m-806	46	429	�	�	PROPN
m-806	46	430	�	�	PROPN
m-806	46	431	�	�	PROPN
m-806	46	432	2	2	NUM
m-806	46	433	�	�	PROPN
m-806	46	434	�	�	PROPN
m-806	46	435	)	)	PUNCT
m-806	46	436	�	�	PROPN
m-806	46	437	�	�	PROPN
m-806	46	438	�	�	PROPN
m-806	46	439	�	�	PROPN
m-806	46	440	�	�	PROPN
m-806	46	441	=	=	SYM
m-806	46	442	�	�	PROPN
m-806	46	443	�	�	PROPN
m-806	46	444	�	�	PROPN
m-806	46	445	(	(	PUNCT
m-806	46	446	�	�	PROPN
m-806	46	447	)	)	PUNCT
m-806	46	448	�	�	PROPN
m-806	46	449	�	�	PROPN
m-806	46	450	�	�	PROPN
m-806	46	451	�	�	PROPN
m-806	46	452	�	�	PROPN
m-806	46	453	−	−	PROPN
m-806	46	454	�	�	PROPN
m-806	46	455	�	�	PROPN
m-806	46	456	�	�	PROPN
m-806	46	457	�	�	PROPN
m-806	46	458	�	�	PROPN
m-806	46	459	�	�	PROPN
m-806	46	460	2	2	NUM
m-806	46	461	�	�	PROPN
m-806	46	462	�	�	PROPN
m-806	46	463	+	+	CCONJ
m-806	46	464	�	�	PROPN
m-806	46	465	�	�	PROPN
m-806	46	466	�	�	PROPN
m-806	46	467	�	�	PROPN
m-806	46	468	�	�	PROPN
m-806	46	469	4	4	NUM
m-806	46	470	�	�	PROPN
m-806	46	471	�	�	PROPN
m-806	46	472	−	−	PROPN
m-806	46	473	�	�	PROPN
m-806	46	474	�	�	PROPN
m-806	46	475	�	�	PROPN
m-806	46	476	�	�	PROPN
m-806	46	477	�	�	PROPN
m-806	46	478	6	6	NUM
m-806	46	479	�	�	PROPN
m-806	46	480	�	�	NOUN
m-806	46	481	�	�	NOUN
m-806	46	482	(5.11	(5.11	NOUN
m-806	46	483	)	)	PUNCT
m-806	46	484	we	we	PRON
m-806	46	485	multiply	multiply	VERB
m-806	46	486	(	(	PUNCT
m-806	46	487	5.11	5.11	NUM
m-806	46	488	)	)	PUNCT
m-806	46	489	through	through	ADP
m-806	46	490	by	by	ADP
m-806	46	491	cos2mx	cos2mx	PROPN
m-806	46	492	and	and	CCONJ
m-806	46	493	integrate	integrate	VERB
m-806	46	494	from	from	ADP
m-806	46	495	0	0	NUM
m-806	46	496	to	to	ADP
m-806	46	497	π	π	PROPN
m-806	46	498	,	,	PUNCT
m-806	46	499	to	to	PART
m-806	46	500	get	get	VERB
m-806	46	501	�	�	PROPN
m-806	46	502	�	�	PROPN
m-806	46	503	(	(	PUNCT
m-806	46	504	�	�	PROPN
m-806	46	505	)	)	PUNCT
m-806	46	506	=	=	SYM
m-806	46	507	�	�	PROPN
m-806	46	508	�	�	PROPN
m-806	46	509	�	�	PROPN
m-806	46	510	�	�	PROPN
m-806	46	511	�	�	PROPN
m-806	46	512	�	�	PROPN
m-806	46	513	(	(	PUNCT
m-806	46	514	�	�	PROPN
m-806	46	515	�	�	PROPN
m-806	46	516	�	�	PROPN
m-806	46	517	�	�	PROPN
m-806	46	518	�	�	PROPN
m-806	46	519	�	�	PROPN
m-806	46	520	�	�	PROPN
m-806	46	521	�	�	PROPN
m-806	46	522	�	�	PROPN
m-806	46	523	�	�	PROPN
m-806	46	524	�	�	PROPN
m-806	46	525	)	)	PUNCT
m-806	46	526	(	(	PUNCT
m-806	46	527	5.12	5.12	NUM
m-806	46	528	)	)	PUNCT
m-806	46	529	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	46	530	ijo	ijo	PROPN
m-806	46	531	journals	journal	NOUN
m-806	46	532	volume	volume	NOUN
m-806	46	533	07	07	NUM
m-806	46	534	|	|	ADV
m-806	46	535	issue	issue	NOUN
m-806	46	536	02	02	NUM
m-806	46	537	|	|	CCONJ
m-806	46	538	february	february	PROPN
m-806	46	539	2024	2024	NUM
m-806	46	540	|	|	ADV
m-806	46	541	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	46	542	4	4	NUM
m-806	46	543	ijo	ijo	PROPN
m-806	46	544	international	international	ADJ
m-806	46	545	journal	journal	PROPN
m-806	46	546	of	of	ADP
m-806	46	547	mathematics	mathematics	PROPN
m-806	46	548	(	(	PUNCT
m-806	46	549	issn	issn	PROPN
m-806	46	550	:	:	PUNCT
m-806	46	551	2992	2992	NUM
m-806	46	552	-	-	SYM
m-806	46	553	4421	4421	NUM
m-806	46	554	)	)	PUNCT
m-806	47	1	i.u	i.u	PROPN
m-806	47	2	.	.	PROPN
m-806	47	3	udo	udo	PROPN
m-806	47	4	-	-	PROPN
m-806	47	5	akpan1	akpan1	ADJ
m-806	47	6	*	*	PUNCT
m-806	47	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	47	8	volume	volume	NOUN
m-806	47	9	07	07	NUM
m-806	47	10	issue	issue	NOUN
m-806	47	11	02	02	NUM
m-806	47	12	||	||	NUM
m-806	47	13	february	february	PROPN
m-806	47	14	,	,	PUNCT
m-806	47	15	2024	2024	NUM
m-806	47	16	||	||	NOUN
m-806	48	1	on	on	ADP
m-806	48	2	a	a	DET
m-806	48	3	-	-	PUNCT
m-806	48	4	two	two	NUM
m-806	48	5	-	-	PUNCT
m-806	48	6	parameter	parameter	NOUN
m-806	48	7	dynamic	dynamic	ADJ
m-806	48	8	buckling	buckling	NOUN
m-806	48	9	of	of	ADP
m-806	48	10	a	a	DET
m-806	48	11	viscously	viscously	ADV
m-806	48	12	damped	damp	VERB
m-806	48	13	but	but	CCONJ
m-806	48	14	clamped	clamp	VERB
m-806	48	15	column	column	NOUN
m-806	48	16	stressed	stress	VERB
m-806	48	17	by	by	ADP
m-806	48	18	a	a	DET
m-806	48	19	step	step	NOUN
m-806	48	20	load	load	NOUN
m-806	48	21	next	next	ADV
m-806	48	22	,	,	PUNCT
m-806	48	23	we	we	PRON
m-806	48	24	multiply	multiply	VERB
m-806	48	25	(	(	PUNCT
m-806	48	26	5.11	5.11	NUM
m-806	48	27	)	)	PUNCT
m-806	48	28	by	by	ADP
m-806	48	29	cos4mx	cos4mx	NOUN
m-806	48	30	and	and	CCONJ
m-806	48	31	integrate	integrate	VERB
m-806	48	32	from	from	ADP
m-806	48	33	0	0	NUM
m-806	48	34	to	to	ADP
m-806	48	35	π	π	PROPN
m-806	48	36	to	to	PART
m-806	48	37	get	get	VERB
m-806	48	38	�	�	PROPN
m-806	48	39	�	�	PROPN
m-806	48	40	�	�	PROPN
m-806	48	41	(	(	PUNCT
m-806	48	42	�	�	PROPN
m-806	48	43	)	)	PUNCT
m-806	48	44	=	=	SYM
m-806	48	45	�	�	PROPN
m-806	48	46	�	�	PROPN
m-806	48	47	�	�	PROPN
m-806	48	48	�	�	PROPN
m-806	48	49	�	�	PROPN
m-806	48	50	�	�	PROPN
m-806	48	51	(	(	PUNCT
m-806	48	52	�	�	PROPN
m-806	48	53	�	�	PROPN
m-806	48	54	�	�	PROPN
m-806	48	55	�	�	PROPN
m-806	48	56	�	�	PROPN
m-806	48	57	�	�	PROPN
m-806	48	58	�	�	PROPN
m-806	48	59	�	�	PROPN
m-806	48	60	�	�	PROPN
m-806	48	61	�	�	PROPN
m-806	48	62	�	�	PROPN
m-806	48	63	�	�	PROPN
m-806	48	64	�	�	PROPN
m-806	48	65	)	)	PUNCT
m-806	48	66	(	(	PUNCT
m-806	48	67	5.13	5.13	NUM
m-806	48	68	)	)	PUNCT
m-806	48	69	lastly	lastly	ADV
m-806	48	70	,	,	PUNCT
m-806	48	71	we	we	PRON
m-806	48	72	multiply	multiply	VERB
m-806	48	73	(	(	PUNCT
m-806	48	74	5.11	5.11	NUM
m-806	48	75	)	)	PUNCT
m-806	48	76	by	by	ADP
m-806	48	77	cos6mx	cos6mx	NOUN
m-806	48	78	and	and	CCONJ
m-806	48	79	integrate	integrate	VERB
m-806	48	80	from	from	ADP
m-806	48	81	0	0	NUM
m-806	48	82	to	to	ADP
m-806	48	83	π	π	PROPN
m-806	48	84	and	and	CCONJ
m-806	48	85	get	get	VERB
m-806	48	86	,	,	PUNCT
m-806	48	87	�	�	PROPN
m-806	48	88	�	�	PROPN
m-806	48	89	�	�	PROPN
m-806	48	90	(	(	PUNCT
m-806	48	91	�	�	PROPN
m-806	48	92	)	)	PUNCT
m-806	48	93	=	=	SYM
m-806	48	94	�	�	PROPN
m-806	48	95	�	�	PROPN
m-806	48	96	�	�	PROPN
m-806	48	97	�	�	PROPN
m-806	48	98	�	�	PROPN
m-806	48	99	�	�	PROPN
m-806	48	100	�	�	PROPN
m-806	48	101	�	�	PROPN
m-806	48	102	�	�	PROPN
m-806	48	103	�	�	PROPN
m-806	48	104	�	�	PROPN
m-806	48	105	�	�	PROPN
m-806	48	106	�	�	PROPN
m-806	48	107	�	�	PROPN
m-806	48	108	�	�	PROPN
m-806	48	109	�	�	PROPN
m-806	48	110	�	�	PROPN
m-806	48	111	�	�	PROPN
m-806	48	112	�	�	PROPN
m-806	48	113	(	(	PUNCT
m-806	48	114	5.14	5.14	NUM
m-806	48	115	)	)	PUNCT
m-806	48	116	thus	thus	ADV
m-806	48	117	,	,	PUNCT
m-806	48	118	we	we	PRON
m-806	48	119	get	get	VERB
m-806	48	120	�	�	PROPN
m-806	48	121	(	(	PUNCT
m-806	48	122	�	�	PROPN
m-806	48	123	)	)	PUNCT
m-806	48	124	=	=	SYM
m-806	48	125	�	�	PROPN
m-806	48	126	�	�	PROPN
m-806	48	127	(	(	PUNCT
m-806	48	128	�	�	PROPN
m-806	48	129	)	)	PUNCT
m-806	48	130	(	(	PUNCT
m-806	48	131	1	1	NUM
m-806	48	132	−	−	PROPN
m-806	48	133	�	�	PROPN
m-806	48	134	�	�	PROPN
m-806	48	135	�	�	PROPN
m-806	48	136	2	2	NUM
m-806	48	137	�	�	PROPN
m-806	48	138	�	�	PROPN
m-806	48	139	)	)	PUNCT
m-806	48	140	+	+	SYM
m-806	48	141	�	�	PROPN
m-806	48	142	�	�	PROPN
m-806	48	143	�	�	PROPN
m-806	48	144	(	(	PUNCT
m-806	48	145	�	�	PROPN
m-806	48	146	)	)	PUNCT
m-806	48	147	(	(	PUNCT
m-806	48	148	1	1	NUM
m-806	48	149	−	−	PROPN
m-806	48	150	�	�	PROPN
m-806	48	151	�	�	PROPN
m-806	48	152	�	�	PROPN
m-806	48	153	4	4	NUM
m-806	48	154	�	�	PROPN
m-806	48	155	�	�	PROPN
m-806	48	156	)	)	PUNCT
m-806	48	157	+	+	SYM
m-806	48	158	�	�	PROPN
m-806	48	159	�	�	PROPN
m-806	48	160	�	�	PROPN
m-806	48	161	(	(	PUNCT
m-806	48	162	�	�	PROPN
m-806	48	163	)	)	PUNCT
m-806	48	164	(	(	PUNCT
m-806	48	165	1	1	NUM
m-806	48	166	−	−	PROPN
m-806	48	167	�	�	PROPN
m-806	48	168	�	�	PROPN
m-806	48	169	�	�	PROPN
m-806	48	170	6	6	NUM
m-806	48	171	�	�	PROPN
m-806	48	172	�	�	PROPN
m-806	48	173	)(5.15	)(5.15	NOUN
m-806	48	174	)	)	PUNCT
m-806	48	175	so	so	SCONJ
m-806	48	176	that	that	SCONJ
m-806	48	177	�	�	PROPN
m-806	48	178	(	(	PUNCT
m-806	48	179	�	�	PROPN
m-806	48	180	)	)	PUNCT
m-806	48	181	=	=	SYM
m-806	48	182	�	�	PROPN
m-806	48	183	�	�	PROPN
m-806	48	184	�	�	PROPN
m-806	48	185	(	(	PUNCT
m-806	48	186	�	�	PROPN
m-806	48	187	)	)	PUNCT
m-806	48	188	(	(	PUNCT
m-806	48	189	1	1	NUM
m-806	48	190	−	−	PROPN
m-806	48	191	�	�	PROPN
m-806	48	192	�	�	PROPN
m-806	48	193	�	�	PROPN
m-806	48	194	2	2	NUM
m-806	48	195	�	�	PROPN
m-806	48	196	�	�	PROPN
m-806	48	197	)	)	PUNCT
m-806	48	198	+	+	SYM
m-806	48	199	�	�	PROPN
m-806	48	200	�	�	PROPN
m-806	48	201	�	�	PROPN
m-806	48	202	�	�	PROPN
m-806	48	203	�	�	PROPN
m-806	48	204	(	(	PUNCT
m-806	48	205	�	�	PROPN
m-806	48	206	)	)	PUNCT
m-806	48	207	(	(	PUNCT
m-806	48	208	1	1	NUM
m-806	48	209	−	−	PROPN
m-806	48	210	�	�	PROPN
m-806	48	211	�	�	PROPN
m-806	48	212	�	�	PROPN
m-806	48	213	2	2	NUM
m-806	48	214	�	�	PROPN
m-806	48	215	�	�	PROPN
m-806	48	216	)	)	PUNCT
m-806	48	217	�	�	PROPN
m-806	48	218	+	+	SYM
m-806	48	219	�	�	PROPN
m-806	48	220	�	�	PROPN
m-806	48	221	�	�	PROPN
m-806	48	222	(	(	PUNCT
m-806	48	223	�	�	PROPN
m-806	48	224	)	)	PUNCT
m-806	48	225	(	(	PUNCT
m-806	48	226	1	1	NUM
m-806	48	227	−	−	PROPN
m-806	48	228	�	�	PROPN
m-806	48	229	�	�	PROPN
m-806	48	230	�	�	PROPN
m-806	48	231	4	4	NUM
m-806	48	232	�	�	PROPN
m-806	48	233	�	�	PROPN
m-806	48	234	)	)	PUNCT
m-806	48	235	�	�	PROPN
m-806	48	236	+	+	SYM
m-806	48	237	�	�	PROPN
m-806	48	238	�	�	PROPN
m-806	48	239	�	�	PROPN
m-806	48	240	(	(	PUNCT
m-806	48	241	�	�	PROPN
m-806	48	242	)	)	PUNCT
m-806	48	243	(	(	PUNCT
m-806	48	244	1	1	NUM
m-806	48	245	−	−	PROPN
m-806	48	246	�	�	PROPN
m-806	48	247	�	�	PROPN
m-806	48	248	�	�	PROPN
m-806	48	249	6	6	NUM
m-806	48	250	�	�	PROPN
m-806	48	251	�	�	NOUN
m-806	48	252	)	)	PUNCT
m-806	48	253	�	�	PROPN
m-806	48	254	+	+	CCONJ
m-806	48	255	…	…	PUNCT
m-806	48	256	(	(	PUNCT
m-806	48	257	5.16	5.16	NUM
m-806	48	258	)	)	PUNCT
m-806	48	259	before	before	ADP
m-806	48	260	determining	determine	VERB
m-806	48	261	the	the	DET
m-806	48	262	static	static	ADJ
m-806	48	263	buckling	buckling	NOUN
m-806	48	264	load	load	NOUN
m-806	48	265	,	,	PUNCT
m-806	48	266	we	we	PRON
m-806	48	267	need	need	VERB
m-806	48	268	to	to	PART
m-806	48	269	evaluate	evaluate	VERB
m-806	48	270	(	(	PUNCT
m-806	48	271	5.16	5.16	NUM
m-806	48	272	)	)	PUNCT
m-806	48	273	at	at	ADP
m-806	48	274	�	�	PROPN
m-806	48	275	=	=	SYM
m-806	48	276	�	�	PROPN
m-806	48	277	�	�	PROPN
m-806	48	278	�	�	PROPN
m-806	48	279	.	.	PUNCT
m-806	49	1	this	this	PRON
m-806	49	2	is	be	AUX
m-806	49	3	informed	inform	VERB
m-806	49	4	by	by	ADP
m-806	49	5	the	the	DET
m-806	49	6	fact	fact	NOUN
m-806	49	7	that	that	SCONJ
m-806	49	8	eventually	eventually	ADV
m-806	49	9	,	,	PUNCT
m-806	49	10	we	we	PRON
m-806	49	11	shall	shall	AUX
m-806	49	12	need	need	VERB
m-806	49	13	to	to	PART
m-806	49	14	determine	determine	VERB
m-806	49	15	the	the	DET
m-806	49	16	associated	associated	ADJ
m-806	49	17	dynamic	dynamic	ADJ
m-806	49	18	problem	problem	NOUN
m-806	49	19	at	at	ADP
m-806	49	20	�	�	PROPN
m-806	49	21	=	=	SYM
m-806	49	22	�	�	PROPN
m-806	49	23	�	�	PROPN
m-806	49	24	�	�	PROPN
m-806	49	25	(	(	PUNCT
m-806	49	26	which	which	PRON
m-806	49	27	also	also	ADV
m-806	49	28	means	mean	VERB
m-806	49	29	finding	find	VERB
m-806	49	30	the	the	DET
m-806	49	31	maximum	maximum	NOUN
m-806	49	32	of	of	ADP
m-806	49	33	(	(	PUNCT
m-806	49	34	5.16	5.16	NUM
m-806	49	35	)	)	PUNCT
m-806	49	36	)	)	PUNCT
m-806	49	37	.	.	PUNCT
m-806	50	1	such	such	ADJ
m-806	50	2	evaluation	evaluation	NOUN
m-806	50	3	yields	yield	VERB
m-806	50	4	�	�	PROPN
m-806	50	5	=	=	SYM
m-806	50	6	2	2	NUM
m-806	50	7	�	�	PROPN
m-806	50	8	�	�	PROPN
m-806	50	9	�	�	PROPN
m-806	50	10	(	(	PUNCT
m-806	50	11	�	�	PROPN
m-806	50	12	)	)	PUNCT
m-806	50	13	+	+	CCONJ
m-806	50	14	2	2	NUM
m-806	50	15	�	�	PROPN
m-806	50	16	�	�	PROPN
m-806	50	17	�	�	PROPN
m-806	50	18	�	�	PROPN
m-806	50	19	�	�	PROPN
m-806	50	20	(	(	PUNCT
m-806	50	21	�	�	PROPN
m-806	50	22	)	)	PUNCT
m-806	50	23	−	−	PROPN
m-806	50	24	�	�	PROPN
m-806	50	25	�	�	PROPN
m-806	50	26	�	�	PROPN
m-806	50	27	(	(	PUNCT
m-806	50	28	�	�	PROPN
m-806	50	29	)	)	PUNCT
m-806	50	30	�	�	PROPN
m-806	50	31	+	+	CCONJ
m-806	50	32	…	…	PUNCT
m-806	50	33	(	(	PUNCT
m-806	50	34	5.17	5.17	NUM
m-806	50	35	)	)	PUNCT
m-806	50	36	we	we	PRON
m-806	50	37	can	can	AUX
m-806	50	38	write	write	VERB
m-806	50	39	(	(	PUNCT
m-806	50	40	5.17	5.17	NUM
m-806	50	41	)	)	PUNCT
m-806	50	42	as	as	ADP
m-806	50	43	�	�	PROPN
m-806	50	44	=	=	SYM
m-806	50	45	�	�	PROPN
m-806	50	46	�	�	PROPN
m-806	50	47	�	�	PROPN
m-806	50	48	+	+	SYM
m-806	50	49	�	�	PROPN
m-806	50	50	�	�	PROPN
m-806	50	51	�	�	PROPN
m-806	50	52	�	�	PROPN
m-806	50	53	+	+	CCONJ
m-806	50	54	…	…	PUNCT
m-806	50	55	(	(	PUNCT
m-806	50	56	5.18	5.18	NUM
m-806	50	57	)	)	PUNCT
m-806	50	58	where	where	SCONJ
m-806	50	59	,	,	PUNCT
m-806	50	60	�	�	PROPN
m-806	50	61	�	�	PROPN
m-806	50	62	=	=	SYM
m-806	50	63	2	2	NUM
m-806	50	64	�	�	PROPN
m-806	50	65	�	�	PROPN
m-806	50	66	(	(	PUNCT
m-806	50	67	�	�	PROPN
m-806	50	68	)	)	PUNCT
m-806	50	69	,	,	PUNCT
m-806	50	70	�	�	PROPN
m-806	50	71	�	�	PROPN
m-806	50	72	=	=	SYM
m-806	50	73	2	2	NUM
m-806	50	74	�	�	PROPN
m-806	50	75	�	�	PROPN
m-806	50	76	�	�	PROPN
m-806	50	77	(	(	PUNCT
m-806	50	78	�	�	PROPN
m-806	50	79	)	)	PUNCT
m-806	50	80	−	−	PROPN
m-806	50	81	�	�	PROPN
m-806	50	82	�	�	PROPN
m-806	50	83	�	�	PROPN
m-806	50	84	(	(	PUNCT
m-806	50	85	�	�	PROPN
m-806	50	86	)	)	PUNCT
m-806	50	87	�	�	PROPN
m-806	50	88	(	(	PUNCT
m-806	50	89	5.19	5.19	NUM
m-806	50	90	)	)	PUNCT
m-806	50	91	as	as	ADP
m-806	50	92	in	in	ADP
m-806	50	93	[	[	X
m-806	50	94	18	18	NUM
m-806	50	95	]	]	PUNCT
m-806	50	96	,	,	PUNCT
m-806	50	97	the	the	DET
m-806	50	98	static	static	ADJ
m-806	50	99	buckling	buckling	NOUN
m-806	50	100	load	load	NOUN
m-806	50	101	is	be	AUX
m-806	50	102	obtained	obtain	VERB
m-806	50	103	by	by	ADP
m-806	50	104	first	first	ADV
m-806	50	105	reversing	reverse	VERB
m-806	50	106	the	the	DET
m-806	50	107	series	series	NOUN
m-806	50	108	(	(	PUNCT
m-806	50	109	5.18	5.18	NUM
m-806	50	110	)	)	PUNCT
m-806	50	111	in	in	ADP
m-806	50	112	the	the	DET
m-806	50	113	form	form	NOUN
m-806	50	114	,	,	PUNCT
m-806	50	115	�	�	PROPN
m-806	50	116	=	=	SYM
m-806	50	117	�	�	PROPN
m-806	50	118	�	�	PROPN
m-806	50	119	�	�	PROPN
m-806	50	120	+	+	SYM
m-806	50	121	�	�	PROPN
m-806	50	122	�	�	PROPN
m-806	50	123	�	�	PROPN
m-806	50	124	�	�	PROPN
m-806	50	125	+	+	CCONJ
m-806	50	126	…	…	PUNCT
m-806	50	127	(	(	PUNCT
m-806	50	128	5.20	5.20	NUM
m-806	50	129	)	)	PUNCT
m-806	50	130	on	on	ADP
m-806	50	131	substituting	substitute	VERB
m-806	50	132	for	for	ADP
m-806	50	133	w	w	NOUN
m-806	50	134	from	from	ADP
m-806	50	135	(	(	PUNCT
m-806	50	136	5.18	5.18	NUM
m-806	50	137	)	)	PUNCT
m-806	50	138	in	in	ADP
m-806	50	139	(	(	PUNCT
m-806	50	140	5.20	5.20	NUM
m-806	50	141	)	)	PUNCT
m-806	50	142	and	and	CCONJ
m-806	50	143	equating	equate	VERB
m-806	50	144	the	the	DET
m-806	50	145	coefficients	coefficient	NOUN
m-806	50	146	of	of	ADP
m-806	50	147	powers	power	NOUN
m-806	50	148	of	of	ADP
m-806	50	149	ϵ	ϵ	NUM
m-806	50	150	,	,	PUNCT
m-806	50	151	we	we	PRON
m-806	50	152	get	get	VERB
m-806	50	153	�	�	NOUN
m-806	50	154	�	�	PROPN
m-806	50	155	=	=	SYM
m-806	50	156	�	�	PROPN
m-806	50	157	�	�	PROPN
m-806	50	158	�	�	PROPN
m-806	50	159	,	,	PUNCT
m-806	50	160	�	�	PROPN
m-806	50	161	�	�	PROPN
m-806	50	162	=	=	SYM
m-806	50	163	�	�	PROPN
m-806	50	164	�	�	PROPN
m-806	50	165	�	�	PROPN
m-806	50	166	�	�	PROPN
m-806	50	167	�	�	PROPN
m-806	50	168	�	�	PROPN
m-806	50	169	(	(	PUNCT
m-806	50	170	5.21	5.21	NUM
m-806	50	171	)	)	PUNCT
m-806	50	172	the	the	DET
m-806	50	173	maximization	maximization	NOUN
m-806	50	174	(	(	PUNCT
m-806	50	175	4.4	4.4	NUM
m-806	50	176	)	)	PUNCT
m-806	50	177	is	be	AUX
m-806	50	178	now	now	ADV
m-806	50	179	easily	easily	ADV
m-806	50	180	executed	execute	VERB
m-806	50	181	from	from	ADP
m-806	50	182	(	(	PUNCT
m-806	50	183	5.20	5.20	NUM
m-806	50	184	)	)	PUNCT
m-806	50	185	to	to	PART
m-806	50	186	yield	yield	VERB
m-806	50	187	�	�	PROPN
m-806	50	188	�	�	PROPN
m-806	50	189	+	+	CCONJ
m-806	50	190	3	3	NUM
m-806	50	191	�	�	PROPN
m-806	50	192	�	�	PROPN
m-806	50	193	�	�	PROPN
m-806	50	194	�	�	PROPN
m-806	50	195	�	�	PROPN
m-806	50	196	=	=	SYM
m-806	50	197	0	0	PUNCT
m-806	50	198	(	(	PUNCT
m-806	50	199	5.22	5.22	NUM
m-806	50	200	)	)	PUNCT
m-806	50	201	where	where	SCONJ
m-806	50	202	,	,	PUNCT
m-806	50	203	�	�	PROPN
m-806	50	204	�	�	PROPN
m-806	50	205	is	be	AUX
m-806	50	206	the	the	DET
m-806	50	207	value	value	NOUN
m-806	50	208	of	of	ADP
m-806	50	209	�	�	PROPN
m-806	50	210	evaluated	evaluate	VERB
m-806	50	211	at	at	ADP
m-806	50	212	static	static	ADJ
m-806	50	213	buckling	buckling	NOUN
m-806	50	214	.	.	PUNCT
m-806	51	1	from	from	ADP
m-806	51	2	(	(	PUNCT
m-806	51	3	5.18	5.18	NUM
m-806	51	4	)	)	PUNCT
m-806	51	5	,	,	PUNCT
m-806	51	6	we	we	PRON
m-806	51	7	get	get	VERB
m-806	51	8	�	�	NOUN
m-806	51	9	�	�	PROPN
m-806	51	10	=	=	SYM
m-806	51	11	�	�	PROPN
m-806	51	12	�	�	PROPN
m-806	51	13	�	�	PROPN
m-806	51	14	�	�	PROPN
m-806	51	15	�	�	PROPN
m-806	51	16	�	�	PROPN
m-806	51	17	�	�	PROPN
m-806	51	18	=	=	SYM
m-806	51	19	�	�	PROPN
m-806	51	20	√	√	NUM
m-806	51	21	�	�	PROPN
m-806	51	22	�	�	PROPN
m-806	51	23	�	�	PROPN
m-806	51	24	�	�	PROPN
m-806	51	25	�	�	PROPN
m-806	51	26	�	�	PROPN
m-806	51	27	�	�	PROPN
m-806	51	28	�	�	PROPN
m-806	51	29	�	�	PROPN
m-806	51	30	�	�	PROPN
m-806	51	31	(	(	PUNCT
m-806	51	32	5.23	5.23	NUM
m-806	51	33	)	)	PUNCT
m-806	51	34	next	next	ADV
m-806	51	35	,	,	PUNCT
m-806	51	36	we	we	PRON
m-806	51	37	determine	determine	VERB
m-806	51	38	(	(	PUNCT
m-806	51	39	5.20	5.20	NUM
m-806	51	40	)	)	PUNCT
m-806	51	41	at	at	ADP
m-806	51	42	static	static	ADJ
m-806	51	43	buckling	buckling	NOUN
m-806	51	44	and	and	CCONJ
m-806	51	45	get	get	VERB
m-806	51	46	�	�	PROPN
m-806	51	47	=	=	SYM
m-806	51	48	�	�	PROPN
m-806	51	49	�	�	PROPN
m-806	51	50	�	�	PROPN
m-806	51	51	+	+	SYM
m-806	51	52	�	�	PROPN
m-806	51	53	�	�	PROPN
m-806	51	54	�	�	PROPN
m-806	51	55	�	�	PROPN
m-806	51	56	+	+	CCONJ
m-806	51	57	…	…	PUNCT
m-806	51	58	=	=	SYM
m-806	51	59	�	�	PROPN
m-806	51	60	�	�	PROPN
m-806	51	61	(	(	PUNCT
m-806	51	62	�	�	PROPN
m-806	51	63	�	�	PROPN
m-806	51	64	+	+	SYM
m-806	51	65	�	�	PROPN
m-806	51	66	�	�	PROPN
m-806	51	67	�	�	PROPN
m-806	51	68	�	�	PROPN
m-806	51	69	�	�	PROPN
m-806	51	70	)	)	PUNCT
m-806	51	71	=	=	SYM
m-806	51	72	�	�	PROPN
m-806	51	73	�	�	PROPN
m-806	51	74	√	√	NUM
m-806	51	75	�	�	PROPN
m-806	51	76	�	�	PROPN
m-806	51	77	�	�	PROPN
m-806	51	78	�	�	PROPN
m-806	51	79	�	�	PROPN
m-806	51	80	�	�	PROPN
m-806	51	81	�	�	PROPN
m-806	51	82	�	�	PROPN
m-806	51	83	�	�	PROPN
m-806	51	84	(	(	PUNCT
m-806	51	85	5.24	5.24	NUM
m-806	51	86	)	)	PUNCT
m-806	51	87	on	on	ADP
m-806	51	88	substituting	substitute	VERB
m-806	51	89	in	in	ADP
m-806	51	90	(	(	PUNCT
m-806	51	91	5.24	5.24	NUM
m-806	51	92	)	)	PUNCT
m-806	51	93	for	for	ADP
m-806	51	94	�	�	PROPN
m-806	51	95	�	�	PROPN
m-806	51	96	and	and	CCONJ
m-806	51	97	�	�	PROPN
m-806	51	98	�	�	PROPN
m-806	51	99	,	,	PUNCT
m-806	51	100	we	we	PRON
m-806	51	101	get	get	VERB
m-806	51	102	(	(	PUNCT
m-806	51	103	16	16	NUM
m-806	51	104	�	�	PROPN
m-806	51	105	�	�	PROPN
m-806	51	106	−	−	PROPN
m-806	51	107	8	8	NUM
m-806	51	108	�	�	PROPN
m-806	51	109	�	�	PROPN
m-806	51	110	�	�	PROPN
m-806	51	111	�	�	PROPN
m-806	51	112	+	+	CCONJ
m-806	51	113	1	1	NUM
m-806	51	114	)	)	PUNCT
m-806	51	115	�	�	PROPN
m-806	51	116	�	�	PROPN
m-806	51	117	=	=	SYM
m-806	51	118	18√5	18√5	NUM
m-806	51	119	�	�	PROPN
m-806	51	120	�	�	PROPN
m-806	51	121	�	�	PROPN
m-806	51	122	�	�	PROPN
m-806	51	123	�	�	PROPN
m-806	51	124	�	�	PROPN
m-806	51	125	�	�	PROPN
m-806	51	126	�	�	PROPN
m-806	51	127	�	�	PROPN
m-806	51	128	�	�	PROPN
m-806	51	129	�	�	PROPN
m-806	51	130	�	�	PROPN
m-806	51	131	1	1	NUM
m-806	51	132	+	+	NUM
m-806	51	133	�	�	PROPN
m-806	51	134	�	�	PROPN
m-806	51	135	�	�	PROPN
m-806	51	136	�	�	PROPN
m-806	51	137	�	�	PROPN
m-806	51	138	�	�	PROPN
m-806	51	139	�	�	PROPN
m-806	51	140	�	�	PROPN
m-806	51	141	�	�	PROPN
m-806	51	142	�	�	PROPN
m-806	51	143	�	�	PROPN
m-806	51	144	�	�	PROPN
m-806	51	145	�	�	PROPN
m-806	51	146	�	�	PROPN
m-806	51	147	�	�	PROPN
m-806	51	148	�	�	PROPN
m-806	51	149	�	�	PROPN
m-806	51	150	�	�	PROPN
m-806	51	151	�	�	PROPN
m-806	51	152	�	�	PROPN
m-806	51	153	�	�	PROPN
m-806	51	154	�	�	PROPN
m-806	51	155	�	�	PROPN
m-806	51	156	�	�	PROPN
m-806	51	157	�	�	PROPN
m-806	51	158	�	�	PROPN
m-806	51	159	�	�	PROPN
m-806	51	160	�	�	PROPN
m-806	51	161	�	�	PROPN
m-806	51	162	�	�	PROPN
m-806	51	163	�	�	PROPN
m-806	51	164	�	�	PROPN
m-806	51	165	�	�	PROPN
m-806	51	166	�	�	PROPN
m-806	51	167	�	�	PROPN
m-806	51	168	(	(	PUNCT
m-806	51	169	5.25	5.25	NUM
m-806	51	170	)	)	PUNCT
m-806	51	171	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	51	172	ijo	ijo	PROPN
m-806	51	173	journals	journal	NOUN
m-806	51	174	volume	volume	NOUN
m-806	51	175	07	07	NUM
m-806	51	176	|	|	ADV
m-806	51	177	issue	issue	NOUN
m-806	51	178	02	02	NUM
m-806	51	179	|	|	CCONJ
m-806	51	180	february	february	PROPN
m-806	51	181	2024	2024	NUM
m-806	52	1	|	|	ADV
m-806	52	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	52	3	5	5	NUM
m-806	52	4	ijo	ijo	PROPN
m-806	52	5	international	international	ADJ
m-806	52	6	journal	journal	PROPN
m-806	52	7	of	of	ADP
m-806	52	8	mathematics	mathematics	PROPN
m-806	52	9	(	(	PUNCT
m-806	52	10	issn	issn	PROPN
m-806	52	11	:	:	PUNCT
m-806	52	12	2992	2992	NUM
m-806	52	13	-	-	SYM
m-806	52	14	4421	4421	NUM
m-806	52	15	)	)	PUNCT
m-806	52	16	i.u	i.u	PROPN
m-806	52	17	.	.	PROPN
m-806	52	18	udo	udo	PROPN
m-806	52	19	-	-	PROPN
m-806	52	20	akpan1	akpan1	ADJ
m-806	52	21	*	*	PUNCT
m-806	52	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	52	23	volume	volume	NOUN
m-806	52	24	07	07	NUM
m-806	52	25	issue	issue	NOUN
m-806	52	26	02	02	NUM
m-806	52	27	||	||	NUM
m-806	52	28	february	february	PROPN
m-806	52	29	,	,	PUNCT
m-806	52	30	2024	2024	NUM
m-806	52	31	||	||	NOUN
m-806	52	32	on	on	ADP
m-806	52	33	a	a	DET
m-806	52	34	-	-	PUNCT
m-806	52	35	two	two	NUM
m-806	52	36	-	-	PUNCT
m-806	52	37	parameter	parameter	NOUN
m-806	52	38	dynamic	dynamic	ADJ
m-806	52	39	buckling	buckling	NOUN
m-806	52	40	of	of	ADP
m-806	52	41	a	a	DET
m-806	52	42	viscously	viscously	ADV
m-806	52	43	damped	damp	VERB
m-806	52	44	but	but	CCONJ
m-806	52	45	clamped	clamp	VERB
m-806	52	46	column	column	NOUN
m-806	52	47	stressed	stress	VERB
m-806	52	48	by	by	ADP
m-806	52	49	a	a	DET
m-806	52	50	step	step	NOUN
m-806	52	51	load	load	NOUN
m-806	52	52	where	where	SCONJ
m-806	52	53	�	�	PROPN
m-806	52	54	�	�	PROPN
m-806	52	55	is	be	AUX
m-806	52	56	the	the	DET
m-806	52	57	static	static	ADJ
m-806	52	58	buckling	buckling	NOUN
m-806	52	59	load	load	NOUN
m-806	52	60	.	.	PUNCT
m-806	53	1	the	the	DET
m-806	53	2	least	least	ADJ
m-806	53	3	value	value	NOUN
m-806	53	4	of	of	ADP
m-806	53	5	�	�	PROPN
m-806	53	6	�	�	PROPN
m-806	53	7	is	be	AUX
m-806	53	8	obtained	obtain	VERB
m-806	53	9	when	when	SCONJ
m-806	53	10	�	�	PROPN
m-806	53	11	=	=	SYM
m-806	53	12	1	1	NUM
m-806	53	13	,	,	PUNCT
m-806	53	14	and	and	CCONJ
m-806	53	15	for	for	ADP
m-806	53	16	this	this	PRON
m-806	53	17	,	,	PUNCT
m-806	53	18	we	we	PRON
m-806	53	19	get	get	VERB
m-806	53	20	(	(	PUNCT
m-806	53	21	17	17	NUM
m-806	53	22	−	−	NUM
m-806	53	23	8	8	NUM
m-806	53	24	�	�	PROPN
m-806	53	25	�	�	PROPN
m-806	53	26	)	)	PUNCT
m-806	53	27	�	�	PROPN
m-806	53	28	�	�	PROPN
m-806	53	29	=	=	SYM
m-806	53	30	18√5	18√5	NUM
m-806	53	31	�	�	PROPN
m-806	53	32	�	�	PROPN
m-806	53	33	�	�	PROPN
m-806	53	34	�	�	PROPN
m-806	53	35	�	�	PROPN
m-806	53	36	�	�	PROPN
m-806	53	37	�	�	PROPN
m-806	53	38	�	�	PROPN
m-806	53	39	�	�	PROPN
m-806	53	40	�	�	PROPN
m-806	53	41	1	1	NUM
m-806	53	42	+	+	NUM
m-806	53	43	�	�	PROPN
m-806	53	44	�	�	PROPN
m-806	53	45	�	�	PROPN
m-806	53	46	�	�	PROPN
m-806	53	47	�	�	PROPN
m-806	53	48	�	�	PROPN
m-806	53	49	�	�	PROPN
m-806	53	50	�	�	PROPN
m-806	53	51	�	�	PROPN
m-806	53	52	�	�	PROPN
m-806	53	53	�	�	PROPN
m-806	53	54	�	�	PROPN
m-806	53	55	�	�	PROPN
m-806	53	56	�	�	PROPN
m-806	53	57	�	�	PROPN
m-806	53	58	�	�	PROPN
m-806	53	59	�	�	PROPN
m-806	53	60	�	�	PROPN
m-806	53	61	�	�	PROPN
m-806	53	62	�	�	PROPN
m-806	53	63	�	�	PROPN
m-806	53	64	�	�	PROPN
m-806	53	65	(	(	PUNCT
m-806	53	66	5.26	5.26	NUM
m-806	53	67	)	)	PUNCT
m-806	53	68	if	if	SCONJ
m-806	53	69	it	it	PRON
m-806	53	70	is	be	AUX
m-806	53	71	required	require	VERB
m-806	53	72	that	that	SCONJ
m-806	53	73	the	the	DET
m-806	53	74	buckling	buckle	VERB
m-806	53	75	mode	mode	NOUN
m-806	53	76	be	be	AUX
m-806	53	77	strictly	strictly	ADV
m-806	53	78	in	in	ADP
m-806	53	79	the	the	DET
m-806	53	80	shape	shape	NOUN
m-806	53	81	of	of	ADP
m-806	53	82	imperfection	imperfection	NOUN
m-806	53	83	,	,	PUNCT
m-806	53	84	then	then	ADV
m-806	53	85	the	the	DET
m-806	53	86	results	result	NOUN
m-806	53	87	corresponding	correspond	VERB
m-806	53	88	to	to	ADP
m-806	53	89	(	(	PUNCT
m-806	53	90	5.25	5.25	NUM
m-806	53	91	)	)	PUNCT
m-806	53	92	and	and	CCONJ
m-806	53	93	(	(	PUNCT
m-806	53	94	5.26	5.26	NUM
m-806	53	95	)	)	PUNCT
m-806	53	96	respectively	respectively	ADV
m-806	53	97	become	become	VERB
m-806	53	98	(	(	PUNCT
m-806	53	99	16	16	NUM
m-806	53	100	�	�	PROPN
m-806	53	101	�	�	PROPN
m-806	53	102	−	−	PROPN
m-806	53	103	8	8	NUM
m-806	53	104	�	�	PROPN
m-806	53	105	�	�	PROPN
m-806	53	106	�	�	PROPN
m-806	53	107	�	�	PROPN
m-806	53	108	+	+	CCONJ
m-806	53	109	1	1	NUM
m-806	53	110	)	)	PUNCT
m-806	53	111	�	�	PROPN
m-806	53	112	�	�	PROPN
m-806	53	113	=	=	SYM
m-806	53	114	18√5	18√5	NUM
m-806	53	115	�	�	PROPN
m-806	53	116	�	�	PROPN
m-806	53	117	�	�	PROPN
m-806	53	118	�	�	PROPN
m-806	53	119	�	�	PROPN
m-806	53	120	�	�	PROPN
m-806	53	121	�	�	PROPN
m-806	53	122	�	�	PROPN
m-806	53	123	�	�	PROPN
m-806	53	124	�	�	PROPN
m-806	53	125	�	�	PROPN
m-806	53	126	(	(	PUNCT
m-806	53	127	5.27	5.27	NUM
m-806	53	128	)	)	PUNCT
m-806	53	129	and	and	CCONJ
m-806	53	130	(	(	PUNCT
m-806	53	131	17	17	NUM
m-806	53	132	−	−	PROPN
m-806	53	133	8	8	NUM
m-806	53	134	�	�	PROPN
m-806	53	135	�	�	PROPN
m-806	53	136	)	)	PUNCT
m-806	53	137	�	�	PROPN
m-806	53	138	�	�	PROPN
m-806	53	139	=	=	SYM
m-806	53	140	18√5	18√5	NUM
m-806	53	141	�	�	PROPN
m-806	53	142	�	�	PROPN
m-806	53	143	�	�	PROPN
m-806	53	144	�	�	PROPN
m-806	53	145	�	�	PROPN
m-806	53	146	�	�	PROPN
m-806	53	147	�	�	PROPN
m-806	53	148	�	�	PROPN
m-806	53	149	�	�	PROPN
m-806	53	150	(	(	PUNCT
m-806	53	151	5.28	5.28	NUM
m-806	53	152	)	)	PUNCT
m-806	53	153	by	by	ADP
m-806	53	154	way	way	NOUN
m-806	53	155	of	of	ADP
m-806	53	156	comparison	comparison	NOUN
m-806	53	157	,	,	PUNCT
m-806	53	158	we	we	PRON
m-806	53	159	can	can	AUX
m-806	53	160	perform	perform	VERB
m-806	53	161	a	a	DET
m-806	53	162	similar	similar	ADJ
m-806	53	163	analysis	analysis	NOUN
m-806	53	164	on	on	ADP
m-806	53	165	the	the	DET
m-806	53	166	same	same	ADJ
m-806	53	167	column	column	NOUN
m-806	53	168	but	but	CCONJ
m-806	53	169	with	with	ADP
m-806	53	170	simply	simply	ADV
m-806	53	171	-	-	PUNCT
m-806	53	172	supported	support	VERB
m-806	53	173	end	end	NOUN
m-806	53	174	conditions	condition	NOUN
m-806	53	175	and	and	CCONJ
m-806	53	176	the	the	DET
m-806	53	177	results	result	NOUN
m-806	53	178	corresponding	correspond	VERB
m-806	53	179	to	to	ADP
m-806	53	180	those	those	PRON
m-806	53	181	of	of	ADP
m-806	53	182	(	(	PUNCT
m-806	53	183	5.25	5.25	NUM
m-806	53	184	)	)	PUNCT
m-806	53	185	,	,	PUNCT
m-806	53	186	(	(	PUNCT
m-806	53	187	5.26	5.26	NUM
m-806	53	188	)	)	PUNCT
m-806	53	189	,	,	PUNCT
m-806	53	190	(	(	PUNCT
m-806	53	191	5.27	5.27	NUM
m-806	53	192	)	)	PUNCT
m-806	53	193	and	and	CCONJ
m-806	53	194	(	(	PUNCT
m-806	53	195	5.28	5.28	NUM
m-806	53	196	)	)	PUNCT
m-806	53	197	are	be	AUX
m-806	53	198	respectively	respectively	ADV
m-806	53	199	given	give	VERB
m-806	53	200	by	by	ADP
m-806	53	201	(	(	PUNCT
m-806	53	202	�	�	PROPN
m-806	53	203	�	�	PROPN
m-806	53	204	−	−	PROPN
m-806	53	205	2	2	NUM
m-806	53	206	�	�	PROPN
m-806	53	207	�	�	PROPN
m-806	53	208	�	�	PROPN
m-806	53	209	�	�	PROPN
m-806	53	210	+	+	CCONJ
m-806	53	211	1	1	NUM
m-806	53	212	)	)	PUNCT
m-806	53	213	�	�	PROPN
m-806	53	214	�	�	PROPN
m-806	53	215	=	=	SYM
m-806	53	216	�	�	PROPN
m-806	53	217	�	�	PROPN
m-806	53	218	�	�	PROPN
m-806	53	219	�	�	PROPN
m-806	53	220	�	�	PROPN
m-806	53	221	�	�	PROPN
m-806	53	222	�	�	PROPN
m-806	53	223	�	�	PROPN
m-806	53	224	�	�	PROPN
m-806	53	225	�	�	PROPN
m-806	53	226	�	�	PROPN
m-806	53	227	�	�	PROPN
m-806	53	228	�	�	PROPN
m-806	53	229	�	�	PROPN
m-806	53	230	1	1	NUM
m-806	53	231	+	+	NUM
m-806	53	232	�	�	PROPN
m-806	53	233	�	�	PROPN
m-806	53	234	�	�	PROPN
m-806	53	235	�	�	PROPN
m-806	53	236	�	�	PROPN
m-806	53	237	�	�	PROPN
m-806	53	238	�	�	PROPN
m-806	53	239	�	�	PROPN
m-806	53	240	�	�	PROPN
m-806	53	241	�	�	PROPN
m-806	53	242	�	�	PROPN
m-806	53	243	�	�	PROPN
m-806	53	244	�	�	PROPN
m-806	53	245	�	�	PROPN
m-806	53	246	�	�	PROPN
m-806	53	247	�	�	PROPN
m-806	53	248	�	�	PROPN
m-806	53	249	�	�	PROPN
m-806	53	250	�	�	PROPN
m-806	53	251	�	�	PROPN
m-806	53	252	�	�	PROPN
m-806	53	253	�	�	PROPN
m-806	53	254	�	�	PROPN
m-806	53	255	�	�	PROPN
m-806	53	256	�	�	PROPN
m-806	53	257	�	�	PROPN
m-806	53	258	�	�	PROPN
m-806	53	259	�	�	PROPN
m-806	53	260	(	(	PUNCT
m-806	53	261	5.29	5.29	NUM
m-806	53	262	)	)	PUNCT
m-806	53	263	(	(	PUNCT
m-806	53	264	1	1	NUM
m-806	53	265	−	−	PROPN
m-806	53	266	�	�	PROPN
m-806	53	267	�	�	PROPN
m-806	53	268	)	)	PUNCT
m-806	53	269	�	�	PROPN
m-806	53	270	�	�	PROPN
m-806	53	271	=	=	SYM
m-806	53	272	�	�	PROPN
m-806	53	273	�	�	PROPN
m-806	53	274	√	√	NUM
m-806	53	275	�	�	PROPN
m-806	53	276	�	�	PROPN
m-806	53	277	�	�	PROPN
m-806	53	278	�	�	PROPN
m-806	53	279	�	�	PROPN
m-806	53	280	�	�	PROPN
m-806	53	281	�	�	PROPN
m-806	53	282	�	�	PROPN
m-806	53	283	�	�	PROPN
m-806	53	284	�	�	PROPN
m-806	53	285	�	�	PROPN
m-806	53	286	1	1	NUM
m-806	53	287	+	+	NUM
m-806	53	288	�	�	PROPN
m-806	53	289	�	�	PROPN
m-806	53	290	�	�	PROPN
m-806	53	291	�	�	PROPN
m-806	53	292	�	�	PROPN
m-806	53	293	�	�	PROPN
m-806	53	294	�	�	PROPN
m-806	53	295	�	�	PROPN
m-806	53	296	�	�	PROPN
m-806	53	297	�	�	PROPN
m-806	53	298	�	�	PROPN
m-806	53	299	�	�	PROPN
m-806	53	300	�	�	PROPN
m-806	53	301	�	�	PROPN
m-806	53	302	�	�	PROPN
m-806	53	303	(	(	PUNCT
m-806	53	304	5.30	5.30	NUM
m-806	53	305	)	)	PUNCT
m-806	53	306	(	(	PUNCT
m-806	53	307	�	�	PROPN
m-806	53	308	�	�	PROPN
m-806	53	309	−	−	PROPN
m-806	53	310	2	2	NUM
m-806	53	311	�	�	PROPN
m-806	53	312	�	�	PROPN
m-806	53	313	�	�	PROPN
m-806	53	314	�	�	PROPN
m-806	53	315	+	+	CCONJ
m-806	53	316	1	1	NUM
m-806	53	317	)	)	PUNCT
m-806	53	318	�	�	PROPN
m-806	53	319	�	�	PROPN
m-806	53	320	=	=	SYM
m-806	53	321	�	�	PROPN
m-806	53	322	�	�	PROPN
m-806	53	323	�	�	PROPN
m-806	53	324	�	�	PROPN
m-806	53	325	�	�	PROPN
m-806	53	326	�	�	PROPN
m-806	53	327	�	�	PROPN
m-806	53	328	�	�	PROPN
m-806	53	329	�	�	PROPN
m-806	53	330	�	�	PROPN
m-806	53	331	�	�	PROPN
m-806	53	332	�	�	PROPN
m-806	53	333	�	�	PROPN
m-806	53	334	(	(	PUNCT
m-806	53	335	5.31	5.31	NUM
m-806	53	336	)	)	PUNCT
m-806	53	337	and	and	CCONJ
m-806	53	338	(	(	PUNCT
m-806	53	339	1	1	NUM
m-806	53	340	−	−	PROPN
m-806	53	341	�	�	PROPN
m-806	53	342	�	�	PROPN
m-806	53	343	)	)	PUNCT
m-806	53	344	�	�	PROPN
m-806	53	345	�	�	PROPN
m-806	53	346	=	=	SYM
m-806	53	347	�	�	PROPN
m-806	53	348	�	�	PROPN
m-806	53	349	√	√	NUM
m-806	53	350	�	�	PROPN
m-806	53	351	�	�	PROPN
m-806	53	352	�	�	PROPN
m-806	53	353	�	�	PROPN
m-806	53	354	�	�	PROPN
m-806	53	355	�	�	PROPN
m-806	53	356	�	�	PROPN
m-806	53	357	�	�	PROPN
m-806	53	358	�	�	PROPN
m-806	53	359	�	�	PROPN
m-806	53	360	(	(	PUNCT
m-806	53	361	5.32	5.32	NUM
m-806	53	362	)	)	PUNCT
m-806	53	363	the	the	DET
m-806	53	364	result	result	NOUN
m-806	53	365	(	(	PUNCT
m-806	53	366	5.32	5.32	NUM
m-806	53	367	)	)	PUNCT
m-806	53	368	was	be	AUX
m-806	53	369	first	first	ADV
m-806	53	370	obtained	obtain	VERB
m-806	53	371	by	by	ADP
m-806	53	372	[	[	X
m-806	53	373	6	6	NUM
m-806	53	374	]	]	PUNCT
m-806	53	375	.	.	PUNCT
m-806	54	1	so	so	ADV
m-806	54	2	far	far	ADV
m-806	54	3	,	,	PUNCT
m-806	54	4	we	we	PRON
m-806	54	5	conclude	conclude	VERB
m-806	54	6	that	that	SCONJ
m-806	54	7	the	the	DET
m-806	54	8	static	static	ADJ
m-806	54	9	buckling	buckling	NOUN
m-806	54	10	load	load	NOUN
m-806	54	11	of	of	ADP
m-806	54	12	structures	structure	NOUN
m-806	54	13	largely	largely	ADV
m-806	54	14	depends	depend	VERB
m-806	54	15	,	,	PUNCT
m-806	54	16	among	among	ADP
m-806	54	17	other	other	ADJ
m-806	54	18	things	thing	NOUN
m-806	54	19	,	,	PUNCT
m-806	54	20	on	on	ADP
m-806	54	21	the	the	DET
m-806	54	22	type	type	NOUN
m-806	54	23	of	of	ADP
m-806	54	24	end	end	NOUN
m-806	54	25	constraints	constraint	NOUN
m-806	54	26	of	of	ADP
m-806	54	27	the	the	DET
m-806	54	28	structures	structure	NOUN
m-806	54	29	.	.	PUNCT
m-806	55	1	6	6	X
m-806	55	2	.	.	X
m-806	55	3	the	the	DET
m-806	55	4	dynamic	dynamic	ADJ
m-806	55	5	problem	problem	NOUN
m-806	55	6	the	the	DET
m-806	55	7	associated	associated	ADJ
m-806	55	8	dynamic	dynamic	ADJ
m-806	55	9	problem	problem	NOUN
m-806	55	10	follows	follow	VERB
m-806	55	11	from	from	ADP
m-806	55	12	(	(	PUNCT
m-806	55	13	3.1a	3.1a	NOUN
m-806	55	14	)	)	PUNCT
m-806	55	15	which	which	PRON
m-806	55	16	we	we	PRON
m-806	55	17	now	now	ADV
m-806	55	18	recast	recast	VERB
m-806	55	19	as	as	ADP
m-806	55	20	�	�	PROPN
m-806	55	21	,	,	PUNCT
m-806	55	22	�	�	PROPN
m-806	55	23	�	�	PROPN
m-806	55	24	+	+	CCONJ
m-806	55	25	2	2	NUM
m-806	55	26	�	�	PROPN
m-806	55	27	�	�	PROPN
m-806	55	28	,	,	PUNCT
m-806	55	29	�	�	PROPN
m-806	55	30	+	+	SYM
m-806	55	31	�	�	PROPN
m-806	55	32	,	,	PUNCT
m-806	55	33	�	�	PROPN
m-806	55	34	�	�	PROPN
m-806	55	35	�	�	PROPN
m-806	55	36	�	�	PROPN
m-806	55	37	+	+	CCONJ
m-806	55	38	2	2	NUM
m-806	55	39	�	�	PROPN
m-806	55	40	�	�	PROPN
m-806	55	41	(	(	PUNCT
m-806	55	42	�	�	PROPN
m-806	55	43	)	)	PUNCT
m-806	55	44	�	�	PROPN
m-806	55	45	,	,	PUNCT
m-806	55	46	�	�	PROPN
m-806	55	47	�	�	PROPN
m-806	55	48	+	+	CCONJ
m-806	55	49	�	�	PROPN
m-806	55	50	−	−	PROPN
m-806	55	51	�	�	PROPN
m-806	55	52	�	�	PROPN
m-806	55	53	�	�	PROPN
m-806	55	54	=	=	PUNCT
m-806	55	55	−2	−2	PROPN
m-806	55	56	�	�	PROPN
m-806	55	57	�	�	PROPN
m-806	55	58	�	�	PROPN
m-806	55	59	(	(	PUNCT
m-806	55	60	�	�	PROPN
m-806	55	61	)	)	PUNCT
m-806	55	62	�	�	PROPN
m-806	55	63	�	�	PROPN
m-806	55	64	�	�	PROPN
m-806	55	65	�	�	PROPN
m-806	55	66	�	�	PROPN
m-806	55	67	�	�	PROPN
m-806	55	68	�	�	PROPN
m-806	55	69	,	,	PUNCT
m-806	55	70	�	�	PROPN
m-806	55	71	>	>	X
m-806	55	72	0	0	NUM
m-806	55	73	,	,	PUNCT
m-806	55	74	0	0	NUM
m-806	55	75	<	<	X
m-806	55	76	�	�	PROPN
m-806	55	77	<	<	X
m-806	55	78	π	π	PROPN
m-806	55	79	(	(	PUNCT
m-806	55	80	6.1a	6.1a	NOUN
m-806	55	81	)	)	PUNCT
m-806	55	82	�	�	PROPN
m-806	55	83	(	(	PUNCT
m-806	55	84	�	�	PROPN
m-806	55	85	,	,	PUNCT
m-806	55	86	0	0	NUM
m-806	55	87	)	)	PUNCT
m-806	55	88	=	=	SYM
m-806	55	89	�	�	PROPN
m-806	55	90	,	,	PUNCT
m-806	55	91	�	�	PROPN
m-806	55	92	(	(	PUNCT
m-806	55	93	�	�	PROPN
m-806	55	94	,	,	PUNCT
m-806	55	95	0	0	NUM
m-806	55	96	)	)	PUNCT
m-806	55	97	=	=	SYM
m-806	55	98	0	0	NUM
m-806	55	99	,	,	PUNCT
m-806	55	100	0	0	NUM
m-806	55	101	<	<	X
m-806	55	102	�	�	PROPN
m-806	55	103	<	<	X
m-806	55	104	π	π	PROPN
m-806	55	105	(	(	PUNCT
m-806	55	106	6.1b	6.1b	PROPN
m-806	55	107	)	)	PUNCT
m-806	55	108	�	�	PROPN
m-806	55	109	=	=	SYM
m-806	55	110	�	�	PROPN
m-806	55	111	,	,	PUNCT
m-806	55	112	�	�	PROPN
m-806	55	113	=	=	SYM
m-806	55	114	0	0	NUM
m-806	55	115	,	,	PUNCT
m-806	55	116	�	�	PROPN
m-806	55	117	�	�	PROPN
m-806	55	118	�	�	PROPN
m-806	55	119	=	=	SYM
m-806	55	120	0	0	NUM
m-806	55	121	,	,	PUNCT
m-806	55	122	π	π	PROPN
m-806	55	123	,	,	PUNCT
m-806	55	124	�	�	PROPN
m-806	55	125	>	>	X
m-806	55	126	0	0	PUNCT
m-806	56	1	(	(	PUNCT
m-806	56	2	6.1c	6.1c	NUM
m-806	56	3	)	)	PUNCT
m-806	56	4	henceforth	henceforth	ADV
m-806	56	5	,	,	PUNCT
m-806	56	6	we	we	PRON
m-806	56	7	shall	shall	AUX
m-806	56	8	substitute	substitute	VERB
m-806	56	9	for	for	ADP
m-806	56	10	the	the	DET
m-806	56	11	step	step	NOUN
m-806	56	12	load	load	NOUN
m-806	56	13	�	�	PROPN
m-806	56	14	(	(	PUNCT
m-806	56	15	�	�	PROPN
m-806	56	16	)	)	PUNCT
m-806	56	17	as	as	ADP
m-806	56	18	in	in	ADP
m-806	56	19	(	(	PUNCT
m-806	56	20	3.2	3.2	NUM
m-806	56	21	)	)	PUNCT
m-806	56	22	.	.	PUNCT
m-806	57	1	we	we	PRON
m-806	57	2	let	let	VERB
m-806	57	3	�	�	PROPN
m-806	57	4	=	=	SYM
m-806	57	5	�	�	PROPN
m-806	57	6	�	�	PROPN
m-806	57	7	,	,	PUNCT
m-806	57	8	(	(	PUNCT
m-806	57	9	6.2a	6.2a	NOUN
m-806	57	10	)	)	PUNCT
m-806	57	11	�	�	PROPN
m-806	57	12	̂	̂	VERB
m-806	57	13	=	=	SYM
m-806	57	14	�	�	PROPN
m-806	57	15	+	+	CCONJ
m-806	57	16	�	�	PROPN
m-806	57	17	�	�	PROPN
m-806	57	18	�	�	PROPN
m-806	57	19	(	(	PUNCT
m-806	57	20	�	�	PROPN
m-806	57	21	)	)	PUNCT
m-806	57	22	�	�	PROPN
m-806	57	23	�	�	PROPN
m-806	57	24	�	�	PROPN
m-806	57	25	�	�	PROPN
m-806	57	26	�	�	PROPN
m-806	57	27	(	(	PUNCT
m-806	57	28	�	�	PROPN
m-806	57	29	)	)	PUNCT
m-806	57	30	�	�	PROPN
m-806	57	31	�	�	PROPN
m-806	57	32	�	�	PROPN
m-806	57	33	⋯	⋯	PROPN
m-806	57	34	�	�	PROPN
m-806	57	35	�	�	PROPN
m-806	57	36	(	(	PUNCT
m-806	57	37	6.2b	6.2b	NOUN
m-806	57	38	)	)	PUNCT
m-806	57	39	where	where	SCONJ
m-806	57	40	,	,	PUNCT
m-806	57	41	�	�	PROPN
m-806	57	42	�	�	PROPN
m-806	57	43	(	(	PUNCT
m-806	57	44	0	0	NUM
m-806	57	45	)	)	PUNCT
m-806	57	46	=	=	SYM
m-806	58	1	0	0	NUM
m-806	58	2	,	,	PUNCT
m-806	58	3	i	i	PRON
m-806	58	4	=	=	NOUN
m-806	58	5	1	1	NUM
m-806	58	6	,	,	PUNCT
m-806	58	7	2	2	NUM
m-806	58	8	,	,	PUNCT
m-806	58	9	3	3	NUM
m-806	58	10	,	,	PUNCT
m-806	58	11	…	…	PUNCT
m-806	58	12	,	,	PUNCT
m-806	58	13	�	�	PROPN
m-806	58	14	�	�	PROPN
m-806	58	15	=	=	SYM
m-806	58	16	�	�	PROPN
m-806	58	17	�	�	PROPN
m-806	58	18	(	(	PUNCT
m-806	58	19	�	�	PROPN
m-806	58	20	)	)	PUNCT
m-806	58	21	we	we	PRON
m-806	58	22	stress	stress	VERB
m-806	58	23	that	that	SCONJ
m-806	58	24	ϵ	ϵ	PROPN
m-806	58	25	and	and	CCONJ
m-806	58	26	δ	δ	PROPN
m-806	58	27	are	be	AUX
m-806	58	28	small	small	ADJ
m-806	58	29	and	and	CCONJ
m-806	58	30	unrelated	unrelated	ADJ
m-806	58	31	parameters	parameter	NOUN
m-806	58	32	.	.	PUNCT
m-806	59	1	thus	thus	ADV
m-806	59	2	,	,	PUNCT
m-806	59	3	from	from	ADP
m-806	59	4	(	(	PUNCT
m-806	59	5	6.2a	6.2a	PROPN
m-806	59	6	,	,	PUNCT
m-806	59	7	b	b	NOUN
m-806	59	8	)	)	PUNCT
m-806	59	9	,	,	PUNCT
m-806	59	10	we	we	PRON
m-806	59	11	get	get	VERB
m-806	59	12	�	�	PROPN
m-806	59	13	�	�	PROPN
m-806	59	14	�	�	PROPN
m-806	59	15	�	�	PROPN
m-806	59	16	=	=	SYM
m-806	59	17	�	�	PROPN
m-806	59	18	�	�	PROPN
m-806	59	19	�	�	PROPN
m-806	59	20	�	�	PROPN
m-806	59	21	̂	̂	SYM
m-806	59	22	�	�	PROPN
m-806	59	23	�	�	PROPN
m-806	59	24	̂	̂	SYM
m-806	59	25	�	�	NOUN
m-806	59	26	�	�	PROPN
m-806	59	27	+	+	SYM
m-806	59	28	�	�	PROPN
m-806	59	29	�	�	PROPN
m-806	59	30	�	�	PROPN
m-806	59	31	�	�	PROPN
m-806	59	32	̂	̂	SYM
m-806	59	33	�	�	PROPN
m-806	59	34	�	�	PROPN
m-806	59	35	̂	̂	SYM
m-806	59	36	�	�	PROPN
m-806	59	37	�	�	PROPN
m-806	59	38	�	�	PROPN
m-806	59	39	�	�	PROPN
m-806	59	40	�	�	PROPN
m-806	59	41	�	�	PROPN
m-806	59	42	+	+	CCONJ
m-806	59	43	�	�	PROPN
m-806	59	44	�	�	PROPN
m-806	59	45	�	�	PROPN
m-806	59	46	�	�	PROPN
m-806	59	47	�	�	PROPN
m-806	59	48	�	�	PROPN
m-806	59	49	�	�	PROPN
m-806	59	50	�	�	PROPN
m-806	59	51	=	=	PUNCT
m-806	59	52	(	(	PUNCT
m-806	59	53	1	1	NUM
m-806	59	54	+	+	NUM
m-806	59	55	�	�	PROPN
m-806	59	56	�	�	PROPN
m-806	59	57	�	�	PROPN
m-806	59	58	�	�	PROPN
m-806	59	59	�	�	PROPN
m-806	59	60	+	+	CCONJ
m-806	59	61	�	�	PROPN
m-806	59	62	�	�	PROPN
m-806	59	63	�	�	PROPN
m-806	59	64	�	�	PROPN
m-806	59	65	�	�	PROPN
m-806	59	66	+	+	CCONJ
m-806	59	67	⋯	⋯	PROPN
m-806	59	68	)	)	PUNCT
m-806	59	69	�	�	PROPN
m-806	59	70	,	,	PUNCT
m-806	59	71	�	�	PROPN
m-806	59	72	�	�	PROPN
m-806	59	73	+	+	SYM
m-806	59	74	�	�	PROPN
m-806	59	75	�	�	PROPN
m-806	59	76	,	,	PUNCT
m-806	59	77	�	�	PROPN
m-806	59	78	(	(	PUNCT
m-806	59	79	6.3a	6.3a	PROPN
m-806	59	80	)	)	PUNCT
m-806	59	81	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	59	82	ijo	ijo	PROPN
m-806	59	83	journals	journal	NOUN
m-806	59	84	volume	volume	NOUN
m-806	59	85	07	07	NUM
m-806	59	86	|	|	ADV
m-806	59	87	issue	issue	NOUN
m-806	59	88	02	02	NUM
m-806	59	89	|	|	CCONJ
m-806	59	90	february	february	PROPN
m-806	59	91	2024	2024	NUM
m-806	60	1	|	|	ADV
m-806	60	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	60	3	6	6	NUM
m-806	60	4	ijo	ijo	PROPN
m-806	60	5	international	international	ADJ
m-806	60	6	journal	journal	PROPN
m-806	60	7	of	of	ADP
m-806	60	8	mathematics	mathematics	PROPN
m-806	60	9	(	(	PUNCT
m-806	60	10	issn	issn	PROPN
m-806	60	11	:	:	PUNCT
m-806	60	12	2992	2992	NUM
m-806	60	13	-	-	SYM
m-806	60	14	4421	4421	NUM
m-806	60	15	)	)	PUNCT
m-806	60	16	i.u	i.u	PROPN
m-806	60	17	.	.	PROPN
m-806	60	18	udo	udo	PROPN
m-806	60	19	-	-	PROPN
m-806	60	20	akpan1	akpan1	ADJ
m-806	60	21	*	*	PUNCT
m-806	60	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	60	23	volume	volume	NOUN
m-806	60	24	07	07	NUM
m-806	60	25	issue	issue	NOUN
m-806	60	26	02	02	NUM
m-806	60	27	||	||	NUM
m-806	60	28	february	february	PROPN
m-806	60	29	,	,	PUNCT
m-806	60	30	2024	2024	NUM
m-806	60	31	||	||	NOUN
m-806	60	32	on	on	ADP
m-806	60	33	a	a	DET
m-806	60	34	-	-	PUNCT
m-806	60	35	two	two	NUM
m-806	60	36	-	-	PUNCT
m-806	60	37	parameter	parameter	NOUN
m-806	60	38	dynamic	dynamic	ADJ
m-806	60	39	buckling	buckling	NOUN
m-806	60	40	of	of	ADP
m-806	60	41	a	a	DET
m-806	60	42	viscously	viscously	ADV
m-806	60	43	damped	damp	VERB
m-806	60	44	but	but	CCONJ
m-806	60	45	clamped	clamp	VERB
m-806	60	46	column	column	NOUN
m-806	60	47	stressed	stress	VERB
m-806	60	48	by	by	ADP
m-806	60	49	a	a	DET
m-806	60	50	step	step	NOUN
m-806	60	51	load	load	NOUN
m-806	60	52	where	where	SCONJ
m-806	60	53	,	,	PUNCT
m-806	60	54	(	(	PUNCT
m-806	60	55	…	…	PUNCT
m-806	60	56	)	)	PUNCT
m-806	60	57	�	�	PROPN
m-806	60	58	=	=	SYM
m-806	60	59	�	�	PROPN
m-806	60	60	(	(	PUNCT
m-806	60	61	…	…	PUNCT
m-806	60	62	)	)	PUNCT
m-806	60	63	�	�	PROPN
m-806	60	64	�	�	PROPN
m-806	60	65	and	and	CCONJ
m-806	60	66	a	a	DET
m-806	60	67	subscript	subscript	NOUN
m-806	60	68	after	after	SCONJ
m-806	60	69	a	a	DET
m-806	60	70	comma	comma	NOUN
m-806	60	71	indicates	indicate	VERB
m-806	60	72	partial	partial	ADJ
m-806	60	73	differentiation	differentiation	NOUN
m-806	60	74	.	.	PUNCT
m-806	61	1	∴	∴	PROPN
m-806	61	2	�	�	PROPN
m-806	61	3	�	�	PROPN
m-806	61	4	�	�	PROPN
m-806	61	5	�	�	PROPN
m-806	61	6	�	�	PROPN
m-806	61	7	�	�	PROPN
m-806	61	8	=	=	PUNCT
m-806	61	9	(	(	PUNCT
m-806	61	10	1	1	NUM
m-806	61	11	+	+	NUM
m-806	61	12	�	�	PROPN
m-806	61	13	�	�	PROPN
m-806	61	14	�	�	PROPN
m-806	61	15	�	�	PROPN
m-806	61	16	�	�	PROPN
m-806	61	17	+	+	CCONJ
m-806	61	18	�	�	PROPN
m-806	61	19	�	�	PROPN
m-806	61	20	�	�	PROPN
m-806	61	21	�	�	PROPN
m-806	61	22	�	�	PROPN
m-806	61	23	+	+	CCONJ
m-806	61	24	⋯	⋯	PROPN
m-806	61	25	)	)	PUNCT
m-806	61	26	�	�	PROPN
m-806	61	27	�	�	PROPN
m-806	61	28	,	,	PUNCT
m-806	61	29	�	�	PROPN
m-806	61	30	�	�	PROPN
m-806	61	31	�	�	PROPN
m-806	61	32	�	�	PROPN
m-806	61	33	+	+	SYM
m-806	61	34	�	�	PROPN
m-806	61	35	�	�	PROPN
m-806	61	36	�	�	PROPN
m-806	61	37	,	,	PUNCT
m-806	61	38	�	�	PROPN
m-806	61	39	�	�	PROPN
m-806	61	40	+	+	CCONJ
m-806	61	41	2	2	NUM
m-806	61	42	�	�	PROPN
m-806	61	43	(1	(1	ADJ
m-806	61	44	+	+	SYM
m-806	61	45	�	�	PROPN
m-806	61	46	�	�	PROPN
m-806	61	47	�	�	PROPN
m-806	61	48	�	�	PROPN
m-806	61	49	�	�	PROPN
m-806	61	50	+	+	CCONJ
m-806	61	51	�	�	PROPN
m-806	61	52	�	�	PROPN
m-806	61	53	�	�	PROPN
m-806	61	54	�	�	PROPN
m-806	61	55	�	�	PROPN
m-806	61	56	+	+	CCONJ
m-806	61	57	⋯	⋯	PROPN
m-806	61	58	)	)	PUNCT
m-806	61	59	�	�	PROPN
m-806	61	60	,	,	PUNCT
m-806	61	61	�	�	PROPN
m-806	61	62	�	�	PROPN
m-806	61	63	�	�	PROPN
m-806	61	64	+	+	SYM
m-806	61	65	�	�	PROPN
m-806	61	66	(	(	PUNCT
m-806	61	67	�	�	PROPN
m-806	61	68	�	�	PROPN
m-806	61	69	�	�	PROPN
m-806	61	70	�	�	PROPN
m-806	61	71	�	�	PROPN
m-806	61	72	�	�	PROPN
m-806	61	73	+	+	SYM
m-806	61	74	�	�	PROPN
m-806	61	75	�	�	PROPN
m-806	61	76	�	�	PROPN
m-806	61	77	�	�	PROPN
m-806	61	78	�	�	PROPN
m-806	61	79	�	�	PROPN
m-806	61	80	+	+	CCONJ
m-806	61	81	⋯	⋯	PROPN
m-806	61	82	)	)	PUNCT
m-806	61	83	�	�	PROPN
m-806	61	84	,	,	PUNCT
m-806	61	85	�	�	PROPN
m-806	61	86	�	�	PROPN
m-806	61	87	(	(	PUNCT
m-806	61	88	6.3b	6.3b	NUM
m-806	61	89	)	)	PUNCT
m-806	61	90	on	on	ADP
m-806	61	91	substituting	substitute	VERB
m-806	61	92	(	(	PUNCT
m-806	61	93	6.3a	6.3a	NOUN
m-806	61	94	,	,	PUNCT
m-806	61	95	b	b	NOUN
m-806	61	96	)	)	PUNCT
m-806	61	97	into	into	ADP
m-806	61	98	(	(	PUNCT
m-806	61	99	6.1a	6.1a	NOUN
m-806	61	100	)	)	PUNCT
m-806	61	101	for	for	ADP
m-806	61	102	�	�	PROPN
m-806	61	103	(	(	PUNCT
m-806	61	104	�	�	PROPN
m-806	61	105	)	)	PUNCT
m-806	61	106	=	=	SYM
m-806	62	1	1	1	NUM
m-806	62	2	,	,	PUNCT
m-806	62	3	we	we	PRON
m-806	62	4	get	get	VERB
m-806	62	5	�	�	PROPN
m-806	62	6	(	(	PUNCT
m-806	62	7	1	1	NUM
m-806	62	8	+	+	NUM
m-806	62	9	�	�	PROPN
m-806	62	10	�	�	PROPN
m-806	62	11	�	�	PROPN
m-806	62	12	�	�	PROPN
m-806	62	13	�	�	PROPN
m-806	62	14	+	+	CCONJ
m-806	62	15	�	�	PROPN
m-806	62	16	�	�	PROPN
m-806	62	17	�	�	PROPN
m-806	62	18	�	�	PROPN
m-806	62	19	�	�	PROPN
m-806	62	20	+	+	CCONJ
m-806	62	21	⋯	⋯	PROPN
m-806	62	22	)	)	PUNCT
m-806	62	23	�	�	PROPN
m-806	62	24	�	�	PROPN
m-806	62	25	,	,	PUNCT
m-806	62	26	�	�	PROPN
m-806	62	27	�	�	PROPN
m-806	62	28	�	�	PROPN
m-806	62	29	�	�	PROPN
m-806	62	30	�	�	PROPN
m-806	62	31	+	+	CCONJ
m-806	62	32	�	�	PROPN
m-806	62	33	�	�	PROPN
m-806	62	34	�	�	PROPN
m-806	62	35	,	,	PUNCT
m-806	62	36	�	�	PROPN
m-806	62	37	�	�	PROPN
m-806	62	38	+	+	CCONJ
m-806	62	39	2	2	NUM
m-806	62	40	�	�	PROPN
m-806	62	41	(1	(1	ADJ
m-806	62	42	+	+	SYM
m-806	62	43	�	�	PROPN
m-806	62	44	�	�	PROPN
m-806	62	45	�	�	PROPN
m-806	62	46	�	�	PROPN
m-806	62	47	�	�	PROPN
m-806	62	48	+	+	CCONJ
m-806	62	49	�	�	PROPN
m-806	62	50	�	�	PROPN
m-806	62	51	�	�	PROPN
m-806	62	52	�	�	PROPN
m-806	62	53	�	�	PROPN
m-806	62	54	+	+	CCONJ
m-806	62	55	⋯	⋯	PROPN
m-806	62	56	)	)	PUNCT
m-806	62	57	�	�	PROPN
m-806	62	58	,	,	PUNCT
m-806	62	59	�	�	PROPN
m-806	62	60	�	�	PROPN
m-806	62	61	�	�	PROPN
m-806	62	62	+	+	PROPN
m-806	62	63	�	�	PROPN
m-806	62	64	�	�	PROPN
m-806	62	65	(	(	PUNCT
m-806	62	66	�	�	PROPN
m-806	62	67	�	�	PROPN
m-806	62	68	�	�	PROPN
m-806	62	69	�	�	PROPN
m-806	62	70	�	�	PROPN
m-806	62	71	�	�	PROPN
m-806	62	72	+	+	SYM
m-806	62	73	�	�	PROPN
m-806	62	74	�	�	PROPN
m-806	62	75	�	�	PROPN
m-806	62	76	�	�	PROPN
m-806	62	77	�	�	PROPN
m-806	62	78	�	�	PROPN
m-806	62	79	+	+	CCONJ
m-806	62	80	⋯	⋯	PROPN
m-806	62	81	)	)	PUNCT
m-806	62	82	�	�	PROPN
m-806	62	83	,	,	PUNCT
m-806	62	84	�	�	PROPN
m-806	62	85	�	�	PROPN
m-806	62	86	�	�	PROPN
m-806	62	87	+	+	CCONJ
m-806	62	88	2	2	NUM
m-806	62	89	�	�	PROPN
m-806	62	90	�	�	PROPN
m-806	62	91	(1	(1	ADJ
m-806	62	92	+	+	SYM
m-806	62	93	�	�	PROPN
m-806	62	94	�	�	PROPN
m-806	62	95	�	�	PROPN
m-806	62	96	�	�	PROPN
m-806	62	97	�	�	PROPN
m-806	62	98	+	+	CCONJ
m-806	62	99	�	�	PROPN
m-806	62	100	�	�	PROPN
m-806	62	101	�	�	PROPN
m-806	62	102	�	�	PROPN
m-806	62	103	�	�	PROPN
m-806	62	104	+	+	CCONJ
m-806	62	105	⋯	⋯	PROPN
m-806	62	106	)	)	PUNCT
m-806	62	107	�	�	PROPN
m-806	62	108	,	,	PUNCT
m-806	62	109	�	�	PROPN
m-806	62	110	�	�	PROPN
m-806	62	111	+	+	SYM
m-806	62	112	�	�	PROPN
m-806	62	113	�	�	PROPN
m-806	62	114	,	,	PUNCT
m-806	62	115	�	�	PROPN
m-806	62	116	�	�	PROPN
m-806	62	117	+	+	SYM
m-806	62	118	�	�	PROPN
m-806	62	119	,	,	PUNCT
m-806	62	120	�	�	PROPN
m-806	62	121	�	�	PROPN
m-806	62	122	�	�	PROPN
m-806	62	123	�	�	PROPN
m-806	62	124	+	+	CCONJ
m-806	62	125	2	2	NUM
m-806	62	126	�	�	PROPN
m-806	62	127	�	�	PROPN
m-806	62	128	(	(	PUNCT
m-806	62	129	�	�	PROPN
m-806	62	130	)	)	PUNCT
m-806	62	131	�	�	PROPN
m-806	62	132	,	,	PUNCT
m-806	62	133	�	�	PROPN
m-806	62	134	�	�	PROPN
m-806	62	135	+	+	CCONJ
m-806	62	136	�	�	PROPN
m-806	62	137	−	−	PROPN
m-806	62	138	�	�	PROPN
m-806	62	139	�	�	PROPN
m-806	62	140	�	�	PROPN
m-806	62	141	=	=	PUNCT
m-806	62	142	−2	−2	PROPN
m-806	62	143	�	�	PROPN
m-806	62	144	�	�	PROPN
m-806	62	145	�	�	PROPN
m-806	62	146	(	(	PUNCT
m-806	62	147	�	�	PROPN
m-806	62	148	)	)	PUNCT
m-806	62	149	�	�	PROPN
m-806	62	150	�	�	PROPN
m-806	62	151	�	�	PROPN
m-806	62	152	�	�	PROPN
m-806	62	153	�	�	PROPN
m-806	62	154	�	�	PROPN
m-806	62	155	�	�	PROPN
m-806	62	156	(	(	PUNCT
m-806	62	157	6.4	6.4	NUM
m-806	62	158	)	)	PUNCT
m-806	62	159	next	next	ADV
m-806	62	160	,	,	PUNCT
m-806	62	161	we	we	PRON
m-806	62	162	adopt	adopt	VERB
m-806	62	163	the	the	DET
m-806	62	164	asymptotic	asymptotic	ADJ
m-806	62	165	series	series	NOUN
m-806	62	166	�	�	PROPN
m-806	62	167	=	=	SYM
m-806	62	168	∑	∑	PROPN
m-806	62	169	∑	∑	PROPN
m-806	62	170	�	�	PROPN
m-806	62	171	(	(	PUNCT
m-806	62	172	�	�	PROPN
m-806	62	173	�	�	PROPN
m-806	62	174	)	)	PUNCT
m-806	62	175	(	(	PUNCT
m-806	62	176	�	�	PROPN
m-806	62	177	,	,	PUNCT
m-806	62	178	�	�	PROPN
m-806	62	179	̂	̂	SYM
m-806	62	180	�	�	PROPN
m-806	62	181	�	�	PROPN
m-806	62	182	�	�	PROPN
m-806	62	183	�	�	PROPN
m-806	62	184	�	�	PROPN
m-806	62	185	�	�	PROPN
m-806	62	186	�	�	PROPN
m-806	62	187	�	�	PROPN
m-806	62	188	,	,	PUNCT
m-806	62	189	�	�	PROPN
m-806	62	190	)	)	PUNCT
m-806	62	191	�	�	PROPN
m-806	62	192	�	�	PROPN
m-806	62	193	�	�	PROPN
m-806	62	194	�	�	PROPN
m-806	62	195	(	(	PUNCT
m-806	62	196	6.5	6.5	NUM
m-806	62	197	)	)	PUNCT
m-806	62	198	and	and	CCONJ
m-806	62	199	substitute	substitute	NOUN
m-806	62	200	same	same	ADJ
m-806	62	201	into	into	ADP
m-806	62	202	(	(	PUNCT
m-806	62	203	6.4	6.4	NUM
m-806	62	204	)	)	PUNCT
m-806	62	205	,	,	PUNCT
m-806	62	206	and	and	CCONJ
m-806	62	207	afterwards	afterwards	ADV
m-806	62	208	,	,	PUNCT
m-806	62	209	equate	equate	ADJ
m-806	62	210	powers	power	NOUN
m-806	62	211	of	of	ADP
m-806	62	212	�	�	PROPN
m-806	62	213	�	�	PROPN
m-806	62	214	�	�	PROPN
m-806	62	215	�	�	PROPN
m-806	62	216	to	to	PART
m-806	62	217	get	get	VERB
m-806	62	218	�	�	PROPN
m-806	62	219	(	(	PUNCT
m-806	62	220	�	�	PROPN
m-806	62	221	):	):	PUNCT
m-806	62	222	�	�	PROPN
m-806	62	223	�	�	PROPN
m-806	62	224	(	(	PUNCT
m-806	62	225	�	�	PROPN
m-806	62	226	�	�	PROPN
m-806	62	227	)	)	PUNCT
m-806	62	228	=	=	SYM
m-806	62	229	�	�	PROPN
m-806	62	230	,	,	PUNCT
m-806	62	231	�	�	PROPN
m-806	62	232	�	�	PROPN
m-806	62	233	�	�	PROPN
m-806	62	234	�	�	PROPN
m-806	62	235	(	(	PUNCT
m-806	62	236	�	�	PROPN
m-806	62	237	�	�	PROPN
m-806	62	238	)	)	PUNCT
m-806	62	239	+	+	SYM
m-806	62	240	�	�	PROPN
m-806	62	241	,	,	PUNCT
m-806	62	242	�	�	PROPN
m-806	62	243	�	�	PROPN
m-806	62	244	�	�	PROPN
m-806	62	245	�	�	PROPN
m-806	62	246	(	(	PUNCT
m-806	62	247	�	�	PROPN
m-806	62	248	�	�	PROPN
m-806	62	249	)	)	PUNCT
m-806	62	250	+	+	CCONJ
m-806	62	251	2	2	NUM
m-806	62	252	�	�	PROPN
m-806	62	253	�	�	PROPN
m-806	62	254	,	,	PUNCT
m-806	62	255	�	�	PROPN
m-806	62	256	�	�	PROPN
m-806	62	257	(	(	PUNCT
m-806	62	258	�	�	PROPN
m-806	62	259	�	�	PROPN
m-806	62	260	)	)	PUNCT
m-806	62	261	+	+	SYM
m-806	62	262	�	�	PROPN
m-806	62	263	(	(	PUNCT
m-806	62	264	�	�	NOUN
m-806	62	265	�	�	PROPN
m-806	62	266	)	)	PUNCT
m-806	62	267	=	=	SYM
m-806	62	268	−2	−2	PROPN
m-806	62	269	�	�	PROPN
m-806	62	270	�	�	PROPN
m-806	62	271	(	(	PUNCT
m-806	62	272	�	�	PROPN
m-806	62	273	)	)	PUNCT
m-806	62	274	�	�	PROPN
m-806	62	275	�	�	PROPN
m-806	62	276	�	�	PROPN
m-806	62	277	�	�	PROPN
m-806	62	278	�	�	PROPN
m-806	62	279	�	�	PROPN
m-806	62	280	�	�	PROPN
m-806	62	281	(	(	PUNCT
m-806	62	282	6.6	6.6	NUM
m-806	62	283	)	)	PUNCT
m-806	62	284	�	�	PROPN
m-806	62	285	(	(	PUNCT
m-806	62	286	�	�	PROPN
m-806	62	287	�	�	PROPN
m-806	62	288	):	):	PUNCT
m-806	62	289	�	�	PROPN
m-806	62	290	�	�	PROPN
m-806	62	291	(	(	PUNCT
m-806	62	292	�	�	PROPN
m-806	62	293	�	�	PROPN
m-806	62	294	)	)	PUNCT
m-806	62	295	=	=	SYM
m-806	62	296	−2	−2	PROPN
m-806	62	297	�	�	PROPN
m-806	62	298	�	�	PROPN
m-806	62	299	,	,	PUNCT
m-806	62	300	�	�	PROPN
m-806	62	301	�	�	PROPN
m-806	62	302	�	�	PROPN
m-806	62	303	(	(	PUNCT
m-806	62	304	�	�	PROPN
m-806	62	305	�	�	PROPN
m-806	62	306	)	)	PUNCT
m-806	62	307	+	+	SYM
m-806	62	308	�	�	PROPN
m-806	62	309	,	,	PUNCT
m-806	62	310	�	�	PROPN
m-806	62	311	�	�	PROPN
m-806	62	312	(	(	PUNCT
m-806	62	313	�	�	PROPN
m-806	62	314	�	�	PROPN
m-806	62	315	)	)	PUNCT
m-806	62	316	�	�	PROPN
m-806	62	317	(	(	PUNCT
m-806	62	318	6.7	6.7	NUM
m-806	62	319	)	)	PUNCT
m-806	62	320	�	�	PROPN
m-806	62	321	(	(	PUNCT
m-806	62	322	�	�	PROPN
m-806	62	323	�	�	PROPN
m-806	62	324	�	�	PROPN
m-806	62	325	):	):	PUNCT
m-806	62	326	�	�	PROPN
m-806	62	327	�	�	PROPN
m-806	62	328	(	(	PUNCT
m-806	62	329	�	�	PROPN
m-806	62	330	�	�	PROPN
m-806	62	331	)	)	PUNCT
m-806	62	332	=	=	SYM
m-806	62	333	−2	−2	PROPN
m-806	62	334	�	�	PROPN
m-806	62	335	�	�	PROPN
m-806	62	336	,	,	PUNCT
m-806	62	337	�	�	PROPN
m-806	62	338	�	�	PROPN
m-806	62	339	�	�	PROPN
m-806	62	340	(	(	PUNCT
m-806	62	341	�	�	PROPN
m-806	62	342	�	�	PROPN
m-806	62	343	)	)	PUNCT
m-806	62	344	+	+	SYM
m-806	62	345	�	�	PROPN
m-806	62	346	,	,	PUNCT
m-806	62	347	�	�	PROPN
m-806	62	348	�	�	PROPN
m-806	62	349	(	(	PUNCT
m-806	62	350	�	�	PROPN
m-806	62	351	�	�	PROPN
m-806	62	352	)	)	PUNCT
m-806	62	353	�	�	PROPN
m-806	62	354	−	−	PROPN
m-806	62	355	�	�	PROPN
m-806	62	356	,	,	PUNCT
m-806	62	357	�	�	PROPN
m-806	62	358	�	�	PROPN
m-806	62	359	(	(	PUNCT
m-806	62	360	�	�	PROPN
m-806	62	361	�	�	PROPN
m-806	62	362	)	)	PUNCT
m-806	62	363	(	(	PUNCT
m-806	62	364	6.8	6.8	NUM
m-806	62	365	)	)	PUNCT
m-806	62	366	�	�	PROPN
m-806	62	367	(	(	PUNCT
m-806	62	368	�	�	PROPN
m-806	62	369	�	�	PROPN
m-806	62	370	):	):	PUNCT
m-806	62	371	�	�	PROPN
m-806	62	372	�	�	PROPN
m-806	62	373	(	(	PUNCT
m-806	62	374	�	�	PROPN
m-806	62	375	�	�	PROPN
m-806	62	376	)	)	PUNCT
m-806	62	377	=	=	SYM
m-806	62	378	0	0	NUM
m-806	63	1	(	(	PUNCT
m-806	63	2	6.9	6.9	NUM
m-806	63	3	)	)	PUNCT
m-806	63	4	�	�	PROPN
m-806	63	5	(	(	PUNCT
m-806	63	6	�	�	PROPN
m-806	63	7	�	�	PROPN
m-806	63	8	�	�	PROPN
m-806	63	9	):	):	PUNCT
m-806	63	10	�	�	PROPN
m-806	63	11	�	�	PROPN
m-806	63	12	(	(	PUNCT
m-806	63	13	�	�	PROPN
m-806	63	14	�	�	PROPN
m-806	63	15	)	)	PUNCT
m-806	63	16	=	=	SYM
m-806	63	17	−2	−2	PROPN
m-806	63	18	�	�	PROPN
m-806	63	19	�	�	PROPN
m-806	63	20	,	,	PUNCT
m-806	63	21	�	�	PROPN
m-806	63	22	�	�	PROPN
m-806	63	23	�	�	PROPN
m-806	63	24	(	(	PUNCT
m-806	63	25	�	�	PROPN
m-806	63	26	�	�	PROPN
m-806	63	27	)	)	PUNCT
m-806	63	28	+	+	SYM
m-806	63	29	�	�	PROPN
m-806	63	30	,	,	PUNCT
m-806	63	31	�	�	PROPN
m-806	63	32	�	�	PROPN
m-806	63	33	(	(	PUNCT
m-806	63	34	�	�	PROPN
m-806	63	35	�	�	PROPN
m-806	63	36	)	)	PUNCT
m-806	63	37	�	�	PROPN
m-806	63	38	(	(	PUNCT
m-806	63	39	6.10	6.10	NUM
m-806	63	40	)	)	PUNCT
m-806	63	41	�	�	PROPN
m-806	63	42	(	(	PUNCT
m-806	63	43	�	�	PROPN
m-806	63	44	�	�	PROPN
m-806	63	45	�	�	PROPN
m-806	63	46	�	�	PROPN
m-806	63	47	):	):	PUNCT
m-806	63	48	�	�	PROPN
m-806	63	49	�	�	PROPN
m-806	63	50	(	(	PUNCT
m-806	63	51	�	�	PROPN
m-806	63	52	�	�	PROPN
m-806	63	53	)	)	PUNCT
m-806	63	54	=	=	SYM
m-806	63	55	−2	−2	PROPN
m-806	63	56	�	�	PROPN
m-806	63	57	�	�	PROPN
m-806	63	58	,	,	PUNCT
m-806	63	59	�	�	PROPN
m-806	63	60	�	�	PROPN
m-806	63	61	�	�	PROPN
m-806	63	62	(	(	PUNCT
m-806	63	63	�	�	PROPN
m-806	63	64	�	�	PROPN
m-806	63	65	)	)	PUNCT
m-806	63	66	+	+	SYM
m-806	63	67	�	�	PROPN
m-806	63	68	,	,	PUNCT
m-806	63	69	�	�	PROPN
m-806	63	70	�	�	PROPN
m-806	63	71	(	(	PUNCT
m-806	63	72	�	�	PROPN
m-806	63	73	�	�	PROPN
m-806	63	74	)	)	PUNCT
m-806	63	75	�	�	PROPN
m-806	63	76	−	−	PROPN
m-806	63	77	�	�	PROPN
m-806	63	78	,	,	PUNCT
m-806	63	79	�	�	PROPN
m-806	63	80	�	�	PROPN
m-806	63	81	(	(	PUNCT
m-806	63	82	�	�	PROPN
m-806	63	83	�	�	PROPN
m-806	63	84	)	)	PUNCT
m-806	63	85	(	(	PUNCT
m-806	63	86	6.11	6.11	NUM
m-806	63	87	)	)	PUNCT
m-806	63	88	�	�	PROPN
m-806	63	89	(	(	PUNCT
m-806	63	90	�	�	PROPN
m-806	63	91	�	�	PROPN
m-806	63	92	):	):	PUNCT
m-806	63	93	�	�	PROPN
m-806	63	94	�	�	PROPN
m-806	63	95	(	(	PUNCT
m-806	63	96	�	�	PROPN
m-806	63	97	�	�	PROPN
m-806	63	98	)	)	PUNCT
m-806	63	99	=	=	SYM
m-806	63	100	�	�	PROPN
m-806	63	101	�	�	PROPN
m-806	63	102	�	�	PROPN
m-806	63	103	(	(	PUNCT
m-806	63	104	�	�	PROPN
m-806	63	105	�	�	PROPN
m-806	63	106	)	)	PUNCT
m-806	63	107	�	�	PROPN
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m-806	63	110	2	2	NUM
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m-806	63	115	,	,	PUNCT
m-806	63	116	�	�	PROPN
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m-806	63	118	�	�	PROPN
m-806	63	119	�	�	PROPN
m-806	63	120	(	(	PUNCT
m-806	63	121	�	�	PROPN
m-806	63	122	�	�	PROPN
m-806	63	123	)	)	PUNCT
m-806	63	124	(	(	PUNCT
m-806	63	125	6.12	6.12	NUM
m-806	63	126	)	)	PUNCT
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m-806	63	128	(	(	PUNCT
m-806	63	129	�	�	PROPN
m-806	63	130	�	�	PROPN
m-806	63	131	�	�	PROPN
m-806	63	132	):	):	PUNCT
m-806	63	133	�	�	PROPN
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m-806	63	135	(	(	PUNCT
m-806	63	136	�	�	PROPN
m-806	63	137	�	�	PROPN
m-806	63	138	)	)	PUNCT
m-806	63	139	=	=	SYM
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m-806	63	144	(	(	PUNCT
m-806	63	145	�	�	PROPN
m-806	63	146	�	�	PROPN
m-806	63	147	)	)	PUNCT
m-806	63	148	�	�	PROPN
m-806	63	149	�	�	PROPN
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m-806	63	151	(	(	PUNCT
m-806	63	152	�	�	PROPN
m-806	63	153	�	�	PROPN
m-806	63	154	)	)	PUNCT
m-806	63	155	−	−	PROPN
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m-806	63	157	�	�	PROPN
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m-806	63	163	�	�	PROPN
m-806	63	164	�	�	PROPN
m-806	63	165	+	+	SYM
m-806	63	166	�	�	PROPN
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m-806	63	170	(	(	PUNCT
m-806	63	171	�	�	PROPN
m-806	63	172	�	�	PROPN
m-806	63	173	)	)	PUNCT
m-806	63	174	�	�	PROPN
m-806	63	175	−	−	PROPN
m-806	63	176	�	�	PROPN
m-806	63	177	�	�	PROPN
m-806	63	178	�	�	PROPN
m-806	63	179	�	�	PROPN
m-806	63	180	�	�	PROPN
m-806	63	181	,	,	PUNCT
m-806	63	182	�	�	PROPN
m-806	63	183	�	�	PROPN
m-806	63	184	(	(	PUNCT
m-806	63	185	�	�	PROPN
m-806	63	186	�	�	PROPN
m-806	63	187	)	)	PUNCT
m-806	63	188	−	−	PROPN
m-806	63	189	2	2	NUM
m-806	63	190	�	�	PROPN
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m-806	63	192	�	�	PROPN
m-806	63	193	�	�	PROPN
m-806	63	194	,	,	PUNCT
m-806	63	195	�	�	PROPN
m-806	63	196	�	�	PROPN
m-806	63	197	(	(	PUNCT
m-806	63	198	�	�	PROPN
m-806	63	199	�	�	PROPN
m-806	63	200	)	)	PUNCT
m-806	63	201	(	(	PUNCT
m-806	63	202	6.13	6.13	NUM
m-806	63	203	)	)	PUNCT
m-806	63	204	�	�	PROPN
m-806	63	205	(	(	PUNCT
m-806	63	206	�	�	PROPN
m-806	63	207	�	�	PROPN
m-806	63	208	�	�	PROPN
m-806	63	209	�	�	PROPN
m-806	63	210	):	):	PUNCT
m-806	63	211	�	�	PROPN
m-806	63	212	�	�	PROPN
m-806	63	213	(	(	PUNCT
m-806	63	214	�	�	PROPN
m-806	63	215	�	�	PROPN
m-806	63	216	)	)	PUNCT
m-806	63	217	=	=	SYM
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m-806	63	219	�	�	PROPN
m-806	63	220	�	�	PROPN
m-806	63	221	�	�	PROPN
m-806	63	222	(	(	PUNCT
m-806	63	223	�	�	PROPN
m-806	63	224	�	�	PROPN
m-806	63	225	)	)	PUNCT
m-806	63	226	�	�	PROPN
m-806	63	227	�	�	PROPN
m-806	63	228	(	(	PUNCT
m-806	63	229	�	�	PROPN
m-806	63	230	�	�	PROPN
m-806	63	231	)	)	PUNCT
m-806	63	232	�	�	PROPN
m-806	63	233	�	�	PROPN
m-806	63	234	+	+	CCONJ
m-806	63	235	�	�	PROPN
m-806	63	236	�	�	PROPN
m-806	63	237	(	(	PUNCT
m-806	63	238	�	�	PROPN
m-806	63	239	�	�	PROPN
m-806	63	240	)	)	PUNCT
m-806	63	241	�	�	PROPN
m-806	63	242	�	�	PROPN
m-806	63	243	�	�	PROPN
m-806	63	244	(	(	PUNCT
m-806	63	245	�	�	PROPN
m-806	63	246	�	�	PROPN
m-806	63	247	)	)	PUNCT
m-806	63	248	�	�	PROPN
m-806	63	249	−	−	PROPN
m-806	63	250	�	�	PROPN
m-806	63	251	,	,	PUNCT
m-806	63	252	�	�	PROPN
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m-806	63	254	(	(	PUNCT
m-806	63	255	�	�	PROPN
m-806	63	256	�	�	PROPN
m-806	63	257	)	)	PUNCT
m-806	63	258	−2	−2	PROPN
m-806	63	259	�	�	PROPN
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m-806	63	261	,	,	PUNCT
m-806	63	262	�	�	PROPN
m-806	63	263	�	�	PROPN
m-806	63	264	�	�	PROPN
m-806	63	265	(	(	PUNCT
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m-806	63	267	�	�	PROPN
m-806	63	268	)	)	PUNCT
m-806	63	269	+	+	SYM
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m-806	63	272	�	�	PROPN
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m-806	63	274	,	,	PUNCT
m-806	63	275	�	�	PROPN
m-806	63	276	�	�	PROPN
m-806	63	277	�	�	PROPN
m-806	63	278	(	(	PUNCT
m-806	63	279	�	�	PROPN
m-806	63	280	�	�	PROPN
m-806	63	281	)	)	PUNCT
m-806	63	282	�	�	PROPN
m-806	63	283	−	−	PROPN
m-806	63	284	�	�	PROPN
m-806	63	285	�	�	PROPN
m-806	63	286	�	�	PROPN
m-806	63	287	�	�	PROPN
m-806	63	288	�	�	PROPN
m-806	63	289	,	,	PUNCT
m-806	63	290	�	�	PROPN
m-806	63	291	�	�	PROPN
m-806	63	292	(	(	PUNCT
m-806	63	293	�	�	PROPN
m-806	63	294	�	�	PROPN
m-806	63	295	)	)	PUNCT
m-806	63	296	−	−	PROPN
m-806	63	297	2	2	NUM
m-806	63	298	�	�	PROPN
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m-806	63	300	,	,	PUNCT
m-806	63	301	�	�	PROPN
m-806	63	302	�	�	PROPN
m-806	63	303	(	(	PUNCT
m-806	63	304	�	�	PROPN
m-806	63	305	�	�	PROPN
m-806	63	306	)	)	PUNCT
m-806	63	307	+	+	SYM
m-806	63	308	�	�	PROPN
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m-806	63	310	�	�	PROPN
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m-806	63	312	,	,	PUNCT
m-806	63	313	�	�	PROPN
m-806	63	314	�	�	PROPN
m-806	63	315	(	(	PUNCT
m-806	63	316	�	�	PROPN
m-806	63	317	�	�	PROPN
m-806	63	318	)	)	PUNCT
m-806	63	319	+	+	SYM
m-806	63	320	�	�	PROPN
m-806	63	321	,	,	PUNCT
m-806	63	322	�	�	PROPN
m-806	63	323	(	(	PUNCT
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m-806	63	325	�	�	PROPN
m-806	63	326	)	)	PUNCT
m-806	63	327	�	�	PROPN
m-806	63	328	(	(	PUNCT
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m-806	63	330	)	)	PUNCT
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m-806	63	333	conditions	condition	NOUN
m-806	63	334	,	,	PUNCT
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m-806	63	336	are	be	AUX
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m-806	63	338	at	at	ADP
m-806	63	339	�	�	PROPN
m-806	63	340	̂	̂	VERB
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m-806	63	346	�	�	PROPN
m-806	63	347	(	(	PUNCT
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m-806	63	382	(	(	PUNCT
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m-806	63	385	ο(ϵ	ο(ϵ	PROPN
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m-806	63	391	(	(	PUNCT
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m-806	63	394	)	)	PUNCT
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m-806	63	404	(	(	PUNCT
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m-806	63	407	ο(ϵδ	ο(ϵδ	PROPN
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m-806	63	413	(	(	PUNCT
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m-806	63	416	)	)	PUNCT
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m-806	64	1	+	+	CCONJ
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m-806	64	5	(	(	PUNCT
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m-806	64	9	(	(	PUNCT
m-806	64	10	x	x	X
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m-806	64	18	(	(	PUNCT
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m-806	64	43	(	(	PUNCT
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m-806	64	46	)	)	PUNCT
m-806	64	47	(	(	PUNCT
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m-806	64	84	(	(	PUNCT
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m-806	65	42	07	07	NUM
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m-806	65	45	02	02	NUM
m-806	65	46	|	|	CCONJ
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m-806	66	1	|	|	ADV
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m-806	66	31	||	||	NOUN
m-806	66	32	on	on	ADP
m-806	66	33	a	a	DET
m-806	66	34	-	-	PUNCT
m-806	66	35	two	two	NUM
m-806	66	36	-	-	PUNCT
m-806	66	37	parameter	parameter	NOUN
m-806	66	38	dynamic	dynamic	ADJ
m-806	66	39	buckling	buckling	NOUN
m-806	66	40	of	of	ADP
m-806	66	41	a	a	DET
m-806	66	42	viscously	viscously	ADV
m-806	66	43	damped	damp	VERB
m-806	66	44	but	but	CCONJ
m-806	66	45	clamped	clamp	VERB
m-806	66	46	column	column	NOUN
m-806	66	47	stressed	stress	VERB
m-806	66	48	by	by	ADP
m-806	66	49	a	a	DET
m-806	66	50	step	step	NOUN
m-806	66	51	load	load	NOUN
m-806	66	52	in	in	ADP
m-806	66	53	general	general	ADJ
m-806	66	54	,	,	PUNCT
m-806	66	55	we	we	PRON
m-806	66	56	have	have	VERB
m-806	66	57	�	�	PROPN
m-806	66	58	,	,	PUNCT
m-806	66	59	�	�	PROPN
m-806	66	60	�	�	PROPN
m-806	66	61	(	(	PUNCT
m-806	66	62	�	�	PROPN
m-806	66	63	�	�	PROPN
m-806	66	64	)	)	PUNCT
m-806	66	65	(	(	PUNCT
m-806	66	66	x	x	X
m-806	66	67	,	,	PUNCT
m-806	66	68	0	0	NUM
m-806	66	69	,	,	PUNCT
m-806	66	70	0	0	NUM
m-806	66	71	)	)	PUNCT
m-806	66	72	+	+	CCONJ
m-806	66	73	�	�	PROPN
m-806	66	74	,	,	PUNCT
m-806	66	75	�	�	PROPN
m-806	66	76	�	�	PROPN
m-806	66	77	(	(	PUNCT
m-806	66	78	�	�	PROPN
m-806	66	79	�	�	PROPN
m-806	66	80	�	�	PROPN
m-806	66	81	)	)	PUNCT
m-806	66	82	(	(	PUNCT
m-806	66	83	x	x	X
m-806	66	84	,	,	PUNCT
m-806	66	85	0	0	NUM
m-806	66	86	,	,	PUNCT
m-806	66	87	0	0	NUM
m-806	66	88	)	)	PUNCT
m-806	66	89	=	=	SYM
m-806	67	1	0	0	NUM
m-806	67	2	,	,	PUNCT
m-806	67	3	k	k	NOUN
m-806	67	4	=	=	SYM
m-806	67	5	1	1	NUM
m-806	67	6	,	,	PUNCT
m-806	67	7	2	2	NUM
m-806	67	8	,	,	PUNCT
m-806	67	9	3	3	NUM
m-806	67	10	,	,	PUNCT
m-806	67	11	…	…	PUNCT
m-806	67	12	(	(	PUNCT
m-806	67	13	6.21	6.21	NUM
m-806	67	14	)	)	PUNCT
m-806	67	15	ο(ϵ	ο(ϵ	PROPN
m-806	67	16	�	�	PROPN
m-806	67	17	):	):	PUNCT
m-806	67	18	�	�	PROPN
m-806	67	19	,	,	PUNCT
m-806	67	20	�	�	PROPN
m-806	67	21	�	�	PROPN
m-806	67	22	(	(	PUNCT
m-806	67	23	�	�	PROPN
m-806	67	24	�	�	PROPN
m-806	67	25	)	)	PUNCT
m-806	67	26	(	(	PUNCT
m-806	67	27	x	x	X
m-806	67	28	,	,	PUNCT
m-806	67	29	0	0	NUM
m-806	67	30	,	,	PUNCT
m-806	67	31	0	0	NUM
m-806	67	32	)	)	PUNCT
m-806	67	33	+	+	CCONJ
m-806	67	34	�	�	PROPN
m-806	67	35	�	�	PROPN
m-806	67	36	�	�	PROPN
m-806	67	37	(	(	PUNCT
m-806	67	38	0	0	NUM
m-806	67	39	)	)	PUNCT
m-806	67	40	�	�	PROPN
m-806	67	41	,	,	PUNCT
m-806	67	42	�	�	PROPN
m-806	67	43	�	�	PROPN
m-806	67	44	(	(	PUNCT
m-806	67	45	�	�	PROPN
m-806	67	46	�	�	PROPN
m-806	67	47	)	)	PUNCT
m-806	67	48	(	(	PUNCT
m-806	67	49	x	x	X
m-806	67	50	,	,	PUNCT
m-806	67	51	0	0	NUM
m-806	67	52	,	,	PUNCT
m-806	67	53	0	0	NUM
m-806	67	54	)	)	PUNCT
m-806	67	55	=	=	SYM
m-806	67	56	0	0	PUNCT
m-806	67	57	(	(	PUNCT
m-806	67	58	6.22	6.22	NUM
m-806	67	59	)	)	PUNCT
m-806	67	60	o(ϵ	o(ϵ	PROPN
m-806	67	61	�	�	PROPN
m-806	67	62	�	�	PROPN
m-806	67	63	):	):	PUNCT
m-806	67	64	�	�	PROPN
m-806	67	65	,	,	PUNCT
m-806	67	66	�	�	PROPN
m-806	67	67	�	�	PROPN
m-806	67	68	(	(	PUNCT
m-806	67	69	�	�	PROPN
m-806	67	70	�	�	PROPN
m-806	67	71	)	)	PUNCT
m-806	67	72	(	(	PUNCT
m-806	67	73	x	x	X
m-806	67	74	,	,	PUNCT
m-806	67	75	0	0	NUM
m-806	67	76	,	,	PUNCT
m-806	67	77	0	0	NUM
m-806	67	78	)	)	PUNCT
m-806	67	79	+	+	CCONJ
m-806	67	80	�	�	PROPN
m-806	67	81	�	�	PROPN
m-806	67	82	�	�	PROPN
m-806	67	83	(	(	PUNCT
m-806	67	84	0	0	NUM
m-806	67	85	)	)	PUNCT
m-806	67	86	�	�	PROPN
m-806	67	87	,	,	PUNCT
m-806	67	88	�	�	PROPN
m-806	67	89	�	�	PROPN
m-806	67	90	(	(	PUNCT
m-806	67	91	�	�	PROPN
m-806	67	92	�	�	PROPN
m-806	67	93	)	)	PUNCT
m-806	67	94	(	(	PUNCT
m-806	67	95	x	x	X
m-806	67	96	,	,	PUNCT
m-806	67	97	0	0	NUM
m-806	67	98	,	,	PUNCT
m-806	67	99	0	0	NUM
m-806	67	100	)	)	PUNCT
m-806	67	101	+	+	CCONJ
m-806	67	102	�	�	PROPN
m-806	67	103	,	,	PUNCT
m-806	67	104	�	�	PROPN
m-806	67	105	(	(	PUNCT
m-806	67	106	�	�	PROPN
m-806	67	107	�	�	PROPN
m-806	67	108	)	)	PUNCT
m-806	67	109	(	(	PUNCT
m-806	67	110	x	x	X
m-806	67	111	,	,	PUNCT
m-806	67	112	0	0	NUM
m-806	67	113	,	,	PUNCT
m-806	67	114	0	0	NUM
m-806	67	115	)	)	PUNCT
m-806	67	116	=	=	SYM
m-806	67	117	0	0	NUM
m-806	67	118	(	(	PUNCT
m-806	67	119	6.23	6.23	NUM
m-806	67	120	)	)	PUNCT
m-806	67	121	ο(ϵ	ο(ϵ	PROPN
m-806	67	122	�	�	PROPN
m-806	67	123	�	�	PROPN
m-806	67	124	�	�	PROPN
m-806	67	125	):	):	PUNCT
m-806	67	126	�	�	PROPN
m-806	67	127	,	,	PUNCT
m-806	67	128	�	�	PROPN
m-806	67	129	�	�	PROPN
m-806	67	130	�	�	PROPN
m-806	67	131	�	�	PROPN
m-806	67	132	(	(	PUNCT
m-806	67	133	x	x	NOUN
m-806	67	134	,	,	PUNCT
m-806	67	135	0	0	NUM
m-806	67	136	,	,	PUNCT
m-806	67	137	0	0	NUM
m-806	67	138	)	)	PUNCT
m-806	68	1	+	+	CCONJ
m-806	68	2	�	�	PROPN
m-806	68	3	�	�	PROPN
m-806	68	4	�	�	PROPN
m-806	68	5	(	(	PUNCT
m-806	68	6	0	0	NUM
m-806	68	7	)	)	PUNCT
m-806	68	8	�	�	PROPN
m-806	68	9	,	,	PUNCT
m-806	68	10	�	�	PROPN
m-806	68	11	�	�	PROPN
m-806	68	12	(	(	PUNCT
m-806	68	13	�	�	PROPN
m-806	68	14	�	�	PROPN
m-806	68	15	)	)	PUNCT
m-806	68	16	(	(	PUNCT
m-806	68	17	x	x	X
m-806	68	18	,	,	PUNCT
m-806	68	19	0	0	NUM
m-806	68	20	,	,	PUNCT
m-806	68	21	0	0	NUM
m-806	68	22	)	)	PUNCT
m-806	68	23	+	+	CCONJ
m-806	68	24	�	�	PROPN
m-806	68	25	,	,	PUNCT
m-806	68	26	�	�	PROPN
m-806	68	27	(	(	PUNCT
m-806	68	28	�	�	PROPN
m-806	68	29	�	�	PROPN
m-806	68	30	)	)	PUNCT
m-806	68	31	(	(	PUNCT
m-806	68	32	0	0	NUM
m-806	68	33	,	,	PUNCT
m-806	68	34	0	0	NUM
m-806	68	35	)	)	PUNCT
m-806	68	36	=	=	SYM
m-806	68	37	0	0	PUNCT
m-806	68	38	(	(	PUNCT
m-806	68	39	6.24	6.24	NUM
m-806	68	40	)	)	PUNCT
m-806	68	41	generally	generally	ADV
m-806	68	42	,	,	PUNCT
m-806	68	43	we	we	PRON
m-806	68	44	have	have	VERB
m-806	68	45	�	�	PROPN
m-806	68	46	,	,	PUNCT
m-806	68	47	�	�	PROPN
m-806	68	48	�	�	PROPN
m-806	68	49	(	(	PUNCT
m-806	68	50	�	�	PROPN
m-806	68	51	�	�	PROPN
m-806	68	52	)	)	PUNCT
m-806	68	53	(	(	PUNCT
m-806	68	54	x	x	X
m-806	68	55	,	,	PUNCT
m-806	68	56	0	0	NUM
m-806	68	57	,	,	PUNCT
m-806	68	58	0	0	NUM
m-806	68	59	)	)	PUNCT
m-806	68	60	+	+	CCONJ
m-806	68	61	�	�	PROPN
m-806	68	62	�	�	PROPN
m-806	68	63	�	�	PROPN
m-806	68	64	(	(	PUNCT
m-806	68	65	0	0	NUM
m-806	68	66	)	)	PUNCT
m-806	68	67	�	�	PROPN
m-806	68	68	,	,	PUNCT
m-806	68	69	�	�	PROPN
m-806	68	70	�	�	PROPN
m-806	68	71	(	(	PUNCT
m-806	68	72	�	�	PROPN
m-806	68	73	�	�	PROPN
m-806	68	74	)	)	PUNCT
m-806	68	75	(	(	PUNCT
m-806	68	76	x	x	X
m-806	68	77	,	,	PUNCT
m-806	68	78	0	0	NUM
m-806	68	79	,	,	PUNCT
m-806	68	80	0	0	NUM
m-806	68	81	)	)	PUNCT
m-806	68	82	+	+	CCONJ
m-806	68	83	�	�	PROPN
m-806	68	84	,	,	PUNCT
m-806	68	85	�	�	PROPN
m-806	68	86	�	�	PROPN
m-806	68	87	�	�	PROPN
m-806	68	88	(	(	PUNCT
m-806	68	89	�	�	PROPN
m-806	68	90	�	�	PROPN
m-806	68	91	�	�	PROPN
m-806	68	92	)	)	PUNCT
m-806	68	93	�	�	PROPN
m-806	68	94	(	(	PUNCT
m-806	68	95	x	x	X
m-806	68	96	,	,	PUNCT
m-806	68	97	0	0	NUM
m-806	68	98	,	,	PUNCT
m-806	68	99	0	0	NUM
m-806	68	100	)	)	PUNCT
m-806	68	101	=	=	SYM
m-806	68	102	0	0	NUM
m-806	68	103	,	,	PUNCT
m-806	68	104	k	k	NOUN
m-806	68	105	=	=	SYM
m-806	68	106	1	1	NUM
m-806	68	107	,	,	PUNCT
m-806	68	108	2	2	NUM
m-806	68	109	,	,	PUNCT
m-806	68	110	3	3	NUM
m-806	68	111	,	,	PUNCT
m-806	68	112	…	…	PUNCT
m-806	68	113	(	(	PUNCT
m-806	68	114	6.25	6.25	NUM
m-806	68	115	)	)	PUNCT
m-806	68	116	the	the	DET
m-806	68	117	boundary	boundary	ADJ
m-806	68	118	conditions	condition	NOUN
m-806	68	119	are	be	AUX
m-806	68	120	�	�	PROPN
m-806	68	121	(	(	PUNCT
m-806	68	122	�	�	NOUN
m-806	68	123	�	�	PROPN
m-806	68	124	)	)	PUNCT
m-806	68	125	=	=	SYM
m-806	68	126	u	u	NOUN
m-806	68	127	,	,	PUNCT
m-806	68	128	�	�	PROPN
m-806	68	129	(	(	PUNCT
m-806	68	130	�	�	NOUN
m-806	68	131	�	�	PROPN
m-806	68	132	)	)	PUNCT
m-806	68	133	=	=	SYM
m-806	68	134	0	0	NUM
m-806	68	135	�	�	PROPN
m-806	68	136	�	�	PROPN
m-806	68	137	�	�	PROPN
m-806	68	138	=	=	SYM
m-806	68	139	0	0	NUM
m-806	68	140	,	,	PUNCT
m-806	68	141	�	�	PROPN
m-806	68	142	.	.	PUNCT
m-806	69	1	for	for	ADP
m-806	69	2	solution	solution	NOUN
m-806	69	3	to	to	ADP
m-806	69	4	all	all	DET
m-806	69	5	the	the	DET
m-806	69	6	systems	system	NOUN
m-806	69	7	of	of	ADP
m-806	69	8	equation	equation	NOUN
m-806	69	9	involved	involve	VERB
m-806	69	10	here	here	ADV
m-806	69	11	,	,	PUNCT
m-806	69	12	we	we	PRON
m-806	69	13	set	set	VERB
m-806	69	14	�	�	PROPN
m-806	69	15	(	(	PUNCT
m-806	69	16	�	�	PROPN
m-806	69	17	�	�	PROPN
m-806	69	18	)	)	PUNCT
m-806	69	19	(	(	PUNCT
m-806	69	20	x	x	X
m-806	69	21	,	,	PUNCT
m-806	69	22	t̂	t̂	NUM
m-806	69	23	,	,	PUNCT
m-806	69	24	τ	τ	X
m-806	69	25	)	)	PUNCT
m-806	69	26	=	=	SYM
m-806	69	27	2	2	NUM
m-806	69	28	∑	∑	PART
m-806	69	29	u	u	NOUN
m-806	69	30	�	�	PROPN
m-806	69	31	(	(	PUNCT
m-806	69	32	�	�	PROPN
m-806	69	33	�	�	PROPN
m-806	69	34	)	)	PUNCT
m-806	69	35	(	(	PUNCT
m-806	69	36	t̂	t̂	PROPN
m-806	69	37	,	,	PUNCT
m-806	69	38	τ)sin	τ)sin	PROPN
m-806	69	39	�	�	PROPN
m-806	69	40	nx	nx	PROPN
m-806	69	41	=	=	SYM
m-806	69	42	∑	∑	PUNCT
m-806	69	43	u	u	NOUN
m-806	69	44	�	�	PROPN
m-806	69	45	(	(	PUNCT
m-806	69	46	�	�	PROPN
m-806	69	47	�	�	PROPN
m-806	69	48	)	)	PUNCT
m-806	69	49	(	(	PUNCT
m-806	69	50	t̂	t̂	NUM
m-806	69	51	,	,	PUNCT
m-806	69	52	τ)(1	τ)(1	X
m-806	70	1	−	−	PROPN
m-806	70	2	cos	cos	PROPN
m-806	70	3	2	2	NUM
m-806	70	4	�	�	PROPN
m-806	70	5	�	�	PROPN
m-806	70	6	)	)	PUNCT
m-806	70	7	�	�	PROPN
m-806	70	8	�	�	PROPN
m-806	70	9	�	�	PROPN
m-806	70	10	�	�	PROPN
m-806	70	11	�	�	PROPN
m-806	70	12	�	�	PROPN
m-806	70	13	�	�	PROPN
m-806	70	14	�	�	PROPN
m-806	70	15	(	(	PUNCT
m-806	70	16	6.26a	6.26a	NUM
m-806	70	17	)	)	PUNCT
m-806	70	18	we	we	PRON
m-806	70	19	shall	shall	AUX
m-806	70	20	assume	assume	VERB
m-806	70	21	�	�	PROPN
m-806	70	22	�	�	PROPN
m-806	70	23	(	(	PUNCT
m-806	70	24	�	�	PROPN
m-806	70	25	)	)	PUNCT
m-806	70	26	=	=	SYM
m-806	70	27	�	�	PROPN
m-806	70	28	�	�	PROPN
m-806	70	29	�	�	PROPN
m-806	70	30	(	(	PUNCT
m-806	70	31	1	1	NUM
m-806	70	32	−	−	PROPN
m-806	70	33	cos	cos	PROPN
m-806	70	34	2	2	NUM
m-806	70	35	�	�	PROPN
m-806	70	36	�	�	PROPN
m-806	70	37	)	)	PUNCT
m-806	70	38	(	(	PUNCT
m-806	70	39	6.26b	6.26b	NOUN
m-806	70	40	)	)	PUNCT
m-806	70	41	for	for	ADP
m-806	70	42	�	�	PROPN
m-806	70	43	,	,	PUNCT
m-806	70	44	fixed	fix	VERB
m-806	70	45	.	.	PUNCT
m-806	71	1	on	on	ADP
m-806	71	2	substituting	substitute	VERB
m-806	71	3	(	(	PUNCT
m-806	71	4	6.26a	6.26a	NUM
m-806	71	5	,	,	PUNCT
m-806	71	6	b	b	NOUN
m-806	71	7	)	)	PUNCT
m-806	71	8	into	into	ADP
m-806	71	9	(	(	PUNCT
m-806	71	10	6.6	6.6	NUM
m-806	71	11	)	)	PUNCT
m-806	71	12	and	and	CCONJ
m-806	71	13	simplifying	simplify	VERB
m-806	71	14	,	,	PUNCT
m-806	71	15	we	we	PRON
m-806	71	16	get	get	VERB
m-806	71	17	�	�	PROPN
m-806	71	18	�	�	PROPN
m-806	71	19	u	u	NOUN
m-806	71	20	�	�	PROPN
m-806	71	21	,	,	PUNCT
m-806	71	22	�	�	PROPN
m-806	71	23	�	�	PROPN
m-806	71	24	�	�	PROPN
m-806	71	25	�	�	PROPN
m-806	71	26	(	(	PUNCT
m-806	71	27	�	�	PROPN
m-806	71	28	�	�	PROPN
m-806	71	29	)	)	PUNCT
m-806	71	30	+	+	CCONJ
m-806	71	31	u	u	NOUN
m-806	71	32	�	�	PROPN
m-806	71	33	(	(	PUNCT
m-806	71	34	�	�	PROPN
m-806	71	35	�	�	PROPN
m-806	71	36	)	)	PUNCT
m-806	71	37	�	�	PROPN
m-806	71	38	(	(	PUNCT
m-806	71	39	1	1	NUM
m-806	71	40	−	−	PROPN
m-806	71	41	cos	cos	PROPN
m-806	71	42	2	2	NUM
m-806	71	43	�	�	PROPN
m-806	71	44	�	�	PROPN
m-806	71	45	)	)	PUNCT
m-806	71	46	�	�	PROPN
m-806	71	47	�	�	PROPN
m-806	71	48	�	�	PROPN
m-806	71	49	�	�	PROPN
m-806	71	50	+	+	SYM
m-806	71	51	�	�	PROPN
m-806	71	52	(	(	PUNCT
m-806	71	53	8	8	NUM
m-806	71	54	�	�	PROPN
m-806	71	55	�	�	PROPN
m-806	71	56	�	�	PROPN
m-806	71	57	−	−	PROPN
m-806	71	58	16	16	NUM
m-806	71	59	�	�	PROPN
m-806	71	60	�	�	PROPN
m-806	71	61	)u	)u	PROPN
m-806	71	62	�	�	PROPN
m-806	71	63	(	(	PUNCT
m-806	71	64	�	�	PROPN
m-806	71	65	�	�	PROPN
m-806	71	66	)	)	PUNCT
m-806	71	67	cos	cos	ADP
m-806	71	68	2	2	NUM
m-806	71	69	�	�	PROPN
m-806	71	70	�	�	PROPN
m-806	71	71	�	�	PROPN
m-806	71	72	�	�	PROPN
m-806	71	73	�	�	PROPN
m-806	71	74	�	�	PROPN
m-806	71	75	=	=	SYM
m-806	71	76	−8	−8	X
m-806	71	77	�	�	PROPN
m-806	71	78	�	�	PROPN
m-806	71	79	�	�	PROPN
m-806	71	80	�	�	PROPN
m-806	71	81	�	�	PROPN
m-806	71	82	�	�	PROPN
m-806	71	83	�	�	PROPN
m-806	71	84	�	�	PROPN
m-806	71	85	�	�	PROPN
m-806	71	86	2	2	NUM
m-806	71	87	�	�	PROPN
m-806	71	88	�	�	PROPN
m-806	71	89	(	(	PUNCT
m-806	71	90	6.27a	6.27a	NUM
m-806	71	91	)	)	PUNCT
m-806	71	92	next	next	ADV
m-806	71	93	,	,	PUNCT
m-806	71	94	we	we	PRON
m-806	71	95	multiply	multiply	VERB
m-806	71	96	(	(	PUNCT
m-806	71	97	6.27a	6.27a	NOUN
m-806	71	98	)	)	PUNCT
m-806	71	99	by	by	ADP
m-806	71	100	�	�	PROPN
m-806	71	101	�	�	PROPN
m-806	71	102	�	�	PROPN
m-806	71	103	2	2	NUM
m-806	71	104	�	�	PROPN
m-806	71	105	�	�	PROPN
m-806	71	106	and	and	CCONJ
m-806	71	107	integrate	integrate	VERB
m-806	71	108	from	from	ADP
m-806	71	109	0	0	NUM
m-806	71	110	to	to	ADP
m-806	71	111	π	π	PROPN
m-806	71	112	,	,	PUNCT
m-806	71	113	and	and	CCONJ
m-806	71	114	note	note	VERB
m-806	71	115	that	that	SCONJ
m-806	71	116	for	for	ADP
m-806	71	117	�	�	PROPN
m-806	71	118	=	=	SYM
m-806	71	119	�	�	PROPN
m-806	71	120	,	,	PUNCT
m-806	71	121	we	we	PRON
m-806	71	122	get	get	VERB
m-806	71	123	u	u	NOUN
m-806	71	124	�	�	PROPN
m-806	71	125	,	,	PUNCT
m-806	71	126	�	�	PROPN
m-806	71	127	�	�	PROPN
m-806	71	128	�	�	PROPN
m-806	71	129	�	�	PROPN
m-806	71	130	(	(	PUNCT
m-806	71	131	�	�	PROPN
m-806	71	132	�	�	PROPN
m-806	71	133	)	)	PUNCT
m-806	72	1	+	+	SYM
m-806	72	2	�	�	PROPN
m-806	72	3	�	�	PROPN
m-806	72	4	u	u	NOUN
m-806	72	5	�	�	PROPN
m-806	72	6	(	(	PUNCT
m-806	72	7	�	�	PROPN
m-806	72	8	�	�	PROPN
m-806	72	9	)	)	PUNCT
m-806	72	10	=	=	SYM
m-806	72	11	8	8	NUM
m-806	72	12	�	�	PROPN
m-806	72	13	�	�	PROPN
m-806	72	14	�	�	PROPN
m-806	72	15	�	�	PROPN
m-806	72	16	�	�	PROPN
m-806	72	17	�	�	PROPN
m-806	72	18	(	(	PUNCT
m-806	72	19	6.27b	6.27b	NUM
m-806	72	20	)	)	PUNCT
m-806	72	21	u	u	NOUN
m-806	72	22	�	�	PROPN
m-806	72	23	(	(	PUNCT
m-806	72	24	�	�	PROPN
m-806	72	25	�	�	PROPN
m-806	72	26	)	)	PUNCT
m-806	72	27	(	(	PUNCT
m-806	72	28	0,0	0,0	NUM
m-806	72	29	)	)	PUNCT
m-806	72	30	=	=	SYM
m-806	72	31	0	0	NUM
m-806	72	32	,	,	PUNCT
m-806	72	33	u	u	NOUN
m-806	72	34	�	�	PROPN
m-806	72	35	,	,	PUNCT
m-806	72	36	�	�	PROPN
m-806	72	37	�	�	PROPN
m-806	72	38	(	(	PUNCT
m-806	72	39	�	�	PROPN
m-806	72	40	�	�	PROPN
m-806	72	41	)	)	PUNCT
m-806	72	42	(	(	PUNCT
m-806	72	43	0,0	0,0	NUM
m-806	72	44	)	)	PUNCT
m-806	72	45	=	=	SYM
m-806	72	46	0	0	PUNCT
m-806	72	47	(	(	PUNCT
m-806	72	48	6.27c	6.27c	NOUN
m-806	72	49	)	)	PUNCT
m-806	72	50	where	where	SCONJ
m-806	72	51	,	,	PUNCT
m-806	72	52	�	�	PROPN
m-806	72	53	�	�	PROPN
m-806	72	54	=	=	SYM
m-806	72	55	(	(	PUNCT
m-806	72	56	16	16	NUM
m-806	72	57	�	�	PROPN
m-806	72	58	�	�	PROPN
m-806	72	59	−	−	PROPN
m-806	72	60	8	8	NUM
m-806	72	61	�	�	PROPN
m-806	72	62	�	�	PROPN
m-806	72	63	�	�	PROPN
m-806	72	64	+	+	CCONJ
m-806	72	65	1	1	NUM
m-806	72	66	)	)	PUNCT
m-806	72	67	>	>	X
m-806	72	68	0	0	NUM
m-806	72	69	,	,	PUNCT
m-806	72	70	∀	∀	X
m-806	72	71	�	�	PROPN
m-806	72	72	(	(	PUNCT
m-806	72	73	6.27d	6.27d	NUM
m-806	72	74	)	)	PUNCT
m-806	72	75	the	the	DET
m-806	72	76	solution	solution	NOUN
m-806	72	77	of	of	ADP
m-806	72	78	(	(	PUNCT
m-806	72	79	6.27b	6.27b	NUM
m-806	72	80	-	-	PUNCT
m-806	72	81	d	d	NOUN
m-806	72	82	)	)	PUNCT
m-806	72	83	is	be	AUX
m-806	72	84	u	u	PRON
m-806	72	85	�	�	PROPN
m-806	72	86	(	(	PUNCT
m-806	72	87	�	�	PROPN
m-806	72	88	�	�	PROPN
m-806	72	89	)	)	PUNCT
m-806	72	90	(	(	PUNCT
m-806	72	91	t̂	t̂	PROPN
m-806	72	92	,	,	PUNCT
m-806	72	93	τ	τ	NOUN
m-806	72	94	)	)	PUNCT
m-806	72	95	=	=	SYM
m-806	72	96	�	�	PROPN
m-806	72	97	�	�	PROPN
m-806	72	98	(	(	PUNCT
m-806	72	99	�	�	PROPN
m-806	72	100	)	)	PUNCT
m-806	72	101	cos	cos	PROPN
m-806	72	102	�	�	PROPN
m-806	72	103	�	�	PROPN
m-806	72	104	̂	̂	VERB
m-806	72	105	+	+	NUM
m-806	72	106	�	�	PROPN
m-806	72	107	�	�	PROPN
m-806	72	108	(	(	PUNCT
m-806	72	109	�	�	PROPN
m-806	72	110	)	)	PUNCT
m-806	72	111	sin	sin	PROPN
m-806	72	112	�	�	PROPN
m-806	72	113	�	�	PROPN
m-806	72	114	̂	̂	VERB
m-806	72	115	+	+	NUM
m-806	72	116	�	�	PROPN
m-806	72	117	(	(	PUNCT
m-806	72	118	6.28a	6.28a	NUM
m-806	72	119	)	)	PUNCT
m-806	72	120	�	�	PROPN
m-806	72	121	=	=	SYM
m-806	72	122	�	�	PROPN
m-806	72	123	�	�	PROPN
m-806	72	124	�	�	PROPN
m-806	72	125	�	�	PROPN
m-806	72	126	�	�	PROPN
m-806	72	127	�	�	PROPN
m-806	72	128	�	�	PROPN
m-806	72	129	�	�	PROPN
m-806	72	130	�	�	PROPN
m-806	72	131	=	=	SYM
m-806	72	132	�	�	PROPN
m-806	72	133	�	�	PROPN
m-806	72	134	�	�	PROPN
m-806	72	135	�	�	PROPN
m-806	72	136	�	�	PROPN
m-806	72	137	�	�	PROPN
m-806	72	138	�	�	PROPN
m-806	72	139	�	�	PROPN
m-806	72	140	�	�	PROPN
m-806	72	141	�	�	PROPN
m-806	72	142	�	�	PROPN
m-806	72	143	�	�	PROPN
m-806	72	144	�	�	PROPN
m-806	72	145	�	�	PROPN
m-806	72	146	�	�	PROPN
m-806	72	147	�	�	PROPN
m-806	72	148	�	�	PROPN
m-806	72	149	�	�	PROPN
m-806	72	150	(	(	PUNCT
m-806	72	151	6.28b	6.28b	PROPN
m-806	72	152	)	)	PUNCT
m-806	72	153	where	where	SCONJ
m-806	72	154	,	,	PUNCT
m-806	72	155	�	�	PROPN
m-806	72	156	�	�	PROPN
m-806	72	157	(	(	PUNCT
m-806	72	158	0	0	NUM
m-806	72	159	)	)	PUNCT
m-806	72	160	=	=	SYM
m-806	72	161	−	−	PROPN
m-806	72	162	�	�	PROPN
m-806	72	163	,	,	PUNCT
m-806	72	164	�	�	PROPN
m-806	72	165	�	�	PROPN
m-806	72	166	(	(	PUNCT
m-806	72	167	0	0	NUM
m-806	72	168	)	)	PUNCT
m-806	72	169	=	=	SYM
m-806	72	170	0	0	PUNCT
m-806	72	171	(	(	PUNCT
m-806	72	172	6.28c	6.28c	NUM
m-806	72	173	)	)	PUNCT
m-806	72	174	this	this	PRON
m-806	72	175	means	mean	VERB
m-806	72	176	that	that	SCONJ
m-806	72	177	�	�	PROPN
m-806	72	178	(	(	PUNCT
m-806	72	179	�	�	PROPN
m-806	72	180	�	�	PROPN
m-806	72	181	)	)	PUNCT
m-806	72	182	=	=	SYM
m-806	72	183	u	u	PRON
m-806	72	184	�	�	PROPN
m-806	72	185	(	(	PUNCT
m-806	72	186	�	�	PROPN
m-806	72	187	�	�	PROPN
m-806	72	188	)	)	PUNCT
m-806	72	189	(	(	PUNCT
m-806	72	190	1	1	NUM
m-806	72	191	−	−	PROPN
m-806	72	192	cos	cos	PROPN
m-806	72	193	2	2	NUM
m-806	72	194	�	�	PROPN
m-806	72	195	�	�	PROPN
m-806	72	196	)	)	PUNCT
m-806	72	197	(	(	PUNCT
m-806	72	198	6.28d	6.28d	NUM
m-806	72	199	)	)	PUNCT
m-806	72	200	we	we	PRON
m-806	72	201	next	next	VERB
m-806	72	202	substitute	substitute	NOUN
m-806	72	203	(	(	PUNCT
m-806	72	204	6.28d	6.28d	NUM
m-806	72	205	)	)	PUNCT
m-806	72	206	into	into	ADP
m-806	72	207	(	(	PUNCT
m-806	72	208	6.7	6.7	NUM
m-806	72	209	)	)	PUNCT
m-806	72	210	,	,	PUNCT
m-806	72	211	using	use	VERB
m-806	72	212	(	(	PUNCT
m-806	72	213	6.25	6.25	NUM
m-806	72	214	)	)	PUNCT
m-806	72	215	,	,	PUNCT
m-806	72	216	and	and	CCONJ
m-806	72	217	thereafter	thereafter	ADV
m-806	72	218	,	,	PUNCT
m-806	72	219	multiply	multiply	ADV
m-806	72	220	by	by	ADP
m-806	72	221	cos	cos	PROPN
m-806	72	222	2	2	PROPN
m-806	72	223	�	�	PROPN
m-806	72	224	�	�	PROPN
m-806	72	225	and	and	CCONJ
m-806	72	226	note	note	VERB
m-806	72	227	that	that	SCONJ
m-806	72	228	for	for	ADP
m-806	72	229	�	�	PROPN
m-806	72	230	=	=	SYM
m-806	72	231	2	2	NUM
m-806	72	232	�	�	PROPN
m-806	72	233	,	,	PUNCT
m-806	72	234	we	we	PRON
m-806	72	235	get	get	VERB
m-806	72	236	u	u	PRON
m-806	72	237	�	�	PROPN
m-806	72	238	,	,	PUNCT
m-806	72	239	�	�	PROPN
m-806	72	240	�	�	PROPN
m-806	72	241	�	�	PROPN
m-806	72	242	�	�	PROPN
m-806	72	243	(	(	PUNCT
m-806	72	244	�	�	PROPN
m-806	72	245	�	�	PROPN
m-806	72	246	)	)	PUNCT
m-806	73	1	+	+	SYM
m-806	73	2	�	�	PROPN
m-806	73	3	�	�	PROPN
m-806	73	4	u	u	NOUN
m-806	73	5	�	�	PROPN
m-806	73	6	(	(	PUNCT
m-806	73	7	�	�	PROPN
m-806	73	8	�	�	PROPN
m-806	73	9	)	)	PUNCT
m-806	73	10	=	=	SYM
m-806	73	11	−2	−2	PROPN
m-806	73	12	�	�	PROPN
m-806	73	13	u	u	NOUN
m-806	73	14	�	�	PROPN
m-806	73	15	,	,	PUNCT
m-806	73	16	�	�	PROPN
m-806	73	17	�	�	PROPN
m-806	73	18	�	�	PROPN
m-806	73	19	(	(	PUNCT
m-806	73	20	�	�	PROPN
m-806	73	21	�	�	PROPN
m-806	73	22	)	)	PUNCT
m-806	73	23	+	+	CCONJ
m-806	73	24	u	u	NOUN
m-806	73	25	�	�	PROPN
m-806	73	26	,	,	PUNCT
m-806	73	27	�	�	PROPN
m-806	73	28	�	�	PROPN
m-806	73	29	(	(	PUNCT
m-806	73	30	�	�	PROPN
m-806	73	31	�	�	PROPN
m-806	73	32	)	)	PUNCT
m-806	73	33	�	�	PROPN
m-806	73	34	(	(	PUNCT
m-806	73	35	6.29a	6.29a	NOUN
m-806	73	36	)	)	PUNCT
m-806	73	37	u	u	NOUN
m-806	73	38	�	�	PROPN
m-806	73	39	(	(	PUNCT
m-806	73	40	�	�	PROPN
m-806	73	41	�	�	PROPN
m-806	73	42	)	)	PUNCT
m-806	73	43	(	(	PUNCT
m-806	73	44	0,0	0,0	NUM
m-806	73	45	)	)	PUNCT
m-806	73	46	=	=	SYM
m-806	73	47	0	0	NUM
m-806	73	48	,	,	PUNCT
m-806	73	49	u	u	NOUN
m-806	73	50	�	�	PROPN
m-806	73	51	,	,	PUNCT
m-806	73	52	�	�	PROPN
m-806	73	53	�	�	PROPN
m-806	73	54	(	(	PUNCT
m-806	73	55	�	�	PROPN
m-806	73	56	�	�	PROPN
m-806	73	57	)	)	PUNCT
m-806	73	58	(	(	PUNCT
m-806	73	59	0,0	0,0	NOUN
m-806	73	60	)	)	PUNCT
m-806	73	61	+	+	CCONJ
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m-806	73	63	�	�	PROPN
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m-806	73	65	�	�	PROPN
m-806	73	66	(	(	PUNCT
m-806	73	67	�	�	PROPN
m-806	73	68	�	�	PROPN
m-806	73	69	)	)	PUNCT
m-806	73	70	(	(	PUNCT
m-806	73	71	0,0	0,0	NOUN
m-806	73	72	)	)	PUNCT
m-806	73	73	(	(	PUNCT
m-806	73	74	6.29b	6.29b	NOUN
m-806	73	75	)	)	PUNCT
m-806	73	76	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	73	77	ijo	ijo	PROPN
m-806	73	78	journals	journal	NOUN
m-806	73	79	volume	volume	NOUN
m-806	73	80	07	07	NUM
m-806	73	81	|	|	ADV
m-806	73	82	issue	issue	NOUN
m-806	73	83	02	02	NUM
m-806	73	84	|	|	CCONJ
m-806	73	85	february	february	PROPN
m-806	73	86	2024	2024	NUM
m-806	73	87	|	|	ADV
m-806	73	88	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	73	89	8	8	NUM
m-806	73	90	ijo	ijo	PROPN
m-806	73	91	international	international	ADJ
m-806	73	92	journal	journal	PROPN
m-806	73	93	of	of	ADP
m-806	73	94	mathematics	mathematics	PROPN
m-806	73	95	(	(	PUNCT
m-806	73	96	issn	issn	PROPN
m-806	73	97	:	:	PUNCT
m-806	73	98	2992	2992	NUM
m-806	73	99	-	-	SYM
m-806	73	100	4421	4421	NUM
m-806	73	101	)	)	PUNCT
m-806	74	1	i.u	i.u	PROPN
m-806	74	2	.	.	PROPN
m-806	74	3	udo	udo	PROPN
m-806	74	4	-	-	PROPN
m-806	74	5	akpan1	akpan1	ADJ
m-806	74	6	*	*	PUNCT
m-806	74	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	74	8	volume	volume	NOUN
m-806	74	9	07	07	NUM
m-806	74	10	issue	issue	NOUN
m-806	74	11	02	02	NUM
m-806	74	12	||	||	NUM
m-806	74	13	february	february	PROPN
m-806	74	14	,	,	PUNCT
m-806	74	15	2024	2024	NUM
m-806	74	16	||	||	NOUN
m-806	75	1	on	on	ADP
m-806	75	2	a	a	DET
m-806	75	3	-	-	PUNCT
m-806	75	4	two	two	NUM
m-806	75	5	-	-	PUNCT
m-806	75	6	parameter	parameter	NOUN
m-806	75	7	dynamic	dynamic	ADJ
m-806	75	8	buckling	buckling	NOUN
m-806	75	9	of	of	ADP
m-806	75	10	a	a	DET
m-806	75	11	viscously	viscously	ADV
m-806	75	12	damped	damp	VERB
m-806	75	13	but	but	CCONJ
m-806	75	14	clamped	clamp	VERB
m-806	75	15	column	column	NOUN
m-806	75	16	stressed	stress	VERB
m-806	75	17	by	by	ADP
m-806	75	18	a	a	DET
m-806	75	19	step	step	NOUN
m-806	75	20	load	load	NOUN
m-806	75	21	on	on	ADP
m-806	75	22	substituting	substitute	VERB
m-806	75	23	for	for	ADP
m-806	75	24	u	u	PROPN
m-806	75	25	�	�	PROPN
m-806	75	26	(	(	PUNCT
m-806	75	27	�	�	PROPN
m-806	75	28	�	�	PROPN
m-806	75	29	)	)	PUNCT
m-806	75	30	in	in	ADP
m-806	75	31	(	(	PUNCT
m-806	75	32	6.29	6.29	NUM
m-806	75	33	)	)	PUNCT
m-806	75	34	from	from	ADP
m-806	75	35	(	(	PUNCT
m-806	75	36	6.28a	6.28a	NUM
m-806	75	37	)	)	PUNCT
m-806	75	38	,	,	PUNCT
m-806	75	39	we	we	PRON
m-806	75	40	ensure	ensure	VERB
m-806	75	41	a	a	DET
m-806	75	42	uniformly	uniformly	ADV
m-806	75	43	valid	valid	ADJ
m-806	75	44	solution	solution	NOUN
m-806	75	45	in	in	ADP
m-806	75	46	�	�	PROPN
m-806	75	47	̂	̂	VERB
m-806	75	48	by	by	ADP
m-806	75	49	equating	equate	VERB
m-806	75	50	to	to	ADP
m-806	75	51	zero	zero	NUM
m-806	75	52	the	the	DET
m-806	75	53	coefficients	coefficient	NOUN
m-806	75	54	of	of	ADP
m-806	75	55	cos	cos	PROPN
m-806	75	56	�	�	PROPN
m-806	75	57	�	�	PROPN
m-806	75	58	̂	̂	VERB
m-806	75	59	and	and	CCONJ
m-806	75	60	sin	sin	PROPN
m-806	75	61	�	�	PROPN
m-806	75	62	�	�	PROPN
m-806	75	63	̂	̂	VERB
m-806	75	64	and	and	CCONJ
m-806	75	65	getting	get	VERB
m-806	75	66	�	�	PROPN
m-806	75	67	�	�	PROPN
m-806	75	68	�	�	PROPN
m-806	75	69	+	+	CCONJ
m-806	75	70	�	�	PROPN
m-806	75	71	�	�	PROPN
m-806	75	72	=	=	SYM
m-806	75	73	0	0	NUM
m-806	75	74	,	,	PUNCT
m-806	75	75	�	�	PROPN
m-806	75	76	�	�	PROPN
m-806	75	77	�	�	PROPN
m-806	75	78	+	+	CCONJ
m-806	75	79	�	�	PROPN
m-806	75	80	�	�	PROPN
m-806	75	81	=	=	SYM
m-806	75	82	0	0	NUM
m-806	76	1	(	(	PUNCT
m-806	76	2	6.30a	6.30a	NUM
m-806	76	3	)	)	PUNCT
m-806	76	4	the	the	DET
m-806	76	5	solution	solution	NOUN
m-806	76	6	of	of	ADP
m-806	76	7	(	(	PUNCT
m-806	76	8	6.30a	6.30a	NUM
m-806	76	9	)	)	PUNCT
m-806	76	10	using	use	VERB
m-806	76	11	(	(	PUNCT
m-806	76	12	6.28c	6.28c	ADJ
m-806	76	13	)	)	PUNCT
m-806	76	14	yields	yield	NOUN
m-806	76	15	�	�	PROPN
m-806	76	16	�	�	PROPN
m-806	76	17	(	(	PUNCT
m-806	76	18	�	�	PROPN
m-806	76	19	)	)	PUNCT
m-806	76	20	=	=	SYM
m-806	76	21	0	0	NUM
m-806	76	22	,	,	PUNCT
m-806	76	23	�	�	PROPN
m-806	76	24	�	�	PROPN
m-806	76	25	(	(	PUNCT
m-806	76	26	�	�	PROPN
m-806	76	27	)	)	PUNCT
m-806	76	28	=	=	SYM
m-806	77	1	−	−	PROPN
m-806	77	2	�	�	PROPN
m-806	77	3	�	�	PROPN
m-806	77	4	�	�	PROPN
m-806	77	5	�	�	PROPN
m-806	77	6	(	(	PUNCT
m-806	77	7	6.30b	6.30b	PROPN
m-806	77	8	)	)	PUNCT
m-806	77	9	the	the	DET
m-806	77	10	remaining	remain	VERB
m-806	77	11	equation	equation	NOUN
m-806	77	12	in	in	ADP
m-806	77	13	(	(	PUNCT
m-806	77	14	6.29a	6.29a	PROPN
m-806	77	15	,	,	PUNCT
m-806	77	16	b	b	NOUN
m-806	77	17	)	)	PUNCT
m-806	77	18	is	be	AUX
m-806	77	19	solved	solve	VERB
m-806	77	20	to	to	PART
m-806	77	21	get	get	VERB
m-806	77	22	u	u	NOUN
m-806	77	23	�	�	X
m-806	77	24	(	(	PUNCT
m-806	77	25	�	�	PROPN
m-806	77	26	�	�	PROPN
m-806	77	27	)	)	PUNCT
m-806	77	28	=	=	SYM
m-806	77	29	�	�	PROPN
m-806	77	30	�	�	PROPN
m-806	77	31	(	(	PUNCT
m-806	77	32	�	�	PROPN
m-806	77	33	)	)	PUNCT
m-806	77	34	cos	cos	PROPN
m-806	77	35	�	�	PROPN
m-806	77	36	�	�	PROPN
m-806	77	37	̂	̂	VERB
m-806	77	38	+	+	NUM
m-806	77	39	�	�	PROPN
m-806	77	40	�	�	PROPN
m-806	77	41	(	(	PUNCT
m-806	77	42	�	�	PROPN
m-806	77	43	)	)	PUNCT
m-806	77	44	sin	sin	PROPN
m-806	77	45	�	�	PROPN
m-806	77	46	�	�	PROPN
m-806	77	47	̂	̂	PUNCT
m-806	77	48	(	(	PUNCT
m-806	77	49	6.31a	6.31a	NOUN
m-806	77	50	)	)	PUNCT
m-806	77	51	�	�	PROPN
m-806	77	52	�	�	PROPN
m-806	77	53	(	(	PUNCT
m-806	77	54	0	0	NUM
m-806	77	55	)	)	PUNCT
m-806	77	56	=	=	SYM
m-806	77	57	0	0	NUM
m-806	77	58	,	,	PUNCT
m-806	77	59	�	�	PROPN
m-806	77	60	�	�	PROPN
m-806	77	61	(	(	PUNCT
m-806	77	62	0	0	NUM
m-806	77	63	)	)	PUNCT
m-806	77	64	=	=	SYM
m-806	77	65	�	�	PROPN
m-806	77	66	�	�	PROPN
m-806	77	67	(	(	PUNCT
m-806	77	68	6.31b	6.31b	NOUN
m-806	77	69	)	)	PUNCT
m-806	77	70	we	we	PRON
m-806	77	71	however	however	ADV
m-806	77	72	note	note	VERB
m-806	77	73	that	that	SCONJ
m-806	77	74	�	�	PROPN
m-806	77	75	�	�	PROPN
m-806	77	76	�	�	PROPN
m-806	77	77	(	(	PUNCT
m-806	77	78	0	0	NUM
m-806	77	79	)	)	PUNCT
m-806	77	80	=	=	SYM
m-806	77	81	b	b	PROPN
m-806	77	82	,	,	PUNCT
m-806	77	83	�	�	PROPN
m-806	77	84	�	�	PROPN
m-806	77	85	�	�	PROPN
m-806	77	86	�	�	PROPN
m-806	77	87	(	(	PUNCT
m-806	77	88	0	0	NUM
m-806	77	89	)	)	PUNCT
m-806	77	90	=	=	PRON
m-806	77	91	−b	−b	ADJ
m-806	77	92	(	(	PUNCT
m-806	77	93	6.31c	6.31c	NUM
m-806	77	94	)	)	PUNCT
m-806	77	95	we	we	PRON
m-806	77	96	equally	equally	ADV
m-806	77	97	note	note	VERB
m-806	77	98	at	at	ADP
m-806	77	99	this	this	DET
m-806	77	100	stage	stage	NOUN
m-806	77	101	that	that	SCONJ
m-806	77	102	(	(	PUNCT
m-806	77	103	6.32	6.32	NUM
m-806	77	104	)	)	PUNCT
m-806	77	105	�	�	PROPN
m-806	77	106	(	(	PUNCT
m-806	77	107	�	�	NOUN
m-806	77	108	�	�	PROPN
m-806	77	109	)	)	PUNCT
m-806	77	110	=	=	SYM
m-806	77	111	u	u	PRON
m-806	77	112	�	�	PROPN
m-806	77	113	(	(	PUNCT
m-806	77	114	�	�	PROPN
m-806	77	115	�	�	PROPN
m-806	77	116	)	)	PUNCT
m-806	77	117	(	(	PUNCT
m-806	77	118	1	1	NUM
m-806	77	119	−	−	PROPN
m-806	77	120	cos	cos	PROPN
m-806	77	121	2	2	NUM
m-806	77	122	�	�	PROPN
m-806	77	123	�	�	PROPN
m-806	77	124	)	)	PUNCT
m-806	77	125	on	on	ADP
m-806	77	126	substituting	substitute	VERB
m-806	77	127	from	from	ADP
m-806	77	128	(	(	PUNCT
m-806	77	129	6.32	6.32	NUM
m-806	77	130	)	)	PUNCT
m-806	77	131	and	and	CCONJ
m-806	77	132	(	(	PUNCT
m-806	77	133	6.28d	6.28d	NOUN
m-806	77	134	)	)	PUNCT
m-806	77	135	in	in	ADP
m-806	77	136	(	(	PUNCT
m-806	77	137	6.8	6.8	NUM
m-806	77	138	)	)	PUNCT
m-806	77	139	,	,	PUNCT
m-806	77	140	multiplying	multiply	VERB
m-806	77	141	thereafter	thereafter	ADV
m-806	77	142	by	by	ADP
m-806	77	143	cos	cos	PROPN
m-806	77	144	2	2	PROPN
m-806	77	145	�	�	PROPN
m-806	77	146	�	�	PROPN
m-806	77	147	and	and	CCONJ
m-806	77	148	integrating	integrate	VERB
m-806	77	149	from	from	ADP
m-806	77	150	0	0	NUM
m-806	77	151	to	to	ADP
m-806	77	152	π	π	PROPN
m-806	77	153	,	,	PUNCT
m-806	77	154	we	we	PRON
m-806	77	155	get	get	VERB
m-806	77	156	,	,	PUNCT
m-806	77	157	(	(	PUNCT
m-806	77	158	for	for	ADP
m-806	77	159	�	�	PROPN
m-806	77	160	=	=	SYM
m-806	77	161	�	�	PROPN
m-806	77	162	)	)	PUNCT
m-806	77	163	u	u	PROPN
m-806	77	164	�	�	PROPN
m-806	77	165	,	,	PUNCT
m-806	77	166	�	�	PROPN
m-806	77	167	�	�	PROPN
m-806	77	168	�	�	PROPN
m-806	77	169	�	�	PROPN
m-806	77	170	(	(	PUNCT
m-806	77	171	�	�	PROPN
m-806	77	172	�	�	PROPN
m-806	77	173	)	)	PUNCT
m-806	78	1	+	+	SYM
m-806	78	2	�	�	PROPN
m-806	78	3	�	�	PROPN
m-806	78	4	u	u	NOUN
m-806	78	5	�	�	PROPN
m-806	78	6	(	(	PUNCT
m-806	78	7	�	�	PROPN
m-806	78	8	�	�	PROPN
m-806	78	9	)	)	PUNCT
m-806	78	10	=	=	SYM
m-806	78	11	−2	−2	PROPN
m-806	78	12	�	�	PROPN
m-806	78	13	u	u	NOUN
m-806	78	14	�	�	PROPN
m-806	78	15	,	,	PUNCT
m-806	78	16	�	�	PROPN
m-806	78	17	�	�	PROPN
m-806	78	18	�	�	PROPN
m-806	78	19	(	(	PUNCT
m-806	78	20	�	�	PROPN
m-806	78	21	�	�	PROPN
m-806	78	22	)	)	PUNCT
m-806	78	23	+	+	CCONJ
m-806	78	24	u	u	NOUN
m-806	78	25	�	�	PROPN
m-806	78	26	,	,	PUNCT
m-806	78	27	�	�	PROPN
m-806	78	28	�	�	PROPN
m-806	78	29	(	(	PUNCT
m-806	78	30	�	�	PROPN
m-806	78	31	�	�	PROPN
m-806	78	32	)	)	PUNCT
m-806	78	33	�	�	PROPN
m-806	78	34	−	−	PROPN
m-806	78	35	u	u	NOUN
m-806	78	36	�	�	PROPN
m-806	78	37	,	,	PUNCT
m-806	78	38	�	�	PROPN
m-806	78	39	�	�	PROPN
m-806	78	40	(	(	PUNCT
m-806	78	41	�	�	PROPN
m-806	78	42	�	�	PROPN
m-806	78	43	)	)	PUNCT
m-806	78	44	(	(	PUNCT
m-806	78	45	6.33a	6.33a	NOUN
m-806	78	46	)	)	PUNCT
m-806	78	47	u	u	NOUN
m-806	78	48	�	�	PROPN
m-806	78	49	(	(	PUNCT
m-806	78	50	�	�	PROPN
m-806	78	51	�	�	PROPN
m-806	78	52	)	)	PUNCT
m-806	78	53	(	(	PUNCT
m-806	78	54	0,0	0,0	NUM
m-806	78	55	)	)	PUNCT
m-806	78	56	=	=	SYM
m-806	78	57	0	0	NUM
m-806	78	58	,	,	PUNCT
m-806	78	59	u	u	NOUN
m-806	78	60	�	�	PROPN
m-806	78	61	,	,	PUNCT
m-806	78	62	�	�	PROPN
m-806	78	63	�	�	PROPN
m-806	78	64	(	(	PUNCT
m-806	78	65	�	�	PROPN
m-806	78	66	�	�	PROPN
m-806	78	67	)	)	PUNCT
m-806	78	68	(	(	PUNCT
m-806	78	69	0,0	0,0	NOUN
m-806	78	70	)	)	PUNCT
m-806	78	71	+	+	CCONJ
m-806	78	72	u	u	NOUN
m-806	78	73	�	�	PROPN
m-806	78	74	,	,	PUNCT
m-806	78	75	�	�	PROPN
m-806	78	76	(	(	PUNCT
m-806	78	77	�	�	PROPN
m-806	78	78	�	�	PROPN
m-806	78	79	)	)	PUNCT
m-806	78	80	(	(	PUNCT
m-806	78	81	0,0	0,0	NUM
m-806	78	82	)	)	PUNCT
m-806	78	83	(	(	PUNCT
m-806	78	84	6.33b	6.33b	NUM
m-806	78	85	)	)	PUNCT
m-806	78	86	next	next	ADV
m-806	78	87	,	,	PUNCT
m-806	78	88	we	we	PRON
m-806	78	89	substitute	substitute	VERB
m-806	78	90	in	in	ADP
m-806	78	91	(	(	PUNCT
m-806	78	92	6.33a	6.33a	NOUN
m-806	78	93	)	)	PUNCT
m-806	78	94	for	for	ADP
m-806	78	95	u	u	PROPN
m-806	78	96	�	�	PROPN
m-806	78	97	(	(	PUNCT
m-806	78	98	�	�	PROPN
m-806	78	99	�	�	PROPN
m-806	78	100	)	)	PUNCT
m-806	78	101	and	and	CCONJ
m-806	78	102	u	u	NOUN
m-806	78	103	�	�	PROPN
m-806	78	104	(	(	PUNCT
m-806	78	105	�	�	PROPN
m-806	78	106	�	�	PROPN
m-806	78	107	)	)	PUNCT
m-806	78	108	from	from	ADP
m-806	78	109	(	(	PUNCT
m-806	78	110	6.31a	6.31a	NOUN
m-806	78	111	)	)	PUNCT
m-806	78	112	and	and	CCONJ
m-806	78	113	(	(	PUNCT
m-806	78	114	6.28a	6.28a	NUM
m-806	78	115	)	)	PUNCT
m-806	78	116	and	and	CCONJ
m-806	78	117	ensure	ensure	VERB
m-806	78	118	a	a	DET
m-806	78	119	uniformly	uniformly	ADV
m-806	78	120	valid	valid	ADJ
m-806	78	121	solution	solution	NOUN
m-806	78	122	in	in	ADP
m-806	78	123	�	�	PROPN
m-806	78	124	̂	̂	VERB
m-806	78	125	by	by	ADP
m-806	78	126	equating	equate	VERB
m-806	78	127	to	to	ADP
m-806	78	128	zero	zero	NUM
m-806	78	129	the	the	DET
m-806	78	130	coefficients	coefficient	NOUN
m-806	78	131	of	of	ADP
m-806	78	132	cos	cos	PROPN
m-806	78	133	�	�	PROPN
m-806	78	134	�	�	PROPN
m-806	78	135	̂	̂	VERB
m-806	78	136	and	and	CCONJ
m-806	78	137	sin	sin	PROPN
m-806	78	138	�	�	PROPN
m-806	78	139	�	�	PROPN
m-806	78	140	̂	̂	PUNCT
m-806	78	141	and	and	CCONJ
m-806	78	142	so	so	ADV
m-806	78	143	,	,	PUNCT
m-806	78	144	get	get	VERB
m-806	78	145	,	,	PUNCT
m-806	78	146	respectively	respectively	ADV
m-806	78	147	�	�	PROPN
m-806	78	148	�	�	PROPN
m-806	78	149	�	�	PROPN
m-806	78	150	+	+	CCONJ
m-806	78	151	�	�	PROPN
m-806	78	152	�	�	PROPN
m-806	78	153	=	=	SYM
m-806	78	154	�	�	PROPN
m-806	78	155	�	�	PROPN
m-806	78	156	�	�	PROPN
m-806	78	157	�	�	PROPN
m-806	78	158	�	�	PROPN
m-806	78	159	�	�	PROPN
m-806	78	160	�	�	PROPN
m-806	78	161	and	and	CCONJ
m-806	78	162	�	�	PROPN
m-806	78	163	�	�	PROPN
m-806	78	164	�	�	PROPN
m-806	78	165	+	+	CCONJ
m-806	78	166	�	�	PROPN
m-806	78	167	�	�	PROPN
m-806	78	168	=	=	SYM
m-806	78	169	0	0	NUM
m-806	78	170	(	(	PUNCT
m-806	78	171	6.33c	6.33c	NUM
m-806	78	172	)	)	PUNCT
m-806	78	173	on	on	ADP
m-806	78	174	solving	solve	VERB
m-806	78	175	(	(	PUNCT
m-806	78	176	6.33c	6.33c	PROPN
m-806	78	177	)	)	PUNCT
m-806	78	178	,	,	PUNCT
m-806	78	179	we	we	PRON
m-806	78	180	get	get	VERB
m-806	78	181	�	�	PROPN
m-806	78	182	�	�	PROPN
m-806	78	183	(	(	PUNCT
m-806	78	184	τ	τ	NOUN
m-806	78	185	)	)	PUNCT
m-806	78	186	=	=	SYM
m-806	78	187	�	�	PROPN
m-806	78	188	�	�	PROPN
m-806	78	189	�	�	PROPN
m-806	78	190	�	�	PROPN
m-806	78	191	∫	∫	PROPN
m-806	78	192	�	�	PROPN
m-806	78	193	�	�	PROPN
m-806	78	194	�	�	PROPN
m-806	78	195	�	�	PROPN
m-806	78	196	�	�	PROPN
m-806	78	197	(	(	PUNCT
m-806	78	198	�	�	PROPN
m-806	78	199	)	)	PUNCT
m-806	78	200	�	�	PROPN
m-806	78	201	�	�	PROPN
m-806	78	202	�	�	PROPN
m-806	78	203	�	�	PROPN
m-806	78	204	�	�	PROPN
m-806	78	205	�	�	PROPN
m-806	78	206	+	+	CCONJ
m-806	78	207	�	�	PROPN
m-806	78	208	�	�	PROPN
m-806	78	209	(	(	PUNCT
m-806	78	210	0	0	NUM
m-806	78	211	)	)	PUNCT
m-806	78	212	�	�	PROPN
m-806	78	213	,	,	PUNCT
m-806	78	214	�	�	PROPN
m-806	78	215	�	�	PROPN
m-806	78	216	(	(	PUNCT
m-806	78	217	τ	τ	X
m-806	78	218	)	)	PUNCT
m-806	78	219	=	=	SYM
m-806	78	220	0	0	NUM
m-806	78	221	(	(	PUNCT
m-806	78	222	6.33d	6.33d	NUM
m-806	78	223	)	)	PUNCT
m-806	78	224	the	the	DET
m-806	78	225	remaining	remain	VERB
m-806	78	226	equation	equation	NOUN
m-806	78	227	in	in	ADP
m-806	78	228	the	the	DET
m-806	78	229	substitution	substitution	NOUN
m-806	78	230	into	into	ADP
m-806	78	231	(	(	PUNCT
m-806	78	232	6.33a	6.33a	NOUN
m-806	78	233	)	)	PUNCT
m-806	78	234	is	be	AUX
m-806	78	235	solved	solve	VERB
m-806	78	236	to	to	PART
m-806	78	237	yield	yield	VERB
m-806	78	238	u	u	PRON
m-806	78	239	�	�	PROPN
m-806	78	240	(	(	PUNCT
m-806	78	241	�	�	PROPN
m-806	78	242	�	�	PROPN
m-806	78	243	)	)	PUNCT
m-806	78	244	(	(	PUNCT
m-806	78	245	t̂	t̂	NUM
m-806	78	246	,	,	PUNCT
m-806	78	247	τ	τ	NOUN
m-806	78	248	)	)	PUNCT
m-806	78	249	=	=	SYM
m-806	78	250	�	�	PROPN
m-806	78	251	�	�	PROPN
m-806	78	252	(	(	PUNCT
m-806	78	253	�	�	PROPN
m-806	78	254	)	)	PUNCT
m-806	78	255	cos	cos	PROPN
m-806	78	256	�	�	PROPN
m-806	78	257	�	�	PROPN
m-806	78	258	̂	̂	VERB
m-806	78	259	+	+	NUM
m-806	78	260	�	�	PROPN
m-806	78	261	�	�	PROPN
m-806	78	262	(	(	PUNCT
m-806	78	263	�	�	PROPN
m-806	78	264	)	)	PUNCT
m-806	78	265	sin	sin	PROPN
m-806	78	266	�	�	PROPN
m-806	78	267	�	�	PROPN
m-806	78	268	̂	̂	PUNCT
m-806	78	269	(	(	PUNCT
m-806	78	270	6.34a	6.34a	NOUN
m-806	78	271	)	)	PUNCT
m-806	79	1	where	where	SCONJ
m-806	79	2	,	,	PUNCT
m-806	79	3	�	�	PROPN
m-806	79	4	�	�	PROPN
m-806	79	5	(	(	PUNCT
m-806	79	6	0	0	NUM
m-806	79	7	)	)	PUNCT
m-806	79	8	=	=	SYM
m-806	79	9	0	0	NUM
m-806	79	10	,	,	PUNCT
m-806	79	11	�	�	PROPN
m-806	79	12	�	�	PROPN
m-806	79	13	(	(	PUNCT
m-806	79	14	0	0	NUM
m-806	79	15	)	)	PUNCT
m-806	79	16	=	=	SYM
m-806	79	17	0	0	NUM
m-806	79	18	(	(	PUNCT
m-806	79	19	6.34b	6.34b	NUM
m-806	79	20	)	)	PUNCT
m-806	79	21	in	in	ADP
m-806	79	22	passing	pass	VERB
m-806	79	23	,	,	PUNCT
m-806	79	24	we	we	PRON
m-806	79	25	note	note	VERB
m-806	79	26	from	from	ADP
m-806	79	27	(	(	PUNCT
m-806	79	28	6.33c	6.33c	PROPN
m-806	79	29	)	)	PUNCT
m-806	80	1	that	that	PRON
m-806	80	2	�	�	PROPN
m-806	80	3	�	�	PROPN
m-806	80	4	�	�	PROPN
m-806	80	5	(	(	PUNCT
m-806	80	6	0	0	NUM
m-806	80	7	)	)	PUNCT
m-806	80	8	=	=	SYM
m-806	80	9	−	−	NUM
m-806	80	10	�	�	PROPN
m-806	80	11	�	�	PROPN
m-806	80	12	(0	(0	NOUN
m-806	80	13	)	)	PUNCT
m-806	80	14	�	�	PROPN
m-806	80	15	�	�	PROPN
m-806	80	16	�	�	PROPN
m-806	80	17	�	�	PROPN
m-806	80	18	�	�	PROPN
m-806	80	19	(	(	PUNCT
m-806	80	20	�	�	PROPN
m-806	80	21	)	)	PUNCT
m-806	80	22	�	�	PROPN
m-806	80	23	�	�	PROPN
m-806	80	24	=	=	SYM
m-806	80	25	�	�	PROPN
m-806	80	26	�	�	PROPN
m-806	80	27	�	�	PROPN
m-806	80	28	�	�	PROPN
m-806	80	29	�	�	PROPN
m-806	80	30	,	,	PUNCT
m-806	80	31	�	�	PROPN
m-806	80	32	�	�	PROPN
m-806	80	33	�	�	PROPN
m-806	80	34	�	�	PROPN
m-806	80	35	(	(	PUNCT
m-806	80	36	0	0	NUM
m-806	80	37	)	)	PUNCT
m-806	80	38	=	=	SYM
m-806	80	39	�	�	PROPN
m-806	80	40	�	�	PROPN
m-806	80	41	(	(	PUNCT
m-806	80	42	6.34c	6.34c	NOUN
m-806	80	43	)	)	PUNCT
m-806	80	44	we	we	PRON
m-806	80	45	conclude	conclude	VERB
m-806	80	46	that	that	SCONJ
m-806	80	47	�	�	PROPN
m-806	80	48	(	(	PUNCT
m-806	80	49	�	�	PROPN
m-806	80	50	�	�	PROPN
m-806	80	51	)	)	PUNCT
m-806	80	52	=	=	SYM
m-806	80	53	u	u	PRON
m-806	80	54	�	�	PROPN
m-806	80	55	(	(	PUNCT
m-806	80	56	�	�	PROPN
m-806	80	57	�	�	PROPN
m-806	80	58	)	)	PUNCT
m-806	80	59	(	(	PUNCT
m-806	80	60	1	1	NUM
m-806	80	61	−	−	PROPN
m-806	80	62	cos	cos	PROPN
m-806	80	63	2	2	NUM
m-806	80	64	�	�	PROPN
m-806	80	65	�	�	PROPN
m-806	80	66	)	)	PUNCT
m-806	80	67	(	(	PUNCT
m-806	80	68	6.35	6.35	NUM
m-806	80	69	)	)	PUNCT
m-806	80	70	on	on	ADP
m-806	80	71	solving	solve	VERB
m-806	80	72	equations	equation	NOUN
m-806	80	73	(	(	PUNCT
m-806	80	74	6.9	6.9	NUM
m-806	80	75	)	)	PUNCT
m-806	80	76	to	to	ADP
m-806	80	77	(	(	PUNCT
m-806	80	78	6.11	6.11	NUM
m-806	80	79	)	)	PUNCT
m-806	80	80	,	,	PUNCT
m-806	80	81	using	use	VERB
m-806	80	82	the	the	DET
m-806	80	83	appropriate	appropriate	ADJ
m-806	80	84	initial	initial	ADJ
m-806	80	85	and	and	CCONJ
m-806	80	86	boundary	boundary	ADJ
m-806	80	87	conditions	condition	NOUN
m-806	80	88	,	,	PUNCT
m-806	80	89	we	we	PRON
m-806	80	90	get	get	VERB
m-806	80	91	�	�	PROPN
m-806	80	92	(	(	PUNCT
m-806	80	93	�	�	PROPN
m-806	80	94	�	�	PROPN
m-806	80	95	)	)	PUNCT
m-806	80	96	(	(	PUNCT
m-806	80	97	�	�	PROPN
m-806	80	98	,	,	PUNCT
m-806	80	99	�	�	PROPN
m-806	80	100	̂	̂	NUM
m-806	80	101	,	,	PUNCT
m-806	80	102	�	�	NOUN
m-806	80	103	)	)	PUNCT
m-806	80	104	=	=	SYM
m-806	80	105	�	�	PROPN
m-806	80	106	(	(	PUNCT
m-806	80	107	�	�	PROPN
m-806	80	108	�	�	PROPN
m-806	80	109	)	)	PUNCT
m-806	80	110	(	(	PUNCT
m-806	80	111	�	�	PROPN
m-806	80	112	,	,	PUNCT
m-806	80	113	�	�	PROPN
m-806	80	114	̂	̂	NUM
m-806	80	115	,	,	PUNCT
m-806	80	116	�	�	NOUN
m-806	80	117	)	)	PUNCT
m-806	80	118	=	=	SYM
m-806	80	119	�	�	PROPN
m-806	80	120	(	(	PUNCT
m-806	80	121	�	�	PROPN
m-806	80	122	�	�	PROPN
m-806	80	123	)	)	PUNCT
m-806	80	124	(	(	PUNCT
m-806	80	125	�	�	PROPN
m-806	80	126	,	,	PUNCT
m-806	80	127	�	�	PROPN
m-806	80	128	̂	̂	NUM
m-806	80	129	,	,	PUNCT
m-806	80	130	�	�	X
m-806	80	131	)	)	PUNCT
m-806	80	132	=	=	SYM
m-806	80	133	0	0	NUM
m-806	80	134	(	(	PUNCT
m-806	80	135	6.36	6.36	NUM
m-806	80	136	)	)	PUNCT
m-806	80	137	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	80	138	ijo	ijo	PROPN
m-806	80	139	journals	journal	NOUN
m-806	80	140	volume	volume	NOUN
m-806	80	141	07	07	NUM
m-806	80	142	|	|	ADV
m-806	80	143	issue	issue	NOUN
m-806	80	144	02	02	NUM
m-806	80	145	|	|	CCONJ
m-806	80	146	february	february	PROPN
m-806	80	147	2024	2024	NUM
m-806	81	1	|	|	ADV
m-806	81	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	81	3	9	9	NUM
m-806	81	4	ijo	ijo	PROPN
m-806	81	5	international	international	ADJ
m-806	81	6	journal	journal	PROPN
m-806	81	7	of	of	ADP
m-806	81	8	mathematics	mathematics	PROPN
m-806	81	9	(	(	PUNCT
m-806	81	10	issn	issn	PROPN
m-806	81	11	:	:	PUNCT
m-806	81	12	2992	2992	NUM
m-806	81	13	-	-	SYM
m-806	81	14	4421	4421	NUM
m-806	81	15	)	)	PUNCT
m-806	81	16	i.u	i.u	PROPN
m-806	81	17	.	.	PROPN
m-806	81	18	udo	udo	PROPN
m-806	81	19	-	-	PROPN
m-806	81	20	akpan1	akpan1	ADJ
m-806	81	21	*	*	PUNCT
m-806	81	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	81	23	volume	volume	NOUN
m-806	81	24	07	07	NUM
m-806	81	25	issue	issue	NOUN
m-806	81	26	02	02	NUM
m-806	81	27	||	||	NUM
m-806	81	28	february	february	PROPN
m-806	81	29	,	,	PUNCT
m-806	81	30	2024	2024	NUM
m-806	81	31	||	||	NOUN
m-806	81	32	on	on	ADP
m-806	81	33	a	a	DET
m-806	81	34	-	-	PUNCT
m-806	81	35	two	two	NUM
m-806	81	36	-	-	PUNCT
m-806	81	37	parameter	parameter	NOUN
m-806	81	38	dynamic	dynamic	ADJ
m-806	81	39	buckling	buckling	NOUN
m-806	81	40	of	of	ADP
m-806	81	41	a	a	DET
m-806	81	42	viscously	viscously	ADV
m-806	81	43	damped	damp	VERB
m-806	81	44	but	but	CCONJ
m-806	81	45	clamped	clamp	VERB
m-806	81	46	column	column	NOUN
m-806	81	47	stressed	stress	VERB
m-806	81	48	by	by	ADP
m-806	81	49	a	a	DET
m-806	81	50	step	step	NOUN
m-806	81	51	load	load	NOUN
m-806	81	52	we	we	PRON
m-806	81	53	next	next	VERB
m-806	81	54	substitute	substitute	NOUN
m-806	81	55	on	on	ADP
m-806	81	56	the	the	DET
m-806	81	57	right	right	ADJ
m-806	81	58	hand	hand	NOUN
m-806	81	59	side	side	NOUN
m-806	81	60	of	of	ADP
m-806	81	61	(	(	PUNCT
m-806	81	62	6.12	6.12	NUM
m-806	81	63	)	)	PUNCT
m-806	81	64	,	,	PUNCT
m-806	81	65	using	use	VERB
m-806	81	66	(	(	PUNCT
m-806	81	67	6.25	6.25	NUM
m-806	81	68	)	)	PUNCT
m-806	81	69	and	and	CCONJ
m-806	81	70	simplify	simplify	VERB
m-806	81	71	to	to	PART
m-806	81	72	get	get	VERB
m-806	81	73	�	�	PROPN
m-806	81	74	�	�	PROPN
m-806	81	75	(	(	PUNCT
m-806	81	76	�	�	PROPN
m-806	81	77	�	�	PROPN
m-806	81	78	)	)	PUNCT
m-806	81	79	=	=	PROPN
m-806	81	80	�	�	PROPN
m-806	81	81	�	�	PROPN
m-806	81	82	�	�	PROPN
m-806	81	83	�	�	PROPN
m-806	81	84	�	�	PROPN
m-806	81	85	+	+	CCONJ
m-806	81	86	3	3	NUM
m-806	81	87	�	�	PROPN
m-806	81	88	�	�	PROPN
m-806	81	89	�	�	PROPN
m-806	81	90	�	�	PROPN
m-806	81	91	2	2	NUM
m-806	81	92	�	�	PROPN
m-806	81	93	+	+	CCONJ
m-806	81	94	3	3	NUM
m-806	81	95	�	�	PROPN
m-806	81	96	�	�	PROPN
m-806	81	97	�	�	PROPN
m-806	81	98	�	�	PROPN
m-806	81	99	�	�	PROPN
m-806	81	100	+	+	SYM
m-806	81	101	�	�	PROPN
m-806	81	102	�	�	PROPN
m-806	81	103	�	�	PROPN
m-806	81	104	4	4	NUM
m-806	81	105	�	�	PROPN
m-806	81	106	cos	cos	PROPN
m-806	81	107	�	�	PROPN
m-806	81	108	�	�	PROPN
m-806	81	109	̂	̂	VERB
m-806	81	110	+	+	NOUN
m-806	81	111	3	3	NUM
m-806	81	112	�	�	PROPN
m-806	81	113	�	�	PROPN
m-806	81	114	�	�	PROPN
m-806	81	115	�	�	PROPN
m-806	81	116	cos	cos	PROPN
m-806	81	117	2	2	PROPN
m-806	81	118	�	�	PROPN
m-806	81	119	�	�	PROPN
m-806	81	120	̂	̂	SYM
m-806	81	121	2	2	NUM
m-806	81	122	�	�	PROPN
m-806	81	123	+	+	CCONJ
m-806	81	124	�	�	PROPN
m-806	81	125	�	�	PROPN
m-806	81	126	�	�	PROPN
m-806	81	127	�	�	PROPN
m-806	81	128	cos	cos	PROPN
m-806	81	129	3	3	PROPN
m-806	81	130	�	�	PROPN
m-806	81	131	�	�	PROPN
m-806	81	132	̂	̂	NUM
m-806	81	133	4	4	NUM
m-806	81	134	�	�	PROPN
m-806	81	135	�	�	PROPN
m-806	81	136	5	5	NUM
m-806	81	137	2	2	NUM
m-806	81	138	−	−	NUM
m-806	81	139	15	15	NUM
m-806	81	140	cos	cos	PROPN
m-806	81	141	2	2	NUM
m-806	81	142	�	�	PROPN
m-806	81	143	�	�	NOUN
m-806	81	144	4	4	NUM
m-806	81	145	+	+	SYM
m-806	81	146	3	3	NUM
m-806	81	147	2	2	NUM
m-806	81	148	cos	cos	PROPN
m-806	81	149	4	4	NUM
m-806	81	150	�	�	PROPN
m-806	81	151	�	�	PROPN
m-806	81	152	−	−	PROPN
m-806	81	153	1	1	NUM
m-806	81	154	4	4	NUM
m-806	81	155	cos	cos	PROPN
m-806	81	156	6	6	NUM
m-806	81	157	�	�	PROPN
m-806	81	158	�	�	PROPN
m-806	81	159	�	�	PROPN
m-806	81	160	−2	−2	PROPN
m-806	81	161	�	�	PROPN
m-806	81	162	�	�	PROPN
m-806	81	163	�	�	PROPN
m-806	81	164	u	u	PROPN
m-806	81	165	�	�	PROPN
m-806	81	166	,	,	PUNCT
m-806	81	167	�	�	PROPN
m-806	81	168	�	�	PROPN
m-806	81	169	�	�	PROPN
m-806	81	170	�	�	PROPN
m-806	81	171	(	(	PUNCT
m-806	81	172	�	�	PROPN
m-806	81	173	�	�	PROPN
m-806	81	174	)	)	PUNCT
m-806	81	175	(	(	PUNCT
m-806	81	176	1	1	NUM
m-806	81	177	−	−	PROPN
m-806	81	178	cos	cos	PROPN
m-806	81	179	2	2	NUM
m-806	81	180	�	�	PROPN
m-806	81	181	�	�	PROPN
m-806	81	182	)	)	PUNCT
m-806	81	183	(	(	PUNCT
m-806	81	184	6.37	6.37	NUM
m-806	81	185	)	)	PUNCT
m-806	81	186	next	next	ADV
m-806	81	187	,	,	PUNCT
m-806	81	188	we	we	PRON
m-806	81	189	assume	assume	VERB
m-806	81	190	�	�	PROPN
m-806	81	191	(	(	PUNCT
m-806	81	192	�	�	NOUN
m-806	81	193	�	�	PROPN
m-806	81	194	)	)	PUNCT
m-806	81	195	=	=	PUNCT
m-806	82	1	∑	∑	PUNCT
m-806	82	2	u	u	NOUN
m-806	82	3	�	�	PROPN
m-806	82	4	(	(	PUNCT
m-806	82	5	�	�	PROPN
m-806	82	6	�	�	PROPN
m-806	82	7	)	)	PUNCT
m-806	82	8	(	(	PUNCT
m-806	82	9	1	1	NUM
m-806	82	10	−	−	PROPN
m-806	82	11	cos	cos	PROPN
m-806	82	12	2	2	NUM
m-806	82	13	�	�	PROPN
m-806	82	14	�	�	PROPN
m-806	82	15	)	)	PUNCT
m-806	82	16	�	�	PROPN
m-806	82	17	�	�	PROPN
m-806	82	18	�	�	PROPN
m-806	82	19	�	�	PROPN
m-806	82	20	(	(	PUNCT
m-806	82	21	6.38	6.38	NUM
m-806	82	22	)	)	PUNCT
m-806	82	23	on	on	ADP
m-806	82	24	substituting	substitute	VERB
m-806	82	25	(	(	PUNCT
m-806	82	26	6.38	6.38	NUM
m-806	82	27	)	)	PUNCT
m-806	82	28	into	into	ADP
m-806	82	29	(	(	PUNCT
m-806	82	30	6.37	6.37	NUM
m-806	82	31	)	)	PUNCT
m-806	82	32	and	and	CCONJ
m-806	82	33	first	first	ADV
m-806	82	34	multiplying	multiply	VERB
m-806	82	35	through	through	ADP
m-806	82	36	by	by	ADP
m-806	82	37	cos	cos	PROPN
m-806	82	38	2	2	PROPN
m-806	82	39	�	�	PROPN
m-806	82	40	�	�	PROPN
m-806	82	41	,	,	PUNCT
m-806	82	42	and	and	CCONJ
m-806	82	43	thereafter	thereafter	ADV
m-806	82	44	integrating	integrate	VERB
m-806	82	45	from	from	ADP
m-806	82	46	0	0	NUM
m-806	82	47	to	to	ADP
m-806	82	48	π	π	PROPN
m-806	82	49	,	,	PUNCT
m-806	82	50	we	we	PRON
m-806	82	51	see	see	VERB
m-806	82	52	that	that	SCONJ
m-806	82	53	,	,	PUNCT
m-806	82	54	for	for	ADP
m-806	82	55	�	�	PROPN
m-806	82	56	=	=	SYM
m-806	82	57	�	�	PROPN
m-806	82	58	,	,	PUNCT
m-806	82	59	we	we	PRON
m-806	82	60	get	get	VERB
m-806	82	61	u	u	NOUN
m-806	82	62	�	�	PROPN
m-806	82	63	,	,	PUNCT
m-806	82	64	�	�	PROPN
m-806	82	65	�	�	PROPN
m-806	82	66	�	�	PROPN
m-806	82	67	�	�	PROPN
m-806	82	68	(	(	PUNCT
m-806	82	69	�	�	PROPN
m-806	82	70	�	�	PROPN
m-806	82	71	)	)	PUNCT
m-806	83	1	+	+	SYM
m-806	83	2	�	�	PROPN
m-806	83	3	�	�	PROPN
m-806	83	4	u	u	NOUN
m-806	83	5	�	�	PROPN
m-806	83	6	(	(	PUNCT
m-806	83	7	�	�	PROPN
m-806	83	8	�	�	PROPN
m-806	83	9	)	)	PUNCT
m-806	83	10	=	=	SYM
m-806	83	11	15	15	NUM
m-806	83	12	�	�	PROPN
m-806	83	13	4	4	NUM
m-806	83	14	�	�	PROPN
m-806	83	15	�	�	PROPN
m-806	83	16	�	�	PROPN
m-806	83	17	�	�	PROPN
m-806	83	18	+	+	CCONJ
m-806	83	19	3	3	NUM
m-806	83	20	�	�	PROPN
m-806	83	21	�	�	PROPN
m-806	83	22	�	�	PROPN
m-806	83	23	�	�	PROPN
m-806	83	24	2	2	NUM
m-806	83	25	�	�	PROPN
m-806	83	26	+	+	CCONJ
m-806	83	27	3	3	NUM
m-806	83	28	�	�	PROPN
m-806	83	29	�	�	PROPN
m-806	83	30	�	�	PROPN
m-806	83	31	�	�	PROPN
m-806	83	32	�	�	PROPN
m-806	83	33	+	+	SYM
m-806	83	34	�	�	PROPN
m-806	83	35	�	�	PROPN
m-806	83	36	�	�	PROPN
m-806	83	37	4	4	NUM
m-806	83	38	�	�	PROPN
m-806	83	39	cos	cos	PROPN
m-806	83	40	�	�	PROPN
m-806	83	41	�	�	PROPN
m-806	83	42	̂	̂	VERB
m-806	83	43	+	+	NOUN
m-806	83	44	3	3	NUM
m-806	83	45	�	�	PROPN
m-806	83	46	�	�	PROPN
m-806	83	47	�	�	PROPN
m-806	83	48	�	�	PROPN
m-806	83	49	cos	cos	PROPN
m-806	83	50	2	2	PROPN
m-806	83	51	�	�	PROPN
m-806	83	52	�	�	PROPN
m-806	83	53	̂	̂	SYM
m-806	83	54	2	2	NUM
m-806	83	55	�	�	PROPN
m-806	83	56	+	+	CCONJ
m-806	83	57	�	�	PROPN
m-806	83	58	�	�	PROPN
m-806	83	59	�	�	PROPN
m-806	83	60	�	�	PROPN
m-806	83	61	�	�	PROPN
m-806	83	62	�	�	PROPN
m-806	83	63	�	�	PROPN
m-806	83	64	�	�	PROPN
m-806	83	65	�	�	PROPN
m-806	83	66	�	�	PROPN
m-806	83	67	�	�	PROPN
m-806	83	68	�	�	PROPN
m-806	83	69	�	�	PROPN
m-806	83	70	−	−	PROPN
m-806	83	71	2	2	NUM
m-806	83	72	�	�	PROPN
m-806	83	73	�	�	PROPN
m-806	83	74	�	�	PROPN
m-806	83	75	u	u	PROPN
m-806	83	76	�	�	PROPN
m-806	83	77	,	,	PUNCT
m-806	83	78	�	�	PROPN
m-806	83	79	�	�	PROPN
m-806	83	80	�	�	PROPN
m-806	83	81	�	�	PROPN
m-806	83	82	(	(	PUNCT
m-806	83	83	�	�	PROPN
m-806	83	84	�	�	PROPN
m-806	83	85	)	)	PUNCT
m-806	83	86	(	(	PUNCT
m-806	83	87	6.39a	6.39a	NUM
m-806	83	88	)	)	PUNCT
m-806	83	89	u	u	NOUN
m-806	83	90	�	�	PROPN
m-806	83	91	(	(	PUNCT
m-806	83	92	�	�	PROPN
m-806	83	93	�	�	PROPN
m-806	83	94	)	)	PUNCT
m-806	83	95	(	(	PUNCT
m-806	83	96	0,0	0,0	NUM
m-806	83	97	)	)	PUNCT
m-806	83	98	=	=	SYM
m-806	83	99	0	0	NUM
m-806	83	100	,	,	PUNCT
m-806	83	101	�	�	PROPN
m-806	83	102	�	�	PROPN
m-806	83	103	,	,	PUNCT
m-806	83	104	�	�	PROPN
m-806	83	105	�	�	PROPN
m-806	83	106	(	(	PUNCT
m-806	83	107	�	�	PROPN
m-806	83	108	�	�	PROPN
m-806	83	109	)	)	PUNCT
m-806	83	110	(	(	PUNCT
m-806	83	111	0	0	NUM
m-806	83	112	,	,	PUNCT
m-806	83	113	0	0	NUM
m-806	83	114	)	)	PUNCT
m-806	83	115	+	+	CCONJ
m-806	83	116	�	�	PROPN
m-806	83	117	�	�	PROPN
m-806	83	118	�	�	PROPN
m-806	83	119	(	(	PUNCT
m-806	83	120	0	0	NUM
m-806	83	121	)	)	PUNCT
m-806	83	122	�	�	PROPN
m-806	83	123	�	�	PROPN
m-806	83	124	,	,	PUNCT
m-806	83	125	�	�	PROPN
m-806	83	126	�	�	PROPN
m-806	83	127	(	(	PUNCT
m-806	83	128	�	�	PROPN
m-806	83	129	�	�	PROPN
m-806	83	130	)	)	PUNCT
m-806	83	131	(	(	PUNCT
m-806	83	132	0	0	NUM
m-806	83	133	,	,	PUNCT
m-806	83	134	0	0	NUM
m-806	83	135	)	)	PUNCT
m-806	83	136	=	=	SYM
m-806	83	137	0	0	NUM
m-806	83	138	(	(	PUNCT
m-806	83	139	6.39b	6.39b	NUM
m-806	83	140	)	)	PUNCT
m-806	83	141	next	next	ADV
m-806	83	142	,	,	PUNCT
m-806	83	143	if	if	SCONJ
m-806	83	144	in	in	ADP
m-806	83	145	the	the	DET
m-806	83	146	substitution	substitution	NOUN
m-806	83	147	in	in	ADP
m-806	83	148	(	(	PUNCT
m-806	83	149	6.12	6.12	NUM
m-806	83	150	)	)	PUNCT
m-806	83	151	,	,	PUNCT
m-806	83	152	we	we	PRON
m-806	83	153	multiply	multiply	VERB
m-806	83	154	through	through	ADP
m-806	83	155	by	by	ADP
m-806	83	156	�	�	PROPN
m-806	83	157	�	�	PROPN
m-806	83	158	�	�	PROPN
m-806	83	159	4	4	NUM
m-806	83	160	�	�	PROPN
m-806	83	161	�	�	PROPN
m-806	83	162	and	and	CCONJ
m-806	83	163	thereafter	thereafter	ADV
m-806	83	164	integrate	integrate	VERB
m-806	83	165	from	from	ADP
m-806	83	166	0	0	NUM
m-806	83	167	to	to	ADP
m-806	83	168	π	π	PROPN
m-806	83	169	,	,	PUNCT
m-806	83	170	we	we	PRON
m-806	83	171	get	get	VERB
m-806	83	172	(	(	PUNCT
m-806	83	173	for	for	ADP
m-806	83	174	�	�	PROPN
m-806	83	175	=	=	SYM
m-806	83	176	2	2	NUM
m-806	83	177	�	�	PROPN
m-806	83	178	)	)	PUNCT
m-806	83	179	u	u	NOUN
m-806	83	180	�	�	PROPN
m-806	83	181	�	�	PROPN
m-806	83	182	,	,	PUNCT
m-806	83	183	�	�	PROPN
m-806	83	184	�	�	PROPN
m-806	83	185	�	�	PROPN
m-806	83	186	�	�	PROPN
m-806	83	187	(	(	PUNCT
m-806	83	188	�	�	PROPN
m-806	83	189	�	�	PROPN
m-806	83	190	)	)	PUNCT
m-806	83	191	+	+	SYM
m-806	84	1	�	�	PROPN
m-806	84	2	�	�	PROPN
m-806	84	3	�	�	PROPN
m-806	84	4	�	�	PROPN
m-806	84	5	u	u	PROPN
m-806	84	6	�	�	PROPN
m-806	84	7	�	�	PROPN
m-806	84	8	(	(	PUNCT
m-806	84	9	�	�	PROPN
m-806	84	10	�	�	PROPN
m-806	84	11	)	)	PUNCT
m-806	84	12	=	=	PUNCT
m-806	84	13	−3	−3	PROPN
m-806	84	14	�	�	PROPN
m-806	84	15	2	2	NUM
m-806	84	16	�	�	PROPN
m-806	84	17	�	�	PROPN
m-806	84	18	�	�	PROPN
m-806	84	19	�	�	PROPN
m-806	84	20	+	+	CCONJ
m-806	84	21	3	3	NUM
m-806	84	22	�	�	PROPN
m-806	84	23	�	�	PROPN
m-806	84	24	�	�	PROPN
m-806	84	25	�	�	PROPN
m-806	84	26	2	2	NUM
m-806	84	27	�	�	PROPN
m-806	84	28	+	+	CCONJ
m-806	84	29	3	3	NUM
m-806	84	30	�	�	PROPN
m-806	84	31	�	�	PROPN
m-806	84	32	�	�	PROPN
m-806	84	33	�	�	PROPN
m-806	84	34	�	�	PROPN
m-806	84	35	+	+	SYM
m-806	84	36	�	�	PROPN
m-806	84	37	�	�	PROPN
m-806	84	38	�	�	PROPN
m-806	84	39	4	4	NUM
m-806	84	40	�	�	PROPN
m-806	84	41	cos	cos	PROPN
m-806	84	42	�	�	PROPN
m-806	84	43	�	�	PROPN
m-806	84	44	̂	̂	VERB
m-806	84	45	+	+	NOUN
m-806	84	46	3	3	NUM
m-806	84	47	�	�	PROPN
m-806	84	48	�	�	PROPN
m-806	84	49	�	�	PROPN
m-806	84	50	�	�	PROPN
m-806	84	51	cos	cos	PROPN
m-806	84	52	2	2	PROPN
m-806	84	53	�	�	PROPN
m-806	84	54	�	�	PROPN
m-806	84	55	̂	̂	SYM
m-806	84	56	2	2	NUM
m-806	84	57	�	�	PROPN
m-806	84	58	+	+	CCONJ
m-806	84	59	�	�	PROPN
m-806	84	60	�	�	PROPN
m-806	84	61	�	�	PROPN
m-806	84	62	�	�	PROPN
m-806	84	63	�	�	PROPN
m-806	84	64	�	�	PROPN
m-806	84	65	�	�	PROPN
m-806	84	66	�	�	PROPN
m-806	84	67	�	�	PROPN
m-806	84	68	�	�	PROPN
m-806	84	69	�	�	PROPN
m-806	84	70	�	�	PROPN
m-806	84	71	�	�	PROPN
m-806	84	72	(	(	PUNCT
m-806	84	73	6.40a	6.40a	NOUN
m-806	84	74	)	)	PUNCT
m-806	84	75	u	u	PROPN
m-806	84	76	�	�	PROPN
m-806	84	77	�	�	PROPN
m-806	84	78	(	(	PUNCT
m-806	84	79	�	�	PROPN
m-806	84	80	�	�	PROPN
m-806	84	81	)	)	PUNCT
m-806	84	82	(	(	PUNCT
m-806	84	83	0,0	0,0	NUM
m-806	84	84	)	)	PUNCT
m-806	84	85	=	=	SYM
m-806	84	86	0	0	NUM
m-806	84	87	,	,	PUNCT
m-806	84	88	�	�	PROPN
m-806	84	89	�	�	PROPN
m-806	84	90	�	�	PROPN
m-806	84	91	,	,	PUNCT
m-806	84	92	�	�	PROPN
m-806	84	93	�	�	PROPN
m-806	84	94	(	(	PUNCT
m-806	84	95	�	�	PROPN
m-806	84	96	�	�	PROPN
m-806	84	97	)	)	PUNCT
m-806	84	98	(	(	PUNCT
m-806	84	99	0	0	NUM
m-806	84	100	,	,	PUNCT
m-806	84	101	0	0	NUM
m-806	84	102	)	)	PUNCT
m-806	84	103	=	=	SYM
m-806	84	104	0	0	PUNCT
m-806	84	105	(	(	PUNCT
m-806	84	106	6.40b	6.40b	NUM
m-806	84	107	)	)	PUNCT
m-806	84	108	where	where	SCONJ
m-806	84	109	,	,	PUNCT
m-806	84	110	�	�	PROPN
m-806	84	111	�	�	PROPN
m-806	84	112	�	�	PROPN
m-806	84	113	�	�	PROPN
m-806	84	114	=	=	SYM
m-806	84	115	(	(	PUNCT
m-806	84	116	256	256	NUM
m-806	84	117	�	�	PROPN
m-806	84	118	�	�	PROPN
m-806	84	119	−	−	PROPN
m-806	84	120	32	32	NUM
m-806	84	121	�	�	PROPN
m-806	84	122	�	�	PROPN
m-806	84	123	�	�	PROPN
m-806	84	124	+	+	CCONJ
m-806	84	125	1	1	NUM
m-806	84	126	)	)	PUNCT
m-806	84	127	>	>	X
m-806	84	128	0	0	NUM
m-806	84	129	,	,	PUNCT
m-806	84	130	∀	∀	X
m-806	84	131	�	�	PROPN
m-806	84	132	(	(	PUNCT
m-806	84	133	6.40	6.40	NUM
m-806	84	134	�	�	NOUN
m-806	84	135	)	)	PUNCT
m-806	84	136	lastly	lastly	ADV
m-806	84	137	,	,	PUNCT
m-806	84	138	if	if	SCONJ
m-806	84	139	in	in	ADP
m-806	84	140	the	the	DET
m-806	84	141	substitution	substitution	NOUN
m-806	84	142	into	into	ADP
m-806	84	143	(	(	PUNCT
m-806	84	144	6.12	6.12	NUM
m-806	84	145	)	)	PUNCT
m-806	84	146	,	,	PUNCT
m-806	84	147	we	we	PRON
m-806	84	148	multiply	multiply	VERB
m-806	84	149	through	through	ADP
m-806	84	150	by	by	ADP
m-806	84	151	cos	cos	PROPN
m-806	84	152	6	6	PROPN
m-806	84	153	�	�	PROPN
m-806	84	154	�	�	PROPN
m-806	84	155	,	,	PUNCT
m-806	84	156	and	and	CCONJ
m-806	84	157	integrate	integrate	VERB
m-806	84	158	from	from	ADP
m-806	84	159	0	0	NUM
m-806	84	160	to	to	ADP
m-806	84	161	π	π	PROPN
m-806	84	162	,	,	PUNCT
m-806	84	163	we	we	PRON
m-806	84	164	see	see	VERB
m-806	84	165	that	that	SCONJ
m-806	84	166	,	,	PUNCT
m-806	84	167	for	for	ADP
m-806	84	168	�	�	PROPN
m-806	84	169	=	=	SYM
m-806	84	170	3	3	NUM
m-806	84	171	�	�	PROPN
m-806	84	172	,	,	PUNCT
m-806	84	173	we	we	PRON
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m-806	84	176	�	�	PROPN
m-806	84	177	�	�	PROPN
m-806	84	178	,	,	PUNCT
m-806	84	179	�	�	PROPN
m-806	84	180	�	�	PROPN
m-806	84	181	�	�	PROPN
m-806	84	182	�	�	PROPN
m-806	84	183	(	(	PUNCT
m-806	84	184	�	�	PROPN
m-806	84	185	�	�	PROPN
m-806	84	186	)	)	PUNCT
m-806	85	1	+	+	SYM
m-806	85	2	�	�	PROPN
m-806	85	3	�	�	PROPN
m-806	85	4	�	�	PROPN
m-806	85	5	�	�	PROPN
m-806	85	6	u	u	PROPN
m-806	85	7	�	�	PROPN
m-806	85	8	�	�	PROPN
m-806	85	9	(	(	PUNCT
m-806	85	10	�	�	PROPN
m-806	85	11	�	�	PROPN
m-806	85	12	)	)	PUNCT
m-806	85	13	=	=	SYM
m-806	85	14	�	�	PROPN
m-806	85	15	4	4	NUM
m-806	85	16	�	�	PROPN
m-806	85	17	�	�	PROPN
m-806	85	18	�	�	PROPN
m-806	85	19	�	�	PROPN
m-806	85	20	+	+	CCONJ
m-806	85	21	3	3	NUM
m-806	85	22	�	�	PROPN
m-806	85	23	�	�	PROPN
m-806	85	24	�	�	PROPN
m-806	85	25	�	�	PROPN
m-806	85	26	2	2	NUM
m-806	85	27	�	�	PROPN
m-806	85	28	+	+	CCONJ
m-806	85	29	3	3	NUM
m-806	85	30	�	�	PROPN
m-806	85	31	�	�	PROPN
m-806	85	32	�	�	PROPN
m-806	85	33	�	�	PROPN
m-806	85	34	�	�	PROPN
m-806	85	35	+	+	SYM
m-806	85	36	�	�	PROPN
m-806	85	37	�	�	PROPN
m-806	85	38	�	�	PROPN
m-806	85	39	4	4	NUM
m-806	85	40	�	�	PROPN
m-806	85	41	cos	cos	PROPN
m-806	85	42	�	�	PROPN
m-806	85	43	�	�	PROPN
m-806	85	44	̂	̂	VERB
m-806	85	45	+	+	NOUN
m-806	85	46	3	3	NUM
m-806	85	47	�	�	PROPN
m-806	85	48	�	�	PROPN
m-806	85	49	�	�	PROPN
m-806	85	50	�	�	PROPN
m-806	85	51	cos	cos	PROPN
m-806	85	52	2	2	PROPN
m-806	85	53	�	�	PROPN
m-806	85	54	�	�	PROPN
m-806	85	55	̂	̂	SYM
m-806	85	56	2	2	NUM
m-806	85	57	�	�	PROPN
m-806	85	58	+	+	SYM
m-806	85	59	�	�	PROPN
m-806	85	60	�	�	PROPN
m-806	85	61	�	�	PROPN
m-806	85	62	�	�	PROPN
m-806	85	63	�	�	PROPN
m-806	85	64	�	�	PROPN
m-806	85	65	�	�	PROPN
m-806	85	66	�	�	PROPN
m-806	85	67	�	�	PROPN
m-806	85	68	�	�	PROPN
m-806	85	69	�	�	PROPN
m-806	85	70	�	�	PROPN
m-806	85	71	�	�	PROPN
m-806	85	72	(	(	PUNCT
m-806	85	73	6.41a	6.41a	NUM
m-806	85	74	)	)	PUNCT
m-806	85	75	u	u	PROPN
m-806	85	76	�	�	PROPN
m-806	85	77	�	�	PROPN
m-806	85	78	(	(	PUNCT
m-806	85	79	�	�	PROPN
m-806	85	80	�	�	PROPN
m-806	85	81	)	)	PUNCT
m-806	85	82	(	(	PUNCT
m-806	85	83	0,0	0,0	NUM
m-806	85	84	)	)	PUNCT
m-806	85	85	=	=	SYM
m-806	85	86	0	0	NUM
m-806	85	87	,	,	PUNCT
m-806	85	88	�	�	PROPN
m-806	85	89	�	�	PROPN
m-806	85	90	�	�	PROPN
m-806	85	91	,	,	PUNCT
m-806	85	92	�	�	PROPN
m-806	85	93	�	�	PROPN
m-806	85	94	(	(	PUNCT
m-806	85	95	�	�	PROPN
m-806	85	96	�	�	PROPN
m-806	85	97	)	)	PUNCT
m-806	85	98	(	(	PUNCT
m-806	85	99	0	0	NUM
m-806	85	100	,	,	PUNCT
m-806	85	101	0	0	NUM
m-806	85	102	)	)	PUNCT
m-806	85	103	=	=	SYM
m-806	85	104	0	0	PUNCT
m-806	85	105	(	(	PUNCT
m-806	85	106	6.41b	6.41b	NOUN
m-806	85	107	)	)	PUNCT
m-806	85	108	where	where	SCONJ
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m-806	85	110	�	�	PROPN
m-806	85	111	�	�	PROPN
m-806	85	112	�	�	PROPN
m-806	85	113	�	�	PROPN
m-806	85	114	=	=	SYM
m-806	85	115	(	(	PUNCT
m-806	85	116	1296	1296	NUM
m-806	85	117	�	�	PROPN
m-806	85	118	�	�	PROPN
m-806	85	119	−	−	PROPN
m-806	85	120	72	72	NUM
m-806	85	121	�	�	PROPN
m-806	85	122	�	�	PROPN
m-806	85	123	�	�	PROPN
m-806	85	124	+	+	CCONJ
m-806	85	125	1	1	NUM
m-806	85	126	)	)	PUNCT
m-806	85	127	>	>	X
m-806	85	128	0	0	NUM
m-806	85	129	,	,	PUNCT
m-806	85	130	∀	∀	X
m-806	85	131	�	�	PROPN
m-806	85	132	(	(	PUNCT
m-806	85	133	6.41	6.41	NUM
m-806	85	134	�	�	NOUN
m-806	85	135	)	)	PUNCT
m-806	85	136	to	to	PART
m-806	85	137	solve	solve	VERB
m-806	85	138	(	(	PUNCT
m-806	85	139	6.39a	6.39a	NUM
m-806	85	140	,	,	PUNCT
m-806	85	141	b	b	NOUN
m-806	85	142	)	)	PUNCT
m-806	85	143	,	,	PUNCT
m-806	85	144	we	we	PRON
m-806	85	145	substitute	substitute	VERB
m-806	85	146	for	for	ADP
m-806	85	147	u	u	PROPN
m-806	85	148	�	�	PROPN
m-806	85	149	(	(	PUNCT
m-806	85	150	�	�	PROPN
m-806	85	151	�	�	PROPN
m-806	85	152	)	)	PUNCT
m-806	85	153	from	from	ADP
m-806	85	154	(	(	PUNCT
m-806	85	155	6.28a	6.28a	NUM
m-806	85	156	)	)	PUNCT
m-806	85	157	,	,	PUNCT
m-806	85	158	(	(	PUNCT
m-806	85	159	noting	note	VERB
m-806	85	160	(	(	PUNCT
m-806	85	161	6.28c	6.28c	NUM
m-806	85	162	)	)	PUNCT
m-806	85	163	)	)	PUNCT
m-806	85	164	,	,	PUNCT
m-806	85	165	and	and	CCONJ
m-806	85	166	ensure	ensure	VERB
m-806	85	167	a	a	DET
m-806	85	168	uniformly	uniformly	ADV
m-806	85	169	valid	valid	ADJ
m-806	85	170	solution	solution	NOUN
m-806	85	171	in	in	ADP
m-806	85	172	�	�	PROPN
m-806	85	173	̂	̂	VERB
m-806	85	174	by	by	ADP
m-806	85	175	equating	equate	VERB
m-806	85	176	to	to	ADP
m-806	85	177	zero	zero	NUM
m-806	85	178	,	,	PUNCT
m-806	85	179	the	the	DET
m-806	85	180	coefficient	coefficient	NOUN
m-806	85	181	of	of	ADP
m-806	85	182	cos	cos	PROPN
m-806	85	183	�	�	PROPN
m-806	85	184	�	�	PROPN
m-806	85	185	̂	̂	PUNCT
m-806	85	186	and	and	CCONJ
m-806	85	187	get	get	VERB
m-806	85	188	�	�	PROPN
m-806	85	189	�	�	PROPN
m-806	85	190	�	�	PROPN
m-806	85	191	(	(	PUNCT
m-806	85	192	�	�	PROPN
m-806	85	193	)	)	PUNCT
m-806	85	194	=	=	SYM
m-806	85	195	�	�	PROPN
m-806	85	196	�	�	PROPN
m-806	85	197	�	�	PROPN
m-806	85	198	�	�	PROPN
m-806	85	199	�	�	PROPN
m-806	85	200	�	�	PROPN
m-806	85	201	�	�	PROPN
m-806	85	202	�	�	PROPN
m-806	85	203	�	�	PROPN
m-806	85	204	+	+	SYM
m-806	85	205	�	�	PROPN
m-806	85	206	�	�	PROPN
m-806	85	207	�	�	PROPN
m-806	85	208	�	�	PROPN
m-806	85	209	�	�	PROPN
m-806	85	210	,	,	PUNCT
m-806	85	211	�	�	PROPN
m-806	85	212	�	�	PROPN
m-806	85	213	�	�	PROPN
m-806	85	214	(	(	PUNCT
m-806	85	215	0	0	NUM
m-806	85	216	)	)	PUNCT
m-806	85	217	=	=	SYM
m-806	85	218	�	�	PROPN
m-806	85	219	�	�	PROPN
m-806	85	220	�	�	PROPN
m-806	85	221	�	�	PROPN
m-806	85	222	�	�	PROPN
m-806	85	223	�	�	PROPN
m-806	85	224	�	�	PROPN
m-806	85	225	�	�	PROPN
m-806	85	226	�	�	PROPN
m-806	85	227	�	�	PROPN
m-806	85	228	�	�	PROPN
m-806	85	229	(	(	PUNCT
m-806	85	230	6.42a	6.42a	PROPN
m-806	85	231	)	)	PUNCT
m-806	85	232	�	�	PROPN
m-806	85	233	�	�	PROPN
m-806	85	234	�	�	PROPN
m-806	85	235	�	�	PROPN
m-806	85	236	(	(	PUNCT
m-806	85	237	0	0	NUM
m-806	85	238	)	)	PUNCT
m-806	85	239	=	=	SYM
m-806	85	240	�	�	PROPN
m-806	85	241	�	�	PROPN
m-806	85	242	�	�	PROPN
m-806	85	243	�	�	PROPN
m-806	85	244	�	�	PROPN
m-806	85	245	�	�	PROPN
m-806	85	246	�	�	PROPN
m-806	85	247	�	�	PROPN
m-806	85	248	�	�	PROPN
m-806	85	249	(	(	PUNCT
m-806	85	250	6.42b	6.42b	NUM
m-806	85	251	)	)	PUNCT
m-806	85	252	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	85	253	ijo	ijo	PROPN
m-806	85	254	journals	journal	NOUN
m-806	85	255	volume	volume	NOUN
m-806	85	256	07	07	NUM
m-806	86	1	|	|	ADV
m-806	86	2	issue	issue	NOUN
m-806	86	3	02	02	NUM
m-806	86	4	|	|	CCONJ
m-806	86	5	february	february	PROPN
m-806	86	6	2024	2024	NUM
m-806	86	7	|	|	ADV
m-806	86	8	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	86	9	10	10	NUM
m-806	86	10	ijo	ijo	PROPN
m-806	86	11	international	international	ADJ
m-806	86	12	journal	journal	PROPN
m-806	86	13	of	of	ADP
m-806	86	14	mathematics	mathematics	PROPN
m-806	86	15	(	(	PUNCT
m-806	86	16	issn	issn	PROPN
m-806	86	17	:	:	PUNCT
m-806	86	18	2992	2992	NUM
m-806	86	19	-	-	SYM
m-806	86	20	4421	4421	NUM
m-806	86	21	)	)	PUNCT
m-806	87	1	i.u	i.u	PROPN
m-806	87	2	.	.	PROPN
m-806	87	3	udo	udo	PROPN
m-806	87	4	-	-	PROPN
m-806	87	5	akpan1	akpan1	ADJ
m-806	87	6	*	*	PUNCT
m-806	87	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	87	8	volume	volume	NOUN
m-806	87	9	07	07	NUM
m-806	87	10	issue	issue	NOUN
m-806	87	11	02	02	NUM
m-806	87	12	||	||	NUM
m-806	87	13	february	february	PROPN
m-806	87	14	,	,	PUNCT
m-806	87	15	2024	2024	NUM
m-806	87	16	||	||	NOUN
m-806	88	1	on	on	ADP
m-806	88	2	a	a	DET
m-806	88	3	-	-	PUNCT
m-806	88	4	two	two	NUM
m-806	88	5	-	-	PUNCT
m-806	88	6	parameter	parameter	NOUN
m-806	88	7	dynamic	dynamic	ADJ
m-806	88	8	buckling	buckling	NOUN
m-806	88	9	of	of	ADP
m-806	88	10	a	a	DET
m-806	88	11	viscously	viscously	ADV
m-806	88	12	damped	damp	VERB
m-806	88	13	but	but	CCONJ
m-806	88	14	clamped	clamp	VERB
m-806	88	15	column	column	NOUN
m-806	88	16	stressed	stress	VERB
m-806	88	17	by	by	ADP
m-806	88	18	a	a	DET
m-806	88	19	step	step	NOUN
m-806	88	20	load	load	NOUN
m-806	88	21	the	the	DET
m-806	88	22	remaining	remain	VERB
m-806	88	23	equation	equation	NOUN
m-806	88	24	in	in	ADP
m-806	88	25	(	(	PUNCT
m-806	88	26	6.39a	6.39a	NOUN
m-806	88	27	)	)	PUNCT
m-806	88	28	is	be	AUX
m-806	88	29	now	now	ADV
m-806	88	30	solved	solve	VERB
m-806	88	31	to	to	PART
m-806	88	32	get	get	VERB
m-806	88	33	u	u	NOUN
m-806	88	34	�	�	X
m-806	88	35	(	(	PUNCT
m-806	88	36	�	�	PROPN
m-806	88	37	�	�	PROPN
m-806	88	38	)	)	PUNCT
m-806	88	39	(	(	PUNCT
m-806	88	40	�	�	PROPN
m-806	88	41	̂	̂	NUM
m-806	88	42	,	,	PUNCT
m-806	88	43	�	�	NOUN
m-806	88	44	)	)	PUNCT
m-806	88	45	=	=	SYM
m-806	88	46	�	�	PROPN
m-806	88	47	�	�	PROPN
m-806	88	48	cos	cos	PROPN
m-806	88	49	�	�	PROPN
m-806	88	50	�	�	PROPN
m-806	88	51	̂	̂	VERB
m-806	88	52	+	+	NUM
m-806	88	53	�	�	PROPN
m-806	88	54	�	�	PROPN
m-806	88	55	sin	sin	PROPN
m-806	88	56	�	�	PROPN
m-806	88	57	�	�	PROPN
m-806	88	58	̂	̂	VERB
m-806	88	59	+	+	CCONJ
m-806	88	60	15	15	NUM
m-806	88	61	�	�	PROPN
m-806	88	62	4	4	NUM
m-806	88	63	�	�	PROPN
m-806	88	64	�	�	PROPN
m-806	88	65	�	�	PROPN
m-806	88	66	�	�	PROPN
m-806	88	67	�	�	PROPN
m-806	88	68	−	−	PROPN
m-806	88	69	3	3	NUM
m-806	88	70	�	�	PROPN
m-806	88	71	�	�	PROPN
m-806	88	72	�	�	PROPN
m-806	88	73	�	�	PROPN
m-806	88	74	cos	cos	PROPN
m-806	88	75	2	2	PROPN
m-806	88	76	�	�	PROPN
m-806	88	77	�	�	PROPN
m-806	88	78	̂	̂	VERB
m-806	88	79	2	2	NUM
m-806	88	80	�	�	PROPN
m-806	88	81	�	�	PROPN
m-806	88	82	�	�	PROPN
m-806	88	83	−	−	PROPN
m-806	88	84	�	�	PROPN
m-806	88	85	�	�	PROPN
m-806	88	86	�	�	PROPN
m-806	88	87	�	�	PROPN
m-806	88	88	cos	cos	PROPN
m-806	88	89	3	3	PROPN
m-806	88	90	�	�	PROPN
m-806	88	91	�	�	PROPN
m-806	88	92	̂	̂	VERB
m-806	88	93	32	32	NUM
m-806	88	94	�	�	PROPN
m-806	88	95	�	�	PROPN
m-806	88	96	�	�	PROPN
m-806	88	97	(	(	PUNCT
m-806	88	98	6.43	6.43	NUM
m-806	88	99	�	�	NOUN
m-806	88	100	)	)	PUNCT
m-806	88	101	where	where	SCONJ
m-806	88	102	�	�	PROPN
m-806	88	103	�	�	PROPN
m-806	88	104	(	(	PUNCT
m-806	88	105	�	�	PROPN
m-806	88	106	)	)	PUNCT
m-806	88	107	=	=	SYM
m-806	88	108	�	�	PROPN
m-806	88	109	�	�	PROPN
m-806	88	110	�	�	PROPN
m-806	88	111	+	+	CCONJ
m-806	88	112	�	�	PROPN
m-806	88	113	�	�	PROPN
m-806	88	114	�	�	PROPN
m-806	88	115	�	�	PROPN
m-806	88	116	�	�	PROPN
m-806	88	117	�	�	PROPN
m-806	88	118	�	�	PROPN
m-806	88	119	(	(	PUNCT
m-806	88	120	6.43b	6.43b	NOUN
m-806	88	121	)	)	PUNCT
m-806	88	122	�	�	PROPN
m-806	88	123	�	�	PROPN
m-806	88	124	(	(	PUNCT
m-806	88	125	0	0	NUM
m-806	88	126	)	)	PUNCT
m-806	88	127	=	=	SYM
m-806	88	128	�	�	PROPN
m-806	88	129	�	�	PROPN
m-806	88	130	�	�	PROPN
m-806	88	131	�	�	PROPN
m-806	88	132	�	�	PROPN
m-806	88	133	�	�	PROPN
m-806	88	134	�	�	PROPN
m-806	88	135	�	�	PROPN
m-806	88	136	�	�	PROPN
m-806	88	137	,	,	PUNCT
m-806	88	138	(	(	PUNCT
m-806	88	139	0	0	NUM
m-806	88	140	)	)	PUNCT
m-806	88	141	=	=	SYM
m-806	88	142	0	0	PUNCT
m-806	88	143	(	(	PUNCT
m-806	88	144	6.43c	6.43c	NUM
m-806	88	145	)	)	PUNCT
m-806	88	146	�	�	PROPN
m-806	88	147	�	�	PROPN
m-806	88	148	(	(	PUNCT
m-806	88	149	0	0	NUM
m-806	88	150	)	)	PUNCT
m-806	89	1	=	=	SYM
m-806	89	2	�	�	PROPN
m-806	89	3	�	�	PROPN
m-806	89	4	�	�	PROPN
m-806	89	5	�	�	PROPN
m-806	89	6	,	,	PUNCT
m-806	89	7	�	�	PROPN
m-806	89	8	�	�	PROPN
m-806	89	9	�	�	PROPN
m-806	89	10	(	(	PUNCT
m-806	89	11	0	0	NUM
m-806	89	12	)	)	PUNCT
m-806	89	13	=	=	SYM
m-806	89	14	−3	−3	PROPN
m-806	89	15	�	�	PROPN
m-806	89	16	�	�	PROPN
m-806	89	17	,	,	PUNCT
m-806	89	18	�	�	PROPN
m-806	89	19	�	�	PROPN
m-806	89	20	�	�	PROPN
m-806	89	21	�	�	PROPN
m-806	89	22	(	(	PUNCT
m-806	89	23	0	0	NUM
m-806	89	24	)	)	PUNCT
m-806	89	25	=	=	SYM
m-806	89	26	6	6	NUM
m-806	89	27	�	�	PROPN
m-806	89	28	�	�	PROPN
m-806	89	29	(	(	PUNCT
m-806	89	30	6.43d	6.43d	NOUN
m-806	89	31	)	)	PUNCT
m-806	89	32	turning	turn	VERB
m-806	89	33	to	to	ADP
m-806	89	34	(	(	PUNCT
m-806	89	35	6.40a	6.40a	NOUN
m-806	89	36	,	,	PUNCT
m-806	89	37	b	b	NOUN
m-806	89	38	)	)	PUNCT
m-806	89	39	,	,	PUNCT
m-806	89	40	we	we	PRON
m-806	89	41	solve	solve	VERB
m-806	89	42	to	to	PART
m-806	89	43	get	get	VERB
m-806	89	44	u	u	NOUN
m-806	89	45	�	�	PROPN
m-806	89	46	�	�	PROPN
m-806	89	47	(	(	PUNCT
m-806	89	48	�	�	PROPN
m-806	89	49	�	�	PROPN
m-806	89	50	)	)	PUNCT
m-806	89	51	(	(	PUNCT
m-806	89	52	�	�	PROPN
m-806	89	53	̂	̂	NUM
m-806	89	54	,	,	PUNCT
m-806	89	55	�	�	NOUN
m-806	89	56	)	)	PUNCT
m-806	89	57	=	=	SYM
m-806	89	58	�	�	PROPN
m-806	89	59	�	�	PROPN
m-806	89	60	cos	cos	PROPN
m-806	89	61	�	�	PROPN
m-806	89	62	�	�	PROPN
m-806	89	63	�	�	PROPN
m-806	89	64	�	�	PROPN
m-806	89	65	̂	̂	VERB
m-806	89	66	+	+	NUM
m-806	89	67	�	�	PROPN
m-806	89	68	�	�	PROPN
m-806	89	69	sin	sin	PROPN
m-806	89	70	�	�	PROPN
m-806	89	71	�	�	PROPN
m-806	89	72	�	�	PROPN
m-806	89	73	�	�	PROPN
m-806	89	74	̂	̂	VERB
m-806	89	75	−	−	PROPN
m-806	89	76	3	3	NUM
m-806	89	77	�	�	PROPN
m-806	89	78	2	2	NUM
m-806	89	79	�	�	PROPN
m-806	89	80	�	�	PROPN
m-806	89	81	�	�	PROPN
m-806	89	82	�	�	PROPN
m-806	89	83	�	�	PROPN
m-806	89	84	�	�	PROPN
m-806	89	85	�	�	PROPN
m-806	89	86	+	+	CCONJ
m-806	89	87	�	�	PROPN
m-806	89	88	�	�	PROPN
m-806	89	89	cos	cos	PROPN
m-806	89	90	�	�	PROPN
m-806	89	91	�	�	PROPN
m-806	89	92	̂	̂	SYM
m-806	89	93	�	�	PROPN
m-806	89	94	�	�	PROPN
m-806	89	95	�	�	PROPN
m-806	89	96	�	�	PROPN
m-806	89	97	−	−	PROPN
m-806	89	98	�	�	PROPN
m-806	89	99	�	�	PROPN
m-806	89	100	+	+	CCONJ
m-806	89	101	3	3	NUM
m-806	89	102	�	�	PROPN
m-806	89	103	�	�	PROPN
m-806	89	104	�	�	PROPN
m-806	89	105	�	�	PROPN
m-806	89	106	cos	cos	PROPN
m-806	89	107	2	2	PROPN
m-806	89	108	�	�	PROPN
m-806	89	109	�	�	PROPN
m-806	89	110	̂	̂	VERB
m-806	89	111	2	2	NUM
m-806	89	112	(	(	PUNCT
m-806	89	113	�	�	PROPN
m-806	89	114	�	�	PROPN
m-806	89	115	�	�	PROPN
m-806	89	116	�	�	PROPN
m-806	89	117	−	−	PROPN
m-806	89	118	4	4	NUM
m-806	89	119	�	�	PROPN
m-806	89	120	�	�	PROPN
m-806	89	121	)	)	PUNCT
m-806	89	122	�	�	PROPN
m-806	89	123	+	+	CCONJ
m-806	89	124	�	�	PROPN
m-806	89	125	�	�	PROPN
m-806	89	126	�	�	PROPN
m-806	89	127	�	�	PROPN
m-806	89	128	�	�	PROPN
m-806	89	129	�	�	PROPN
m-806	89	130	�	�	PROPN
m-806	89	131	�	�	PROPN
m-806	89	132	�	�	PROPN
m-806	89	133	�	�	PROPN
m-806	89	134	�	�	PROPN
m-806	89	135	�	�	PROPN
m-806	89	136	�	�	PROPN
m-806	89	137	�	�	PROPN
m-806	89	138	�	�	PROPN
m-806	89	139	�	�	PROPN
m-806	89	140	�	�	PROPN
m-806	89	141	�	�	PROPN
m-806	89	142	�	�	PROPN
m-806	89	143	�	�	PROPN
m-806	89	144	�	�	PROPN
m-806	89	145	�	�	PROPN
m-806	89	146	�	�	PROPN
m-806	89	147	(	(	PUNCT
m-806	89	148	6.44a	6.44a	PROPN
m-806	89	149	)	)	PUNCT
m-806	90	1	where	where	SCONJ
m-806	90	2	,	,	PUNCT
m-806	90	3	�	�	PROPN
m-806	90	4	�	�	PROPN
m-806	90	5	(	(	PUNCT
m-806	90	6	�	�	PROPN
m-806	90	7	)	)	PUNCT
m-806	90	8	=	=	SYM
m-806	90	9	3	3	NUM
m-806	90	10	�	�	PROPN
m-806	90	11	�	�	PROPN
m-806	90	12	�	�	PROPN
m-806	90	13	�	�	PROPN
m-806	90	14	�	�	PROPN
m-806	90	15	+	+	SYM
m-806	90	16	�	�	PROPN
m-806	90	17	�	�	PROPN
m-806	90	18	�	�	PROPN
m-806	90	19	�	�	PROPN
m-806	90	20	�	�	PROPN
m-806	90	21	,	,	PUNCT
m-806	90	22	�	�	PROPN
m-806	90	23	�	�	PROPN
m-806	90	24	(	(	PUNCT
m-806	90	25	0	0	NUM
m-806	90	26	)	)	PUNCT
m-806	90	27	=	=	SYM
m-806	90	28	�	�	PROPN
m-806	90	29	�	�	PROPN
m-806	90	30	�	�	PROPN
m-806	90	31	�	�	PROPN
m-806	90	32	�	�	PROPN
m-806	90	33	�	�	PROPN
m-806	90	34	,	,	PUNCT
m-806	90	35	�	�	PROPN
m-806	90	36	�	�	PROPN
m-806	90	37	�	�	PROPN
m-806	90	38	(	(	PUNCT
m-806	90	39	0	0	NUM
m-806	90	40	)	)	PUNCT
m-806	90	41	=	=	SYM
m-806	90	42	�	�	PROPN
m-806	90	43	�	�	PROPN
m-806	90	44	�	�	PROPN
m-806	90	45	�	�	PROPN
m-806	90	46	�	�	PROPN
m-806	90	47	,	,	PUNCT
m-806	90	48	�	�	PROPN
m-806	90	49	�	�	PROPN
m-806	90	50	�	�	PROPN
m-806	90	51	�	�	PROPN
m-806	90	52	(	(	PUNCT
m-806	90	53	0	0	NUM
m-806	90	54	)	)	PUNCT
m-806	90	55	=	=	SYM
m-806	90	56	�	�	PROPN
m-806	90	57	�	�	PROPN
m-806	90	58	�	�	PROPN
m-806	90	59	�	�	PROPN
m-806	90	60	�	�	PROPN
m-806	90	61	�	�	PROPN
m-806	90	62	(	(	PUNCT
m-806	90	63	6.44b	6.44b	PROPN
m-806	90	64	)	)	PUNCT
m-806	90	65	�	�	PROPN
m-806	90	66	�	�	PROPN
m-806	90	67	(	(	PUNCT
m-806	90	68	0	0	NUM
m-806	90	69	)	)	PUNCT
m-806	90	70	=	=	SYM
m-806	90	71	�	�	PROPN
m-806	90	72	�	�	PROPN
m-806	90	73	�	�	PROPN
m-806	90	74	�	�	PROPN
m-806	90	75	�	�	PROPN
m-806	90	76	�	�	PROPN
m-806	90	77	�	�	PROPN
m-806	90	78	,	,	PUNCT
m-806	90	79	�	�	PROPN
m-806	90	80	�	�	PROPN
m-806	90	81	(	(	PUNCT
m-806	90	82	0	0	NUM
m-806	90	83	)	)	PUNCT
m-806	90	84	=	=	SYM
m-806	90	85	0	0	PUNCT
m-806	90	86	(	(	PUNCT
m-806	90	87	6.44c	6.44c	NUM
m-806	90	88	)	)	PUNCT
m-806	90	89	�	�	PROPN
m-806	90	90	�	�	PROPN
m-806	90	91	=	=	SYM
m-806	90	92	�	�	PROPN
m-806	90	93	�	�	PROPN
m-806	90	94	�	�	PROPN
m-806	90	95	�	�	PROPN
m-806	90	96	�	�	PROPN
m-806	90	97	�	�	PROPN
m-806	90	98	+	+	CCONJ
m-806	90	99	�	�	PROPN
m-806	90	100	�	�	PROPN
m-806	90	101	�	�	PROPN
m-806	90	102	�	�	PROPN
m-806	90	103	�	�	PROPN
m-806	90	104	�	�	PROPN
m-806	90	105	�	�	PROPN
m-806	90	106	�	�	PROPN
m-806	90	107	�	�	PROPN
m-806	90	108	�	�	PROPN
m-806	90	109	�	�	PROPN
m-806	90	110	�	�	PROPN
m-806	90	111	�	�	PROPN
m-806	90	112	−	−	PROPN
m-806	90	113	�	�	PROPN
m-806	90	114	�	�	PROPN
m-806	90	115	�	�	PROPN
m-806	90	116	�	�	PROPN
m-806	90	117	�	�	PROPN
m-806	90	118	�	�	PROPN
m-806	90	119	�	�	PROPN
m-806	90	120	�	�	PROPN
m-806	90	121	�	�	PROPN
m-806	90	122	+	+	CCONJ
m-806	90	123	�	�	PROPN
m-806	90	124	�	�	PROPN
m-806	90	125	�	�	PROPN
m-806	90	126	�	�	PROPN
m-806	90	127	�	�	PROPN
m-806	90	128	�	�	PROPN
m-806	90	129	�	�	PROPN
m-806	90	130	�	�	PROPN
m-806	90	131	�	�	PROPN
m-806	90	132	�	�	PROPN
m-806	90	133	�	�	PROPN
m-806	90	134	�	�	PROPN
m-806	90	135	(	(	PUNCT
m-806	90	136	6.44d	6.44d	PROPN
m-806	90	137	)	)	PUNCT
m-806	90	138	we	we	PRON
m-806	90	139	next	next	ADV
m-806	90	140	solve	solve	NOUN
m-806	90	141	(	(	PUNCT
m-806	90	142	6.41a	6.41a	NOUN
m-806	90	143	)	)	PUNCT
m-806	90	144	and	and	CCONJ
m-806	90	145	get	get	VERB
m-806	90	146	u	u	NOUN
m-806	90	147	�	�	PROPN
m-806	90	148	�	�	PROPN
m-806	90	149	(	(	PUNCT
m-806	90	150	�	�	PROPN
m-806	90	151	�	�	PROPN
m-806	90	152	)	)	PUNCT
m-806	90	153	(	(	PUNCT
m-806	90	154	�	�	PROPN
m-806	90	155	̂	̂	NUM
m-806	90	156	,	,	PUNCT
m-806	90	157	�	�	NOUN
m-806	90	158	)	)	PUNCT
m-806	90	159	=	=	SYM
m-806	90	160	�	�	PROPN
m-806	90	161	�	�	PROPN
m-806	90	162	cos	cos	PROPN
m-806	90	163	�	�	PROPN
m-806	90	164	�	�	PROPN
m-806	90	165	�	�	PROPN
m-806	90	166	�	�	PROPN
m-806	90	167	̂	̂	VERB
m-806	90	168	+	+	NUM
m-806	90	169	�	�	PROPN
m-806	90	170	�	�	PROPN
m-806	90	171	sin	sin	PROPN
m-806	90	172	�	�	PROPN
m-806	90	173	�	�	PROPN
m-806	90	174	�	�	PROPN
m-806	90	175	�	�	PROPN
m-806	90	176	̂	̂	VERB
m-806	90	177	+	+	NUM
m-806	90	178	�	�	PROPN
m-806	90	179	4	4	NUM
m-806	90	180	�	�	PROPN
m-806	90	181	�	�	PROPN
m-806	90	182	�	�	PROPN
m-806	90	183	�	�	PROPN
m-806	90	184	�	�	PROPN
m-806	90	185	�	�	PROPN
m-806	90	186	�	�	PROPN
m-806	90	187	+	+	CCONJ
m-806	90	188	�	�	PROPN
m-806	90	189	�	�	PROPN
m-806	90	190	cos	cos	PROPN
m-806	90	191	�	�	PROPN
m-806	90	192	�	�	PROPN
m-806	90	193	̂	̂	SYM
m-806	90	194	�	�	PROPN
m-806	90	195	�	�	PROPN
m-806	90	196	�	�	PROPN
m-806	90	197	�	�	PROPN
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m-806	90	199	�	�	PROPN
m-806	90	200	�	�	PROPN
m-806	90	201	+	+	CCONJ
m-806	90	202	3	3	NUM
m-806	90	203	�	�	PROPN
m-806	90	204	�	�	PROPN
m-806	90	205	�	�	PROPN
m-806	90	206	�	�	PROPN
m-806	90	207	cos	cos	PROPN
m-806	90	208	2	2	PROPN
m-806	90	209	�	�	PROPN
m-806	90	210	�	�	PROPN
m-806	90	211	̂	̂	VERB
m-806	90	212	2	2	NUM
m-806	90	213	(	(	PUNCT
m-806	90	214	�	�	PROPN
m-806	90	215	�	�	PROPN
m-806	90	216	�	�	PROPN
m-806	90	217	�	�	PROPN
m-806	90	218	−	−	PROPN
m-806	90	219	4	4	NUM
m-806	90	220	�	�	PROPN
m-806	90	221	�	�	NOUN
m-806	90	222	)	)	PUNCT
m-806	90	223	�	�	PROPN
m-806	90	224	+	+	CCONJ
m-806	90	225	�	�	PROPN
m-806	90	226	�	�	PROPN
m-806	90	227	�	�	PROPN
m-806	90	228	�	�	PROPN
m-806	90	229	�	�	PROPN
m-806	90	230	�	�	PROPN
m-806	90	231	�	�	PROPN
m-806	90	232	�	�	PROPN
m-806	90	233	�	�	PROPN
m-806	90	234	�	�	PROPN
m-806	90	235	�	�	PROPN
m-806	90	236	�	�	PROPN
m-806	90	237	�	�	PROPN
m-806	90	238	�	�	PROPN
m-806	90	239	�	�	PROPN
m-806	90	240	�	�	PROPN
m-806	90	241	�	�	PROPN
m-806	90	242	�	�	PROPN
m-806	90	243	�	�	PROPN
m-806	90	244	�	�	PROPN
m-806	90	245	�	�	PROPN
m-806	90	246	�	�	PROPN
m-806	90	247	�	�	PROPN
m-806	90	248	(	(	PUNCT
m-806	90	249	6.45a	6.45a	NUM
m-806	90	250	)	)	PUNCT
m-806	90	251	where	where	SCONJ
m-806	90	252	,	,	PUNCT
m-806	90	253	�	�	PROPN
m-806	90	254	�	�	PROPN
m-806	90	255	(	(	PUNCT
m-806	90	256	0	0	NUM
m-806	90	257	)	)	PUNCT
m-806	90	258	=	=	SYM
m-806	90	259	�	�	PROPN
m-806	90	260	�	�	PROPN
m-806	90	261	�	�	PROPN
m-806	90	262	�	�	PROPN
m-806	90	263	�	�	PROPN
m-806	90	264	4	4	NUM
m-806	90	265	,	,	PUNCT
m-806	90	266	�	�	PROPN
m-806	90	267	�	�	PROPN
m-806	90	268	=	=	SYM
m-806	90	269	�	�	PROPN
m-806	90	270	1	1	NUM
m-806	90	271	�	�	PROPN
m-806	90	272	�	�	PROPN
m-806	90	273	�	�	PROPN
m-806	90	274	�	�	PROPN
m-806	90	275	+	+	CCONJ
m-806	90	276	15	15	NUM
m-806	90	277	�	�	PROPN
m-806	90	278	�	�	PROPN
m-806	90	279	�	�	PROPN
m-806	90	280	�	�	PROPN
m-806	90	281	−	−	PROPN
m-806	90	282	�	�	PROPN
m-806	90	283	�	�	PROPN
m-806	90	284	−	−	PROPN
m-806	90	285	3	3	NUM
m-806	90	286	�	�	PROPN
m-806	90	287	�	�	PROPN
m-806	90	288	�	�	PROPN
m-806	90	289	�	�	PROPN
m-806	90	290	−	−	PROPN
m-806	90	291	4	4	NUM
m-806	90	292	�	�	PROPN
m-806	90	293	�	�	PROPN
m-806	90	294	�	�	PROPN
m-806	90	295	+	+	CCONJ
m-806	90	296	�	�	PROPN
m-806	90	297	1	1	NUM
m-806	90	298	2	2	NUM
m-806	90	299	(	(	PUNCT
m-806	90	300	�	�	PROPN
m-806	90	301	�	�	PROPN
m-806	90	302	�	�	PROPN
m-806	90	303	�	�	PROPN
m-806	90	304	−	−	PROPN
m-806	90	305	9	9	NUM
m-806	90	306	�	�	PROPN
m-806	90	307	�	�	PROPN
m-806	90	308	)	)	PUNCT
m-806	90	309	�	�	PROPN
m-806	90	310	,	,	PUNCT
m-806	90	311	�	�	PROPN
m-806	90	312	�	�	PROPN
m-806	90	313	(	(	PUNCT
m-806	90	314	0	0	NUM
m-806	90	315	)	)	PUNCT
m-806	90	316	=	=	SYM
m-806	90	317	0	0	NUM
m-806	90	318	(	(	PUNCT
m-806	90	319	6.45	6.45	NUM
m-806	90	320	�	�	NOUN
m-806	90	321	)	)	PUNCT
m-806	90	322	thus	thus	ADV
m-806	90	323	,	,	PUNCT
m-806	90	324	we	we	PRON
m-806	90	325	have	have	VERB
m-806	90	326	�	�	PROPN
m-806	90	327	(	(	PUNCT
m-806	90	328	�	�	NOUN
m-806	90	329	�	�	PROPN
m-806	90	330	)	)	PUNCT
m-806	90	331	=	=	SYM
m-806	91	1	u	u	PRON
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m-806	91	3	(	(	PUNCT
m-806	91	4	�	�	PROPN
m-806	91	5	�	�	PROPN
m-806	91	6	)	)	PUNCT
m-806	91	7	(	(	PUNCT
m-806	91	8	1	1	NUM
m-806	91	9	−	−	PROPN
m-806	91	10	cos	cos	PROPN
m-806	91	11	2	2	NUM
m-806	91	12	�	�	PROPN
m-806	91	13	�	�	PROPN
m-806	91	14	)	)	PUNCT
m-806	91	15	+	+	CCONJ
m-806	91	16	u	u	NOUN
m-806	91	17	�	�	PROPN
m-806	91	18	�	�	PROPN
m-806	91	19	(	(	PUNCT
m-806	91	20	�	�	PROPN
m-806	91	21	�	�	PROPN
m-806	91	22	)	)	PUNCT
m-806	91	23	(	(	PUNCT
m-806	91	24	1	1	NUM
m-806	91	25	−	−	PROPN
m-806	91	26	cos	cos	PROPN
m-806	91	27	4	4	NUM
m-806	91	28	�	�	PROPN
m-806	91	29	�	�	PROPN
m-806	91	30	)	)	PUNCT
m-806	91	31	+	+	CCONJ
m-806	91	32	u	u	NOUN
m-806	91	33	�	�	PROPN
m-806	91	34	�	�	PROPN
m-806	91	35	(	(	PUNCT
m-806	91	36	�	�	PROPN
m-806	91	37	�	�	PROPN
m-806	91	38	)	)	PUNCT
m-806	91	39	(	(	PUNCT
m-806	91	40	1	1	NUM
m-806	91	41	−	−	PROPN
m-806	91	42	cos	cos	PROPN
m-806	91	43	6	6	NUM
m-806	91	44	�	�	PROPN
m-806	91	45	�	�	PROPN
m-806	91	46	)	)	PUNCT
m-806	91	47	(	(	PUNCT
m-806	91	48	6.45	6.45	NUM
m-806	91	49	�	�	NOUN
m-806	91	50	)	)	PUNCT
m-806	91	51	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	91	52	ijo	ijo	PROPN
m-806	91	53	journals	journal	NOUN
m-806	91	54	volume	volume	NOUN
m-806	91	55	07	07	NUM
m-806	91	56	|	|	ADV
m-806	91	57	issue	issue	NOUN
m-806	91	58	02	02	NUM
m-806	91	59	|	|	CCONJ
m-806	91	60	february	february	PROPN
m-806	91	61	2024	2024	NUM
m-806	91	62	|	|	ADV
m-806	91	63	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	91	64	11	11	NUM
m-806	91	65	ijo	ijo	PROPN
m-806	91	66	international	international	PROPN
m-806	91	67	journal	journal	PROPN
m-806	91	68	of	of	ADP
m-806	91	69	mathematics	mathematics	PROPN
m-806	91	70	(	(	PUNCT
m-806	91	71	issn	issn	PROPN
m-806	91	72	:	:	PUNCT
m-806	91	73	2992	2992	NUM
m-806	91	74	-	-	SYM
m-806	91	75	4421	4421	NUM
m-806	91	76	)	)	PUNCT
m-806	92	1	i.u	i.u	PROPN
m-806	92	2	.	.	PROPN
m-806	92	3	udo	udo	PROPN
m-806	92	4	-	-	PROPN
m-806	92	5	akpan1	akpan1	ADJ
m-806	92	6	*	*	PUNCT
m-806	92	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	92	8	volume	volume	NOUN
m-806	92	9	07	07	NUM
m-806	92	10	issue	issue	NOUN
m-806	92	11	02	02	NUM
m-806	92	12	||	||	NUM
m-806	92	13	february	february	PROPN
m-806	92	14	,	,	PUNCT
m-806	92	15	2024	2024	NUM
m-806	92	16	||	||	NOUN
m-806	93	1	on	on	ADP
m-806	93	2	a	a	DET
m-806	93	3	-	-	PUNCT
m-806	93	4	two	two	NUM
m-806	93	5	-	-	PUNCT
m-806	93	6	parameter	parameter	NOUN
m-806	93	7	dynamic	dynamic	ADJ
m-806	93	8	buckling	buckling	NOUN
m-806	93	9	of	of	ADP
m-806	93	10	a	a	DET
m-806	93	11	viscously	viscously	ADV
m-806	93	12	damped	damp	VERB
m-806	93	13	but	but	CCONJ
m-806	93	14	clamped	clamp	VERB
m-806	93	15	column	column	NOUN
m-806	93	16	stressed	stress	VERB
m-806	93	17	by	by	ADP
m-806	93	18	a	a	DET
m-806	93	19	step	step	NOUN
m-806	93	20	load	load	NOUN
m-806	93	21	we	we	PRON
m-806	93	22	next	next	VERB
m-806	93	23	substitute	substitute	NOUN
m-806	93	24	on	on	ADP
m-806	93	25	the	the	DET
m-806	93	26	right	right	ADJ
m-806	93	27	hand	hand	NOUN
m-806	93	28	side	side	NOUN
m-806	93	29	of	of	ADP
m-806	93	30	(	(	PUNCT
m-806	93	31	6.13	6.13	NUM
m-806	93	32	)	)	PUNCT
m-806	93	33	and	and	CCONJ
m-806	93	34	get	get	VERB
m-806	93	35	�	�	PROPN
m-806	93	36	�	�	PROPN
m-806	93	37	(	(	PUNCT
m-806	93	38	�	�	PROPN
m-806	93	39	�	�	PROPN
m-806	93	40	)	)	PUNCT
m-806	93	41	=	=	PUNCT
m-806	93	42	3	3	NUM
m-806	93	43	�	�	PROPN
m-806	93	44	4	4	NUM
m-806	93	45	�	�	PROPN
m-806	93	46	�	�	PROPN
m-806	93	47	�	�	PROPN
m-806	93	48	�	�	PROPN
m-806	93	49	�	�	PROPN
m-806	93	50	�	�	PROPN
m-806	93	51	�	�	PROPN
m-806	93	52	+	+	SYM
m-806	93	53	�	�	PROPN
m-806	93	54	�	�	PROPN
m-806	93	55	�	�	PROPN
m-806	93	56	4	4	NUM
m-806	93	57	�	�	PROPN
m-806	93	58	sin	sin	PROPN
m-806	93	59	�	�	PROPN
m-806	93	60	�	�	PROPN
m-806	93	61	̂	̂	VERB
m-806	93	62	+	+	NUM
m-806	93	63	�	�	PROPN
m-806	93	64	�	�	PROPN
m-806	93	65	�	�	PROPN
m-806	93	66	sin2	sin2	PROPN
m-806	93	67	�	�	PROPN
m-806	93	68	�	�	PROPN
m-806	93	69	̂	̂	VERB
m-806	93	70	−	−	PROPN
m-806	93	71	�	�	PROPN
m-806	93	72	�	�	PROPN
m-806	93	73	�	�	PROPN
m-806	93	74	4	4	NUM
m-806	93	75	sin3	sin3	PROPN
m-806	93	76	�	�	PROPN
m-806	93	77	�	�	PROPN
m-806	93	78	̂	̂	PROPN
m-806	93	79	�	�	PROPN
m-806	93	80	�	�	PROPN
m-806	93	81	�	�	PROPN
m-806	93	82	5	5	NUM
m-806	93	83	2	2	NUM
m-806	93	84	−	−	NUM
m-806	93	85	15	15	NUM
m-806	93	86	cos	cos	PROPN
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m-806	93	88	�	�	PROPN
m-806	93	89	�	�	PROPN
m-806	93	90	4	4	NUM
m-806	93	91	�	�	PROPN
m-806	93	92	�	�	PROPN
m-806	93	93	�	�	PROPN
m-806	93	94	+	+	CCONJ
m-806	93	95	3	3	NUM
m-806	93	96	cos	cos	PROPN
m-806	93	97	4	4	NUM
m-806	93	98	�	�	PROPN
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m-806	93	104	�	�	PROPN
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m-806	93	107	�	�	PROPN
m-806	93	108	�	�	PROPN
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m-806	93	111	�	�	PROPN
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m-806	93	119	�	�	PROPN
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m-806	93	121	)	)	PUNCT
m-806	93	122	(	(	PUNCT
m-806	93	123	1	1	NUM
m-806	93	124	−	−	PROPN
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m-806	93	127	�	�	PROPN
m-806	93	128	�	�	PROPN
m-806	93	129	)	)	PUNCT
m-806	93	130	+	+	CCONJ
m-806	93	131	u	u	NOUN
m-806	93	132	�	�	PROPN
m-806	93	133	�	�	PROPN
m-806	93	134	,	,	PUNCT
m-806	93	135	�	�	PROPN
m-806	93	136	�	�	PROPN
m-806	93	137	�	�	PROPN
m-806	93	138	(	(	PUNCT
m-806	93	139	�	�	PROPN
m-806	93	140	�	�	PROPN
m-806	93	141	)	)	PUNCT
m-806	93	142	(	(	PUNCT
m-806	93	143	1	1	NUM
m-806	93	144	−	−	PROPN
m-806	93	145	cos	cos	PROPN
m-806	93	146	4	4	NUM
m-806	93	147	�	�	PROPN
m-806	93	148	�	�	PROPN
m-806	93	149	)	)	PUNCT
m-806	93	150	�	�	PROPN
m-806	93	151	+	+	CCONJ
m-806	93	152	u	u	PROPN
m-806	93	153	�	�	PROPN
m-806	93	154	�	�	PROPN
m-806	93	155	,	,	PUNCT
m-806	93	156	�	�	PROPN
m-806	93	157	�	�	PROPN
m-806	93	158	�	�	PROPN
m-806	93	159	(	(	PUNCT
m-806	93	160	�	�	PROPN
m-806	93	161	�	�	PROPN
m-806	93	162	)	)	PUNCT
m-806	93	163	(	(	PUNCT
m-806	93	164	1	1	NUM
m-806	93	165	−	−	PROPN
m-806	93	166	cos	cos	PROPN
m-806	93	167	6	6	NUM
m-806	93	168	�	�	PROPN
m-806	93	169	�	�	PROPN
m-806	93	170	)	)	PUNCT
m-806	93	171	+	+	CCONJ
m-806	93	172	u	u	NOUN
m-806	93	173	�	�	PROPN
m-806	93	174	,	,	PUNCT
m-806	93	175	�	�	PROPN
m-806	93	176	�	�	PROPN
m-806	93	177	(	(	PUNCT
m-806	93	178	�	�	PROPN
m-806	93	179	�	�	PROPN
m-806	93	180	)	)	PUNCT
m-806	93	181	(	(	PUNCT
m-806	93	182	1	1	NUM
m-806	93	183	−	−	PROPN
m-806	93	184	cos	cos	PROPN
m-806	93	185	2	2	NUM
m-806	93	186	�	�	PROPN
m-806	93	187	�	�	PROPN
m-806	93	188	)	)	PUNCT
m-806	93	189	+	+	CCONJ
m-806	93	190	u	u	NOUN
m-806	93	191	�	�	PROPN
m-806	93	192	�	�	PROPN
m-806	93	193	,	,	PUNCT
m-806	93	194	�	�	PROPN
m-806	93	195	�	�	PROPN
m-806	93	196	(	(	PUNCT
m-806	93	197	�	�	PROPN
m-806	93	198	�	�	PROPN
m-806	93	199	)	)	PUNCT
m-806	93	200	(	(	PUNCT
m-806	93	201	1	1	NUM
m-806	93	202	−	−	PROPN
m-806	93	203	cos	cos	PROPN
m-806	93	204	4	4	NUM
m-806	93	205	�	�	PROPN
m-806	93	206	�	�	PROPN
m-806	93	207	)	)	PUNCT
m-806	93	208	�	�	PROPN
m-806	93	209	+	+	CCONJ
m-806	93	210	u	u	NOUN
m-806	93	211	�	�	PROPN
m-806	93	212	�	�	PROPN
m-806	93	213	,	,	PUNCT
m-806	93	214	�	�	PROPN
m-806	93	215	�	�	PROPN
m-806	93	216	(	(	PUNCT
m-806	93	217	�	�	PROPN
m-806	93	218	�	�	PROPN
m-806	93	219	)	)	PUNCT
m-806	93	220	(	(	PUNCT
m-806	93	221	1	1	NUM
m-806	93	222	−	−	PROPN
m-806	93	223	cos	cos	PROPN
m-806	93	224	6	6	NUM
m-806	93	225	�	�	PROPN
m-806	93	226	�	�	NOUN
m-806	93	227	)	)	PUNCT
m-806	93	228	�	�	PROPN
m-806	93	229	−	−	PROPN
m-806	93	230	�	�	PROPN
m-806	93	231	�	�	PROPN
m-806	93	232	�	�	PROPN
m-806	93	233	�	�	PROPN
m-806	93	234	u	u	NOUN
m-806	93	235	�	�	PROPN
m-806	93	236	,	,	PUNCT
m-806	93	237	�	�	PROPN
m-806	93	238	�	�	PROPN
m-806	93	239	(	(	PUNCT
m-806	93	240	�	�	PROPN
m-806	93	241	�	�	PROPN
m-806	93	242	)	)	PUNCT
m-806	93	243	(	(	PUNCT
m-806	93	244	1	1	NUM
m-806	93	245	−	−	PROPN
m-806	93	246	cos	cos	PROPN
m-806	93	247	2	2	NUM
m-806	93	248	�	�	PROPN
m-806	93	249	�	�	PROPN
m-806	93	250	)	)	PUNCT
m-806	93	251	−2	−2	PROPN
m-806	93	252	�	�	PROPN
m-806	93	253	�	�	PROPN
m-806	93	254	�	�	PROPN
m-806	93	255	u	u	PROPN
m-806	93	256	�	�	PROPN
m-806	93	257	,	,	PUNCT
m-806	93	258	�	�	PROPN
m-806	93	259	�	�	PROPN
m-806	93	260	(	(	PUNCT
m-806	93	261	�	�	PROPN
m-806	93	262	�	�	PROPN
m-806	93	263	)	)	PUNCT
m-806	93	264	(	(	PUNCT
m-806	93	265	1	1	NUM
m-806	93	266	−	−	PROPN
m-806	93	267	cos	cos	PROPN
m-806	93	268	2	2	NUM
m-806	93	269	�	�	PROPN
m-806	93	270	�	�	PROPN
m-806	93	271	)	)	PUNCT
m-806	93	272	(	(	PUNCT
m-806	93	273	6.46	6.46	X
m-806	93	274	)	)	PUNCT
m-806	93	275	let	let	VERB
m-806	93	276	�	�	PROPN
m-806	93	277	(	(	PUNCT
m-806	93	278	�	�	PROPN
m-806	93	279	�	�	PROPN
m-806	93	280	)	)	PUNCT
m-806	93	281	=	=	SYM
m-806	93	282	�	�	PROPN
m-806	93	283	u	u	PRON
m-806	93	284	�	�	PROPN
m-806	93	285	(	(	PUNCT
m-806	93	286	�	�	PROPN
m-806	93	287	�	�	PROPN
m-806	93	288	)	)	PUNCT
m-806	93	289	(	(	PUNCT
m-806	93	290	1	1	NUM
m-806	93	291	−	−	PROPN
m-806	93	292	cos	cos	PROPN
m-806	93	293	2	2	NUM
m-806	93	294	�	�	PROPN
m-806	93	295	�	�	PROPN
m-806	93	296	)	)	PUNCT
m-806	93	297	(	(	PUNCT
m-806	93	298	6.47	6.47	NUM
m-806	93	299	)	)	PUNCT
m-806	93	300	�	�	PROPN
m-806	93	301	�	�	PROPN
m-806	93	302	�	�	PROPN
m-806	93	303	�	�	PROPN
m-806	93	304	on	on	ADP
m-806	93	305	substituting	substitute	VERB
m-806	93	306	(	(	PUNCT
m-806	93	307	6.47	6.47	NUM
m-806	93	308	)	)	PUNCT
m-806	93	309	into	into	ADP
m-806	93	310	(	(	PUNCT
m-806	93	311	6.46	6.46	NUM
m-806	93	312	)	)	PUNCT
m-806	93	313	,	,	PUNCT
m-806	93	314	first	first	ADV
m-806	93	315	multiplying	multiply	VERB
m-806	93	316	through	through	ADP
m-806	93	317	by	by	ADP
m-806	93	318	cos	cos	PROPN
m-806	93	319	2	2	PROPN
m-806	93	320	�	�	PROPN
m-806	93	321	�	�	PROPN
m-806	93	322	and	and	CCONJ
m-806	93	323	integrating	integrate	VERB
m-806	93	324	from	from	ADP
m-806	93	325	0	0	NUM
m-806	93	326	to	to	ADP
m-806	93	327	π	π	PROPN
m-806	93	328	,	,	PUNCT
m-806	93	329	we	we	PRON
m-806	93	330	get	get	VERB
m-806	93	331	,	,	PUNCT
m-806	93	332	for	for	ADP
m-806	93	333	�	�	PROPN
m-806	93	334	=	=	SYM
m-806	93	335	�	�	PROPN
m-806	93	336	u	u	NOUN
m-806	93	337	�	�	PROPN
m-806	93	338	,	,	PUNCT
m-806	93	339	�	�	PROPN
m-806	93	340	�	�	PROPN
m-806	93	341	�	�	PROPN
m-806	93	342	�	�	PROPN
m-806	93	343	(	(	PUNCT
m-806	93	344	�	�	PROPN
m-806	93	345	�	�	PROPN
m-806	93	346	)	)	PUNCT
m-806	93	347	+	+	SYM
m-806	93	348	�	�	PROPN
m-806	93	349	�	�	PROPN
m-806	93	350	u	u	NOUN
m-806	93	351	�	�	PROPN
m-806	93	352	(	(	PUNCT
m-806	93	353	�	�	PROPN
m-806	93	354	�	�	PROPN
m-806	93	355	)	)	PUNCT
m-806	93	356	=	=	SYM
m-806	93	357	45	45	NUM
m-806	93	358	�	�	PROPN
m-806	93	359	4	4	NUM
m-806	93	360	�	�	PROPN
m-806	93	361	�	�	PROPN
m-806	93	362	�	�	PROPN
m-806	93	363	�	�	PROPN
m-806	93	364	�	�	PROPN
m-806	93	365	�	�	PROPN
m-806	93	366	�	�	PROPN
m-806	93	367	+	+	SYM
m-806	93	368	�	�	PROPN
m-806	93	369	�	�	PROPN
m-806	93	370	�	�	PROPN
m-806	93	371	4	4	NUM
m-806	93	372	�	�	PROPN
m-806	93	373	sin	sin	PROPN
m-806	93	374	�	�	PROPN
m-806	93	375	�	�	PROPN
m-806	93	376	̂	̂	VERB
m-806	93	377	+	+	NUM
m-806	93	378	�	�	PROPN
m-806	93	379	�	�	PROPN
m-806	93	380	�	�	PROPN
m-806	93	381	sin2	sin2	PROPN
m-806	93	382	�	�	PROPN
m-806	93	383	�	�	PROPN
m-806	93	384	̂	̂	VERB
m-806	93	385	−	−	PROPN
m-806	93	386	�	�	PROPN
m-806	93	387	�	�	PROPN
m-806	93	388	�	�	PROPN
m-806	93	389	4	4	NUM
m-806	93	390	sin3	sin3	PROPN
m-806	93	391	�	�	PROPN
m-806	93	392	�	�	PROPN
m-806	93	393	̂	̂	PROPN
m-806	93	394	�	�	PROPN
m-806	93	395	�	�	PROPN
m-806	93	396	−	−	PROPN
m-806	93	397	�	�	PROPN
m-806	93	398	�	�	PROPN
m-806	93	399	�	�	PROPN
m-806	93	400	�	�	PROPN
m-806	93	401	u	u	NOUN
m-806	93	402	�	�	PROPN
m-806	93	403	,	,	PUNCT
m-806	93	404	�	�	PROPN
m-806	93	405	�	�	PROPN
m-806	93	406	(	(	PUNCT
m-806	93	407	�	�	PROPN
m-806	93	408	�	�	PROPN
m-806	93	409	)	)	PUNCT
m-806	93	410	−	−	PROPN
m-806	93	411	2	2	NUM
m-806	93	412	�	�	PROPN
m-806	93	413	�	�	PROPN
m-806	93	414	�	�	PROPN
m-806	93	415	u	u	PROPN
m-806	93	416	�	�	PROPN
m-806	93	417	,	,	PUNCT
m-806	93	418	�	�	PROPN
m-806	93	419	�	�	PROPN
m-806	93	420	(	(	PUNCT
m-806	93	421	�	�	PROPN
m-806	93	422	�	�	PROPN
m-806	93	423	)	)	PUNCT
m-806	93	424	−	−	PROPN
m-806	93	425	2	2	NUM
m-806	93	426	�	�	PROPN
m-806	93	427	u	u	NOUN
m-806	93	428	�	�	PROPN
m-806	93	429	�	�	PROPN
m-806	93	430	,	,	PUNCT
m-806	93	431	�	�	PROPN
m-806	93	432	�	�	PROPN
m-806	93	433	�	�	PROPN
m-806	93	434	(	(	PUNCT
m-806	93	435	�	�	PROPN
m-806	93	436	�	�	PROPN
m-806	93	437	)	)	PUNCT
m-806	93	438	+	+	CCONJ
m-806	93	439	u	u	NOUN
m-806	93	440	�	�	PROPN
m-806	93	441	�	�	PROPN
m-806	93	442	,	,	PUNCT
m-806	93	443	�	�	PROPN
m-806	93	444	�	�	PROPN
m-806	93	445	(	(	PUNCT
m-806	93	446	�	�	PROPN
m-806	93	447	�	�	PROPN
m-806	93	448	)	)	PUNCT
m-806	93	449	�	�	PROPN
m-806	93	450	(	(	PUNCT
m-806	93	451	6.48a	6.48a	NUM
m-806	93	452	)	)	PUNCT
m-806	93	453	u	u	NOUN
m-806	93	454	�	�	PROPN
m-806	93	455	(	(	PUNCT
m-806	93	456	�	�	PROPN
m-806	93	457	�	�	PROPN
m-806	93	458	)	)	PUNCT
m-806	93	459	(	(	PUNCT
m-806	93	460	0,0	0,0	NUM
m-806	93	461	)	)	PUNCT
m-806	93	462	=	=	SYM
m-806	93	463	0	0	NUM
m-806	93	464	,	,	PUNCT
m-806	93	465	�	�	PROPN
m-806	93	466	�	�	PROPN
m-806	93	467	,	,	PUNCT
m-806	93	468	�	�	PROPN
m-806	93	469	�	�	PROPN
m-806	93	470	(	(	PUNCT
m-806	93	471	�	�	PROPN
m-806	93	472	�	�	PROPN
m-806	93	473	)	)	PUNCT
m-806	93	474	(	(	PUNCT
m-806	93	475	0	0	NUM
m-806	93	476	,	,	PUNCT
m-806	93	477	0	0	NUM
m-806	93	478	)	)	PUNCT
m-806	94	1	+	+	CCONJ
m-806	94	2	�	�	PROPN
m-806	94	3	�	�	PROPN
m-806	94	4	�	�	PROPN
m-806	94	5	(	(	PUNCT
m-806	94	6	0	0	NUM
m-806	94	7	)	)	PUNCT
m-806	94	8	�	�	PROPN
m-806	94	9	�	�	PROPN
m-806	94	10	,	,	PUNCT
m-806	94	11	�	�	PROPN
m-806	94	12	�	�	PROPN
m-806	94	13	(	(	PUNCT
m-806	94	14	�	�	PROPN
m-806	94	15	�	�	PROPN
m-806	94	16	)	)	PUNCT
m-806	94	17	(	(	PUNCT
m-806	94	18	0	0	NUM
m-806	94	19	,	,	PUNCT
m-806	94	20	0	0	NUM
m-806	94	21	)	)	PUNCT
m-806	94	22	+	+	CCONJ
m-806	94	23	�	�	PROPN
m-806	94	24	�	�	PROPN
m-806	94	25	,	,	PUNCT
m-806	94	26	�	�	PROPN
m-806	94	27	(	(	PUNCT
m-806	94	28	�	�	PROPN
m-806	94	29	�	�	PROPN
m-806	94	30	)	)	PUNCT
m-806	94	31	(	(	PUNCT
m-806	94	32	0	0	NUM
m-806	94	33	,	,	PUNCT
m-806	94	34	0	0	NUM
m-806	94	35	)	)	PUNCT
m-806	94	36	=	=	SYM
m-806	94	37	0	0	NUM
m-806	94	38	(	(	PUNCT
m-806	94	39	6.48b	6.48b	NUM
m-806	94	40	)	)	PUNCT
m-806	94	41	next	next	ADV
m-806	94	42	,	,	PUNCT
m-806	94	43	we	we	PRON
m-806	94	44	multiply	multiply	VERB
m-806	94	45	(	(	PUNCT
m-806	94	46	6.46	6.46	NUM
m-806	94	47	)	)	PUNCT
m-806	94	48	by	by	ADP
m-806	94	49	cos	cos	PROPN
m-806	94	50	4	4	PROPN
m-806	94	51	�	�	PROPN
m-806	94	52	�	�	NOUN
m-806	94	53	,	,	PUNCT
m-806	94	54	integrate	integrate	VERB
m-806	94	55	from	from	ADP
m-806	94	56	0	0	NUM
m-806	94	57	to	to	ADP
m-806	94	58	π	π	PROPN
m-806	94	59	,	,	PUNCT
m-806	94	60	we	we	PRON
m-806	94	61	get	get	VERB
m-806	94	62	,	,	PUNCT
m-806	94	63	for	for	ADP
m-806	94	64	�	�	PROPN
m-806	94	65	=	=	SYM
m-806	94	66	2	2	NUM
m-806	94	67	�	�	PROPN
m-806	94	68	u	u	NOUN
m-806	94	69	�	�	PROPN
m-806	94	70	�	�	PROPN
m-806	94	71	,	,	PUNCT
m-806	94	72	�	�	PROPN
m-806	94	73	�	�	PROPN
m-806	94	74	�	�	PROPN
m-806	94	75	�	�	PROPN
m-806	94	76	(	(	PUNCT
m-806	94	77	�	�	PROPN
m-806	94	78	�	�	PROPN
m-806	94	79	)	)	PUNCT
m-806	95	1	+	+	SYM
m-806	95	2	�	�	PROPN
m-806	95	3	�	�	PROPN
m-806	95	4	�	�	PROPN
m-806	95	5	�	�	PROPN
m-806	95	6	u	u	PROPN
m-806	95	7	�	�	PROPN
m-806	95	8	�	�	PROPN
m-806	95	9	(	(	PUNCT
m-806	95	10	�	�	PROPN
m-806	95	11	�	�	PROPN
m-806	95	12	)	)	PUNCT
m-806	95	13	=	=	SYM
m-806	95	14	−9	−9	NOUN
m-806	95	15	�	�	PROPN
m-806	95	16	�	�	PROPN
m-806	95	17	�	�	PROPN
m-806	95	18	8	8	NUM
m-806	95	19	�	�	PROPN
m-806	95	20	�	�	PROPN
m-806	95	21	�	�	PROPN
m-806	95	22	�	�	PROPN
m-806	95	23	�	�	PROPN
m-806	95	24	+	+	SYM
m-806	95	25	�	�	PROPN
m-806	95	26	�	�	PROPN
m-806	95	27	�	�	PROPN
m-806	95	28	4	4	NUM
m-806	95	29	�	�	PROPN
m-806	95	30	sin	sin	PROPN
m-806	95	31	�	�	PROPN
m-806	95	32	�	�	PROPN
m-806	95	33	̂	̂	VERB
m-806	95	34	+	+	NUM
m-806	95	35	�	�	PROPN
m-806	95	36	�	�	PROPN
m-806	95	37	�	�	PROPN
m-806	95	38	sin2	sin2	PROPN
m-806	95	39	�	�	PROPN
m-806	95	40	�	�	PROPN
m-806	95	41	̂	̂	VERB
m-806	95	42	−	−	PROPN
m-806	95	43	�	�	PROPN
m-806	95	44	�	�	PROPN
m-806	95	45	�	�	PROPN
m-806	95	46	4	4	NUM
m-806	95	47	sin3	sin3	PROPN
m-806	95	48	�	�	PROPN
m-806	95	49	�	�	PROPN
m-806	95	50	̂	̂	PROPN
m-806	95	51	�	�	NOUN
m-806	95	52	�	�	PROPN
m-806	95	53	−	−	PROPN
m-806	95	54	2	2	NUM
m-806	95	55	�	�	PROPN
m-806	95	56	u	u	NOUN
m-806	95	57	�	�	PROPN
m-806	95	58	�	�	PROPN
m-806	95	59	,	,	PUNCT
m-806	95	60	�	�	PROPN
m-806	95	61	�	�	PROPN
m-806	95	62	�	�	PROPN
m-806	95	63	(	(	PUNCT
m-806	95	64	�	�	PROPN
m-806	95	65	�	�	PROPN
m-806	95	66	)	)	PUNCT
m-806	95	67	+	+	CCONJ
m-806	95	68	u	u	NOUN
m-806	95	69	�	�	PROPN
m-806	95	70	�	�	PROPN
m-806	95	71	,	,	PUNCT
m-806	95	72	�	�	PROPN
m-806	95	73	�	�	PROPN
m-806	95	74	(	(	PUNCT
m-806	95	75	�	�	PROPN
m-806	95	76	�	�	PROPN
m-806	95	77	)	)	PUNCT
m-806	95	78	�	�	PROPN
m-806	95	79	(	(	PUNCT
m-806	95	80	6.49a	6.49a	NUM
m-806	95	81	)	)	PUNCT
m-806	95	82	u	u	PROPN
m-806	95	83	�	�	PROPN
m-806	95	84	�	�	PROPN
m-806	95	85	(	(	PUNCT
m-806	95	86	�	�	PROPN
m-806	95	87	�	�	PROPN
m-806	95	88	)	)	PUNCT
m-806	95	89	(	(	PUNCT
m-806	95	90	0,0	0,0	NUM
m-806	95	91	)	)	PUNCT
m-806	95	92	=	=	SYM
m-806	95	93	0	0	NUM
m-806	95	94	,	,	PUNCT
m-806	95	95	�	�	PROPN
m-806	95	96	�	�	PROPN
m-806	95	97	�	�	PROPN
m-806	95	98	,	,	PUNCT
m-806	95	99	�	�	PROPN
m-806	95	100	�	�	PROPN
m-806	95	101	(	(	PUNCT
m-806	95	102	�	�	PROPN
m-806	95	103	�	�	PROPN
m-806	95	104	)	)	PUNCT
m-806	95	105	(	(	PUNCT
m-806	95	106	0	0	NUM
m-806	95	107	,	,	PUNCT
m-806	95	108	0	0	NUM
m-806	95	109	)	)	PUNCT
m-806	95	110	+	+	CCONJ
m-806	95	111	�	�	PROPN
m-806	95	112	�	�	PROPN
m-806	95	113	�	�	PROPN
m-806	95	114	,	,	PUNCT
m-806	95	115	�	�	PROPN
m-806	95	116	(	(	PUNCT
m-806	95	117	�	�	PROPN
m-806	95	118	�	�	PROPN
m-806	95	119	)	)	PUNCT
m-806	95	120	(	(	PUNCT
m-806	95	121	0	0	NUM
m-806	95	122	,	,	PUNCT
m-806	95	123	0	0	NUM
m-806	95	124	)	)	PUNCT
m-806	95	125	=	=	SYM
m-806	95	126	0	0	NUM
m-806	95	127	(	(	PUNCT
m-806	95	128	6.49b	6.49b	NUM
m-806	95	129	)	)	PUNCT
m-806	95	130	similarly	similarly	ADV
m-806	95	131	,	,	PUNCT
m-806	95	132	we	we	PRON
m-806	95	133	multiply	multiply	VERB
m-806	95	134	(	(	PUNCT
m-806	95	135	6.46	6.46	NUM
m-806	95	136	)	)	PUNCT
m-806	95	137	by	by	ADP
m-806	95	138	cos	cos	PROPN
m-806	95	139	6	6	PROPN
m-806	95	140	�	�	PROPN
m-806	95	141	�	�	NOUN
m-806	95	142	,	,	PUNCT
m-806	95	143	integrate	integrate	VERB
m-806	95	144	from	from	ADP
m-806	95	145	0	0	NUM
m-806	95	146	to	to	ADP
m-806	95	147	π	π	PROPN
m-806	95	148	,	,	PUNCT
m-806	95	149	we	we	PRON
m-806	95	150	get	get	VERB
m-806	95	151	,	,	PUNCT
m-806	95	152	for	for	ADP
m-806	95	153	�	�	PROPN
m-806	95	154	=	=	SYM
m-806	95	155	3	3	NUM
m-806	95	156	�	�	PROPN
m-806	95	157	u	u	NOUN
m-806	95	158	�	�	PROPN
m-806	95	159	�	�	PROPN
m-806	95	160	,	,	PUNCT
m-806	95	161	�	�	PROPN
m-806	95	162	�	�	PROPN
m-806	95	163	�	�	PROPN
m-806	95	164	�	�	PROPN
m-806	95	165	(	(	PUNCT
m-806	95	166	�	�	PROPN
m-806	95	167	�	�	PROPN
m-806	95	168	)	)	PUNCT
m-806	96	1	+	+	SYM
m-806	96	2	�	�	PROPN
m-806	96	3	�	�	PROPN
m-806	96	4	�	�	PROPN
m-806	96	5	�	�	PROPN
m-806	96	6	u	u	PROPN
m-806	96	7	�	�	PROPN
m-806	96	8	�	�	PROPN
m-806	96	9	(	(	PUNCT
m-806	96	10	�	�	PROPN
m-806	96	11	�	�	PROPN
m-806	96	12	)	)	PUNCT
m-806	96	13	=	=	SYM
m-806	96	14	3	3	NUM
m-806	96	15	�	�	PROPN
m-806	96	16	�	�	PROPN
m-806	96	17	�	�	PROPN
m-806	96	18	16	16	NUM
m-806	96	19	�	�	PROPN
m-806	96	20	�	�	PROPN
m-806	96	21	�	�	PROPN
m-806	96	22	�	�	PROPN
m-806	96	23	�	�	PROPN
m-806	96	24	+	+	SYM
m-806	96	25	�	�	PROPN
m-806	96	26	�	�	PROPN
m-806	96	27	�	�	PROPN
m-806	96	28	4	4	NUM
m-806	96	29	�	�	PROPN
m-806	96	30	sin	sin	PROPN
m-806	96	31	�	�	PROPN
m-806	96	32	�	�	PROPN
m-806	96	33	̂	̂	VERB
m-806	96	34	+	+	NUM
m-806	96	35	�	�	PROPN
m-806	96	36	�	�	PROPN
m-806	96	37	�	�	PROPN
m-806	96	38	sin2	sin2	PROPN
m-806	96	39	�	�	PROPN
m-806	96	40	�	�	PROPN
m-806	96	41	̂	̂	VERB
m-806	96	42	−	−	PROPN
m-806	96	43	�	�	PROPN
m-806	96	44	�	�	PROPN
m-806	96	45	�	�	PROPN
m-806	96	46	4	4	NUM
m-806	96	47	sin3	sin3	PROPN
m-806	96	48	�	�	PROPN
m-806	96	49	�	�	PROPN
m-806	96	50	̂	̂	PROPN
m-806	96	51	�	�	NOUN
m-806	96	52	�	�	PROPN
m-806	96	53	−	−	PROPN
m-806	96	54	2	2	NUM
m-806	96	55	�	�	PROPN
m-806	96	56	u	u	NOUN
m-806	96	57	�	�	PROPN
m-806	96	58	�	�	PROPN
m-806	96	59	,	,	PUNCT
m-806	96	60	�	�	PROPN
m-806	96	61	�	�	PROPN
m-806	96	62	�	�	PROPN
m-806	96	63	(	(	PUNCT
m-806	96	64	�	�	PROPN
m-806	96	65	�	�	PROPN
m-806	96	66	)	)	PUNCT
m-806	96	67	+	+	CCONJ
m-806	96	68	u	u	NOUN
m-806	96	69	�	�	PROPN
m-806	96	70	�	�	PROPN
m-806	96	71	,	,	PUNCT
m-806	96	72	�	�	PROPN
m-806	96	73	�	�	PROPN
m-806	96	74	(	(	PUNCT
m-806	96	75	�	�	PROPN
m-806	96	76	�	�	PROPN
m-806	96	77	)	)	PUNCT
m-806	96	78	�	�	PROPN
m-806	96	79	(	(	PUNCT
m-806	96	80	6.50a	6.50a	PROPN
m-806	96	81	)	)	PUNCT
m-806	96	82	u	u	PROPN
m-806	96	83	�	�	PROPN
m-806	96	84	�	�	PROPN
m-806	96	85	(	(	PUNCT
m-806	96	86	�	�	PROPN
m-806	96	87	�	�	PROPN
m-806	96	88	)	)	PUNCT
m-806	96	89	(	(	PUNCT
m-806	96	90	0,0	0,0	NUM
m-806	96	91	)	)	PUNCT
m-806	96	92	=	=	SYM
m-806	96	93	0	0	NUM
m-806	96	94	,	,	PUNCT
m-806	96	95	�	�	PROPN
m-806	96	96	�	�	PROPN
m-806	96	97	�	�	PROPN
m-806	96	98	,	,	PUNCT
m-806	96	99	�	�	PROPN
m-806	96	100	�	�	PROPN
m-806	96	101	(	(	PUNCT
m-806	96	102	�	�	PROPN
m-806	96	103	�	�	PROPN
m-806	96	104	)	)	PUNCT
m-806	96	105	(	(	PUNCT
m-806	96	106	0	0	NUM
m-806	96	107	,	,	PUNCT
m-806	96	108	0	0	NUM
m-806	96	109	)	)	PUNCT
m-806	96	110	+	+	CCONJ
m-806	96	111	�	�	PROPN
m-806	96	112	�	�	PROPN
m-806	96	113	�	�	PROPN
m-806	96	114	,	,	PUNCT
m-806	96	115	�	�	PROPN
m-806	96	116	(	(	PUNCT
m-806	96	117	�	�	PROPN
m-806	96	118	�	�	PROPN
m-806	96	119	)	)	PUNCT
m-806	96	120	(	(	PUNCT
m-806	96	121	0	0	NUM
m-806	96	122	,	,	PUNCT
m-806	96	123	0	0	NUM
m-806	96	124	)	)	PUNCT
m-806	96	125	=	=	SYM
m-806	96	126	0	0	PUNCT
m-806	96	127	(	(	PUNCT
m-806	96	128	6.50b	6.50b	NUM
m-806	96	129	)	)	PUNCT
m-806	96	130	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	96	131	ijo	ijo	PROPN
m-806	96	132	journals	journal	NOUN
m-806	96	133	volume	volume	NOUN
m-806	96	134	07	07	NUM
m-806	96	135	|	|	ADV
m-806	96	136	issue	issue	NOUN
m-806	96	137	02	02	NUM
m-806	96	138	|	|	CCONJ
m-806	96	139	february	february	PROPN
m-806	96	140	2024	2024	NUM
m-806	96	141	|	|	ADV
m-806	96	142	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	96	143	12	12	NUM
m-806	96	144	ijo	ijo	PROPN
m-806	96	145	international	international	PROPN
m-806	96	146	journal	journal	PROPN
m-806	96	147	of	of	ADP
m-806	96	148	mathematics	mathematics	PROPN
m-806	96	149	(	(	PUNCT
m-806	96	150	issn	issn	PROPN
m-806	96	151	:	:	PUNCT
m-806	96	152	2992	2992	NUM
m-806	96	153	-	-	SYM
m-806	96	154	4421	4421	NUM
m-806	96	155	)	)	PUNCT
m-806	97	1	i.u	i.u	PROPN
m-806	97	2	.	.	PROPN
m-806	97	3	udo	udo	PROPN
m-806	97	4	-	-	PROPN
m-806	97	5	akpan1	akpan1	ADJ
m-806	97	6	*	*	PUNCT
m-806	97	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	97	8	volume	volume	NOUN
m-806	97	9	07	07	NUM
m-806	97	10	issue	issue	NOUN
m-806	97	11	02	02	NUM
m-806	97	12	||	||	NUM
m-806	97	13	february	february	PROPN
m-806	97	14	,	,	PUNCT
m-806	97	15	2024	2024	NUM
m-806	97	16	||	||	NOUN
m-806	98	1	on	on	ADP
m-806	98	2	a	a	DET
m-806	98	3	-	-	PUNCT
m-806	98	4	two	two	NUM
m-806	98	5	-	-	PUNCT
m-806	98	6	parameter	parameter	NOUN
m-806	98	7	dynamic	dynamic	ADJ
m-806	98	8	buckling	buckling	NOUN
m-806	98	9	of	of	ADP
m-806	98	10	a	a	DET
m-806	98	11	viscously	viscously	ADV
m-806	98	12	damped	damp	VERB
m-806	98	13	but	but	CCONJ
m-806	98	14	clamped	clamp	VERB
m-806	98	15	column	column	NOUN
m-806	98	16	stressed	stress	VERB
m-806	98	17	by	by	ADP
m-806	98	18	a	a	DET
m-806	98	19	step	step	NOUN
m-806	98	20	load	load	NOUN
m-806	98	21	to	to	PART
m-806	98	22	solve	solve	VERB
m-806	98	23	(	(	PUNCT
m-806	98	24	6.48a	6.48a	NUM
m-806	98	25	)	)	PUNCT
m-806	98	26	,	,	PUNCT
m-806	98	27	we	we	PRON
m-806	98	28	substitute	substitute	VERB
m-806	98	29	for	for	ADP
m-806	98	30	terms	term	NOUN
m-806	98	31	there	there	ADV
m-806	98	32	and	and	CCONJ
m-806	98	33	after	after	ADV
m-806	98	34	,	,	PUNCT
m-806	98	35	ensure	ensure	VERB
m-806	98	36	a	a	DET
m-806	98	37	uniformly	uniformly	ADV
m-806	98	38	valid	valid	ADJ
m-806	98	39	solution	solution	NOUN
m-806	98	40	by	by	ADP
m-806	98	41	equating	equate	VERB
m-806	98	42	to	to	ADP
m-806	98	43	zero	zero	NUM
m-806	98	44	the	the	DET
m-806	98	45	coefficients	coefficient	NOUN
m-806	98	46	of	of	ADP
m-806	98	47	cos	cos	PROPN
m-806	98	48	�	�	PROPN
m-806	98	49	�	�	PROPN
m-806	98	50	̂	̂	VERB
m-806	98	51	and	and	CCONJ
m-806	98	52	sin	sin	PROPN
m-806	98	53	�	�	PROPN
m-806	98	54	�	�	PROPN
m-806	98	55	̂.	̂.	PROPN
m-806	98	56	this	this	PRON
m-806	98	57	gives	give	VERB
m-806	98	58	,	,	PUNCT
m-806	98	59	for	for	ADP
m-806	98	60	cos	cos	PROPN
m-806	98	61	�	�	PROPN
m-806	98	62	�	�	PROPN
m-806	98	63	̂	̂	VERB
m-806	98	64	�	�	PROPN
m-806	98	65	�	�	PROPN
m-806	98	66	�	�	PROPN
m-806	98	67	+	+	CCONJ
m-806	98	68	�	�	PROPN
m-806	98	69	�	�	PROPN
m-806	98	70	=	=	SYM
m-806	98	71	0	0	NUM
m-806	98	72	(	(	PUNCT
m-806	98	73	6.51	6.51	NUM
m-806	98	74	�	�	NOUN
m-806	98	75	)	)	PUNCT
m-806	98	76	forsin	forsin	NOUN
m-806	98	77	�	�	PROPN
m-806	98	78	�	�	PROPN
m-806	98	79	̂	̂	NUM
m-806	98	80	:	:	PUNCT
m-806	98	81	�	�	PROPN
m-806	98	82	�	�	PROPN
m-806	98	83	�	�	PROPN
m-806	98	84	+	+	CCONJ
m-806	98	85	�	�	PROPN
m-806	98	86	�	�	PROPN
m-806	98	87	=	=	SYM
m-806	98	88	�	�	PROPN
m-806	98	89	�	�	PROPN
m-806	98	90	2	2	NUM
m-806	98	91	(	(	PUNCT
m-806	98	92	�	�	PROPN
m-806	98	93	�	�	PROPN
m-806	98	94	�	�	PROPN
m-806	98	95	�	�	PROPN
m-806	98	96	+	+	CCONJ
m-806	98	97	2	2	NUM
m-806	98	98	�	�	PROPN
m-806	98	99	�	�	PROPN
m-806	98	100	�	�	PROPN
m-806	98	101	)	)	PUNCT
m-806	98	102	−	−	PROPN
m-806	99	1	45	45	NUM
m-806	99	2	�	�	PROPN
m-806	99	3	32	32	NUM
m-806	99	4	�	�	PROPN
m-806	99	5	(	(	PUNCT
m-806	99	6	�	�	PROPN
m-806	99	7	�	�	PROPN
m-806	99	8	+	+	SYM
m-806	99	9	�	�	PROPN
m-806	99	10	�	�	PROPN
m-806	99	11	�	�	PROPN
m-806	99	12	)	)	PUNCT
m-806	99	13	�	�	PROPN
m-806	99	14	�	�	PROPN
m-806	99	15	(	(	PUNCT
m-806	99	16	6.51	6.51	NUM
m-806	99	17	�	�	NOUN
m-806	99	18	)	)	PUNCT
m-806	99	19	on	on	ADP
m-806	99	20	solving	solve	VERB
m-806	99	21	(	(	PUNCT
m-806	99	22	6.51a	6.51a	NOUN
m-806	99	23	,	,	PUNCT
m-806	99	24	b	b	NOUN
m-806	99	25	)	)	PUNCT
m-806	99	26	,	,	PUNCT
m-806	99	27	we	we	PRON
m-806	99	28	get	get	VERB
m-806	99	29	�	�	NOUN
m-806	99	30	�	�	X
m-806	99	31	=	=	SYM
m-806	99	32	0	0	NUM
m-806	99	33	;	;	PUNCT
m-806	99	34	�	�	PROPN
m-806	99	35	�	�	PROPN
m-806	99	36	=	=	SYM
m-806	99	37	�	�	PROPN
m-806	99	38	�	�	PROPN
m-806	99	39	�	�	PROPN
m-806	99	40	�	�	PROPN
m-806	99	41	�	�	PROPN
m-806	99	42	�	�	PROPN
m-806	99	43	(	(	PUNCT
m-806	99	44	0	0	NUM
m-806	99	45	)	)	PUNCT
m-806	99	46	−	−	PROPN
m-806	99	47	�	�	PROPN
m-806	99	48	�	�	PROPN
m-806	99	49	�	�	PROPN
m-806	99	50	�	�	PROPN
m-806	99	51	�	�	PROPN
m-806	99	52	�	�	PROPN
m-806	99	53	2	2	NUM
m-806	99	54	(	(	PUNCT
m-806	99	55	�	�	PROPN
m-806	99	56	�	�	PROPN
m-806	99	57	�	�	PROPN
m-806	99	58	�	�	PROPN
m-806	99	59	+	+	CCONJ
m-806	99	60	2	2	NUM
m-806	99	61	�	�	PROPN
m-806	99	62	�	�	PROPN
m-806	99	63	�	�	PROPN
m-806	99	64	)	)	PUNCT
m-806	100	1	+	+	CCONJ
m-806	100	2	45	45	NUM
m-806	100	3	�	�	PROPN
m-806	100	4	32	32	NUM
m-806	100	5	�	�	PROPN
m-806	100	6	(	(	PUNCT
m-806	100	7	�	�	PROPN
m-806	100	8	�	�	PROPN
m-806	100	9	+	+	SYM
m-806	100	10	�	�	PROPN
m-806	100	11	�	�	PROPN
m-806	100	12	�	�	PROPN
m-806	100	13	)	)	PUNCT
m-806	100	14	�	�	PROPN
m-806	100	15	�	�	PROPN
m-806	100	16	�	�	PROPN
m-806	100	17	�	�	PROPN
m-806	100	18	�	�	PROPN
m-806	100	19	�	�	PROPN
m-806	100	20	�	�	PROPN
m-806	100	21	�	�	PROPN
m-806	100	22	(	(	PUNCT
m-806	100	23	6.51	6.51	NUM
m-806	100	24	�	�	NOUN
m-806	100	25	)	)	PUNCT
m-806	100	26	�	�	PROPN
m-806	100	27	�	�	PROPN
m-806	100	28	�	�	PROPN
m-806	100	29	(	(	PUNCT
m-806	100	30	0	0	NUM
m-806	100	31	)	)	PUNCT
m-806	100	32	=	=	SYM
m-806	100	33	�	�	PROPN
m-806	100	34	�	�	PROPN
m-806	100	35	�	�	PROPN
m-806	100	36	�	�	PROPN
m-806	100	37	�	�	PROPN
m-806	100	38	�	�	PROPN
m-806	100	39	�	�	PROPN
m-806	100	40	�	�	PROPN
m-806	100	41	�	�	PROPN
m-806	100	42	�	�	PROPN
m-806	100	43	�	�	PROPN
m-806	100	44	�	�	PROPN
m-806	100	45	�	�	PROPN
m-806	100	46	(	(	PUNCT
m-806	100	47	6.52d	6.52d	NUM
m-806	100	48	)	)	PUNCT
m-806	100	49	the	the	DET
m-806	100	50	remaining	remain	VERB
m-806	100	51	equations	equation	NOUN
m-806	100	52	,	,	PUNCT
m-806	100	53	having	having	AUX
m-806	100	54	ensured	ensure	VERB
m-806	100	55	a	a	DET
m-806	100	56	uniformly	uniformly	ADV
m-806	100	57	valid	valid	ADJ
m-806	100	58	solution	solution	NOUN
m-806	100	59	in	in	ADP
m-806	100	60	(	(	PUNCT
m-806	100	61	6.48a	6.48a	NUM
m-806	100	62	)	)	PUNCT
m-806	100	63	are	be	AUX
m-806	100	64	u	u	PRON
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m-806	100	71	(	(	PUNCT
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m-806	100	73	�	�	PROPN
m-806	100	74	)	)	PUNCT
m-806	101	1	+	+	SYM
m-806	101	2	�	�	PROPN
m-806	101	3	�	�	PROPN
m-806	101	4	u	u	NOUN
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m-806	101	6	(	(	PUNCT
m-806	101	7	�	�	PROPN
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m-806	101	9	)	)	PUNCT
m-806	101	10	=	=	SYM
m-806	101	11	�	�	PROPN
m-806	101	12	�	�	PROPN
m-806	101	13	sin2	sin2	PROPN
m-806	101	14	�	�	PROPN
m-806	101	15	�	�	PROPN
m-806	101	16	̂	̂	VERB
m-806	101	17	+	+	NUM
m-806	101	18	�	�	PROPN
m-806	101	19	�	�	PROPN
m-806	101	20	sin3	sin3	PROPN
m-806	101	21	�	�	PROPN
m-806	101	22	�	�	PROPN
m-806	101	23	̂	̂	PUNCT
m-806	101	24	(	(	PUNCT
m-806	101	25	6.52	6.52	NUM
m-806	101	26	�	�	NOUN
m-806	101	27	)	)	PUNCT
m-806	101	28	u	u	NOUN
m-806	101	29	�	�	PROPN
m-806	101	30	(	(	PUNCT
m-806	101	31	�	�	PROPN
m-806	101	32	�	�	PROPN
m-806	101	33	)	)	PUNCT
m-806	101	34	(	(	PUNCT
m-806	101	35	0,0	0,0	NUM
m-806	101	36	)	)	PUNCT
m-806	101	37	=	=	SYM
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m-806	101	42	,	,	PUNCT
m-806	101	43	�	�	PROPN
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m-806	101	45	(	(	PUNCT
m-806	101	46	�	�	PROPN
m-806	101	47	�	�	PROPN
m-806	101	48	)	)	PUNCT
m-806	101	49	(	(	PUNCT
m-806	101	50	0	0	NUM
m-806	101	51	,	,	PUNCT
m-806	101	52	0	0	NUM
m-806	101	53	)	)	PUNCT
m-806	101	54	+	+	CCONJ
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m-806	101	57	�	�	PROPN
m-806	101	58	(	(	PUNCT
m-806	101	59	0	0	NUM
m-806	101	60	)	)	PUNCT
m-806	101	61	�	�	PROPN
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m-806	101	63	,	,	PUNCT
m-806	101	64	�	�	PROPN
m-806	101	65	�	�	PROPN
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m-806	101	67	�	�	PROPN
m-806	101	68	�	�	PROPN
m-806	101	69	)	)	PUNCT
m-806	101	70	(	(	PUNCT
m-806	101	71	0	0	NUM
m-806	101	72	,	,	PUNCT
m-806	101	73	0	0	NUM
m-806	101	74	)	)	PUNCT
m-806	101	75	+	+	CCONJ
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m-806	101	78	,	,	PUNCT
m-806	101	79	�	�	PROPN
m-806	101	80	(	(	PUNCT
m-806	101	81	�	�	PROPN
m-806	101	82	�	�	PROPN
m-806	101	83	)	)	PUNCT
m-806	101	84	(	(	PUNCT
m-806	101	85	0	0	NUM
m-806	101	86	,	,	PUNCT
m-806	101	87	0	0	NUM
m-806	101	88	)	)	PUNCT
m-806	101	89	=	=	SYM
m-806	101	90	0	0	PUNCT
m-806	101	91	(	(	PUNCT
m-806	101	92	6.52b	6.52b	NUM
m-806	101	93	)	)	PUNCT
m-806	102	1	where	where	SCONJ
m-806	102	2	,	,	PUNCT
m-806	102	3	�	�	PROPN
m-806	102	4	�	�	PROPN
m-806	102	5	=	=	SYM
m-806	102	6	�	�	PROPN
m-806	102	7	�	�	PROPN
m-806	102	8	�	�	PROPN
m-806	102	9	�	�	PROPN
m-806	102	10	�	�	PROPN
m-806	102	11	�	�	PROPN
m-806	102	12	�	�	PROPN
m-806	102	13	�	�	PROPN
m-806	102	14	�	�	PROPN
m-806	102	15	�	�	PROPN
m-806	102	16	−	−	PROPN
m-806	102	17	�	�	PROPN
m-806	102	18	�	�	PROPN
m-806	102	19	�	�	PROPN
m-806	102	20	�	�	PROPN
m-806	102	21	�	�	PROPN
m-806	102	22	�	�	PROPN
m-806	102	23	{	{	PUNCT
m-806	102	24	(	(	PUNCT
m-806	102	25	�	�	PROPN
m-806	102	26	�	�	PROPN
m-806	102	27	�	�	PROPN
m-806	102	28	)	)	PUNCT
m-806	102	29	�	�	PROPN
m-806	102	30	+	+	CCONJ
m-806	102	31	(	(	PUNCT
m-806	102	32	�	�	PROPN
m-806	102	33	�	�	PROPN
m-806	102	34	�	�	PROPN
m-806	102	35	)	)	PUNCT
m-806	102	36	}	}	PUNCT
m-806	102	37	(	(	PUNCT
m-806	102	38	6.52c	6.52c	NUM
m-806	102	39	)	)	PUNCT
m-806	102	40	�	�	PROPN
m-806	102	41	�	�	PROPN
m-806	102	42	=	=	SYM
m-806	102	43	−45	−45	PROPN
m-806	102	44	�	�	PROPN
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m-806	102	46	�	�	PROPN
m-806	102	47	�	�	PROPN
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m-806	102	49	�	�	PROPN
m-806	102	50	�	�	PROPN
m-806	102	51	64	64	NUM
m-806	102	52	−	−	NUM
m-806	102	53	15	15	NUM
m-806	102	54	�	�	PROPN
m-806	102	55	32	32	NUM
m-806	102	56	�	�	PROPN
m-806	102	57	{	{	PUNCT
m-806	102	58	(	(	PUNCT
m-806	102	59	�	�	PROPN
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m-806	102	61	�	�	PROPN
m-806	102	62	)	)	PUNCT
m-806	102	63	�	�	PROPN
m-806	102	64	+	+	CCONJ
m-806	102	65	(	(	PUNCT
m-806	102	66	�	�	PROPN
m-806	102	67	�	�	PROPN
m-806	102	68	�	�	PROPN
m-806	102	69	)	)	PUNCT
m-806	102	70	}	}	PUNCT
m-806	102	71	(	(	PUNCT
m-806	102	72	6.52	6.52	NUM
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m-806	102	74	)	)	PUNCT
m-806	102	75	(	(	PUNCT
m-806	102	76	0	0	NUM
m-806	102	77	)	)	PUNCT
m-806	102	78	=	=	NOUN
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m-806	102	86	�	�	PROPN
m-806	102	87	�	�	PROPN
m-806	102	88	(	(	PUNCT
m-806	102	89	0	0	NUM
m-806	102	90	)	)	PUNCT
m-806	102	91	=	=	SYM
m-806	102	92	−225	−225	PROPN
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m-806	102	95	�	�	PROPN
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m-806	102	97	�	�	PROPN
m-806	102	98	(	(	PUNCT
m-806	102	99	6.52	6.52	NUM
m-806	102	100	�	�	NOUN
m-806	102	101	)	)	PUNCT
m-806	102	102	we	we	PRON
m-806	102	103	note	note	VERB
m-806	102	104	the	the	DET
m-806	102	105	following	follow	VERB
m-806	102	106	r	r	PROPN
m-806	102	107	�	�	PROPN
m-806	102	108	�	�	PROPN
m-806	102	109	(	(	PUNCT
m-806	102	110	0	0	NUM
m-806	102	111	)	)	PUNCT
m-806	102	112	=	=	SYM
m-806	102	113	−345	−345	PROPN
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m-806	102	115	�	�	PROPN
m-806	102	116	�	�	PROPN
m-806	102	117	128	128	NUM
m-806	102	118	�	�	PROPN
m-806	102	119	,	,	PUNCT
m-806	102	120	r	r	PROPN
m-806	102	121	�	�	PROPN
m-806	102	122	�	�	PROPN
m-806	102	123	(	(	PUNCT
m-806	102	124	0	0	NUM
m-806	102	125	)	)	PUNCT
m-806	102	126	=	=	SYM
m-806	102	127	465	465	NUM
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m-806	102	129	�	�	NOUN
m-806	102	130	�	�	PROPN
m-806	102	131	32	32	NUM
m-806	102	132	�	�	PROPN
m-806	102	133	,	,	PUNCT
m-806	102	134	r	r	PROPN
m-806	102	135	�	�	PROPN
m-806	102	136	�	�	PROPN
m-806	102	137	(	(	PUNCT
m-806	102	138	0	0	NUM
m-806	102	139	)	)	PUNCT
m-806	102	140	=	=	SYM
m-806	102	141	−45	−45	ADP
m-806	102	142	�	�	PROPN
m-806	102	143	�	�	PROPN
m-806	102	144	�	�	PROPN
m-806	102	145	128	128	NUM
m-806	102	146	�	�	PROPN
m-806	102	147	(	(	PUNCT
m-806	102	148	6.52	6.52	NUM
m-806	102	149	�	�	NOUN
m-806	102	150	)	)	PUNCT
m-806	102	151	on	on	ADP
m-806	102	152	solving	solve	VERB
m-806	102	153	(	(	PUNCT
m-806	102	154	6.52a	6.52a	NUM
m-806	102	155	,	,	PUNCT
m-806	102	156	b	b	NOUN
m-806	102	157	)	)	PUNCT
m-806	102	158	,	,	PUNCT
m-806	102	159	we	we	PRON
m-806	102	160	get	get	VERB
m-806	102	161	u	u	NOUN
m-806	102	162	�	�	PROPN
m-806	102	163	(	(	PUNCT
m-806	102	164	�	�	PROPN
m-806	102	165	�	�	PROPN
m-806	102	166	)	)	PUNCT
m-806	102	167	=	=	SYM
m-806	102	168	�	�	PROPN
m-806	102	169	�	�	PROPN
m-806	102	170	cos	cos	PROPN
m-806	102	171	�	�	PROPN
m-806	102	172	�	�	PROPN
m-806	102	173	̂	̂	VERB
m-806	102	174	+	+	NUM
m-806	102	175	�	�	PROPN
m-806	102	176	�	�	PROPN
m-806	102	177	sin	sin	PROPN
m-806	102	178	�	�	PROPN
m-806	102	179	�	�	PROPN
m-806	102	180	̂	̂	VERB
m-806	102	181	−	−	PROPN
m-806	102	182	�	�	PROPN
m-806	102	183	�	�	PROPN
m-806	102	184	sin2	sin2	PROPN
m-806	102	185	�	�	PROPN
m-806	102	186	�	�	PROPN
m-806	102	187	̂	̂	VERB
m-806	102	188	3	3	NUM
m-806	102	189	�	�	PROPN
m-806	102	190	�	�	PROPN
m-806	102	191	−	−	PROPN
m-806	102	192	�	�	PROPN
m-806	102	193	�	�	PROPN
m-806	102	194	sin3	sin3	PROPN
m-806	102	195	�	�	PROPN
m-806	102	196	�	�	PROPN
m-806	102	197	̂	̂	VERB
m-806	102	198	8	8	NUM
m-806	102	199	�	�	PROPN
m-806	102	200	�	�	PROPN
m-806	102	201	(	(	PUNCT
m-806	102	202	6.53	6.53	NUM
m-806	102	203	�	�	NOUN
m-806	102	204	)	)	PUNCT
m-806	103	1	where	where	SCONJ
m-806	103	2	,	,	PUNCT
m-806	103	3	�	�	PROPN
m-806	103	4	�	�	PROPN
m-806	103	5	(	(	PUNCT
m-806	103	6	0	0	NUM
m-806	103	7	)	)	PUNCT
m-806	103	8	=	=	SYM
m-806	103	9	0	0	NUM
m-806	103	10	(	(	PUNCT
m-806	103	11	6.53	6.53	NUM
m-806	103	12	�	�	NOUN
m-806	103	13	)	)	PUNCT
m-806	103	14	�	�	PROPN
m-806	103	15	�	�	PROPN
m-806	103	16	�	�	PROPN
m-806	103	17	(	(	PUNCT
m-806	103	18	0	0	NUM
m-806	103	19	)	)	PUNCT
m-806	103	20	−	−	PROPN
m-806	103	21	2	2	NUM
m-806	103	22	�	�	PROPN
m-806	103	23	�	�	PROPN
m-806	103	24	(0	(0	NOUN
m-806	103	25	)	)	PUNCT
m-806	103	26	3	3	NUM
m-806	103	27	�	�	NOUN
m-806	103	28	−	−	NUM
m-806	103	29	3	3	NUM
m-806	103	30	�	�	PROPN
m-806	103	31	�	�	PROPN
m-806	103	32	(0	(0	NOUN
m-806	103	33	)	)	PUNCT
m-806	103	34	8	8	NUM
m-806	103	35	�	�	PROPN
m-806	103	36	+	+	SYM
m-806	103	37	�	�	PROPN
m-806	103	38	�	�	PROPN
m-806	103	39	(	(	PUNCT
m-806	103	40	0)	0)	PROPN
m-806	103	41	�	�	PROPN
m-806	103	42	�	�	PROPN
m-806	103	43	�	�	PROPN
m-806	103	44	(0	(0	X
m-806	103	45	)	)	PUNCT
m-806	103	46	+	+	CCONJ
m-806	103	47	15	15	NUM
m-806	103	48	�	�	PROPN
m-806	103	49	4	4	NUM
m-806	103	50	�	�	PROPN
m-806	103	51	�	�	PROPN
m-806	103	52	�	�	PROPN
m-806	103	53	�	�	PROPN
m-806	103	54	�	�	PROPN
m-806	103	55	�	�	PROPN
m-806	103	56	−	−	PROPN
m-806	103	57	�	�	PROPN
m-806	103	58	�	�	PROPN
m-806	103	59	�	�	PROPN
m-806	103	60	�	�	PROPN
m-806	103	61	�	�	PROPN
m-806	103	62	�	�	PROPN
m-806	103	63	�	�	PROPN
m-806	103	64	�	�	PROPN
m-806	103	65	−	−	PROPN
m-806	103	66	3	3	NUM
m-806	103	67	�	�	PROPN
m-806	103	68	�	�	PROPN
m-806	103	69	�	�	PROPN
m-806	103	70	�	�	PROPN
m-806	103	71	�	�	PROPN
m-806	103	72	�	�	PROPN
m-806	103	73	�	�	PROPN
m-806	103	74	�	�	PROPN
m-806	103	75	�	�	PROPN
m-806	103	76	│	│	SYM
m-806	103	77	�	�	PROPN
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m-806	103	79	�	�	PROPN
m-806	103	80	=	=	SYM
m-806	103	81	0	0	PROPN
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m-806	103	83	yields	yield	NOUN
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m-806	103	85	�	�	PROPN
m-806	103	86	(	(	PUNCT
m-806	103	87	0	0	NUM
m-806	103	88	)	)	PUNCT
m-806	103	89	=	=	SYM
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m-806	103	92	�	�	PROPN
m-806	103	93	512	512	NUM
m-806	103	94	�	�	PROPN
m-806	103	95	�	�	PROPN
m-806	103	96	(	(	PUNCT
m-806	103	97	6.53	6.53	NUM
m-806	103	98	�	�	NOUN
m-806	103	99	)	)	PUNCT
m-806	103	100	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	103	101	ijo	ijo	PROPN
m-806	103	102	journals	journal	NOUN
m-806	103	103	volume	volume	NOUN
m-806	103	104	07	07	NUM
m-806	103	105	|	|	ADV
m-806	103	106	issue	issue	NOUN
m-806	103	107	02	02	NUM
m-806	103	108	|	|	CCONJ
m-806	103	109	february	february	PROPN
m-806	103	110	2024	2024	NUM
m-806	104	1	|	|	ADV
m-806	104	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-806	104	3	13	13	NUM
m-806	104	4	ijo	ijo	PROPN
m-806	104	5	international	international	PROPN
m-806	104	6	journal	journal	PROPN
m-806	104	7	of	of	ADP
m-806	104	8	mathematics	mathematics	PROPN
m-806	104	9	(	(	PUNCT
m-806	104	10	issn	issn	PROPN
m-806	104	11	:	:	PUNCT
m-806	104	12	2992	2992	NUM
m-806	104	13	-	-	SYM
m-806	104	14	4421	4421	NUM
m-806	104	15	)	)	PUNCT
m-806	104	16	i.u	i.u	PROPN
m-806	104	17	.	.	PROPN
m-806	104	18	udo	udo	PROPN
m-806	104	19	-	-	PROPN
m-806	104	20	akpan1	akpan1	ADJ
m-806	104	21	*	*	PUNCT
m-806	104	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	104	23	volume	volume	NOUN
m-806	104	24	07	07	NUM
m-806	104	25	issue	issue	NOUN
m-806	104	26	02	02	NUM
m-806	104	27	||	||	NUM
m-806	104	28	february	february	PROPN
m-806	104	29	,	,	PUNCT
m-806	104	30	2024	2024	NUM
m-806	104	31	||	||	NOUN
m-806	104	32	on	on	ADP
m-806	104	33	a	a	DET
m-806	104	34	-	-	PUNCT
m-806	104	35	two	two	NUM
m-806	104	36	-	-	PUNCT
m-806	104	37	parameter	parameter	NOUN
m-806	104	38	dynamic	dynamic	ADJ
m-806	104	39	buckling	buckling	NOUN
m-806	104	40	of	of	ADP
m-806	104	41	a	a	DET
m-806	104	42	viscously	viscously	ADV
m-806	104	43	damped	damp	VERB
m-806	104	44	but	but	CCONJ
m-806	104	45	clamped	clamp	VERB
m-806	104	46	column	column	NOUN
m-806	104	47	stressed	stress	VERB
m-806	104	48	by	by	ADP
m-806	104	49	a	a	DET
m-806	104	50	step	step	NOUN
m-806	104	51	load	load	NOUN
m-806	104	52	to	to	PART
m-806	104	53	ensure	ensure	VERB
m-806	104	54	a	a	DET
m-806	104	55	uniformly	uniformly	ADV
m-806	104	56	valid	valid	ADJ
m-806	104	57	solution	solution	NOUN
m-806	104	58	in	in	ADP
m-806	104	59	terms	term	NOUN
m-806	104	60	of	of	ADP
m-806	104	61	�	�	PROPN
m-806	104	62	̂	̂	VERB
m-806	104	63	in	in	ADP
m-806	104	64	(	(	PUNCT
m-806	104	65	6.49a	6.49a	NUM
m-806	104	66	)	)	PUNCT
m-806	104	67	,	,	PUNCT
m-806	104	68	we	we	PRON
m-806	104	69	equate	equate	VERB
m-806	104	70	to	to	ADP
m-806	104	71	zero	zero	NUM
m-806	104	72	the	the	DET
m-806	104	73	coefficients	coefficient	NOUN
m-806	104	74	of	of	ADP
m-806	104	75	cos2	cos2	PROPN
m-806	104	76	�	�	PROPN
m-806	104	77	�	�	PROPN
m-806	104	78	�	�	PROPN
m-806	104	79	�	�	PROPN
m-806	104	80	̂and	̂and	PROPN
m-806	104	81	sin2	sin2	PROPN
m-806	104	82	�	�	PROPN
m-806	104	83	�	�	PROPN
m-806	104	84	�	�	PROPN
m-806	104	85	�	�	PROPN
m-806	104	86	̂	̂	VERB
m-806	104	87	and	and	CCONJ
m-806	104	88	respectively	respectively	ADV
m-806	104	89	get	get	VERB
m-806	104	90	�	�	PROPN
m-806	104	91	�	�	PROPN
m-806	104	92	�	�	PROPN
m-806	104	93	+	+	CCONJ
m-806	104	94	�	�	PROPN
m-806	104	95	�	�	PROPN
m-806	104	96	=	=	SYM
m-806	104	97	0	0	NUM
m-806	104	98	(	(	PUNCT
m-806	104	99	6.53	6.53	NUM
m-806	104	100	�	�	NOUN
m-806	104	101	)	)	PUNCT
m-806	104	102	and	and	CCONJ
m-806	104	103	�	�	PROPN
m-806	104	104	�	�	PROPN
m-806	104	105	�	�	PROPN
m-806	104	106	+	+	CCONJ
m-806	104	107	�	�	PROPN
m-806	104	108	�	�	PROPN
m-806	104	109	=	=	SYM
m-806	104	110	�	�	PROPN
m-806	104	111	�	�	PROPN
m-806	104	112	�	�	PROPN
m-806	104	113	�	�	PROPN
m-806	104	114	�	�	PROPN
m-806	104	115	�	�	PROPN
m-806	104	116	�	�	PROPN
m-806	104	117	�	�	PROPN
m-806	104	118	�	�	PROPN
m-806	104	119	�	�	PROPN
m-806	104	120	�	�	PROPN
m-806	104	121	�	�	PROPN
m-806	104	122	�	�	PROPN
m-806	104	123	+	+	SYM
m-806	104	124	�	�	PROPN
m-806	104	125	�	�	PROPN
m-806	104	126	�	�	PROPN
m-806	104	127	�	�	PROPN
m-806	104	128	�	�	PROPN
m-806	104	129	+	+	CCONJ
m-806	104	130	�	�	PROPN
m-806	104	131	�	�	PROPN
m-806	104	132	�	�	PROPN
m-806	104	133	�	�	PROPN
m-806	104	134	�	�	PROPN
m-806	104	135	�	�	PROPN
m-806	104	136	�	�	PROPN
m-806	104	137	�	�	PROPN
m-806	104	138	�	�	PROPN
m-806	104	139	�	�	PROPN
m-806	104	140	�	�	PROPN
m-806	104	141	�	�	PROPN
m-806	104	142	�	�	PROPN
m-806	104	143	�	�	PROPN
m-806	104	144	�	�	PROPN
m-806	104	145	�	�	PROPN
m-806	104	146	�	�	PROPN
m-806	104	147	�	�	PROPN
m-806	104	148	(	(	PUNCT
m-806	104	149	6.53e	6.53e	PROPN
m-806	104	150	)	)	PUNCT
m-806	104	151	on	on	ADP
m-806	104	152	solving	solve	VERB
m-806	104	153	(	(	PUNCT
m-806	104	154	6.53d	6.53d	NUM
m-806	104	155	,	,	PUNCT
m-806	104	156	e	e	NOUN
m-806	104	157	)	)	PUNCT
m-806	104	158	,	,	PUNCT
m-806	104	159	we	we	PRON
m-806	104	160	get	get	VERB
m-806	104	161	�	�	NOUN
m-806	104	162	�	�	PROPN
m-806	104	163	=	=	SYM
m-806	104	164	0	0	NUM
m-806	104	165	,	,	PUNCT
m-806	104	166	�	�	PROPN
m-806	104	167	�	�	PROPN
m-806	104	168	=	=	SYM
m-806	104	169	�	�	PROPN
m-806	104	170	�	�	PROPN
m-806	104	171	�	�	PROPN
m-806	104	172	�	�	PROPN
m-806	104	173	�	�	PROPN
m-806	104	174	�	�	PROPN
m-806	104	175	(	(	PUNCT
m-806	104	176	0	0	NUM
m-806	104	177	)	)	PUNCT
m-806	105	1	+	+	CCONJ
m-806	105	2	∫	∫	PROPN
m-806	105	3	�	�	PROPN
m-806	105	4	�	�	PROPN
m-806	105	5	�	�	PROPN
m-806	105	6	�	�	PROPN
m-806	105	7	�	�	PROPN
m-806	105	8	�	�	PROPN
m-806	105	9	�	�	PROPN
m-806	105	10	�	�	PROPN
m-806	105	11	�	�	PROPN
m-806	105	12	(	(	PUNCT
m-806	105	13	6.53f	6.53f	PROPN
m-806	105	14	)	)	PUNCT
m-806	105	15	where	where	SCONJ
m-806	105	16	,	,	PUNCT
m-806	105	17	�	�	PROPN
m-806	105	18	�	�	PROPN
m-806	105	19	=	=	SYM
m-806	105	20	�	�	PROPN
m-806	105	21	�	�	PROPN
m-806	105	22	�	�	PROPN
m-806	105	23	�	�	PROPN
m-806	105	24	�	�	PROPN
m-806	105	25	�	�	PROPN
m-806	105	26	�	�	PROPN
m-806	105	27	�	�	PROPN
m-806	105	28	�	�	PROPN
m-806	105	29	�	�	PROPN
m-806	105	30	�	�	PROPN
m-806	105	31	�	�	PROPN
m-806	105	32	�	�	PROPN
m-806	105	33	+	+	SYM
m-806	105	34	�	�	PROPN
m-806	105	35	�	�	PROPN
m-806	105	36	�	�	PROPN
m-806	105	37	�	�	PROPN
m-806	105	38	�	�	PROPN
m-806	105	39	+	+	CCONJ
m-806	105	40	�	�	PROPN
m-806	105	41	�	�	PROPN
m-806	105	42	�	�	PROPN
m-806	105	43	�	�	PROPN
m-806	105	44	�	�	PROPN
m-806	105	45	�	�	PROPN
m-806	105	46	�	�	PROPN
m-806	105	47	�	�	PROPN
m-806	105	48	�	�	PROPN
m-806	105	49	�	�	PROPN
m-806	105	50	�	�	PROPN
m-806	105	51	�	�	PROPN
m-806	105	52	�	�	PROPN
m-806	105	53	�	�	PROPN
m-806	105	54	�	�	PROPN
m-806	105	55	�	�	PROPN
m-806	105	56	�	�	PROPN
m-806	105	57	�	�	PROPN
m-806	105	58	(	(	PUNCT
m-806	105	59	6.53	6.53	NUM
m-806	105	60	g	g	NOUN
m-806	105	61	)	)	PUNCT
m-806	105	62	from	from	ADP
m-806	105	63	(	(	PUNCT
m-806	105	64	6.53e	6.53e	PROPN
m-806	105	65	)	)	PUNCT
m-806	105	66	,	,	PUNCT
m-806	105	67	we	we	PRON
m-806	105	68	get	get	VERB
m-806	105	69	�	�	PROPN
m-806	105	70	�	�	PROPN
m-806	105	71	�	�	PROPN
m-806	105	72	(	(	PUNCT
m-806	105	73	0	0	NUM
m-806	105	74	)	)	PUNCT
m-806	105	75	=	=	SYM
m-806	105	76	�	�	PROPN
m-806	105	77	�	�	PROPN
m-806	105	78	�	�	PROPN
m-806	105	79	�	�	PROPN
m-806	105	80	�	�	PROPN
m-806	105	81	,	,	PUNCT
m-806	105	82	�	�	PROPN
m-806	105	83	�	�	PROPN
m-806	105	84	=	=	SYM
m-806	105	85	�	�	PROPN
m-806	105	86	�	�	PROPN
m-806	105	87	�	�	PROPN
m-806	105	88	�	�	PROPN
m-806	105	89	�	�	PROPN
m-806	105	90	�	�	PROPN
m-806	105	91	�	�	PROPN
m-806	105	92	�	�	PROPN
m-806	105	93	�	�	PROPN
m-806	105	94	�	�	PROPN
m-806	105	95	�	�	PROPN
m-806	105	96	+	+	SYM
m-806	105	97	�	�	PROPN
m-806	105	98	�	�	PROPN
m-806	105	99	�	�	PROPN
m-806	105	100	�	�	PROPN
m-806	105	101	�	�	PROPN
m-806	105	102	�	�	PROPN
m-806	105	103	�	�	PROPN
m-806	105	104	�	�	PROPN
m-806	105	105	�	�	PROPN
m-806	105	106	�	�	PROPN
m-806	105	107	�	�	PROPN
m-806	105	108	�	�	PROPN
m-806	105	109	�	�	PROPN
m-806	105	110	−	−	PROPN
m-806	105	111	�	�	PROPN
m-806	105	112	�	�	PROPN
m-806	105	113	�	�	PROPN
m-806	105	114	�	�	PROPN
m-806	105	115	(	(	PUNCT
m-806	105	116	6.53h	6.53h	NUM
m-806	105	117	)	)	PUNCT
m-806	105	118	the	the	DET
m-806	105	119	remaining	remain	VERB
m-806	105	120	equation	equation	NOUN
m-806	105	121	in	in	ADP
m-806	105	122	(	(	PUNCT
m-806	105	123	6.49a	6.49a	NUM
m-806	105	124	)	)	PUNCT
m-806	105	125	is	be	AUX
m-806	105	126	now	now	ADV
m-806	105	127	written	write	VERB
m-806	105	128	as	as	ADP
m-806	105	129	u	u	PROPN
m-806	105	130	�	�	PROPN
m-806	105	131	�	�	PROPN
m-806	105	132	,	,	PUNCT
m-806	105	133	�	�	PROPN
m-806	105	134	�	�	PROPN
m-806	105	135	�	�	PROPN
m-806	105	136	�	�	PROPN
m-806	105	137	(	(	PUNCT
m-806	105	138	�	�	PROPN
m-806	105	139	�	�	PROPN
m-806	105	140	)	)	PUNCT
m-806	105	141	+	+	SYM
m-806	105	142	�	�	PROPN
m-806	105	143	�	�	PROPN
m-806	105	144	�	�	PROPN
m-806	105	145	�	�	PROPN
m-806	105	146	u	u	PROPN
m-806	105	147	�	�	PROPN
m-806	105	148	�	�	PROPN
m-806	105	149	(	(	PUNCT
m-806	105	150	�	�	PROPN
m-806	105	151	�	�	PROPN
m-806	105	152	)	)	PUNCT
m-806	105	153	=	=	SYM
m-806	105	154	�	�	PROPN
m-806	105	155	�	�	PROPN
m-806	105	156	sin	sin	PROPN
m-806	105	157	�	�	PROPN
m-806	105	158	�	�	PROPN
m-806	105	159	̂	̂	VERB
m-806	105	160	+	+	NUM
m-806	105	161	�	�	PROPN
m-806	105	162	�	�	PROPN
m-806	105	163	sin2	sin2	PROPN
m-806	105	164	�	�	PROPN
m-806	105	165	�	�	PROPN
m-806	105	166	̂	̂	VERB
m-806	105	167	+	+	NUM
m-806	105	168	�	�	PROPN
m-806	105	169	�	�	PROPN
m-806	105	170	sin3	sin3	PROPN
m-806	105	171	�	�	PROPN
m-806	105	172	�	�	PROPN
m-806	105	173	̂	̂	PUNCT
m-806	105	174	(	(	PUNCT
m-806	105	175	6.54a	6.54a	NUM
m-806	105	176	)	)	PUNCT
m-806	105	177	u	u	NOUN
m-806	105	178	�	�	PROPN
m-806	105	179	�	�	PROPN
m-806	105	180	(	(	PUNCT
m-806	105	181	�	�	PROPN
m-806	105	182	�	�	PROPN
m-806	105	183	)	)	PUNCT
m-806	105	184	(	(	PUNCT
m-806	105	185	0,0	0,0	NUM
m-806	105	186	)	)	PUNCT
m-806	105	187	=	=	SYM
m-806	105	188	0	0	NUM
m-806	105	189	,	,	PUNCT
m-806	105	190	�	�	PROPN
m-806	105	191	�	�	PROPN
m-806	105	192	�	�	PROPN
m-806	105	193	,	,	PUNCT
m-806	105	194	�	�	PROPN
m-806	105	195	�	�	PROPN
m-806	105	196	(	(	PUNCT
m-806	105	197	�	�	PROPN
m-806	105	198	�	�	PROPN
m-806	105	199	)	)	PUNCT
m-806	105	200	(	(	PUNCT
m-806	105	201	0	0	NUM
m-806	105	202	,	,	PUNCT
m-806	105	203	0	0	NUM
m-806	105	204	)	)	PUNCT
m-806	105	205	+	+	CCONJ
m-806	105	206	�	�	PROPN
m-806	105	207	�	�	PROPN
m-806	105	208	�	�	PROPN
m-806	105	209	,	,	PUNCT
m-806	105	210	�	�	PROPN
m-806	105	211	(	(	PUNCT
m-806	105	212	�	�	PROPN
m-806	105	213	�	�	PROPN
m-806	105	214	)	)	PUNCT
m-806	105	215	(	(	PUNCT
m-806	105	216	0	0	NUM
m-806	105	217	,	,	PUNCT
m-806	105	218	0	0	NUM
m-806	105	219	)	)	PUNCT
m-806	105	220	=	=	SYM
m-806	105	221	0	0	PUNCT
m-806	106	1	(	(	PUNCT
m-806	106	2	6.54b	6.54b	NOUN
m-806	106	3	)	)	PUNCT
m-806	106	4	where	where	SCONJ
m-806	106	5	,	,	PUNCT
m-806	106	6	�	�	PROPN
m-806	106	7	�	�	PROPN
m-806	106	8	=	=	SYM
m-806	106	9	�	�	PROPN
m-806	106	10	�	�	PROPN
m-806	106	11	�	�	PROPN
m-806	106	12	�	�	PROPN
m-806	106	13	�	�	PROPN
m-806	106	14	�	�	PROPN
m-806	106	15	�	�	PROPN
m-806	106	16	�	�	PROPN
m-806	106	17	�	�	PROPN
m-806	106	18	+	+	SYM
m-806	106	19	�	�	PROPN
m-806	106	20	�	�	PROPN
m-806	106	21	�	�	PROPN
m-806	106	22	�	�	PROPN
m-806	106	23	�	�	PROPN
m-806	106	24	+	+	CCONJ
m-806	106	25	�	�	PROPN
m-806	106	26	�	�	PROPN
m-806	106	27	�	�	PROPN
m-806	106	28	�	�	PROPN
m-806	106	29	�	�	PROPN
m-806	106	30	�	�	PROPN
m-806	106	31	�	�	PROPN
m-806	106	32	�	�	PROPN
m-806	106	33	�	�	PROPN
m-806	106	34	�	�	PROPN
m-806	106	35	�	�	PROPN
m-806	106	36	�	�	PROPN
m-806	106	37	�	�	PROPN
m-806	106	38	�	�	PROPN
m-806	106	39	�	�	PROPN
m-806	106	40	�	�	PROPN
m-806	106	41	�	�	PROPN
m-806	106	42	�	�	PROPN
m-806	106	43	(	(	PUNCT
m-806	106	44	6.54c	6.54c	PROPN
m-806	106	45	)	)	PUNCT
m-806	106	46	�	�	PROPN
m-806	106	47	�	�	PROPN
m-806	106	48	=	=	SYM
m-806	106	49	�	�	PROPN
m-806	106	50	�	�	PROPN
m-806	106	51	�	�	PROPN
m-806	106	52	�	�	PROPN
m-806	106	53	�	�	PROPN
m-806	106	54	�	�	PROPN
m-806	106	55	�	�	PROPN
m-806	106	56	�	�	PROPN
m-806	106	57	�	�	PROPN
m-806	106	58	−	−	PROPN
m-806	106	59	�	�	PROPN
m-806	106	60	�	�	PROPN
m-806	106	61	�	�	PROPN
m-806	106	62	�	�	PROPN
m-806	106	63	�	�	PROPN
m-806	106	64	�	�	PROPN
m-806	106	65	�	�	PROPN
m-806	106	66	�	�	PROPN
m-806	106	67	�	�	PROPN
m-806	106	68	�	�	PROPN
m-806	106	69	�	�	PROPN
m-806	106	70	�	�	PROPN
m-806	106	71	�	�	PROPN
m-806	106	72	�	�	PROPN
m-806	106	73	�	�	PROPN
m-806	106	74	�	�	PROPN
m-806	106	75	�	�	PROPN
m-806	106	76	�	�	PROPN
m-806	106	77	�	�	PROPN
m-806	106	78	�	�	PROPN
m-806	106	79	�	�	PROPN
m-806	106	80	�	�	PROPN
m-806	106	81	�	�	PROPN
m-806	106	82	�	�	PROPN
m-806	106	83	�	�	PROPN
m-806	106	84	�	�	PROPN
m-806	106	85	(	(	PUNCT
m-806	106	86	6.54d	6.54d	PROPN
m-806	106	87	)	)	PUNCT
m-806	106	88	�	�	PROPN
m-806	106	89	�	�	PROPN
m-806	106	90	=	=	SYM
m-806	106	91	�	�	PROPN
m-806	106	92	�	�	PROPN
m-806	106	93	�	�	PROPN
m-806	106	94	�	�	PROPN
m-806	106	95	�	�	PROPN
m-806	106	96	�	�	PROPN
m-806	106	97	�	�	PROPN
m-806	106	98	�	�	PROPN
m-806	106	99	�	�	PROPN
m-806	106	100	−	−	PROPN
m-806	106	101	�	�	PROPN
m-806	106	102	�	�	PROPN
m-806	106	103	�	�	PROPN
m-806	106	104	�	�	PROPN
m-806	106	105	�	�	PROPN
m-806	106	106	�	�	PROPN
m-806	106	107	�	�	PROPN
m-806	106	108	�	�	PROPN
m-806	106	109	�	�	PROPN
m-806	106	110	�	�	PROPN
m-806	106	111	�	�	PROPN
m-806	106	112	�	�	PROPN
m-806	106	113	�	�	PROPN
m-806	106	114	�	�	PROPN
m-806	106	115	�	�	PROPN
m-806	106	116	�	�	PROPN
m-806	106	117	�	�	PROPN
m-806	106	118	�	�	PROPN
m-806	106	119	�	�	PROPN
m-806	106	120	�	�	PROPN
m-806	106	121	�	�	PROPN
m-806	106	122	�	�	PROPN
m-806	106	123	�	�	PROPN
m-806	106	124	�	�	PROPN
m-806	106	125	�	�	PROPN
m-806	106	126	�	�	PROPN
m-806	106	127	�	�	PROPN
m-806	106	128	�	�	PROPN
m-806	106	129	(	(	PUNCT
m-806	106	130	6.54e	6.54e	NUM
m-806	106	131	)	)	PUNCT
m-806	106	132	where	where	SCONJ
m-806	106	133	,	,	PUNCT
m-806	106	134	�	�	PROPN
m-806	106	135	�	�	PROPN
m-806	106	136	(	(	PUNCT
m-806	106	137	0	0	NUM
m-806	106	138	)	)	PUNCT
m-806	106	139	=	=	SYM
m-806	106	140	�	�	PROPN
m-806	106	141	�	�	PROPN
m-806	106	142	�	�	PROPN
m-806	106	143	�	�	PROPN
m-806	106	144	�	�	PROPN
m-806	106	145	,	,	PUNCT
m-806	106	146	�	�	PROPN
m-806	106	147	�	�	PROPN
m-806	106	148	=	=	SYM
m-806	106	149	�	�	PROPN
m-806	106	150	�	�	PROPN
m-806	106	151	�	�	PROPN
m-806	106	152	�	�	PROPN
m-806	106	153	�	�	PROPN
m-806	106	154	�	�	PROPN
m-806	106	155	+	+	SYM
m-806	106	156	�	�	PROPN
m-806	106	157	�	�	PROPN
m-806	106	158	�	�	PROPN
m-806	106	159	�	�	PROPN
m-806	106	160	�	�	PROPN
m-806	106	161	�	�	PROPN
m-806	106	162	�	�	PROPN
m-806	106	163	�	�	PROPN
m-806	106	164	�	�	PROPN
m-806	106	165	�	�	PROPN
m-806	106	166	�	�	PROPN
m-806	106	167	�	�	PROPN
m-806	106	168	(	(	PUNCT
m-806	106	169	6.54f	6.54f	NUM
m-806	106	170	)	)	PUNCT
m-806	106	171	�	�	PROPN
m-806	106	172	�	�	PROPN
m-806	106	173	(	(	PUNCT
m-806	106	174	0	0	NUM
m-806	106	175	)	)	PUNCT
m-806	106	176	=	=	SYM
m-806	106	177	�	�	PROPN
m-806	106	178	�	�	PROPN
m-806	106	179	�	�	PROPN
m-806	106	180	�	�	PROPN
m-806	106	181	�	�	PROPN
m-806	106	182	,	,	PUNCT
m-806	106	183	�	�	PROPN
m-806	106	184	�	�	PROPN
m-806	106	185	=	=	SYM
m-806	106	186	9	9	NUM
m-806	106	187	�	�	PROPN
m-806	106	188	�	�	PROPN
m-806	106	189	�	�	PROPN
m-806	106	190	�	�	PROPN
m-806	106	191	+	+	CCONJ
m-806	106	192	�	�	PROPN
m-806	106	193	�	�	PROPN
m-806	106	194	�	�	PROPN
m-806	106	195	�	�	PROPN
m-806	106	196	�	�	PROPN
m-806	106	197	�	�	PROPN
m-806	106	198	�	�	PROPN
m-806	106	199	�	�	PROPN
m-806	106	200	�	�	PROPN
m-806	106	201	�	�	PROPN
m-806	106	202	(	(	PUNCT
m-806	106	203	6.54	6.54	NUM
m-806	106	204	g	g	NOUN
m-806	106	205	)	)	PUNCT
m-806	106	206	�	�	PROPN
m-806	106	207	�	�	PROPN
m-806	106	208	(	(	PUNCT
m-806	106	209	0	0	NUM
m-806	106	210	)	)	PUNCT
m-806	106	211	=	=	SYM
m-806	106	212	�	�	PROPN
m-806	106	213	�	�	PROPN
m-806	106	214	�	�	PROPN
m-806	106	215	�	�	PROPN
m-806	106	216	�	�	PROPN
m-806	106	217	�	�	PROPN
m-806	106	218	,	,	PUNCT
m-806	106	219	�	�	PROPN
m-806	106	220	�	�	PROPN
m-806	106	221	�	�	PROPN
m-806	106	222	=	=	SYM
m-806	106	223	�	�	PROPN
m-806	106	224	�	�	PROPN
m-806	106	225	�	�	PROPN
m-806	106	226	�	�	PROPN
m-806	106	227	−	−	PROPN
m-806	106	228	�	�	PROPN
m-806	106	229	�	�	PROPN
m-806	106	230	�	�	PROPN
m-806	106	231	�	�	PROPN
m-806	106	232	�	�	PROPN
m-806	106	233	�	�	PROPN
m-806	106	234	�	�	PROPN
m-806	106	235	�	�	PROPN
m-806	106	236	�	�	PROPN
m-806	106	237	�	�	PROPN
m-806	106	238	�	�	PROPN
m-806	106	239	�	�	PROPN
m-806	106	240	�	�	PROPN
m-806	106	241	(	(	PUNCT
m-806	106	242	6.54h	6.54h	NUM
m-806	106	243	)	)	PUNCT
m-806	106	244	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	106	245	ijo	ijo	PROPN
m-806	106	246	journals	journal	NOUN
m-806	106	247	volume	volume	NOUN
m-806	106	248	07	07	NUM
m-806	107	1	|	|	ADV
m-806	107	2	issue	issue	NOUN
m-806	107	3	02	02	NUM
m-806	107	4	|	|	CCONJ
m-806	107	5	february	february	PROPN
m-806	107	6	2024	2024	NUM
m-806	107	7	|	|	ADV
m-806	107	8	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-806	107	9	14	14	NUM
m-806	107	10	ijo	ijo	PROPN
m-806	107	11	international	international	PROPN
m-806	107	12	journal	journal	PROPN
m-806	107	13	of	of	ADP
m-806	107	14	mathematics	mathematics	PROPN
m-806	107	15	(	(	PUNCT
m-806	107	16	issn	issn	PROPN
m-806	107	17	:	:	PUNCT
m-806	107	18	2992	2992	NUM
m-806	107	19	-	-	SYM
m-806	107	20	4421	4421	NUM
m-806	107	21	)	)	PUNCT
m-806	108	1	i.u	i.u	PROPN
m-806	108	2	.	.	PROPN
m-806	108	3	udo	udo	PROPN
m-806	108	4	-	-	PROPN
m-806	108	5	akpan1	akpan1	ADJ
m-806	108	6	*	*	PUNCT
m-806	108	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	108	8	volume	volume	NOUN
m-806	108	9	07	07	NUM
m-806	108	10	issue	issue	NOUN
m-806	108	11	02	02	NUM
m-806	108	12	||	||	NUM
m-806	108	13	february	february	PROPN
m-806	108	14	,	,	PUNCT
m-806	108	15	2024	2024	NUM
m-806	108	16	||	||	NOUN
m-806	109	1	on	on	ADP
m-806	109	2	a	a	DET
m-806	109	3	-	-	PUNCT
m-806	109	4	two	two	NUM
m-806	109	5	-	-	PUNCT
m-806	109	6	parameter	parameter	NOUN
m-806	109	7	dynamic	dynamic	ADJ
m-806	109	8	buckling	buckling	NOUN
m-806	109	9	of	of	ADP
m-806	109	10	a	a	DET
m-806	109	11	viscously	viscously	ADV
m-806	109	12	damped	damp	VERB
m-806	109	13	but	but	CCONJ
m-806	109	14	clamped	clamp	VERB
m-806	109	15	column	column	NOUN
m-806	109	16	stressed	stress	VERB
m-806	109	17	by	by	ADP
m-806	109	18	a	a	DET
m-806	109	19	step	step	NOUN
m-806	109	20	load	load	NOUN
m-806	109	21	on	on	ADP
m-806	109	22	solving	solve	VERB
m-806	109	23	(	(	PUNCT
m-806	109	24	6.54a	6.54a	NUM
m-806	109	25	,	,	PUNCT
m-806	109	26	b	b	NOUN
m-806	109	27	)	)	PUNCT
m-806	109	28	,	,	PUNCT
m-806	109	29	we	we	PRON
m-806	109	30	get	get	VERB
m-806	109	31	u	u	NOUN
m-806	109	32	�	�	PROPN
m-806	109	33	�	�	PROPN
m-806	109	34	(	(	PUNCT
m-806	109	35	�	�	PROPN
m-806	109	36	�	�	PROPN
m-806	109	37	)	)	PUNCT
m-806	109	38	=	=	SYM
m-806	109	39	�	�	PROPN
m-806	109	40	�	�	PROPN
m-806	109	41	cos	cos	PROPN
m-806	109	42	�	�	PROPN
m-806	109	43	�	�	PROPN
m-806	109	44	�	�	PROPN
m-806	109	45	�	�	PROPN
m-806	109	46	̂	̂	VERB
m-806	109	47	+	+	NUM
m-806	109	48	�	�	PROPN
m-806	109	49	�	�	PROPN
m-806	109	50	sin	sin	PROPN
m-806	109	51	�	�	PROPN
m-806	109	52	�	�	PROPN
m-806	109	53	�	�	PROPN
m-806	109	54	�	�	PROPN
m-806	109	55	̂	̂	VERB
m-806	109	56	+	+	NUM
m-806	109	57	�	�	PROPN
m-806	109	58	�	�	PROPN
m-806	109	59	�	�	PROPN
m-806	109	60	�	�	PROPN
m-806	109	61	�	�	PROPN
m-806	109	62	�	�	PROPN
m-806	109	63	�	�	PROPN
m-806	109	64	�	�	PROPN
m-806	109	65	�	�	PROPN
m-806	109	66	�	�	PROPN
m-806	109	67	�	�	PROPN
m-806	109	68	�	�	PROPN
m-806	109	69	�	�	PROPN
m-806	109	70	�	�	PROPN
m-806	109	71	�	�	PROPN
m-806	109	72	+	+	CCONJ
m-806	109	73	�	�	PROPN
m-806	109	74	�	�	PROPN
m-806	109	75	�	�	PROPN
m-806	109	76	�	�	PROPN
m-806	109	77	�	�	PROPN
m-806	109	78	�	�	PROPN
m-806	109	79	�	�	PROPN
m-806	109	80	�	�	PROPN
m-806	109	81	�	�	PROPN
m-806	109	82	�	�	PROPN
m-806	109	83	�	�	PROPN
m-806	109	84	�	�	PROPN
m-806	109	85	�	�	PROPN
m-806	109	86	�	�	PROPN
m-806	109	87	�	�	PROPN
m-806	109	88	�	�	PROPN
m-806	109	89	�	�	PROPN
m-806	109	90	+	+	SYM
m-806	109	91	�	�	PROPN
m-806	109	92	�	�	PROPN
m-806	109	93	�	�	PROPN
m-806	109	94	�	�	PROPN
m-806	109	95	�	�	PROPN
m-806	109	96	�	�	PROPN
m-806	109	97	�	�	PROPN
m-806	109	98	�	�	PROPN
m-806	109	99	�	�	PROPN
m-806	109	100	�	�	PROPN
m-806	109	101	�	�	PROPN
m-806	109	102	�	�	PROPN
m-806	109	103	�	�	PROPN
m-806	109	104	�	�	PROPN
m-806	109	105	�	�	PROPN
m-806	109	106	�	�	PROPN
m-806	109	107	�	�	PROPN
m-806	109	108	(	(	PUNCT
m-806	109	109	6.55a	6.55a	PROPN
m-806	109	110	)	)	PUNCT
m-806	109	111	�	�	PROPN
m-806	109	112	�	�	PROPN
m-806	109	113	(	(	PUNCT
m-806	109	114	0	0	NUM
m-806	109	115	)	)	PUNCT
m-806	109	116	=	=	SYM
m-806	109	117	0	0	NUM
m-806	109	118	,	,	PUNCT
m-806	109	119	�	�	PROPN
m-806	109	120	�	�	PROPN
m-806	109	121	(	(	PUNCT
m-806	109	122	0	0	NUM
m-806	109	123	)	)	PUNCT
m-806	109	124	=	=	SYM
m-806	110	1	−	−	PROPN
m-806	110	2	1	1	NUM
m-806	110	3	2	2	NUM
m-806	110	4	�	�	PROPN
m-806	110	5	�	�	PROPN
m-806	110	6	�	�	PROPN
m-806	110	7	�	�	PROPN
m-806	110	8	�	�	PROPN
m-806	110	9	�	�	PROPN
m-806	110	10	�	�	PROPN
m-806	110	11	�	�	PROPN
m-806	110	12	�	�	PROPN
m-806	110	13	�	�	PROPN
m-806	110	14	�	�	PROPN
m-806	110	15	−	−	PROPN
m-806	110	16	�	�	PROPN
m-806	110	17	�	�	PROPN
m-806	110	18	+	+	CCONJ
m-806	110	19	2	2	NUM
m-806	110	20	�	�	PROPN
m-806	110	21	�	�	PROPN
m-806	110	22	�	�	PROPN
m-806	110	23	�	�	PROPN
m-806	110	24	�	�	PROPN
m-806	110	25	�	�	PROPN
m-806	110	26	�	�	PROPN
m-806	110	27	−	−	PROPN
m-806	110	28	4	4	NUM
m-806	110	29	�	�	PROPN
m-806	110	30	�	�	PROPN
m-806	110	31	+	+	CCONJ
m-806	110	32	3	3	NUM
m-806	110	33	�	�	PROPN
m-806	110	34	�	�	PROPN
m-806	110	35	�	�	PROPN
m-806	110	36	�	�	PROPN
m-806	110	37	�	�	PROPN
m-806	110	38	�	�	PROPN
m-806	110	39	�	�	PROPN
m-806	110	40	−	−	PROPN
m-806	110	41	9	9	NUM
m-806	110	42	�	�	PROPN
m-806	110	43	�	�	PROPN
m-806	110	44	+	+	SYM
m-806	110	45	�	�	PROPN
m-806	110	46	�	�	PROPN
m-806	110	47	�	�	PROPN
m-806	110	48	(	(	PUNCT
m-806	110	49	0	0	NUM
m-806	110	50	)	)	PUNCT
m-806	110	51	�	�	PROPN
m-806	110	52	=	=	SYM
m-806	110	53	�	�	PROPN
m-806	110	54	�	�	PROPN
m-806	111	1	−	−	PROPN
m-806	111	2	�	�	PROPN
m-806	111	3	�	�	PROPN
m-806	111	4	�	�	PROPN
m-806	111	5	�	�	PROPN
m-806	111	6	�	�	PROPN
m-806	111	7	�	�	PROPN
m-806	111	8	�	�	PROPN
m-806	111	9	�	�	PROPN
m-806	111	10	�	�	PROPN
m-806	111	11	�	�	PROPN
m-806	111	12	�	�	PROPN
m-806	111	13	+	+	CCONJ
m-806	111	14	�	�	PROPN
m-806	111	15	�	�	PROPN
m-806	111	16	�	�	PROPN
m-806	111	17	�	�	PROPN
m-806	111	18	�	�	PROPN
m-806	111	19	�	�	PROPN
m-806	111	20	�	�	PROPN
m-806	111	21	�	�	PROPN
m-806	111	22	�	�	PROPN
m-806	111	23	�	�	PROPN
m-806	111	24	+	+	CCONJ
m-806	111	25	�	�	PROPN
m-806	111	26	�	�	PROPN
m-806	111	27	�	�	PROPN
m-806	111	28	�	�	PROPN
m-806	111	29	�	�	PROPN
m-806	111	30	�	�	PROPN
m-806	111	31	�	�	PROPN
m-806	111	32	�	�	PROPN
m-806	111	33	�	�	PROPN
m-806	111	34	�	�	PROPN
m-806	111	35	�	�	PROPN
m-806	111	36	�	�	PROPN
m-806	111	37	�	�	PROPN
m-806	111	38	�	�	PROPN
m-806	111	39	�	�	PROPN
m-806	111	40	+	+	CCONJ
m-806	111	41	�	�	PROPN
m-806	111	42	�	�	PROPN
m-806	111	43	�	�	PROPN
m-806	111	44	�	�	PROPN
m-806	111	45	�	�	PROPN
m-806	111	46	�	�	PROPN
m-806	111	47	�	�	PROPN
m-806	111	48	�	�	PROPN
m-806	111	49	�	�	PROPN
m-806	111	50	�	�	PROPN
m-806	111	51	�	�	PROPN
m-806	111	52	�	�	PROPN
m-806	111	53	�	�	PROPN
m-806	111	54	�	�	PROPN
m-806	111	55	�	�	PROPN
m-806	111	56	�	�	PROPN
m-806	111	57	�	�	PROPN
m-806	111	58	�	�	PROPN
m-806	111	59	�	�	PROPN
m-806	111	60	�	�	PROPN
m-806	111	61	�	�	PROPN
m-806	111	62	�	�	PROPN
m-806	111	63	�	�	PROPN
m-806	111	64	(	(	PUNCT
m-806	111	65	6.55b	6.55b	NUM
m-806	111	66	)	)	PUNCT
m-806	111	67	that	that	PRON
m-806	111	68	is	be	AUX
m-806	111	69	�	�	PROPN
m-806	111	70	�	�	PROPN
m-806	111	71	(	(	PUNCT
m-806	111	72	0	0	NUM
m-806	111	73	)	)	PUNCT
m-806	111	74	=	=	SYM
m-806	111	75	�	�	PROPN
m-806	111	76	�	�	PROPN
m-806	111	77	�	�	PROPN
m-806	111	78	�	�	PROPN
m-806	111	79	�	�	PROPN
m-806	111	80	�	�	PROPN
m-806	111	81	,	,	PUNCT
m-806	111	82	(	(	PUNCT
m-806	111	83	6.55c	6.55c	NUM
m-806	111	84	)	)	PUNCT
m-806	111	85	�	�	PROPN
m-806	111	86	�	�	PROPN
m-806	111	87	�	�	PROPN
m-806	111	88	=	=	SYM
m-806	111	89	−	−	PROPN
m-806	111	90	1	1	NUM
m-806	111	91	2	2	NUM
m-806	111	92	�	�	PROPN
m-806	111	93	�	�	PROPN
m-806	111	94	�	�	PROPN
m-806	111	95	�	�	PROPN
m-806	111	96	�	�	PROPN
m-806	111	97	�	�	PROPN
m-806	111	98	�	�	PROPN
m-806	111	99	�	�	PROPN
m-806	111	100	�	�	PROPN
m-806	111	101	�	�	PROPN
m-806	111	102	�	�	PROPN
m-806	111	103	�	�	PROPN
m-806	111	104	−	−	PROPN
m-806	111	105	�	�	PROPN
m-806	111	106	�	�	PROPN
m-806	111	107	+	+	CCONJ
m-806	111	108	2	2	NUM
m-806	111	109	�	�	PROPN
m-806	111	110	�	�	PROPN
m-806	111	111	�	�	PROPN
m-806	111	112	�	�	PROPN
m-806	111	113	�	�	PROPN
m-806	111	114	�	�	PROPN
m-806	111	115	−	−	PROPN
m-806	111	116	4	4	NUM
m-806	111	117	�	�	PROPN
m-806	111	118	�	�	PROPN
m-806	111	119	+	+	CCONJ
m-806	111	120	3	3	NUM
m-806	111	121	�	�	PROPN
m-806	111	122	�	�	PROPN
m-806	111	123	�	�	PROPN
m-806	111	124	�	�	PROPN
m-806	111	125	�	�	PROPN
m-806	111	126	�	�	PROPN
m-806	111	127	�	�	PROPN
m-806	111	128	−	−	PROPN
m-806	111	129	9	9	NUM
m-806	111	130	�	�	PROPN
m-806	111	131	�	�	PROPN
m-806	111	132	�	�	PROPN
m-806	111	133	�	�	PROPN
m-806	111	134	+	+	CCONJ
m-806	111	135	�	�	PROPN
m-806	111	136	�	�	PROPN
m-806	111	137	�	�	PROPN
m-806	111	138	�	�	PROPN
m-806	111	139	�	�	PROPN
m-806	111	140	�	�	PROPN
m-806	111	141	�	�	PROPN
m-806	111	142	�	�	PROPN
m-806	111	143	�	�	PROPN
m-806	111	144	−	−	PROPN
m-806	111	145	�	�	PROPN
m-806	111	146	�	�	PROPN
m-806	111	147	�	�	PROPN
m-806	111	148	�	�	PROPN
m-806	111	149	�	�	PROPN
m-806	111	150	�	�	PROPN
m-806	111	151	�	�	PROPN
m-806	111	152	�	�	PROPN
m-806	111	153	�	�	PROPN
m-806	111	154	�	�	PROPN
m-806	111	155	�	�	PROPN
m-806	111	156	�	�	PROPN
m-806	111	157	+	+	CCONJ
m-806	111	158	�	�	PROPN
m-806	111	159	�	�	PROPN
m-806	111	160	�	�	PROPN
m-806	111	161	�	�	PROPN
m-806	111	162	�	�	PROPN
m-806	111	163	�	�	PROPN
m-806	111	164	�	�	PROPN
m-806	111	165	�	�	PROPN
m-806	111	166	�	�	PROPN
m-806	111	167	−	−	PROPN
m-806	111	168	�	�	PROPN
m-806	111	169	�	�	PROPN
m-806	111	170	�	�	PROPN
m-806	111	171	�	�	PROPN
m-806	111	172	�	�	PROPN
m-806	111	173	�	�	PROPN
m-806	111	174	�	�	PROPN
m-806	111	175	�	�	PROPN
m-806	111	176	�	�	PROPN
m-806	111	177	�	�	PROPN
m-806	111	178	�	�	PROPN
m-806	111	179	(	(	PUNCT
m-806	111	180	6.55d	6.55d	PROPN
m-806	111	181	)	)	PUNCT
m-806	112	1	next	next	ADV
m-806	112	2	we	we	PRON
m-806	112	3	ensure	ensure	VERB
m-806	112	4	a	a	DET
m-806	112	5	uniformly	uniformly	ADV
m-806	112	6	valid	valid	ADJ
m-806	112	7	solution	solution	NOUN
m-806	112	8	in	in	ADP
m-806	112	9	�	�	PROPN
m-806	112	10	̂	̂	VERB
m-806	112	11	in	in	ADP
m-806	112	12	(	(	PUNCT
m-806	112	13	6.50a	6.50a	PROPN
m-806	112	14	)	)	PUNCT
m-806	112	15	by	by	ADP
m-806	112	16	first	first	ADJ
m-806	112	17	substituting	substitute	VERB
m-806	112	18	for	for	ADP
m-806	112	19	the	the	DET
m-806	112	20	relevant	relevant	ADJ
m-806	112	21	terms	term	NOUN
m-806	112	22	there	there	ADV
m-806	112	23	,	,	PUNCT
m-806	112	24	and	and	CCONJ
m-806	112	25	equating	equate	VERB
m-806	112	26	to	to	ADP
m-806	112	27	zero	zero	NUM
m-806	112	28	the	the	DET
m-806	112	29	coefficients	coefficient	NOUN
m-806	112	30	of	of	ADP
m-806	112	31	cos	cos	PROPN
m-806	112	32	�	�	PROPN
m-806	112	33	�	�	PROPN
m-806	112	34	�	�	PROPN
m-806	112	35	�	�	PROPN
m-806	112	36	̂	̂	VERB
m-806	112	37	and	and	CCONJ
m-806	112	38	sin	sin	PROPN
m-806	112	39	�	�	PROPN
m-806	112	40	�	�	PROPN
m-806	112	41	�	�	PROPN
m-806	112	42	�	�	PROPN
m-806	112	43	̂	̂	VERB
m-806	112	44	to	to	PART
m-806	112	45	get	get	VERB
m-806	112	46	�	�	PROPN
m-806	112	47	�	�	PROPN
m-806	112	48	�	�	PROPN
m-806	112	49	+	+	CCONJ
m-806	112	50	�	�	PROPN
m-806	112	51	�	�	PROPN
m-806	112	52	=	=	SYM
m-806	112	53	0	0	NUM
m-806	112	54	,	,	PUNCT
m-806	112	55	�	�	PROPN
m-806	112	56	�	�	PROPN
m-806	112	57	�	�	PROPN
m-806	112	58	+	+	CCONJ
m-806	112	59	�	�	PROPN
m-806	112	60	�	�	PROPN
m-806	112	61	=	=	SYM
m-806	112	62	0	0	NUM
m-806	112	63	(	(	PUNCT
m-806	112	64	6.56a	6.56a	NUM
m-806	112	65	)	)	PUNCT
m-806	112	66	on	on	ADP
m-806	112	67	solving	solve	VERB
m-806	112	68	(	(	PUNCT
m-806	112	69	6.56a	6.56a	NUM
m-806	112	70	)	)	PUNCT
m-806	112	71	,	,	PUNCT
m-806	112	72	we	we	PRON
m-806	112	73	get	get	VERB
m-806	112	74	�	�	PROPN
m-806	112	75	�	�	PROPN
m-806	112	76	(	(	PUNCT
m-806	112	77	�	�	PROPN
m-806	112	78	)	)	PUNCT
m-806	112	79	=	=	SYM
m-806	112	80	0	0	NUM
m-806	112	81	,	,	PUNCT
m-806	112	82	�	�	PROPN
m-806	112	83	�	�	PROPN
m-806	112	84	(	(	PUNCT
m-806	112	85	�	�	PROPN
m-806	112	86	)	)	PUNCT
m-806	112	87	=	=	SYM
m-806	112	88	�	�	PROPN
m-806	112	89	�	�	PROPN
m-806	112	90	(	(	PUNCT
m-806	112	91	0	0	NUM
m-806	112	92	)	)	PUNCT
m-806	112	93	�	�	PROPN
m-806	112	94	�	�	PROPN
m-806	112	95	�	�	PROPN
m-806	112	96	(	(	PUNCT
m-806	112	97	6.56b	6.56b	PROPN
m-806	112	98	)	)	PUNCT
m-806	112	99	where	where	SCONJ
m-806	112	100	,	,	PUNCT
m-806	112	101	�	�	PROPN
m-806	112	102	�	�	PROPN
m-806	112	103	�	�	PROPN
m-806	112	104	(	(	PUNCT
m-806	112	105	0	0	NUM
m-806	112	106	)	)	PUNCT
m-806	112	107	=	=	SYM
m-806	113	1	−	−	NUM
m-806	113	2	�	�	PROPN
m-806	113	3	�	�	PROPN
m-806	113	4	(0	(0	PUNCT
m-806	113	5	)	)	PUNCT
m-806	113	6	,	,	PUNCT
m-806	113	7	�	�	PROPN
m-806	113	8	�	�	PROPN
m-806	113	9	�	�	PROPN
m-806	113	10	�	�	PROPN
m-806	113	11	(	(	PUNCT
m-806	113	12	0	0	NUM
m-806	113	13	)	)	PUNCT
m-806	113	14	=	=	SYM
m-806	113	15	�	�	PROPN
m-806	113	16	�	�	PROPN
m-806	113	17	(	(	PUNCT
m-806	113	18	0	0	NUM
m-806	113	19	)	)	PUNCT
m-806	113	20	(	(	PUNCT
m-806	113	21	6.56c	6.56c	X
m-806	113	22	)	)	PUNCT
m-806	114	1	the	the	DET
m-806	114	2	remaining	remain	VERB
m-806	114	3	equation	equation	NOUN
m-806	114	4	in	in	ADP
m-806	114	5	(	(	PUNCT
m-806	114	6	6.50a	6.50a	PROPN
m-806	114	7	)	)	PUNCT
m-806	114	8	is	be	AUX
m-806	114	9	now	now	ADV
m-806	114	10	written	write	VERB
m-806	114	11	as	as	ADP
m-806	114	12	u	u	NOUN
m-806	114	13	�	�	PROPN
m-806	114	14	�	�	PROPN
m-806	114	15	,	,	PUNCT
m-806	114	16	�	�	PROPN
m-806	114	17	�	�	PROPN
m-806	114	18	�	�	PROPN
m-806	114	19	�	�	PROPN
m-806	114	20	(	(	PUNCT
m-806	114	21	�	�	PROPN
m-806	114	22	�	�	PROPN
m-806	114	23	)	)	PUNCT
m-806	114	24	+	+	SYM
m-806	114	25	�	�	PROPN
m-806	114	26	�	�	PROPN
m-806	114	27	�	�	PROPN
m-806	114	28	�	�	PROPN
m-806	114	29	u	u	PROPN
m-806	114	30	�	�	PROPN
m-806	114	31	�	�	PROPN
m-806	114	32	(	(	PUNCT
m-806	114	33	�	�	PROPN
m-806	114	34	�	�	PROPN
m-806	114	35	)	)	PUNCT
m-806	114	36	=	=	SYM
m-806	114	37	�	�	PROPN
m-806	114	38	�	�	PROPN
m-806	114	39	sin	sin	PROPN
m-806	114	40	�	�	PROPN
m-806	114	41	�	�	PROPN
m-806	114	42	̂	̂	VERB
m-806	114	43	+	+	NUM
m-806	114	44	�	�	PROPN
m-806	114	45	�	�	PROPN
m-806	114	46	sin2	sin2	PROPN
m-806	114	47	�	�	PROPN
m-806	114	48	�	�	PROPN
m-806	114	49	̂	̂	VERB
m-806	114	50	+	+	NUM
m-806	114	51	�	�	PROPN
m-806	114	52	�	�	PROPN
m-806	114	53	�	�	PROPN
m-806	114	54	sin3	sin3	PROPN
m-806	114	55	�	�	PROPN
m-806	114	56	�	�	PROPN
m-806	114	57	̂	̂	PUNCT
m-806	114	58	(	(	PUNCT
m-806	114	59	6.57	6.57	NUM
m-806	114	60	�	�	NOUN
m-806	114	61	)	)	PUNCT
m-806	114	62	u	u	NOUN
m-806	114	63	�	�	PROPN
m-806	114	64	�	�	PROPN
m-806	114	65	(	(	PUNCT
m-806	114	66	�	�	PROPN
m-806	114	67	�	�	PROPN
m-806	114	68	)	)	PUNCT
m-806	114	69	(	(	PUNCT
m-806	114	70	0,0	0,0	NUM
m-806	114	71	)	)	PUNCT
m-806	114	72	=	=	SYM
m-806	114	73	0	0	NUM
m-806	114	74	,	,	PUNCT
m-806	114	75	�	�	PROPN
m-806	114	76	�	�	PROPN
m-806	114	77	�	�	PROPN
m-806	114	78	,	,	PUNCT
m-806	114	79	�	�	PROPN
m-806	114	80	�	�	PROPN
m-806	114	81	(	(	PUNCT
m-806	114	82	�	�	PROPN
m-806	114	83	�	�	PROPN
m-806	114	84	)	)	PUNCT
m-806	114	85	(	(	PUNCT
m-806	114	86	0	0	NUM
m-806	114	87	,	,	PUNCT
m-806	114	88	0	0	NUM
m-806	114	89	)	)	PUNCT
m-806	114	90	+	+	CCONJ
m-806	114	91	�	�	PROPN
m-806	114	92	�	�	PROPN
m-806	114	93	�	�	PROPN
m-806	114	94	,	,	PUNCT
m-806	114	95	�	�	PROPN
m-806	114	96	(	(	PUNCT
m-806	114	97	�	�	PROPN
m-806	114	98	�	�	PROPN
m-806	114	99	)	)	PUNCT
m-806	114	100	(	(	PUNCT
m-806	114	101	0	0	NUM
m-806	114	102	,	,	PUNCT
m-806	114	103	0	0	NUM
m-806	114	104	)	)	PUNCT
m-806	114	105	=	=	SYM
m-806	114	106	0	0	PUNCT
m-806	115	1	(	(	PUNCT
m-806	115	2	6.57b	6.57b	PROPN
m-806	115	3	)	)	PUNCT
m-806	115	4	where	where	SCONJ
m-806	115	5	,	,	PUNCT
m-806	115	6	�	�	PROPN
m-806	115	7	�	�	PROPN
m-806	115	8	=	=	SYM
m-806	115	9	�	�	PROPN
m-806	115	10	�	�	PROPN
m-806	115	11	�	�	PROPN
m-806	115	12	�	�	PROPN
m-806	115	13	�	�	PROPN
m-806	115	14	�	�	PROPN
m-806	115	15	�	�	PROPN
m-806	115	16	�	�	PROPN
m-806	115	17	�	�	PROPN
m-806	115	18	+	+	SYM
m-806	115	19	�	�	PROPN
m-806	115	20	�	�	PROPN
m-806	115	21	�	�	PROPN
m-806	115	22	�	�	PROPN
m-806	115	23	�	�	PROPN
m-806	115	24	+	+	CCONJ
m-806	115	25	�	�	PROPN
m-806	115	26	�	�	PROPN
m-806	115	27	�	�	PROPN
m-806	115	28	�	�	PROPN
m-806	115	29	�	�	PROPN
m-806	115	30	�	�	PROPN
m-806	115	31	�	�	PROPN
m-806	115	32	�	�	PROPN
m-806	115	33	�	�	PROPN
m-806	115	34	�	�	PROPN
m-806	115	35	�	�	PROPN
m-806	115	36	�	�	PROPN
m-806	115	37	�	�	PROPN
m-806	115	38	�	�	PROPN
m-806	115	39	�	�	PROPN
m-806	115	40	�	�	PROPN
m-806	115	41	�	�	PROPN
m-806	115	42	�	�	PROPN
m-806	115	43	�	�	PROPN
m-806	115	44	�	�	PROPN
m-806	115	45	�	�	PROPN
m-806	115	46	�	�	PROPN
m-806	115	47	�	�	PROPN
m-806	115	48	�	�	PROPN
m-806	115	49	�	�	PROPN
m-806	115	50	�	�	PROPN
m-806	115	51	�	�	PROPN
m-806	115	52	�	�	PROPN
m-806	115	53	�	�	PROPN
m-806	115	54	(	(	PUNCT
m-806	115	55	6.57c	6.57c	PROPN
m-806	115	56	)	)	PUNCT
m-806	115	57	�	�	PROPN
m-806	115	58	�	�	PROPN
m-806	115	59	=	=	SYM
m-806	115	60	�	�	PROPN
m-806	115	61	�	�	PROPN
m-806	115	62	�	�	PROPN
m-806	115	63	�	�	PROPN
m-806	115	64	�	�	PROPN
m-806	115	65	�	�	PROPN
m-806	115	66	�	�	PROPN
m-806	115	67	�	�	PROPN
m-806	115	68	�	�	PROPN
m-806	115	69	+	+	CCONJ
m-806	115	70	�	�	PROPN
m-806	115	71	�	�	PROPN
m-806	115	72	�	�	PROPN
m-806	115	73	�	�	PROPN
m-806	115	74	�	�	PROPN
m-806	115	75	�	�	PROPN
m-806	115	76	�	�	PROPN
m-806	115	77	�	�	PROPN
m-806	115	78	�	�	PROPN
m-806	115	79	�	�	PROPN
m-806	115	80	�	�	PROPN
m-806	115	81	�	�	PROPN
m-806	115	82	�	�	PROPN
m-806	115	83	�	�	PROPN
m-806	115	84	�	�	PROPN
m-806	115	85	�	�	PROPN
m-806	115	86	�	�	PROPN
m-806	115	87	�	�	PROPN
m-806	115	88	�	�	PROPN
m-806	115	89	�	�	PROPN
m-806	115	90	�	�	PROPN
m-806	115	91	�	�	PROPN
m-806	115	92	�	�	PROPN
m-806	115	93	�	�	PROPN
m-806	115	94	�	�	PROPN
m-806	115	95	�	�	PROPN
m-806	115	96	(	(	PUNCT
m-806	115	97	6.57d	6.57d	PROPN
m-806	115	98	)	)	PUNCT
m-806	115	99	�	�	PROPN
m-806	115	100	�	�	PROPN
m-806	115	101	�	�	PROPN
m-806	115	102	=	=	SYM
m-806	115	103	�	�	PROPN
m-806	115	104	�	�	PROPN
m-806	115	105	�	�	PROPN
m-806	115	106	�	�	PROPN
m-806	115	107	�	�	PROPN
m-806	115	108	�	�	PROPN
m-806	115	109	�	�	PROPN
m-806	115	110	�	�	PROPN
m-806	115	111	�	�	PROPN
m-806	115	112	�	�	PROPN
m-806	115	113	+	+	CCONJ
m-806	115	114	�	�	PROPN
m-806	115	115	�	�	PROPN
m-806	115	116	�	�	PROPN
m-806	115	117	�	�	PROPN
m-806	115	118	(	(	PUNCT
m-806	115	119	�	�	PROPN
m-806	115	120	�	�	PROPN
m-806	115	121	�	�	PROPN
m-806	115	122	�	�	PROPN
m-806	115	123	�	�	PROPN
m-806	115	124	�	�	PROPN
m-806	115	125	+	+	CCONJ
m-806	115	126	�	�	PROPN
m-806	115	127	�	�	PROPN
m-806	115	128	�	�	PROPN
m-806	115	129	)	)	PUNCT
m-806	115	130	(	(	PUNCT
m-806	115	131	6.57e	6.57e	PROPN
m-806	115	132	)	)	PUNCT
m-806	115	133	�	�	PROPN
m-806	115	134	�	�	PROPN
m-806	115	135	(	(	PUNCT
m-806	115	136	0	0	NUM
m-806	115	137	)	)	PUNCT
m-806	115	138	=	=	SYM
m-806	115	139	�	�	PROPN
m-806	115	140	�	�	PROPN
m-806	115	141	�	�	PROPN
m-806	115	142	�	�	PROPN
m-806	115	143	�	�	PROPN
m-806	115	144	,	,	PUNCT
m-806	115	145	�	�	PROPN
m-806	115	146	�	�	PROPN
m-806	115	147	=	=	SYM
m-806	115	148	�	�	PROPN
m-806	115	149	�	�	PROPN
m-806	115	150	�	�	PROPN
m-806	115	151	�	�	PROPN
m-806	115	152	�	�	PROPN
m-806	115	153	+	+	SYM
m-806	115	154	�	�	PROPN
m-806	115	155	�	�	PROPN
m-806	115	156	�	�	PROPN
m-806	115	157	�	�	PROPN
m-806	115	158	�	�	PROPN
m-806	115	159	�	�	PROPN
m-806	115	160	�	�	PROPN
m-806	115	161	�	�	PROPN
m-806	115	162	�	�	PROPN
m-806	115	163	�	�	PROPN
m-806	115	164	�	�	PROPN
m-806	115	165	�	�	PROPN
m-806	115	166	(	(	PUNCT
m-806	115	167	6.57f	6.57f	PROPN
m-806	115	168	)	)	PUNCT
m-806	115	169	�	�	PROPN
m-806	115	170	�	�	PROPN
m-806	115	171	(	(	PUNCT
m-806	115	172	0	0	NUM
m-806	115	173	)	)	PUNCT
m-806	115	174	=	=	SYM
m-806	115	175	�	�	PROPN
m-806	115	176	�	�	PROPN
m-806	115	177	�	�	PROPN
m-806	115	178	�	�	PROPN
m-806	115	179	�	�	PROPN
m-806	115	180	�	�	PROPN
m-806	115	181	�	�	PROPN
m-806	115	182	�	�	PROPN
m-806	115	183	,	,	PUNCT
m-806	115	184	�	�	PROPN
m-806	115	185	�	�	PROPN
m-806	115	186	�	�	PROPN
m-806	115	187	(	(	PUNCT
m-806	115	188	0	0	NUM
m-806	115	189	)	)	PUNCT
m-806	115	190	=	=	SYM
m-806	115	191	�	�	PROPN
m-806	115	192	�	�	PROPN
m-806	115	193	�	�	PROPN
m-806	115	194	�	�	PROPN
m-806	115	195	�	�	PROPN
m-806	115	196	�	�	PROPN
m-806	115	197	�	�	PROPN
m-806	115	198	(	(	PUNCT
m-806	115	199	6.57	6.57	NUM
m-806	115	200	g	g	NOUN
m-806	115	201	)	)	PUNCT
m-806	115	202	�	�	PROPN
m-806	115	203	�	�	PROPN
m-806	115	204	�	�	PROPN
m-806	115	205	(	(	PUNCT
m-806	115	206	0	0	NUM
m-806	115	207	)	)	PUNCT
m-806	115	208	=	=	SYM
m-806	115	209	�	�	PROPN
m-806	115	210	�	�	PROPN
m-806	115	211	�	�	PROPN
m-806	115	212	�	�	PROPN
m-806	115	213	�	�	PROPN
m-806	115	214	�	�	PROPN
m-806	115	215	�	�	PROPN
m-806	115	216	�	�	PROPN
m-806	115	217	�	�	PROPN
m-806	115	218	�	�	PROPN
m-806	115	219	−	−	PROPN
m-806	115	220	�	�	PROPN
m-806	115	221	�	�	PROPN
m-806	115	222	�	�	PROPN
m-806	115	223	�	�	PROPN
m-806	115	224	�	�	PROPN
m-806	115	225	�	�	PROPN
m-806	115	226	�	�	PROPN
m-806	115	227	�	�	PROPN
m-806	115	228	�	�	PROPN
m-806	115	229	�	�	PROPN
m-806	115	230	�	�	PROPN
m-806	115	231	�	�	PROPN
m-806	115	232	�	�	PROPN
m-806	115	233	�	�	PROPN
m-806	115	234	�	�	PROPN
m-806	115	235	(	(	PUNCT
m-806	115	236	6.57h	6.57h	PROPN
m-806	115	237	)	)	PUNCT
m-806	115	238	�	�	PROPN
m-806	115	239	�	�	PROPN
m-806	115	240	�	�	PROPN
m-806	115	241	(	(	PUNCT
m-806	115	242	0	0	NUM
m-806	115	243	)	)	PUNCT
m-806	115	244	=	=	SYM
m-806	115	245	�	�	PROPN
m-806	115	246	�	�	PROPN
m-806	115	247	�	�	PROPN
m-806	115	248	�	�	PROPN
m-806	115	249	�	�	PROPN
m-806	115	250	�	�	PROPN
m-806	115	251	�	�	PROPN
m-806	115	252	�	�	PROPN
m-806	115	253	�	�	PROPN
m-806	116	1	−	−	PROPN
m-806	116	2	�	�	PROPN
m-806	116	3	�	�	PROPN
m-806	116	4	�	�	PROPN
m-806	116	5	�	�	PROPN
m-806	116	6	�	�	PROPN
m-806	116	7	�	�	PROPN
m-806	116	8	�	�	PROPN
m-806	116	9	�	�	PROPN
m-806	116	10	�	�	PROPN
m-806	116	11	�	�	PROPN
m-806	116	12	(	(	PUNCT
m-806	116	13	6.57i	6.57i	NUM
m-806	116	14	)	)	PUNCT
m-806	116	15	�	�	PROPN
m-806	116	16	�	�	PROPN
m-806	116	17	�	�	PROPN
m-806	116	18	�	�	PROPN
m-806	116	19	(	(	PUNCT
m-806	116	20	0	0	NUM
m-806	116	21	)	)	PUNCT
m-806	116	22	=	=	SYM
m-806	116	23	�	�	PROPN
m-806	116	24	�	�	PROPN
m-806	116	25	�	�	PROPN
m-806	116	26	�	�	PROPN
m-806	116	27	�	�	PROPN
m-806	116	28	�	�	PROPN
m-806	116	29	�	�	PROPN
m-806	116	30	(	(	PUNCT
m-806	116	31	6.57j	6.57j	NUM
m-806	116	32	)	)	PUNCT
m-806	116	33	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	116	34	ijo	ijo	PROPN
m-806	116	35	journals	journal	NOUN
m-806	116	36	volume	volume	NOUN
m-806	116	37	07	07	NUM
m-806	116	38	|	|	ADV
m-806	116	39	issue	issue	NOUN
m-806	116	40	02	02	NUM
m-806	116	41	|	|	CCONJ
m-806	116	42	february	february	PROPN
m-806	116	43	2024	2024	NUM
m-806	116	44	|	|	ADV
m-806	116	45	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	116	46	15	15	NUM
m-806	116	47	ijo	ijo	PROPN
m-806	116	48	international	international	PROPN
m-806	116	49	journal	journal	PROPN
m-806	116	50	of	of	ADP
m-806	116	51	mathematics	mathematics	PROPN
m-806	116	52	(	(	PUNCT
m-806	116	53	issn	issn	PROPN
m-806	116	54	:	:	PUNCT
m-806	116	55	2992	2992	NUM
m-806	116	56	-	-	SYM
m-806	116	57	4421	4421	NUM
m-806	116	58	)	)	PUNCT
m-806	117	1	i.u	i.u	PROPN
m-806	117	2	.	.	PROPN
m-806	117	3	udo	udo	PROPN
m-806	117	4	-	-	PROPN
m-806	117	5	akpan1	akpan1	ADJ
m-806	117	6	*	*	PUNCT
m-806	117	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	117	8	volume	volume	NOUN
m-806	117	9	07	07	NUM
m-806	117	10	issue	issue	NOUN
m-806	117	11	02	02	NUM
m-806	117	12	||	||	NUM
m-806	117	13	february	february	PROPN
m-806	117	14	,	,	PUNCT
m-806	117	15	2024	2024	NUM
m-806	117	16	||	||	NOUN
m-806	118	1	on	on	ADP
m-806	118	2	a	a	DET
m-806	118	3	-	-	PUNCT
m-806	118	4	two	two	NUM
m-806	118	5	-	-	PUNCT
m-806	118	6	parameter	parameter	NOUN
m-806	118	7	dynamic	dynamic	ADJ
m-806	118	8	buckling	buckling	NOUN
m-806	118	9	of	of	ADP
m-806	118	10	a	a	DET
m-806	118	11	viscously	viscously	ADV
m-806	118	12	damped	damp	VERB
m-806	118	13	but	but	CCONJ
m-806	118	14	clamped	clamp	VERB
m-806	118	15	column	column	NOUN
m-806	118	16	stressed	stress	VERB
m-806	118	17	by	by	ADP
m-806	118	18	a	a	DET
m-806	118	19	step	step	NOUN
m-806	118	20	load	load	NOUN
m-806	118	21	on	on	ADP
m-806	118	22	solving	solve	VERB
m-806	118	23	(	(	PUNCT
m-806	118	24	6.57a	6.57a	NUM
m-806	118	25	,	,	PUNCT
m-806	118	26	b	b	NOUN
m-806	118	27	)	)	PUNCT
m-806	118	28	,	,	PUNCT
m-806	118	29	we	we	PRON
m-806	118	30	get	get	VERB
m-806	118	31	u	u	NOUN
m-806	118	32	�	�	PROPN
m-806	118	33	�	�	PROPN
m-806	118	34	(	(	PUNCT
m-806	118	35	�	�	PROPN
m-806	118	36	�	�	PROPN
m-806	118	37	)	)	PUNCT
m-806	118	38	=	=	SYM
m-806	118	39	�	�	PROPN
m-806	118	40	�	�	PROPN
m-806	118	41	cos	cos	PROPN
m-806	118	42	�	�	PROPN
m-806	118	43	�	�	PROPN
m-806	118	44	�	�	PROPN
m-806	118	45	�	�	PROPN
m-806	118	46	̂	̂	VERB
m-806	118	47	+	+	NUM
m-806	118	48	�	�	PROPN
m-806	118	49	�	�	PROPN
m-806	118	50	sin	sin	PROPN
m-806	118	51	�	�	PROPN
m-806	118	52	�	�	PROPN
m-806	118	53	�	�	PROPN
m-806	118	54	�	�	PROPN
m-806	118	55	̂	̂	VERB
m-806	118	56	+	+	NUM
m-806	118	57	�	�	PROPN
m-806	118	58	�	�	PROPN
m-806	118	59	�	�	PROPN
m-806	118	60	�	�	PROPN
m-806	118	61	�	�	PROPN
m-806	118	62	�	�	PROPN
m-806	118	63	�	�	PROPN
m-806	118	64	�	�	PROPN
m-806	118	65	�	�	PROPN
m-806	118	66	�	�	PROPN
m-806	118	67	�	�	PROPN
m-806	118	68	�	�	PROPN
m-806	118	69	�	�	PROPN
m-806	118	70	�	�	PROPN
m-806	118	71	�	�	PROPN
m-806	118	72	+	+	CCONJ
m-806	118	73	�	�	PROPN
m-806	118	74	�	�	PROPN
m-806	118	75	�	�	PROPN
m-806	118	76	�	�	PROPN
m-806	118	77	�	�	PROPN
m-806	118	78	�	�	PROPN
m-806	118	79	�	�	PROPN
m-806	118	80	�	�	PROPN
m-806	118	81	�	�	PROPN
m-806	118	82	�	�	PROPN
m-806	118	83	�	�	PROPN
m-806	118	84	�	�	PROPN
m-806	118	85	�	�	PROPN
m-806	118	86	�	�	PROPN
m-806	118	87	�	�	PROPN
m-806	118	88	�	�	PROPN
m-806	118	89	�	�	PROPN
m-806	118	90	+	+	CCONJ
m-806	118	91	�	�	PROPN
m-806	118	92	�	�	PROPN
m-806	118	93	�	�	PROPN
m-806	118	94	�	�	PROPN
m-806	118	95	�	�	PROPN
m-806	118	96	�	�	PROPN
m-806	118	97	�	�	PROPN
m-806	118	98	�	�	PROPN
m-806	118	99	�	�	PROPN
m-806	118	100	�	�	PROPN
m-806	118	101	�	�	PROPN
m-806	118	102	�	�	PROPN
m-806	118	103	�	�	PROPN
m-806	118	104	�	�	PROPN
m-806	118	105	�	�	PROPN
m-806	118	106	�	�	PROPN
m-806	118	107	�	�	PROPN
m-806	118	108	�	�	PROPN
m-806	118	109	(	(	PUNCT
m-806	118	110	6.58a	6.58a	PROPN
m-806	118	111	)	)	PUNCT
m-806	118	112	with	with	ADP
m-806	118	113	�	�	PROPN
m-806	118	114	�	�	PROPN
m-806	118	115	(	(	PUNCT
m-806	118	116	0	0	NUM
m-806	118	117	)	)	PUNCT
m-806	118	118	=	=	SYM
m-806	119	1	0	0	NUM
m-806	119	2	,	,	PUNCT
m-806	119	3	(	(	PUNCT
m-806	119	4	6.58b	6.58b	NOUN
m-806	119	5	)	)	PUNCT
m-806	119	6	�	�	PROPN
m-806	119	7	�	�	PROPN
m-806	119	8	(	(	PUNCT
m-806	119	9	0	0	NUM
m-806	119	10	)	)	PUNCT
m-806	119	11	=	=	SYM
m-806	120	1	−	−	PROPN
m-806	120	2	1	1	NUM
m-806	120	3	�	�	PROPN
m-806	120	4	�	�	PROPN
m-806	120	5	�	�	PROPN
m-806	120	6	�	�	PROPN
m-806	120	7	�	�	PROPN
m-806	120	8	�	�	PROPN
m-806	120	9	�	�	PROPN
m-806	120	10	�	�	PROPN
m-806	120	11	�	�	PROPN
m-806	120	12	�	�	PROPN
m-806	120	13	�	�	PROPN
m-806	120	14	�	�	PROPN
m-806	120	15	−	−	PROPN
m-806	120	16	�	�	PROPN
m-806	120	17	�	�	PROPN
m-806	120	18	+	+	CCONJ
m-806	120	19	2	2	NUM
m-806	120	20	�	�	PROPN
m-806	120	21	�	�	PROPN
m-806	120	22	�	�	PROPN
m-806	120	23	�	�	PROPN
m-806	120	24	�	�	PROPN
m-806	120	25	�	�	PROPN
m-806	120	26	−	−	PROPN
m-806	120	27	4	4	NUM
m-806	120	28	�	�	PROPN
m-806	120	29	�	�	PROPN
m-806	120	30	+	+	CCONJ
m-806	120	31	3	3	NUM
m-806	120	32	�	�	PROPN
m-806	120	33	�	�	PROPN
m-806	120	34	�	�	PROPN
m-806	120	35	�	�	PROPN
m-806	120	36	�	�	PROPN
m-806	120	37	�	�	PROPN
m-806	120	38	�	�	PROPN
m-806	120	39	−	−	PROPN
m-806	120	40	9	9	NUM
m-806	120	41	�	�	PROPN
m-806	120	42	�	�	PROPN
m-806	120	43	�	�	PROPN
m-806	120	44	+	+	CCONJ
m-806	120	45	�	�	PROPN
m-806	120	46	�	�	PROPN
m-806	120	47	�	�	PROPN
m-806	120	48	�	�	PROPN
m-806	120	49	+	+	CCONJ
m-806	120	50	�	�	PROPN
m-806	120	51	�	�	PROPN
m-806	120	52	�	�	PROPN
m-806	120	53	�	�	PROPN
m-806	120	54	�	�	PROPN
m-806	120	55	�	�	PROPN
m-806	120	56	�	�	PROPN
m-806	120	57	�	�	PROPN
m-806	120	58	�	�	PROPN
m-806	120	59	�	�	PROPN
m-806	120	60	�	�	PROPN
m-806	120	61	�	�	PROPN
m-806	120	62	+	+	CCONJ
m-806	120	63	�	�	PROPN
m-806	120	64	�	�	PROPN
m-806	120	65	�	�	PROPN
m-806	120	66	�	�	PROPN
m-806	120	67	�	�	PROPN
m-806	120	68	�	�	PROPN
m-806	120	69	�	�	PROPN
m-806	120	70	�	�	PROPN
m-806	120	71	�	�	PROPN
m-806	120	72	�	�	PROPN
m-806	120	73	+	+	CCONJ
m-806	120	74	�	�	PROPN
m-806	120	75	�	�	PROPN
m-806	120	76	�	�	PROPN
m-806	120	77	�	�	PROPN
m-806	120	78	�	�	PROPN
m-806	120	79	�	�	PROPN
m-806	120	80	�	�	PROPN
m-806	120	81	�	�	PROPN
m-806	120	82	�	�	PROPN
m-806	120	83	�	�	PROPN
m-806	120	84	�	�	PROPN
m-806	120	85	�	�	PROPN
m-806	120	86	�	�	PROPN
m-806	120	87	�	�	PROPN
m-806	120	88	�	�	PROPN
m-806	120	89	�	�	PROPN
m-806	120	90	�	�	PROPN
m-806	120	91	�	�	PROPN
m-806	120	92	�	�	PROPN
m-806	120	93	�	�	PROPN
m-806	120	94	�	�	PROPN
m-806	120	95	+	+	CCONJ
m-806	120	96	�	�	PROPN
m-806	120	97	�	�	PROPN
m-806	120	98	�	�	PROPN
m-806	120	99	�	�	PROPN
m-806	120	100	�	�	PROPN
m-806	120	101	�	�	PROPN
m-806	120	102	�	�	PROPN
m-806	120	103	�	�	PROPN
m-806	120	104	�	�	PROPN
m-806	120	105	�	�	PROPN
m-806	120	106	�	�	PROPN
m-806	120	107	�	�	PROPN
m-806	120	108	�	�	PROPN
m-806	120	109	�	�	PROPN
m-806	120	110	�	�	PROPN
m-806	120	111	�	�	PROPN
m-806	120	112	�	�	PROPN
m-806	120	113	�	�	PROPN
m-806	120	114	�	�	PROPN
m-806	120	115	�	�	PROPN
m-806	120	116	�	�	PROPN
m-806	120	117	�	�	PROPN
m-806	120	118	�	�	PROPN
m-806	120	119	�	�	PROPN
m-806	120	120	(	(	PUNCT
m-806	120	121	6.58c	6.58c	PROPN
m-806	120	122	)	)	PUNCT
m-806	120	123	we	we	PRON
m-806	120	124	note	note	VERB
m-806	120	125	from	from	ADP
m-806	120	126	(	(	PUNCT
m-806	120	127	6.56a	6.56a	NUM
m-806	120	128	)	)	PUNCT
m-806	121	1	that	that	PRON
m-806	121	2	�	�	PROPN
m-806	121	3	�	�	PROPN
m-806	121	4	�	�	PROPN
m-806	121	5	(	(	PUNCT
m-806	121	6	0	0	NUM
m-806	121	7	)	)	PUNCT
m-806	121	8	=	=	SYM
m-806	121	9	−	−	NUM
m-806	121	10	�	�	PROPN
m-806	121	11	�	�	PROPN
m-806	121	12	(0	(0	X
m-806	121	13	)	)	PUNCT
m-806	121	14	=	=	SYM
m-806	121	15	�	�	PROPN
m-806	121	16	�	�	PROPN
m-806	121	17	�	�	PROPN
m-806	121	18	�	�	PROPN
m-806	121	19	�	�	PROPN
m-806	121	20	�	�	PROPN
m-806	121	21	�	�	PROPN
m-806	121	22	(	(	PUNCT
m-806	121	23	6.58d	6.58d	NOUN
m-806	121	24	)	)	PUNCT
m-806	121	25	on	on	ADP
m-806	121	26	simplifying	simplify	VERB
m-806	121	27	(	(	PUNCT
m-806	121	28	6.58c	6.58c	PROPN
m-806	121	29	)	)	PUNCT
m-806	121	30	,	,	PUNCT
m-806	121	31	we	we	PRON
m-806	121	32	get	get	VERB
m-806	121	33	�	�	PROPN
m-806	121	34	�	�	PROPN
m-806	121	35	(	(	PUNCT
m-806	121	36	0	0	NUM
m-806	121	37	)	)	PUNCT
m-806	121	38	=	=	SYM
m-806	121	39	�	�	PROPN
m-806	121	40	�	�	PROPN
m-806	121	41	�	�	PROPN
m-806	121	42	�	�	PROPN
m-806	121	43	�	�	PROPN
m-806	121	44	,	,	PUNCT
m-806	121	45	(	(	PUNCT
m-806	121	46	6.58e	6.58e	NOUN
m-806	121	47	)	)	PUNCT
m-806	121	48	�	�	PROPN
m-806	121	49	�	�	PROPN
m-806	121	50	=	=	SYM
m-806	121	51	−	−	PROPN
m-806	121	52	1	1	NUM
m-806	121	53	�	�	PROPN
m-806	121	54	�	�	PROPN
m-806	121	55	�	�	PROPN
m-806	121	56	�	�	PROPN
m-806	121	57	�	�	PROPN
m-806	121	58	�	�	PROPN
m-806	121	59	�	�	PROPN
m-806	121	60	�	�	PROPN
m-806	121	61	�	�	PROPN
m-806	121	62	�	�	PROPN
m-806	121	63	�	�	PROPN
m-806	121	64	�	�	PROPN
m-806	121	65	−	−	PROPN
m-806	121	66	�	�	PROPN
m-806	121	67	�	�	PROPN
m-806	121	68	−	−	PROPN
m-806	121	69	3	3	NUM
m-806	121	70	8	8	NUM
m-806	121	71	(	(	PUNCT
m-806	121	72	�	�	PROPN
m-806	121	73	�	�	PROPN
m-806	121	74	�	�	PROPN
m-806	121	75	�	�	PROPN
m-806	121	76	−	−	PROPN
m-806	121	77	4	4	NUM
m-806	121	78	�	�	PROPN
m-806	121	79	�	�	PROPN
m-806	121	80	)	)	PUNCT
m-806	121	81	−	−	PROPN
m-806	121	82	9	9	NUM
m-806	121	83	56	56	NUM
m-806	121	84	(	(	PUNCT
m-806	121	85	�	�	PROPN
m-806	121	86	�	�	PROPN
m-806	121	87	�	�	PROPN
m-806	121	88	�	�	PROPN
m-806	121	89	−	−	PROPN
m-806	121	90	9	9	NUM
m-806	121	91	�	�	PROPN
m-806	121	92	�	�	PROPN
m-806	121	93	)	)	PUNCT
m-806	121	94	�	�	PROPN
m-806	121	95	�	�	PROPN
m-806	121	96	−	−	PROPN
m-806	121	97	�	�	PROPN
m-806	121	98	�	�	PROPN
m-806	121	99	8	8	NUM
m-806	121	100	+	+	NUM
m-806	121	101	�	�	PROPN
m-806	121	102	�	�	PROPN
m-806	121	103	�	�	PROPN
m-806	121	104	�	�	PROPN
m-806	121	105	�	�	PROPN
m-806	121	106	�	�	PROPN
m-806	121	107	�	�	PROPN
m-806	121	108	�	�	PROPN
m-806	121	109	�	�	PROPN
m-806	121	110	�	�	PROPN
m-806	121	111	+	+	CCONJ
m-806	121	112	�	�	PROPN
m-806	121	113	�	�	PROPN
m-806	121	114	�	�	PROPN
m-806	121	115	�	�	PROPN
m-806	121	116	�	�	PROPN
m-806	121	117	�	�	PROPN
m-806	121	118	�	�	PROPN
m-806	121	119	�	�	PROPN
m-806	121	120	�	�	PROPN
m-806	121	121	�	�	PROPN
m-806	121	122	�	�	PROPN
m-806	121	123	�	�	PROPN
m-806	121	124	−	−	PROPN
m-806	121	125	�	�	PROPN
m-806	121	126	�	�	PROPN
m-806	121	127	�	�	PROPN
m-806	121	128	�	�	PROPN
m-806	121	129	�	�	PROPN
m-806	121	130	�	�	PROPN
m-806	121	131	�	�	PROPN
m-806	121	132	�	�	PROPN
m-806	121	133	�	�	PROPN
m-806	121	134	+	+	CCONJ
m-806	121	135	�	�	PROPN
m-806	121	136	�	�	PROPN
m-806	121	137	�	�	PROPN
m-806	121	138	�	�	PROPN
m-806	121	139	�	�	PROPN
m-806	121	140	�	�	PROPN
m-806	121	141	�	�	PROPN
m-806	121	142	�	�	PROPN
m-806	121	143	�	�	PROPN
m-806	121	144	�	�	PROPN
m-806	121	145	�	�	PROPN
m-806	121	146	�	�	PROPN
m-806	121	147	�	�	PROPN
m-806	121	148	�	�	PROPN
m-806	121	149	(	(	PUNCT
m-806	121	150	6.58f	6.58f	NOUN
m-806	121	151	)	)	PUNCT
m-806	121	152	we	we	PRON
m-806	121	153	next	next	VERB
m-806	121	154	substitute	substitute	NOUN
m-806	121	155	on	on	ADP
m-806	121	156	the	the	DET
m-806	121	157	right	right	ADJ
m-806	121	158	hand	hand	NOUN
m-806	121	159	side	side	NOUN
m-806	121	160	of	of	ADP
m-806	121	161	(	(	PUNCT
m-806	121	162	6.14	6.14	NUM
m-806	121	163	)	)	PUNCT
m-806	121	164	and	and	CCONJ
m-806	121	165	get	get	VERB
m-806	121	166	�	�	PROPN
m-806	121	167	�	�	PROPN
m-806	121	168	(	(	PUNCT
m-806	121	169	�	�	PROPN
m-806	121	170	�	�	PROPN
m-806	121	171	)	)	PUNCT
m-806	121	172	=	=	SYM
m-806	121	173	3	3	NUM
m-806	121	174	�	�	PROPN
m-806	121	175	�	�	PROPN
m-806	121	176	�	�	PROPN
m-806	121	177	�	�	PROPN
m-806	121	178	(	(	PUNCT
m-806	121	179	�	�	PROPN
m-806	121	180	�	�	PROPN
m-806	121	181	)	)	PUNCT
m-806	121	182	�	�	PROPN
m-806	121	183	�	�	PROPN
m-806	121	184	�	�	PROPN
m-806	121	185	(	(	PUNCT
m-806	121	186	�	�	PROPN
m-806	121	187	�	�	PROPN
m-806	121	188	)	)	PUNCT
m-806	121	189	�	�	PROPN
m-806	121	190	�	�	PROPN
m-806	121	191	+	+	CCONJ
m-806	121	192	�	�	PROPN
m-806	121	193	�	�	PROPN
m-806	121	194	�	�	PROPN
m-806	121	195	(	(	PUNCT
m-806	121	196	�	�	PROPN
m-806	121	197	�	�	PROPN
m-806	121	198	)	)	PUNCT
m-806	121	199	�	�	PROPN
m-806	121	200	�	�	PROPN
m-806	121	201	�	�	PROPN
m-806	121	202	�	�	PROPN
m-806	121	203	(	(	PUNCT
m-806	121	204	�	�	PROPN
m-806	121	205	�	�	PROPN
m-806	121	206	)	)	PUNCT
m-806	121	207	�	�	PROPN
m-806	121	208	(	(	PUNCT
m-806	121	209	1	1	NUM
m-806	121	210	−	−	PROPN
m-806	121	211	cos	cos	PROPN
m-806	121	212	2	2	NUM
m-806	121	213	�	�	PROPN
m-806	121	214	�	�	PROPN
m-806	121	215	)	)	PUNCT
m-806	121	216	−	−	PROPN
m-806	121	217	�	�	PROPN
m-806	121	218	�	�	PROPN
m-806	121	219	�	�	PROPN
m-806	121	220	,	,	PUNCT
m-806	121	221	�	�	PROPN
m-806	121	222	�	�	PROPN
m-806	121	223	(	(	PUNCT
m-806	121	224	�	�	PROPN
m-806	121	225	�	�	PROPN
m-806	121	226	)	)	PUNCT
m-806	121	227	(	(	PUNCT
m-806	121	228	1	1	NUM
m-806	121	229	−	−	PROPN
m-806	121	230	cos	cos	PROPN
m-806	121	231	2	2	NUM
m-806	121	232	�	�	PROPN
m-806	121	233	�	�	PROPN
m-806	121	234	)	)	PUNCT
m-806	121	235	+	+	SYM
m-806	121	236	�	�	PROPN
m-806	121	237	�	�	PROPN
m-806	121	238	�	�	PROPN
m-806	121	239	,	,	PUNCT
m-806	121	240	�	�	PROPN
m-806	121	241	�	�	PROPN
m-806	121	242	(	(	PUNCT
m-806	121	243	�	�	PROPN
m-806	121	244	�	�	PROPN
m-806	121	245	)	)	PUNCT
m-806	121	246	(	(	PUNCT
m-806	121	247	1	1	NUM
m-806	121	248	−	−	PROPN
m-806	121	249	cos	cos	PROPN
m-806	121	250	4	4	NUM
m-806	121	251	�	�	PROPN
m-806	121	252	�	�	PROPN
m-806	121	253	)	)	PUNCT
m-806	121	254	+	+	SYM
m-806	121	255	�	�	PROPN
m-806	121	256	�	�	PROPN
m-806	121	257	�	�	PROPN
m-806	121	258	,	,	PUNCT
m-806	121	259	�	�	PROPN
m-806	121	260	�	�	PROPN
m-806	121	261	(	(	PUNCT
m-806	121	262	�	�	PROPN
m-806	121	263	�	�	PROPN
m-806	121	264	)	)	PUNCT
m-806	121	265	(	(	PUNCT
m-806	121	266	1	1	NUM
m-806	121	267	−	−	PROPN
m-806	121	268	cos	cos	PROPN
m-806	121	269	6	6	NUM
m-806	121	270	�	�	PROPN
m-806	121	271	�	�	NOUN
m-806	121	272	)	)	PUNCT
m-806	121	273	�	�	PROPN
m-806	121	274	−2	−2	PROPN
m-806	121	275	�	�	PROPN
m-806	121	276	�	�	PROPN
m-806	121	277	�	�	PROPN
m-806	121	278	,	,	PUNCT
m-806	121	279	�	�	PROPN
m-806	121	280	�	�	PROPN
m-806	121	281	�	�	PROPN
m-806	121	282	(	(	PUNCT
m-806	121	283	�	�	PROPN
m-806	121	284	�	�	PROPN
m-806	121	285	)	)	PUNCT
m-806	121	286	(	(	PUNCT
m-806	121	287	1	1	NUM
m-806	121	288	−	−	PROPN
m-806	121	289	cos	cos	PROPN
m-806	121	290	2	2	NUM
m-806	121	291	�	�	PROPN
m-806	121	292	�	�	PROPN
m-806	121	293	)	)	PUNCT
m-806	121	294	+	+	SYM
m-806	121	295	�	�	PROPN
m-806	121	296	�	�	PROPN
m-806	121	297	�	�	PROPN
m-806	121	298	,	,	PUNCT
m-806	121	299	�	�	PROPN
m-806	121	300	�	�	PROPN
m-806	121	301	�	�	PROPN
m-806	121	302	(	(	PUNCT
m-806	121	303	�	�	PROPN
m-806	121	304	�	�	PROPN
m-806	121	305	)	)	PUNCT
m-806	121	306	(	(	PUNCT
m-806	121	307	1	1	NUM
m-806	121	308	−	−	PROPN
m-806	121	309	cos	cos	PROPN
m-806	121	310	4	4	NUM
m-806	121	311	�	�	PROPN
m-806	121	312	�	�	PROPN
m-806	121	313	)	)	PUNCT
m-806	121	314	+	+	SYM
m-806	121	315	�	�	PROPN
m-806	121	316	�	�	PROPN
m-806	121	317	�	�	PROPN
m-806	121	318	,	,	PUNCT
m-806	121	319	�	�	PROPN
m-806	121	320	�	�	PROPN
m-806	121	321	�	�	PROPN
m-806	121	322	(	(	PUNCT
m-806	121	323	�	�	PROPN
m-806	121	324	�	�	PROPN
m-806	121	325	)	)	PUNCT
m-806	121	326	(	(	PUNCT
m-806	121	327	1	1	NUM
m-806	121	328	−	−	PROPN
m-806	121	329	cos	cos	PROPN
m-806	121	330	6	6	NUM
m-806	121	331	�	�	PROPN
m-806	121	332	�	�	NOUN
m-806	121	333	)	)	PUNCT
m-806	121	334	�	�	PROPN
m-806	121	335	+	+	SYM
m-806	121	336	�	�	PROPN
m-806	121	337	�	�	PROPN
m-806	121	338	�	�	PROPN
m-806	121	339	,	,	PUNCT
m-806	121	340	�	�	PROPN
m-806	121	341	�	�	PROPN
m-806	121	342	(	(	PUNCT
m-806	121	343	�	�	PROPN
m-806	121	344	�	�	PROPN
m-806	121	345	)	)	PUNCT
m-806	121	346	(	(	PUNCT
m-806	121	347	1	1	NUM
m-806	121	348	−	−	PROPN
m-806	121	349	cos	cos	PROPN
m-806	121	350	2	2	NUM
m-806	121	351	�	�	PROPN
m-806	121	352	�	�	PROPN
m-806	121	353	)	)	PUNCT
m-806	121	354	+	+	SYM
m-806	121	355	�	�	PROPN
m-806	121	356	�	�	PROPN
m-806	121	357	�	�	PROPN
m-806	121	358	,	,	PUNCT
m-806	121	359	�	�	PROPN
m-806	121	360	�	�	PROPN
m-806	121	361	(	(	PUNCT
m-806	121	362	�	�	PROPN
m-806	121	363	�	�	PROPN
m-806	121	364	)	)	PUNCT
m-806	121	365	(	(	PUNCT
m-806	121	366	1	1	NUM
m-806	121	367	−	−	PROPN
m-806	121	368	cos	cos	PROPN
m-806	121	369	4	4	NUM
m-806	121	370	�	�	PROPN
m-806	121	371	�	�	PROPN
m-806	121	372	)	)	PUNCT
m-806	121	373	+	+	SYM
m-806	121	374	�	�	PROPN
m-806	121	375	�	�	PROPN
m-806	121	376	�	�	PROPN
m-806	121	377	,	,	PUNCT
m-806	121	378	�	�	PROPN
m-806	121	379	�	�	PROPN
m-806	121	380	(	(	PUNCT
m-806	121	381	�	�	PROPN
m-806	121	382	�	�	PROPN
m-806	121	383	)	)	PUNCT
m-806	121	384	(	(	PUNCT
m-806	121	385	1	1	NUM
m-806	121	386	−	−	PROPN
m-806	121	387	cos	cos	PROPN
m-806	121	388	6	6	NUM
m-806	121	389	�	�	PROPN
m-806	121	390	�	�	NOUN
m-806	121	391	)	)	PUNCT
m-806	121	392	�	�	PROPN
m-806	121	393	+	+	SYM
m-806	121	394	�	�	PROPN
m-806	121	395	�	�	PROPN
m-806	121	396	�	�	PROPN
m-806	121	397	�	�	PROPN
m-806	121	398	�	�	PROPN
m-806	121	399	,	,	PUNCT
m-806	121	400	�	�	PROPN
m-806	121	401	�	�	PROPN
m-806	121	402	�	�	PROPN
m-806	121	403	(	(	PUNCT
m-806	121	404	�	�	PROPN
m-806	121	405	�	�	PROPN
m-806	121	406	)	)	PUNCT
m-806	121	407	(	(	PUNCT
m-806	121	408	1	1	NUM
m-806	121	409	−	−	PROPN
m-806	121	410	cos	cos	PROPN
m-806	121	411	2	2	NUM
m-806	121	412	�	�	PROPN
m-806	121	413	�	�	PROPN
m-806	121	414	)	)	PUNCT
m-806	121	415	−	−	PROPN
m-806	121	416	�	�	PROPN
m-806	121	417	�	�	PROPN
m-806	121	418	�	�	PROPN
m-806	121	419	�	�	PROPN
m-806	121	420	�	�	PROPN
m-806	121	421	�	�	PROPN
m-806	121	422	,	,	PUNCT
m-806	121	423	�	�	PROPN
m-806	121	424	�	�	PROPN
m-806	121	425	(	(	PUNCT
m-806	121	426	�	�	PROPN
m-806	121	427	�	�	PROPN
m-806	121	428	)	)	PUNCT
m-806	121	429	(	(	PUNCT
m-806	121	430	1	1	NUM
m-806	121	431	−	−	PROPN
m-806	121	432	cos	cos	PROPN
m-806	121	433	2	2	NUM
m-806	121	434	�	�	PROPN
m-806	121	435	�	�	PROPN
m-806	121	436	)	)	PUNCT
m-806	121	437	−2	−2	PROPN
m-806	121	438	�	�	PROPN
m-806	121	439	�	�	PROPN
m-806	121	440	�	�	PROPN
m-806	121	441	�	�	PROPN
m-806	121	442	�	�	PROPN
m-806	121	443	�	�	PROPN
m-806	121	444	,	,	PUNCT
m-806	121	445	�	�	PROPN
m-806	121	446	�	�	PROPN
m-806	121	447	(	(	PUNCT
m-806	121	448	�	�	PROPN
m-806	121	449	�	�	PROPN
m-806	121	450	)	)	PUNCT
m-806	121	451	(	(	PUNCT
m-806	121	452	1	1	NUM
m-806	121	453	−	−	PROPN
m-806	121	454	cos	cos	PROPN
m-806	121	455	2	2	NUM
m-806	121	456	�	�	PROPN
m-806	121	457	�	�	PROPN
m-806	121	458	)	)	PUNCT
m-806	121	459	+	+	SYM
m-806	121	460	�	�	PROPN
m-806	121	461	�	�	PROPN
m-806	121	462	,	,	PUNCT
m-806	121	463	�	�	PROPN
m-806	121	464	(	(	PUNCT
m-806	121	465	�	�	PROPN
m-806	121	466	�	�	PROPN
m-806	121	467	)	)	PUNCT
m-806	121	468	(	(	PUNCT
m-806	121	469	1	1	NUM
m-806	121	470	−	−	PROPN
m-806	121	471	cos	cos	PROPN
m-806	121	472	2	2	NUM
m-806	121	473	�	�	PROPN
m-806	121	474	�	�	PROPN
m-806	121	475	)	)	PUNCT
m-806	121	476	+	+	SYM
m-806	121	477	�	�	PROPN
m-806	121	478	�	�	PROPN
m-806	121	479	�	�	PROPN
m-806	121	480	,	,	PUNCT
m-806	121	481	�	�	PROPN
m-806	121	482	(	(	PUNCT
m-806	121	483	�	�	PROPN
m-806	121	484	�	�	PROPN
m-806	121	485	)	)	PUNCT
m-806	121	486	(	(	PUNCT
m-806	121	487	1	1	NUM
m-806	121	488	−	−	PROPN
m-806	121	489	cos	cos	PROPN
m-806	121	490	4	4	NUM
m-806	121	491	�	�	PROPN
m-806	121	492	�	�	PROPN
m-806	121	493	)	)	PUNCT
m-806	121	494	�	�	PROPN
m-806	121	495	+	+	NOUN
m-806	121	496	�	�	PROPN
m-806	121	497	�	�	PROPN
m-806	121	498	�	�	PROPN
m-806	121	499	�	�	PROPN
m-806	121	500	,	,	PUNCT
m-806	121	501	�	�	PROPN
m-806	121	502	(	(	PUNCT
m-806	121	503	�	�	PROPN
m-806	121	504	�	�	PROPN
m-806	121	505	)	)	PUNCT
m-806	121	506	(	(	PUNCT
m-806	121	507	1	1	NUM
m-806	121	508	−	−	PROPN
m-806	121	509	cos	cos	PROPN
m-806	121	510	6	6	NUM
m-806	121	511	�	�	PROPN
m-806	121	512	�	�	PROPN
m-806	121	513	)	)	PUNCT
m-806	121	514	�	�	PROPN
m-806	121	515	(	(	PUNCT
m-806	121	516	6.59a	6.59a	NOUN
m-806	121	517	)	)	PUNCT
m-806	121	518	by	by	ADP
m-806	121	519	letting	let	VERB
m-806	121	520	�	�	PROPN
m-806	121	521	(	(	PUNCT
m-806	121	522	�	�	NOUN
m-806	121	523	�	�	PROPN
m-806	121	524	)	)	PUNCT
m-806	121	525	=	=	PUNCT
m-806	122	1	∑	∑	PUNCT
m-806	122	2	u	u	NOUN
m-806	122	3	�	�	PROPN
m-806	122	4	(	(	PUNCT
m-806	122	5	�	�	PROPN
m-806	122	6	�	�	PROPN
m-806	122	7	)	)	PUNCT
m-806	122	8	(	(	PUNCT
m-806	122	9	1	1	NUM
m-806	122	10	−	−	PROPN
m-806	122	11	cos	cos	PROPN
m-806	122	12	2	2	NUM
m-806	122	13	�	�	PROPN
m-806	122	14	�	�	PROPN
m-806	122	15	)	)	PUNCT
m-806	122	16	�	�	PROPN
m-806	122	17	�	�	PROPN
m-806	122	18	�	�	PROPN
m-806	122	19	�	�	PROPN
m-806	122	20	(	(	PUNCT
m-806	122	21	6.59b	6.59b	NUM
m-806	122	22	)	)	PUNCT
m-806	122	23	and	and	CCONJ
m-806	122	24	substituting	substitute	VERB
m-806	122	25	same	same	ADJ
m-806	122	26	into	into	ADP
m-806	122	27	(	(	PUNCT
m-806	122	28	6.59a	6.59a	NOUN
m-806	122	29	)	)	PUNCT
m-806	122	30	,	,	PUNCT
m-806	122	31	multiplying	multiply	VERB
m-806	122	32	the	the	DET
m-806	122	33	resultant	resultant	NOUN
m-806	122	34	equation	equation	NOUN
m-806	122	35	by	by	ADP
m-806	122	36	cos	cos	PROPN
m-806	122	37	2	2	PROPN
m-806	122	38	�	�	PROPN
m-806	122	39	�	�	PROPN
m-806	122	40	and	and	CCONJ
m-806	122	41	integrating	integrate	VERB
m-806	122	42	from	from	ADP
m-806	122	43	0	0	NUM
m-806	122	44	to	to	ADP
m-806	122	45	π	π	PROPN
m-806	122	46	,	,	PUNCT
m-806	122	47	we	we	PRON
m-806	122	48	see	see	VERB
m-806	122	49	that	that	SCONJ
m-806	122	50	,	,	PUNCT
m-806	122	51	for	for	ADP
m-806	122	52	�	�	PROPN
m-806	122	53	=	=	SYM
m-806	122	54	�	�	PROPN
m-806	122	55	,	,	PUNCT
m-806	122	56	we	we	PRON
m-806	122	57	get	get	VERB
m-806	122	58	u	u	NOUN
m-806	122	59	�	�	PROPN
m-806	122	60	,	,	PUNCT
m-806	122	61	�	�	PROPN
m-806	122	62	�	�	PROPN
m-806	122	63	�	�	PROPN
m-806	122	64	�	�	PROPN
m-806	122	65	(	(	PUNCT
m-806	122	66	�	�	PROPN
m-806	122	67	�	�	PROPN
m-806	122	68	)	)	PUNCT
m-806	123	1	+	+	SYM
m-806	123	2	�	�	PROPN
m-806	123	3	�	�	PROPN
m-806	123	4	u	u	NOUN
m-806	123	5	�	�	PROPN
m-806	123	6	(	(	PUNCT
m-806	123	7	�	�	PROPN
m-806	123	8	�	�	PROPN
m-806	123	9	)	)	PUNCT
m-806	123	10	=	=	SYM
m-806	123	11	45	45	NUM
m-806	123	12	�	�	PROPN
m-806	123	13	4	4	NUM
m-806	123	14	�	�	PROPN
m-806	123	15	�	�	PROPN
m-806	123	16	�	�	PROPN
m-806	123	17	(	(	PUNCT
m-806	123	18	�	�	PROPN
m-806	123	19	�	�	PROPN
m-806	123	20	)	)	PUNCT
m-806	123	21	�	�	PROPN
m-806	123	22	�	�	PROPN
m-806	123	23	�	�	PROPN
m-806	123	24	(	(	PUNCT
m-806	123	25	�	�	PROPN
m-806	123	26	�	�	PROPN
m-806	123	27	)	)	PUNCT
m-806	123	28	�	�	PROPN
m-806	123	29	�	�	PROPN
m-806	123	30	+	+	CCONJ
m-806	123	31	�	�	PROPN
m-806	123	32	�	�	PROPN
m-806	123	33	�	�	PROPN
m-806	123	34	(	(	PUNCT
m-806	123	35	�	�	PROPN
m-806	123	36	�	�	PROPN
m-806	123	37	)	)	PUNCT
m-806	123	38	�	�	PROPN
m-806	123	39	�	�	PROPN
m-806	123	40	�	�	PROPN
m-806	123	41	�	�	PROPN
m-806	123	42	(	(	PUNCT
m-806	123	43	�	�	PROPN
m-806	123	44	�	�	PROPN
m-806	123	45	)	)	PUNCT
m-806	123	46	�	�	PROPN
m-806	123	47	−	−	PROPN
m-806	123	48	�	�	PROPN
m-806	123	49	�	�	PROPN
m-806	123	50	,	,	PUNCT
m-806	123	51	�	�	PROPN
m-806	123	52	�	�	PROPN
m-806	123	53	(	(	PUNCT
m-806	123	54	�	�	PROPN
m-806	123	55	�	�	PROPN
m-806	123	56	)	)	PUNCT
m-806	123	57	−	−	PROPN
m-806	123	58	2	2	NUM
m-806	123	59	�	�	PROPN
m-806	123	60	�	�	PROPN
m-806	123	61	�	�	PROPN
m-806	123	62	,	,	PUNCT
m-806	123	63	�	�	PROPN
m-806	123	64	�	�	PROPN
m-806	123	65	�	�	PROPN
m-806	123	66	(	(	PUNCT
m-806	123	67	�	�	PROPN
m-806	123	68	�	�	PROPN
m-806	123	69	)	)	PUNCT
m-806	123	70	+	+	SYM
m-806	123	71	�	�	PROPN
m-806	123	72	�	�	PROPN
m-806	123	73	,	,	PUNCT
m-806	123	74	�	�	PROPN
m-806	123	75	�	�	PROPN
m-806	123	76	(	(	PUNCT
m-806	123	77	�	�	PROPN
m-806	123	78	�	�	PROPN
m-806	123	79	)	)	PUNCT
m-806	123	80	+	+	SYM
m-806	123	81	�	�	PROPN
m-806	123	82	�	�	PROPN
m-806	123	83	�	�	PROPN
m-806	123	84	�	�	PROPN
m-806	123	85	�	�	PROPN
m-806	123	86	,	,	PUNCT
m-806	123	87	�	�	PROPN
m-806	123	88	�	�	PROPN
m-806	123	89	�	�	PROPN
m-806	123	90	(	(	PUNCT
m-806	123	91	�	�	PROPN
m-806	123	92	�	�	PROPN
m-806	123	93	)	)	PUNCT
m-806	123	94	�	�	PROPN
m-806	123	95	−	−	PROPN
m-806	123	96	�	�	PROPN
m-806	123	97	�	�	PROPN
m-806	123	98	�	�	PROPN
m-806	123	99	�	�	PROPN
m-806	123	100	�	�	PROPN
m-806	123	101	�	�	PROPN
m-806	123	102	,	,	PUNCT
m-806	123	103	�	�	PROPN
m-806	123	104	�	�	PROPN
m-806	123	105	(	(	PUNCT
m-806	123	106	�	�	PROPN
m-806	123	107	�	�	PROPN
m-806	123	108	)	)	PUNCT
m-806	123	109	−	−	PROPN
m-806	123	110	2	2	NUM
m-806	123	111	�	�	PROPN
m-806	123	112	�	�	PROPN
m-806	123	113	�	�	PROPN
m-806	123	114	�	�	PROPN
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m-806	123	123	−	−	PROPN
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m-806	123	133	(	(	PUNCT
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m-806	123	192	6.60b	6.60b	NUM
m-806	123	193	)	)	PUNCT
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m-806	123	198	07	07	NUM
m-806	123	199	|	|	ADV
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m-806	123	201	02	02	NUM
m-806	123	202	|	|	CCONJ
m-806	123	203	february	february	PROPN
m-806	123	204	2024	2024	NUM
m-806	124	1	|	|	ADV
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m-806	124	3	16	16	NUM
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m-806	124	10	issn	issn	PROPN
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m-806	124	14	4421	4421	NUM
m-806	124	15	)	)	PUNCT
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m-806	125	2	.	.	PROPN
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m-806	125	11	02	02	NUM
m-806	125	12	||	||	NUM
m-806	125	13	february	february	PROPN
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m-806	125	16	||	||	NOUN
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m-806	126	2	a	a	DET
m-806	126	3	-	-	PUNCT
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m-806	126	5	-	-	PUNCT
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m-806	126	10	a	a	DET
m-806	126	11	viscously	viscously	ADV
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m-806	126	31	6.59a	6.59a	NOUN
m-806	126	32	)	)	PUNCT
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m-806	127	1	+	+	SYM
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m-806	130	3	substitute	substitute	VERB
m-806	130	4	for	for	ADP
m-806	130	5	terms	term	NOUN
m-806	130	6	on	on	ADP
m-806	130	7	the	the	DET
m-806	130	8	right	right	ADJ
m-806	130	9	hand	hand	NOUN
m-806	130	10	side	side	NOUN
m-806	130	11	of	of	ADP
m-806	130	12	(	(	PUNCT
m-806	130	13	6.60a	6.60a	NOUN
m-806	130	14	)	)	PUNCT
m-806	130	15	,	,	PUNCT
m-806	130	16	we	we	PRON
m-806	130	17	get	get	VERB
m-806	130	18	u	u	PRON
m-806	130	19	�	�	PROPN
m-806	130	20	,	,	PUNCT
m-806	130	21	�	�	PROPN
m-806	130	22	�	�	PROPN
m-806	130	23	�	�	PROPN
m-806	130	24	�	�	PROPN
m-806	130	25	(	(	PUNCT
m-806	130	26	�	�	PROPN
m-806	130	27	�	�	PROPN
m-806	130	28	)	)	PUNCT
m-806	130	29	+	+	SYM
m-806	130	30	�	�	PROPN
m-806	130	31	�	�	PROPN
m-806	130	32	u	u	NOUN
m-806	130	33	�	�	PROPN
m-806	130	34	(	(	PUNCT
m-806	130	35	�	�	PROPN
m-806	130	36	�	�	PROPN
m-806	130	37	)	)	PUNCT
m-806	130	38	=	=	SYM
m-806	130	39	45	45	NUM
m-806	130	40	�	�	PROPN
m-806	130	41	4	4	NUM
m-806	130	42	�	�	PROPN
m-806	130	43	�	�	PROPN
m-806	130	44	�	�	PROPN
m-806	130	45	�	�	PROPN
m-806	130	46	�	�	PROPN
m-806	130	47	�	�	PROPN
m-806	130	48	�	�	PROPN
m-806	130	49	cos	cos	PROPN
m-806	130	50	�	�	PROPN
m-806	130	51	�	�	PROPN
m-806	130	52	̂	̂	VERB
m-806	130	53	4	4	NUM
m-806	130	54	+	+	NUM
m-806	130	55	�	�	PROPN
m-806	130	56	2	2	NUM
m-806	130	57	(	(	PUNCT
m-806	130	58	1	1	NUM
m-806	130	59	−	−	PROPN
m-806	130	60	cos	cos	PROPN
m-806	130	61	2	2	NUM
m-806	130	62	�	�	PROPN
m-806	130	63	�	�	NOUN
m-806	130	64	̂	̂	NUM
m-806	130	65	)	)	PUNCT
m-806	130	66	−	−	PROPN
m-806	130	67	�	�	PROPN
m-806	130	68	�	�	PROPN
m-806	130	69	4	4	NUM
m-806	130	70	cos	cos	PROPN
m-806	130	71	3	3	NUM
m-806	130	72	�	�	PROPN
m-806	130	73	�	�	PROPN
m-806	130	74	̂	̂	NOUN
m-806	130	75	�	�	PROPN
m-806	130	76	�	�	PROPN
m-806	130	77	+	+	SYM
m-806	130	78	�	�	PROPN
m-806	130	79	�	�	PROPN
m-806	130	80	�	�	PROPN
m-806	130	81	�	�	PROPN
m-806	130	82	�	�	PROPN
m-806	130	83	�	�	PROPN
m-806	130	84	+	+	SYM
m-806	130	85	�	�	PROPN
m-806	130	86	�	�	PROPN
m-806	130	87	�	�	PROPN
m-806	130	88	�	�	PROPN
m-806	130	89	�	�	PROPN
m-806	130	90	+	+	CCONJ
m-806	130	91	�	�	PROPN
m-806	130	92	�	�	PROPN
m-806	130	93	�	�	PROPN
m-806	130	94	�	�	PROPN
m-806	130	95	�	�	PROPN
m-806	130	96	�	�	PROPN
m-806	130	97	cos	cos	PROPN
m-806	130	98	�	�	PROPN
m-806	130	99	�	�	PROPN
m-806	130	100	̂	̂	VERB
m-806	130	101	+	+	NUM
m-806	130	102	�	�	PROPN
m-806	130	103	�	�	PROPN
m-806	130	104	�	�	PROPN
m-806	130	105	�	�	PROPN
m-806	130	106	�	�	PROPN
m-806	130	107	+	+	SYM
m-806	130	108	�	�	PROPN
m-806	130	109	�	�	PROPN
m-806	130	110	�	�	PROPN
m-806	130	111	�	�	PROPN
m-806	130	112	�	�	PROPN
m-806	130	113	�	�	PROPN
m-806	130	114	�	�	PROPN
m-806	130	115	�	�	PROPN
m-806	130	116	�	�	PROPN
m-806	130	117	�	�	PROPN
m-806	130	118	̂	̂	NUM
m-806	130	119	�	�	PROPN
m-806	130	120	+	+	SYM
m-806	130	121	�	�	PROPN
m-806	130	122	�	�	PROPN
m-806	130	123	�	�	PROPN
m-806	130	124	�	�	PROPN
m-806	130	125	�	�	PROPN
m-806	130	126	�	�	PROPN
m-806	130	127	�	�	PROPN
m-806	130	128	cos	cos	PROPN
m-806	130	129	2	2	PROPN
m-806	130	130	�	�	PROPN
m-806	130	131	�	�	PROPN
m-806	130	132	̂	̂	VERB
m-806	130	133	+	+	NUM
m-806	130	134	�	�	PROPN
m-806	130	135	�	�	PROPN
m-806	130	136	�	�	PROPN
m-806	130	137	�	�	PROPN
m-806	130	138	�	�	PROPN
m-806	130	139	�	�	PROPN
m-806	130	140	�	�	PROPN
m-806	130	141	�	�	PROPN
m-806	130	142	2	2	NUM
m-806	130	143	�	�	PROPN
m-806	130	144	�	�	PROPN
m-806	130	145	̂	̂	VERB
m-806	130	146	+	+	NUM
m-806	130	147	�	�	PROPN
m-806	130	148	�	�	PROPN
m-806	130	149	�	�	PROPN
m-806	130	150	�	�	PROPN
m-806	130	151	�	�	PROPN
m-806	130	152	�	�	PROPN
m-806	130	153	cos	cos	PROPN
m-806	130	154	3	3	PROPN
m-806	130	155	�	�	PROPN
m-806	130	156	�	�	PROPN
m-806	130	157	̂	̂	VERB
m-806	130	158	+	+	NUM
m-806	130	159	�	�	PROPN
m-806	130	160	�	�	PROPN
m-806	130	161	�	�	PROPN
m-806	130	162	�	�	PROPN
m-806	130	163	�	�	PROPN
m-806	130	164	�	�	PROPN
m-806	130	165	sin	sin	VERB
m-806	130	166	3	3	NUM
m-806	130	167	�	�	PROPN
m-806	130	168	�	�	PROPN
m-806	130	169	̂	̂	NOUN
m-806	130	170	�	�	PROPN
m-806	130	171	�	�	PROPN
m-806	130	172	−	−	PROPN
m-806	130	173	�	�	PROPN
m-806	130	174	�	�	PROPN
m-806	130	175	�	�	PROPN
m-806	130	176	�	�	PROPN
m-806	130	177	�	�	PROPN
m-806	130	178	cos	cos	PROPN
m-806	130	179	�	�	PROPN
m-806	130	180	�	�	PROPN
m-806	130	181	̂	̂	VERB
m-806	130	182	+	+	NUM
m-806	130	183	�	�	PROPN
m-806	130	184	�	�	PROPN
m-806	130	185	�	�	PROPN
m-806	130	186	�	�	PROPN
m-806	130	187	�	�	PROPN
m-806	130	188	�	�	PROPN
m-806	130	189	�	�	PROPN
m-806	130	190	�	�	PROPN
m-806	130	191	�	�	PROPN
m-806	130	192	�	�	PROPN
m-806	130	193	�	�	PROPN
m-806	130	194	−	−	PROPN
m-806	130	195	�	�	PROPN
m-806	130	196	�	�	PROPN
m-806	130	197	�	�	PROPN
m-806	130	198	�	�	PROPN
m-806	130	199	�	�	PROPN
m-806	130	200	�	�	PROPN
m-806	130	201	�	�	PROPN
m-806	130	202	�	�	PROPN
m-806	130	203	�	�	PROPN
m-806	130	204	�	�	PROPN
m-806	130	205	�	�	PROPN
m-806	130	206	cos	cos	PROPN
m-806	130	207	2	2	PROPN
m-806	130	208	�	�	PROPN
m-806	130	209	�	�	PROPN
m-806	130	210	̂	̂	VERB
m-806	130	211	−	−	PROPN
m-806	130	212	�	�	PROPN
m-806	130	213	�	�	PROPN
m-806	130	214	�	�	PROPN
m-806	130	215	�	�	PROPN
m-806	130	216	�	�	PROPN
m-806	130	217	�	�	PROPN
m-806	130	218	�	�	PROPN
m-806	130	219	�	�	PROPN
m-806	130	220	�	�	PROPN
m-806	130	221	�	�	PROPN
m-806	130	222	�	�	PROPN
m-806	131	1	cos	cos	PROPN
m-806	131	2	3	3	PROPN
m-806	131	3	�	�	PROPN
m-806	131	4	�	�	PROPN
m-806	131	5	̂	̂	SYM
m-806	131	6	�	�	PROPN
m-806	131	7	�	�	PROPN
m-806	131	8	−2	−2	PROPN
m-806	131	9	�	�	PROPN
m-806	131	10	�	�	PROPN
m-806	131	11	�	�	PROPN
m-806	131	12	�	�	PROPN
m-806	131	13	�	�	PROPN
m-806	131	14	�	�	PROPN
m-806	131	15	cos	cos	PROPN
m-806	131	16	�	�	PROPN
m-806	131	17	�	�	PROPN
m-806	131	18	̂	̂	VERB
m-806	131	19	−	−	PROPN
m-806	131	20	�	�	PROPN
m-806	131	21	�	�	PROPN
m-806	131	22	�	�	PROPN
m-806	131	23	�	�	PROPN
m-806	131	24	sin	sin	PROPN
m-806	131	25	�	�	PROPN
m-806	131	26	�	�	PROPN
m-806	131	27	̂	̂	VERB
m-806	131	28	−	−	PROPN
m-806	131	29	2	2	NUM
m-806	131	30	�	�	PROPN
m-806	131	31	�	�	PROPN
m-806	131	32	�	�	PROPN
m-806	131	33	3	3	NUM
m-806	131	34	�	�	PROPN
m-806	131	35	cos	cos	PROPN
m-806	131	36	2	2	PROPN
m-806	131	37	�	�	PROPN
m-806	131	38	�	�	PROPN
m-806	131	39	̂	̂	VERB
m-806	131	40	−	−	PROPN
m-806	131	41	3	3	NUM
m-806	131	42	�	�	PROPN
m-806	131	43	�	�	PROPN
m-806	131	44	�	�	PROPN
m-806	131	45	8	8	NUM
m-806	131	46	�	�	PROPN
m-806	131	47	cos	cos	PROPN
m-806	131	48	3	3	PROPN
m-806	131	49	�	�	PROPN
m-806	131	50	�	�	PROPN
m-806	131	51	̂	̂	NOUN
m-806	131	52	�	�	PROPN
m-806	131	53	�	�	PROPN
m-806	131	54	−	−	PROPN
m-806	131	55	�	�	PROPN
m-806	131	56	�	�	PROPN
m-806	131	57	�	�	PROPN
m-806	131	58	�	�	PROPN
m-806	131	59	�	�	PROPN
m-806	131	60	�	�	PROPN
m-806	131	61	�	�	PROPN
m-806	131	62	�	�	PROPN
m-806	131	63	cos	cos	PROPN
m-806	131	64	�	�	PROPN
m-806	131	65	�	�	PROPN
m-806	131	66	̂	̂	NUM
m-806	131	67	]	]	PUNCT
m-806	131	68	−	−	PROPN
m-806	131	69	�	�	PROPN
m-806	131	70	�	�	PROPN
m-806	131	71	�	�	PROPN
m-806	131	72	�	�	PROPN
m-806	131	73	�	�	PROPN
m-806	131	74	�	�	PROPN
m-806	131	75	�	�	PROPN
m-806	131	76	cos	cos	PROPN
m-806	131	77	�	�	PROPN
m-806	131	78	�	�	PROPN
m-806	131	79	̂	̂	VERB
m-806	131	80	−	−	PROPN
m-806	131	81	2	2	NUM
m-806	131	82	�	�	PROPN
m-806	131	83	�	�	PROPN
m-806	131	84	�	�	PROPN
m-806	131	85	�	�	PROPN
m-806	131	86	�	�	PROPN
m-806	131	87	�	�	PROPN
m-806	131	88	cos	cos	PROPN
m-806	131	89	�	�	PROPN
m-806	131	90	�	�	PROPN
m-806	131	91	̂	̂	VERB
m-806	131	92	−2	−2	PROPN
m-806	131	93	�	�	PROPN
m-806	131	94	�	�	PROPN
m-806	131	95	�	�	PROPN
m-806	131	96	�	�	PROPN
m-806	131	97	cos	cos	PROPN
m-806	131	98	�	�	PROPN
m-806	131	99	�	�	PROPN
m-806	131	100	̂	̂	VERB
m-806	131	101	+	+	NUM
m-806	131	102	�	�	PROPN
m-806	131	103	�	�	PROPN
m-806	131	104	�	�	PROPN
m-806	131	105	�	�	PROPN
m-806	131	106	�	�	PROPN
m-806	131	107	�	�	PROPN
m-806	131	108	�	�	PROPN
m-806	131	109	�	�	PROPN
m-806	131	110	�	�	PROPN
m-806	131	111	�	�	PROPN
m-806	131	112	−	−	PROPN
m-806	131	113	�	�	PROPN
m-806	131	114	�	�	PROPN
m-806	131	115	�	�	PROPN
m-806	131	116	�	�	PROPN
m-806	131	117	�	�	PROPN
m-806	131	118	�	�	PROPN
m-806	131	119	�	�	PROPN
m-806	131	120	�	�	PROPN
m-806	131	121	�	�	PROPN
m-806	131	122	�	�	PROPN
m-806	131	123	cos	cos	PROPN
m-806	131	124	2	2	PROPN
m-806	131	125	�	�	PROPN
m-806	131	126	�	�	PROPN
m-806	131	127	̂	̂	VERB
m-806	131	128	−	−	PROPN
m-806	131	129	�	�	PROPN
m-806	131	130	�	�	PROPN
m-806	131	131	�	�	PROPN
m-806	131	132	�	�	PROPN
m-806	131	133	�	�	PROPN
m-806	131	134	�	�	PROPN
m-806	131	135	�	�	PROPN
m-806	131	136	�	�	PROPN
m-806	131	137	�	�	PROPN
m-806	131	138	�	�	PROPN
m-806	131	139	cos	cos	PROPN
m-806	131	140	3	3	PROPN
m-806	131	141	�	�	PROPN
m-806	131	142	�	�	PROPN
m-806	131	143	̂	̂	NOUN
m-806	131	144	�	�	NOUN
m-806	131	145	�	�	PROPN
m-806	131	146	(	(	PUNCT
m-806	131	147	6.63a	6.63a	NOUN
m-806	131	148	)	)	PUNCT
m-806	131	149	to	to	PART
m-806	131	150	ensure	ensure	VERB
m-806	131	151	a	a	DET
m-806	131	152	uniformly	uniformly	ADV
m-806	131	153	valid	valid	ADJ
m-806	131	154	solution	solution	NOUN
m-806	131	155	in	in	ADP
m-806	131	156	�	�	PROPN
m-806	131	157	̂	̂	PUNCT
m-806	131	158	as	as	ADV
m-806	131	159	far	far	ADV
m-806	131	160	as	as	ADP
m-806	131	161	(	(	PUNCT
m-806	131	162	6.63a	6.63a	NOUN
m-806	131	163	)	)	PUNCT
m-806	131	164	is	be	AUX
m-806	131	165	concerned	concern	VERB
m-806	131	166	,	,	PUNCT
m-806	131	167	we	we	PRON
m-806	131	168	equate	equate	VERB
m-806	131	169	to	to	ADP
m-806	131	170	zero	zero	NUM
m-806	131	171	the	the	DET
m-806	131	172	coefficients	coefficient	NOUN
m-806	131	173	of	of	ADP
m-806	131	174	cos	cos	PROPN
m-806	131	175	�	�	PROPN
m-806	131	176	�	�	PROPN
m-806	131	177	̂	̂	VERB
m-806	131	178	and	and	CCONJ
m-806	131	179	sin	sin	PROPN
m-806	131	180	�	�	PROPN
m-806	131	181	�	�	PROPN
m-806	131	182	̂	̂	VERB
m-806	131	183	and	and	CCONJ
m-806	131	184	respectively	respectively	ADV
m-806	131	185	get	get	VERB
m-806	131	186	�	�	PROPN
m-806	131	187	�	�	PROPN
m-806	131	188	�	�	PROPN
m-806	131	189	+	+	CCONJ
m-806	131	190	�	�	PROPN
m-806	131	191	�	�	PROPN
m-806	131	192	=	=	PUNCT
m-806	131	193	−ℎ	−ℎ	NOUN
m-806	131	194	�	�	PROPN
m-806	131	195	(	(	PUNCT
m-806	131	196	�	�	PROPN
m-806	131	197	)	)	PUNCT
m-806	131	198	=	=	SYM
m-806	131	199	−	−	PROPN
m-806	131	200	�	�	PROPN
m-806	131	201	�	�	PROPN
m-806	131	202	�	�	PROPN
m-806	131	203	�	�	PROPN
m-806	131	204	�	�	PROPN
m-806	131	205	�	�	PROPN
m-806	131	206	�	�	PROPN
m-806	131	207	�	�	PROPN
m-806	131	208	+	+	SYM
m-806	131	209	�	�	PROPN
m-806	131	210	�	�	PROPN
m-806	131	211	�	�	PROPN
m-806	131	212	�	�	PROPN
m-806	131	213	�	�	PROPN
m-806	131	214	(	(	PUNCT
m-806	131	215	6.63b	6.63b	PROPN
m-806	131	216	)	)	PUNCT
m-806	131	217	and	and	CCONJ
m-806	131	218	�	�	PROPN
m-806	131	219	�	�	PROPN
m-806	131	220	�	�	PROPN
m-806	131	221	+	+	CCONJ
m-806	131	222	�	�	PROPN
m-806	131	223	�	�	PROPN
m-806	131	224	=	=	SYM
m-806	131	225	ℎ	ℎ	PROPN
m-806	131	226	�	�	PROPN
m-806	131	227	(	(	PUNCT
m-806	131	228	�	�	PROPN
m-806	131	229	)	)	PUNCT
m-806	131	230	=	=	SYM
m-806	131	231	−	−	PROPN
m-806	131	232	�	�	PROPN
m-806	131	233	�	�	PROPN
m-806	131	234	�	�	PROPN
m-806	131	235	�	�	PROPN
m-806	131	236	�	�	PROPN
m-806	131	237	�	�	PROPN
m-806	131	238	�	�	PROPN
m-806	131	239	�	�	PROPN
m-806	131	240	�	�	PROPN
m-806	131	241	�	�	PROPN
m-806	131	242	�	�	PROPN
m-806	131	243	�	�	PROPN
m-806	131	244	�	�	PROPN
m-806	131	245	�	�	PROPN
m-806	131	246	�	�	PROPN
m-806	131	247	+	+	CCONJ
m-806	131	248	�	�	PROPN
m-806	131	249	�	�	PROPN
m-806	131	250	�	�	PROPN
m-806	131	251	�	�	PROPN
m-806	131	252	�	�	PROPN
m-806	131	253	+	+	CCONJ
m-806	131	254	�	�	PROPN
m-806	131	255	�	�	PROPN
m-806	131	256	�	�	PROPN
m-806	131	257	�	�	PROPN
m-806	131	258	�	�	PROPN
m-806	131	259	�	�	PROPN
m-806	131	260	�	�	PROPN
m-806	132	1	−	−	PROPN
m-806	132	2	2	2	NUM
m-806	132	3	�	�	PROPN
m-806	132	4	�	�	PROPN
m-806	132	5	�	�	PROPN
m-806	132	6	−	−	PROPN
m-806	132	7	�	�	PROPN
m-806	132	8	�	�	PROPN
m-806	132	9	�	�	PROPN
m-806	132	10	�	�	PROPN
m-806	132	11	−	−	PROPN
m-806	132	12	�	�	PROPN
m-806	132	13	�	�	PROPN
m-806	132	14	�	�	PROPN
m-806	132	15	�	�	PROPN
m-806	132	16	�	�	PROPN
m-806	132	17	�	�	PROPN
m-806	132	18	�	�	PROPN
m-806	132	19	�	�	PROPN
m-806	132	20	−	−	PROPN
m-806	132	21	�	�	PROPN
m-806	132	22	�	�	PROPN
m-806	132	23	�	�	PROPN
m-806	132	24	�	�	PROPN
m-806	132	25	�	�	PROPN
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m-806	132	87	+	+	CCONJ
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m-806	132	106	|	|	ADV
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m-806	132	109	|	|	CCONJ
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m-806	132	112	|	|	ADV
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m-806	132	125	4421	4421	NUM
m-806	132	126	)	)	PUNCT
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m-806	133	9	07	07	NUM
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m-806	133	12	||	||	NUM
m-806	133	13	february	february	PROPN
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m-806	134	5	-	-	PUNCT
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m-806	134	26	6.60a	6.60a	NOUN
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m-806	134	37	�	�	PROPN
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m-806	135	1	+	+	SYM
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m-806	137	95	+	+	CCONJ
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m-806	137	224	�	�	PROPN
m-806	137	225	�	�	PROPN
m-806	137	226	�	�	PROPN
m-806	137	227	�	�	PROPN
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m-806	137	229	,	,	PUNCT
m-806	137	230	�	�	PROPN
m-806	137	231	�	�	PROPN
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m-806	137	233	(	(	PUNCT
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m-806	137	235	)	)	PUNCT
m-806	137	236	=	=	SYM
m-806	137	237	�	�	PROPN
m-806	137	238	�	�	PROPN
m-806	137	239	�	�	PROPN
m-806	137	240	�	�	PROPN
m-806	137	241	�	�	PROPN
m-806	137	242	�	�	PROPN
m-806	137	243	�	�	PROPN
m-806	137	244	�	�	PROPN
m-806	137	245	�	�	PROPN
m-806	137	246	�	�	PROPN
m-806	137	247	,	,	PUNCT
m-806	137	248	�	�	PROPN
m-806	137	249	�	�	PROPN
m-806	137	250	�	�	PROPN
m-806	137	251	(	(	PUNCT
m-806	137	252	0	0	NUM
m-806	137	253	)	)	PUNCT
m-806	137	254	=	=	SYM
m-806	137	255	�	�	PROPN
m-806	137	256	�	�	PROPN
m-806	137	257	�	�	PROPN
m-806	137	258	�	�	PROPN
m-806	137	259	�	�	PROPN
m-806	137	260	�	�	PROPN
m-806	137	261	�	�	PROPN
m-806	137	262	�	�	PROPN
m-806	137	263	,	,	PUNCT
m-806	137	264	(	(	PUNCT
m-806	137	265	6.64h	6.64h	NUM
m-806	137	266	)	)	PUNCT
m-806	137	267	�	�	PROPN
m-806	137	268	�	�	PROPN
m-806	137	269	�	�	PROPN
m-806	137	270	(	(	PUNCT
m-806	137	271	0	0	NUM
m-806	137	272	)	)	PUNCT
m-806	137	273	=	=	SYM
m-806	137	274	�	�	PROPN
m-806	137	275	�	�	PROPN
m-806	137	276	�	�	PROPN
m-806	137	277	�	�	PROPN
m-806	137	278	�	�	PROPN
m-806	137	279	�	�	PROPN
m-806	137	280	�	�	PROPN
m-806	137	281	�	�	PROPN
m-806	137	282	�	�	PROPN
m-806	137	283	�	�	PROPN
m-806	137	284	�	�	PROPN
m-806	137	285	�	�	PROPN
m-806	137	286	,	,	PUNCT
m-806	137	287	�	�	PROPN
m-806	137	288	�	�	PROPN
m-806	137	289	�	�	PROPN
m-806	137	290	(	(	PUNCT
m-806	137	291	0	0	NUM
m-806	137	292	)	)	PUNCT
m-806	137	293	=	=	SYM
m-806	137	294	�	�	PROPN
m-806	137	295	�	�	PROPN
m-806	137	296	�	�	PROPN
m-806	137	297	�	�	PROPN
m-806	137	298	�	�	PROPN
m-806	137	299	�	�	PROPN
m-806	137	300	�	�	PROPN
m-806	137	301	�	�	PROPN
m-806	137	302	�	�	PROPN
m-806	137	303	�	�	PROPN
m-806	137	304	(	(	PUNCT
m-806	137	305	6.64i	6.64i	NUM
m-806	137	306	)	)	PUNCT
m-806	137	307	on	on	ADP
m-806	137	308	solving	solve	VERB
m-806	137	309	(	(	PUNCT
m-806	137	310	6.64a	6.64a	NOUN
m-806	137	311	)	)	PUNCT
m-806	137	312	,	,	PUNCT
m-806	137	313	using	use	VERB
m-806	137	314	(	(	PUNCT
m-806	137	315	6.64b	6.64b	NUM
m-806	137	316	)	)	PUNCT
m-806	137	317	we	we	PRON
m-806	137	318	get	get	VERB
m-806	137	319	u	u	NOUN
m-806	137	320	�	�	PROPN
m-806	137	321	(	(	PUNCT
m-806	137	322	�	�	PROPN
m-806	137	323	�	�	PROPN
m-806	137	324	)	)	PUNCT
m-806	137	325	(	(	PUNCT
m-806	137	326	�	�	PROPN
m-806	137	327	̂	̂	NUM
m-806	137	328	,	,	PUNCT
m-806	137	329	�	�	PROPN
m-806	137	330	)	)	PUNCT
m-806	137	331	=	=	SYM
m-806	137	332	�	�	PROPN
m-806	137	333	�	�	PROPN
m-806	137	334	�	�	PROPN
m-806	137	335	cos	cos	PROPN
m-806	137	336	�	�	PROPN
m-806	137	337	�	�	PROPN
m-806	137	338	̂	̂	VERB
m-806	137	339	+	+	NUM
m-806	137	340	�	�	PROPN
m-806	137	341	�	�	PROPN
m-806	137	342	�	�	PROPN
m-806	137	343	sin	sin	PROPN
m-806	137	344	�	�	PROPN
m-806	137	345	�	�	PROPN
m-806	137	346	̂	̂	VERB
m-806	137	347	+	+	NUM
m-806	137	348	�	�	PROPN
m-806	137	349	�	�	PROPN
m-806	137	350	�	�	PROPN
m-806	137	351	�	�	PROPN
m-806	137	352	�	�	PROPN
m-806	137	353	−	−	PROPN
m-806	137	354	1	1	NUM
m-806	137	355	3	3	NUM
m-806	137	356	�	�	PROPN
m-806	137	357	�	�	PROPN
m-806	137	358	(	(	PUNCT
m-806	137	359	�	�	PROPN
m-806	137	360	�	�	PROPN
m-806	137	361	�	�	PROPN
m-806	137	362	cos	cos	PROPN
m-806	137	363	2	2	PROPN
m-806	137	364	�	�	PROPN
m-806	137	365	�	�	PROPN
m-806	137	366	̂	̂	VERB
m-806	137	367	+	+	NUM
m-806	137	368	�	�	PROPN
m-806	137	369	�	�	PROPN
m-806	137	370	�	�	PROPN
m-806	137	371	sin	sin	NOUN
m-806	137	372	2	2	NUM
m-806	137	373	�	�	PROPN
m-806	137	374	�	�	NOUN
m-806	137	375	̂	̂	NUM
m-806	137	376	)	)	PUNCT
m-806	137	377	−	−	PROPN
m-806	137	378	�	�	PROPN
m-806	137	379	�	�	PROPN
m-806	137	380	�	�	PROPN
m-806	137	381	�	�	PROPN
m-806	137	382	(	(	PUNCT
m-806	137	383	�	�	PROPN
m-806	137	384	�	�	PROPN
m-806	137	385	�	�	PROPN
m-806	137	386	cos	cos	PROPN
m-806	137	387	3	3	PROPN
m-806	137	388	�	�	PROPN
m-806	137	389	�	�	PROPN
m-806	137	390	̂	̂	VERB
m-806	137	391	+	+	NUM
m-806	137	392	�	�	PROPN
m-806	137	393	�	�	PROPN
m-806	137	394	�	�	PROPN
m-806	137	395	sin	sin	NOUN
m-806	137	396	3	3	NUM
m-806	137	397	�	�	PROPN
m-806	137	398	�	�	NOUN
m-806	137	399	̂	̂	NUM
m-806	137	400	)	)	PUNCT
m-806	137	401	(	(	PUNCT
m-806	137	402	6.65a	6.65a	NOUN
m-806	137	403	)	)	PUNCT
m-806	138	1	where	where	SCONJ
m-806	138	2	,	,	PUNCT
m-806	138	3	�	�	PROPN
m-806	138	4	�	�	PROPN
m-806	138	5	�	�	PROPN
m-806	138	6	(	(	PUNCT
m-806	138	7	0	0	NUM
m-806	138	8	)	)	PUNCT
m-806	138	9	=	=	SYM
m-806	138	10	−	−	PROPN
m-806	138	11	�	�	PROPN
m-806	138	12	�	�	PROPN
m-806	138	13	�	�	PROPN
m-806	138	14	(0	(0	NOUN
m-806	138	15	)	)	PUNCT
m-806	138	16	�	�	PROPN
m-806	138	17	�	�	PROPN
m-806	138	18	+	+	CCONJ
m-806	138	19	�	�	PROPN
m-806	138	20	�	�	PROPN
m-806	138	21	�	�	PROPN
m-806	138	22	(	(	PUNCT
m-806	138	23	0	0	NUM
m-806	138	24	)	)	PUNCT
m-806	138	25	3	3	NUM
m-806	138	26	�	�	PROPN
m-806	138	27	�	�	PROPN
m-806	138	28	+	+	SYM
m-806	138	29	�	�	PROPN
m-806	138	30	�	�	PROPN
m-806	138	31	�	�	PROPN
m-806	138	32	(	(	PUNCT
m-806	138	33	0	0	NUM
m-806	138	34	)	)	PUNCT
m-806	138	35	8	8	NUM
m-806	138	36	�	�	PROPN
m-806	138	37	�	�	PROPN
m-806	138	38	�	�	PROPN
m-806	138	39	�	�	PROPN
m-806	138	40	�	�	PROPN
m-806	138	41	(	(	PUNCT
m-806	138	42	0	0	NUM
m-806	138	43	)	)	PUNCT
m-806	138	44	=	=	SYM
m-806	138	45	�	�	PROPN
m-806	138	46	�	�	PROPN
m-806	138	47	�	�	PROPN
m-806	138	48	�	�	PROPN
m-806	138	49	�	�	PROPN
m-806	138	50	�	�	PROPN
m-806	138	51	�	�	PROPN
m-806	138	52	�	�	PROPN
m-806	138	53	�	�	PROPN
m-806	138	54	�	�	PROPN
m-806	138	55	�	�	PROPN
m-806	138	56	�	�	PROPN
m-806	138	57	�	�	PROPN
m-806	138	58	�	�	PROPN
m-806	138	59	,	,	PUNCT
m-806	138	60	�	�	PROPN
m-806	138	61	�	�	PROPN
m-806	138	62	�	�	PROPN
m-806	138	63	(	(	PUNCT
m-806	138	64	0	0	NUM
m-806	138	65	)	)	PUNCT
m-806	138	66	=	=	SYM
m-806	138	67	0	0	PUNCT
m-806	138	68	(	(	PUNCT
m-806	138	69	6.65b	6.65b	NUM
m-806	138	70	)	)	PUNCT
m-806	138	71	as	as	SCONJ
m-806	138	72	was	be	AUX
m-806	138	73	in	in	ADP
m-806	138	74	the	the	DET
m-806	138	75	case	case	NOUN
m-806	138	76	of	of	ADP
m-806	138	77	u	u	PROPN
m-806	138	78	�	�	PROPN
m-806	138	79	(	(	PUNCT
m-806	138	80	�	�	PROPN
m-806	138	81	�	�	PROPN
m-806	138	82	)	)	PUNCT
m-806	138	83	in	in	ADP
m-806	138	84	(	(	PUNCT
m-806	138	85	6.60a	6.60a	NOUN
m-806	138	86	)	)	PUNCT
m-806	138	87	which	which	PRON
m-806	138	88	eventually	eventually	ADV
m-806	138	89	led	lead	VERB
m-806	138	90	to	to	ADP
m-806	138	91	(	(	PUNCT
m-806	138	92	6.65a	6.65a	PROPN
m-806	138	93	)	)	PUNCT
m-806	138	94	,	,	PUNCT
m-806	138	95	we	we	PRON
m-806	138	96	now	now	ADV
m-806	138	97	substitute	substitute	VERB
m-806	138	98	for	for	ADP
m-806	138	99	terms	term	NOUN
m-806	138	100	into	into	ADP
m-806	138	101	(	(	PUNCT
m-806	138	102	6.61a	6.61a	NOUN
m-806	138	103	)	)	PUNCT
m-806	138	104	and	and	CCONJ
m-806	138	105	to	to	PART
m-806	138	106	ensure	ensure	VERB
m-806	138	107	a	a	DET
m-806	138	108	uniformly	uniformly	ADV
m-806	138	109	valid	valid	ADJ
m-806	138	110	solution	solution	NOUN
m-806	138	111	in	in	ADP
m-806	138	112	�	�	PROPN
m-806	138	113	̂	̂	NUM
m-806	138	114	,	,	PUNCT
m-806	138	115	we	we	PRON
m-806	138	116	equate	equate	VERB
m-806	138	117	to	to	ADP
m-806	138	118	zero	zero	NUM
m-806	138	119	the	the	DET
m-806	138	120	coefficients	coefficient	NOUN
m-806	138	121	of	of	ADP
m-806	138	122	cos	cos	PROPN
m-806	138	123	�	�	PROPN
m-806	138	124	�	�	PROPN
m-806	138	125	�	�	PROPN
m-806	138	126	�	�	PROPN
m-806	138	127	̂	̂	VERB
m-806	138	128	and	and	CCONJ
m-806	138	129	sin	sin	PROPN
m-806	138	130	�	�	PROPN
m-806	138	131	�	�	PROPN
m-806	138	132	�	�	PROPN
m-806	138	133	�	�	PROPN
m-806	138	134	̂	̂	VERB
m-806	138	135	and	and	CCONJ
m-806	138	136	respectively	respectively	ADV
m-806	138	137	get	get	VERB
m-806	138	138	�	�	PROPN
m-806	138	139	�	�	PROPN
m-806	138	140	�	�	PROPN
m-806	138	141	+	+	CCONJ
m-806	138	142	�	�	PROPN
m-806	138	143	�	�	PROPN
m-806	138	144	=	=	SYM
m-806	138	145	�	�	PROPN
m-806	138	146	�	�	PROPN
m-806	138	147	�	�	PROPN
m-806	138	148	�	�	PROPN
m-806	138	149	(	(	PUNCT
m-806	138	150	�	�	PROPN
m-806	138	151	�	�	PROPN
m-806	138	152	�	�	PROPN
m-806	138	153	�	�	PROPN
m-806	138	154	+	+	CCONJ
m-806	138	155	2	2	NUM
m-806	138	156	�	�	PROPN
m-806	138	157	�	�	PROPN
m-806	138	158	�	�	PROPN
m-806	138	159	)	)	PUNCT
m-806	138	160	(	(	PUNCT
m-806	138	161	6.66a	6.66a	NOUN
m-806	138	162	)	)	PUNCT
m-806	138	163	and	and	CCONJ
m-806	138	164	�	�	PROPN
m-806	138	165	�	�	PROPN
m-806	138	166	�	�	PROPN
m-806	138	167	+	+	CCONJ
m-806	138	168	�	�	PROPN
m-806	138	169	�	�	PROPN
m-806	138	170	=	=	SYM
m-806	138	171	�	�	PROPN
m-806	138	172	�	�	PROPN
m-806	138	173	�	�	PROPN
m-806	138	174	�	�	PROPN
m-806	138	175	(	(	PUNCT
m-806	138	176	�	�	PROPN
m-806	138	177	�	�	PROPN
m-806	138	178	�	�	PROPN
m-806	138	179	�	�	PROPN
m-806	138	180	+	+	CCONJ
m-806	138	181	2	2	NUM
m-806	138	182	�	�	PROPN
m-806	138	183	�	�	PROPN
m-806	138	184	�	�	PROPN
m-806	138	185	)	)	PUNCT
m-806	138	186	(	(	PUNCT
m-806	138	187	6.66b	6.66b	NUM
m-806	138	188	)	)	PUNCT
m-806	138	189	on	on	ADP
m-806	138	190	solving	solve	VERB
m-806	138	191	,	,	PUNCT
m-806	138	192	we	we	PRON
m-806	138	193	get	get	VERB
m-806	138	194	�	�	PROPN
m-806	138	195	�	�	PROPN
m-806	138	196	=	=	SYM
m-806	138	197	�	�	PROPN
m-806	138	198	�	�	PROPN
m-806	138	199	�	�	PROPN
m-806	138	200	�	�	PROPN
m-806	138	201	�	�	PROPN
m-806	138	202	�	�	PROPN
m-806	138	203	(	(	PUNCT
m-806	138	204	0	0	NUM
m-806	138	205	)	)	PUNCT
m-806	138	206	−	−	PROPN
m-806	138	207	�	�	PROPN
m-806	138	208	�	�	PROPN
m-806	138	209	�	�	PROPN
m-806	138	210	∫	∫	PROPN
m-806	138	211	�	�	PROPN
m-806	138	212	�	�	PROPN
m-806	138	213	(	(	PUNCT
m-806	138	214	�	�	PROPN
m-806	138	215	�	�	PROPN
m-806	138	216	�	�	PROPN
m-806	138	217	�	�	PROPN
m-806	138	218	+	+	CCONJ
m-806	138	219	2	2	NUM
m-806	138	220	�	�	PROPN
m-806	138	221	�	�	PROPN
m-806	138	222	�	�	PROPN
m-806	138	223	)	)	PUNCT
m-806	138	224	�	�	PROPN
m-806	138	225	�	�	PROPN
m-806	138	226	�	�	PROPN
m-806	138	227	�	�	PROPN
m-806	138	228	�	�	PROPN
m-806	138	229	(	(	PUNCT
m-806	138	230	6.66b	6.66b	PROPN
m-806	138	231	)	)	PUNCT
m-806	138	232	�	�	PROPN
m-806	138	233	�	�	PROPN
m-806	138	234	=	=	SYM
m-806	138	235	�	�	PROPN
m-806	138	236	�	�	PROPN
m-806	138	237	�	�	PROPN
m-806	138	238	�	�	PROPN
m-806	138	239	�	�	PROPN
m-806	138	240	�	�	PROPN
m-806	138	241	(	(	PUNCT
m-806	138	242	0	0	NUM
m-806	138	243	)	)	PUNCT
m-806	138	244	−	−	PROPN
m-806	138	245	�	�	PROPN
m-806	138	246	�	�	PROPN
m-806	138	247	�	�	PROPN
m-806	138	248	∫	∫	PROPN
m-806	138	249	�	�	PROPN
m-806	138	250	�	�	PROPN
m-806	138	251	(	(	PUNCT
m-806	138	252	�	�	PROPN
m-806	138	253	�	�	PROPN
m-806	138	254	�	�	PROPN
m-806	138	255	�	�	PROPN
m-806	138	256	+	+	CCONJ
m-806	138	257	2	2	NUM
m-806	138	258	�	�	PROPN
m-806	138	259	�	�	PROPN
m-806	138	260	�	�	PROPN
m-806	138	261	)	)	PUNCT
m-806	138	262	�	�	PROPN
m-806	138	263	�	�	PROPN
m-806	138	264	�	�	PROPN
m-806	138	265	�	�	PROPN
m-806	138	266	�	�	PROPN
m-806	138	267	(	(	PUNCT
m-806	138	268	6.66c	6.66c	PROPN
m-806	138	269	)	)	PUNCT
m-806	138	270	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
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m-806	138	272	journals	journal	NOUN
m-806	138	273	volume	volume	NOUN
m-806	138	274	07	07	NUM
m-806	138	275	|	|	ADV
m-806	138	276	issue	issue	NOUN
m-806	138	277	02	02	NUM
m-806	138	278	|	|	CCONJ
m-806	138	279	february	february	PROPN
m-806	138	280	2024	2024	NUM
m-806	139	1	|	|	ADV
m-806	139	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	139	3	18	18	NUM
m-806	139	4	ijo	ijo	PROPN
m-806	139	5	international	international	ADJ
m-806	139	6	journal	journal	PROPN
m-806	139	7	of	of	ADP
m-806	139	8	mathematics	mathematics	PROPN
m-806	139	9	(	(	PUNCT
m-806	139	10	issn	issn	PROPN
m-806	139	11	:	:	PUNCT
m-806	139	12	2992	2992	NUM
m-806	139	13	-	-	SYM
m-806	139	14	4421	4421	NUM
m-806	139	15	)	)	PUNCT
m-806	139	16	i.u	i.u	PROPN
m-806	139	17	.	.	PROPN
m-806	139	18	udo	udo	PROPN
m-806	139	19	-	-	PROPN
m-806	139	20	akpan1	akpan1	ADJ
m-806	139	21	*	*	PUNCT
m-806	139	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	139	23	volume	volume	NOUN
m-806	139	24	07	07	NUM
m-806	139	25	issue	issue	NOUN
m-806	139	26	02	02	NUM
m-806	139	27	||	||	NUM
m-806	139	28	february	february	PROPN
m-806	139	29	,	,	PUNCT
m-806	139	30	2024	2024	NUM
m-806	139	31	||	||	NOUN
m-806	139	32	on	on	ADP
m-806	139	33	a	a	DET
m-806	139	34	-	-	PUNCT
m-806	139	35	two	two	NUM
m-806	139	36	-	-	PUNCT
m-806	139	37	parameter	parameter	NOUN
m-806	139	38	dynamic	dynamic	ADJ
m-806	139	39	buckling	buckling	NOUN
m-806	139	40	of	of	ADP
m-806	139	41	a	a	DET
m-806	139	42	viscously	viscously	ADV
m-806	139	43	damped	damp	VERB
m-806	139	44	but	but	CCONJ
m-806	139	45	clamped	clamp	VERB
m-806	139	46	column	column	NOUN
m-806	139	47	stressed	stress	VERB
m-806	139	48	by	by	ADP
m-806	139	49	a	a	DET
m-806	139	50	step	step	NOUN
m-806	139	51	load	load	NOUN
m-806	139	52	the	the	DET
m-806	139	53	remaining	remain	VERB
m-806	139	54	equation	equation	NOUN
m-806	139	55	in	in	ADP
m-806	139	56	the	the	DET
m-806	139	57	substitution	substitution	NOUN
m-806	139	58	into	into	ADP
m-806	139	59	(	(	PUNCT
m-806	139	60	6.61a	6.61a	NOUN
m-806	139	61	)	)	PUNCT
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m-806	139	72	�	�	PROPN
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m-806	139	74	)	)	PUNCT
m-806	140	1	+	+	SYM
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m-806	140	9	(	(	PUNCT
m-806	140	10	�	�	PROPN
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m-806	140	12	)	)	PUNCT
m-806	140	13	=	=	SYM
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m-806	140	18	�	�	PROPN
m-806	140	19	�	�	PROPN
m-806	140	20	�	�	PROPN
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m-806	140	22	�	�	PROPN
m-806	140	23	�	�	PROPN
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m-806	140	25	+	+	NUM
m-806	140	26	�	�	PROPN
m-806	140	27	�	�	PROPN
m-806	140	28	�	�	PROPN
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m-806	140	31	�	�	PROPN
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m-806	140	33	+	+	NUM
m-806	140	34	�	�	PROPN
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m-806	140	36	�	�	PROPN
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m-806	140	40	�	�	PROPN
m-806	140	41	̂	̂	VERB
m-806	140	42	+	+	NUM
m-806	140	43	�	�	PROPN
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m-806	140	49	�	�	PROPN
m-806	140	50	̂	̂	VERB
m-806	140	51	+	+	NUM
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m-806	140	53	�	�	PROPN
m-806	140	54	�	�	PROPN
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m-806	140	57	�	�	PROPN
m-806	140	58	�	�	PROPN
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m-806	140	60	+	+	NUM
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m-806	140	70	6.67a	6.67a	NOUN
m-806	140	71	)	)	PUNCT
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m-806	140	77	�	�	PROPN
m-806	140	78	)	)	PUNCT
m-806	140	79	(	(	PUNCT
m-806	140	80	0,0	0,0	NUM
m-806	140	81	)	)	PUNCT
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m-806	140	92	�	�	PROPN
m-806	140	93	�	�	PROPN
m-806	140	94	)	)	PUNCT
m-806	140	95	(	(	PUNCT
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m-806	140	99	)	)	PUNCT
m-806	140	100	+	+	CCONJ
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m-806	140	107	�	�	PROPN
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m-806	140	109	)	)	PUNCT
m-806	140	110	(	(	PUNCT
m-806	140	111	0	0	NUM
m-806	140	112	,	,	PUNCT
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m-806	140	114	)	)	PUNCT
m-806	140	115	(	(	PUNCT
m-806	140	116	6.67b	6.67b	NOUN
m-806	140	117	)	)	PUNCT
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m-806	140	121	�	�	PROPN
m-806	140	122	�	�	PROPN
m-806	140	123	=	=	SYM
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m-806	140	125	�	�	PROPN
m-806	140	126	�	�	PROPN
m-806	140	127	�	�	PROPN
m-806	140	128	(	(	PUNCT
m-806	140	129	�	�	PROPN
m-806	140	130	�	�	PROPN
m-806	140	131	�	�	PROPN
m-806	140	132	�	�	PROPN
m-806	140	133	+	+	CCONJ
m-806	140	134	�	�	PROPN
m-806	140	135	�	�	PROPN
m-806	140	136	�	�	PROPN
m-806	140	137	�	�	PROPN
m-806	140	138	�	�	PROPN
m-806	140	139	)	)	PUNCT
m-806	140	140	+	+	SYM
m-806	140	141	�	�	PROPN
m-806	140	142	�	�	PROPN
m-806	140	143	�	�	PROPN
m-806	140	144	�	�	PROPN
m-806	140	145	�	�	PROPN
m-806	140	146	�	�	PROPN
m-806	140	147	�	�	PROPN
m-806	140	148	�	�	PROPN
m-806	140	149	�	�	PROPN
m-806	140	150	+	+	CCONJ
m-806	140	151	�	�	PROPN
m-806	140	152	�	�	PROPN
m-806	140	153	�	�	PROPN
m-806	140	154	�	�	PROPN
m-806	140	155	�	�	PROPN
m-806	140	156	�	�	PROPN
m-806	140	157	�	�	PROPN
m-806	140	158	�	�	PROPN
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m-806	140	160	�	�	PROPN
m-806	140	161	�	�	PROPN
m-806	140	162	(	(	PUNCT
m-806	140	163	6.67c	6.67c	NUM
m-806	140	164	)	)	PUNCT
m-806	140	165	�	�	PROPN
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m-806	140	168	=	=	SYM
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m-806	140	172	�	�	PROPN
m-806	140	173	�	�	PROPN
m-806	140	174	�	�	PROPN
m-806	140	175	�	�	PROPN
m-806	140	176	�	�	PROPN
m-806	140	177	�	�	PROPN
m-806	140	178	�	�	PROPN
m-806	140	179	�	�	PROPN
m-806	140	180	+	+	CCONJ
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m-806	140	182	�	�	PROPN
m-806	140	183	�	�	PROPN
m-806	140	184	�	�	PROPN
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m-806	140	186	�	�	PROPN
m-806	140	187	�	�	PROPN
m-806	140	188	�	�	PROPN
m-806	140	189	+	+	CCONJ
m-806	140	190	�	�	PROPN
m-806	140	191	�	�	PROPN
m-806	140	192	�	�	PROPN
m-806	140	193	�	�	PROPN
m-806	140	194	+	+	SYM
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m-806	140	196	�	�	PROPN
m-806	140	197	�	�	PROPN
m-806	140	198	�	�	PROPN
m-806	140	199	�	�	PROPN
m-806	140	200	�	�	PROPN
m-806	140	201	�	�	PROPN
m-806	140	202	�	�	PROPN
m-806	140	203	�	�	PROPN
m-806	140	204	�	�	PROPN
m-806	140	205	�	�	PROPN
m-806	140	206	�	�	PROPN
m-806	140	207	�	�	PROPN
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m-806	140	211	+	+	SYM
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m-806	140	213	�	�	PROPN
m-806	140	214	�	�	PROPN
m-806	140	215	�	�	PROPN
m-806	140	216	�	�	PROPN
m-806	140	217	�	�	PROPN
m-806	140	218	�	�	PROPN
m-806	140	219	�	�	PROPN
m-806	140	220	�	�	PROPN
m-806	140	221	�	�	PROPN
m-806	140	222	�	�	PROPN
m-806	140	223	�	�	PROPN
m-806	140	224	�	�	PROPN
m-806	140	225	�	�	PROPN
m-806	140	226	�	�	PROPN
m-806	140	227	−	−	PROPN
m-806	140	228	�	�	PROPN
m-806	140	229	�	�	PROPN
m-806	140	230	�	�	PROPN
m-806	140	231	�	�	PROPN
m-806	140	232	�	�	PROPN
m-806	140	233	�	�	PROPN
m-806	140	234	�	�	PROPN
m-806	140	235	�	�	PROPN
m-806	140	236	�	�	PROPN
m-806	140	237	�	�	PROPN
m-806	140	238	�	�	PROPN
m-806	140	239	�	�	PROPN
m-806	140	240	�	�	PROPN
m-806	140	241	�	�	PROPN
m-806	140	242	�	�	PROPN
m-806	140	243	�	�	PROPN
m-806	140	244	�	�	PROPN
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m-806	140	246	6.67d	6.67d	NOUN
m-806	140	247	)	)	PUNCT
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m-806	140	251	=	=	SYM
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m-806	140	253	�	�	PROPN
m-806	140	254	�	�	PROPN
m-806	140	255	�	�	PROPN
m-806	140	256	�	�	PROPN
m-806	140	257	�	�	PROPN
m-806	140	258	�	�	PROPN
m-806	140	259	�	�	PROPN
m-806	140	260	�	�	PROPN
m-806	140	261	�	�	PROPN
m-806	140	262	�	�	PROPN
m-806	140	263	�	�	PROPN
m-806	140	264	+	+	CCONJ
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m-806	140	266	�	�	PROPN
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m-806	140	269	6.67e	6.67e	PROPN
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m-806	140	274	=	=	SYM
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m-806	140	280	�	�	PROPN
m-806	140	281	�	�	PROPN
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m-806	140	283	+	+	CCONJ
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m-806	140	285	�	�	PROPN
m-806	140	286	�	�	PROPN
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m-806	140	288	�	�	PROPN
m-806	140	289	�	�	PROPN
m-806	140	290	+	+	SYM
m-806	140	291	�	�	PROPN
m-806	140	292	�	�	PROPN
m-806	140	293	�	�	PROPN
m-806	140	294	�	�	PROPN
m-806	140	295	�	�	PROPN
m-806	140	296	�	�	PROPN
m-806	140	297	�	�	PROPN
m-806	140	298	�	�	PROPN
m-806	140	299	�	�	PROPN
m-806	140	300	�	�	PROPN
m-806	140	301	�	�	PROPN
m-806	140	302	�	�	PROPN
m-806	140	303	�	�	PROPN
m-806	140	304	�	�	PROPN
m-806	140	305	�	�	PROPN
m-806	140	306	�	�	PROPN
m-806	140	307	�	�	PROPN
m-806	140	308	�	�	PROPN
m-806	140	309	�	�	PROPN
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m-806	140	311	�	�	PROPN
m-806	140	312	+	+	SYM
m-806	140	313	�	�	PROPN
m-806	140	314	�	�	PROPN
m-806	140	315	�	�	PROPN
m-806	140	316	�	�	PROPN
m-806	140	317	�	�	PROPN
m-806	140	318	�	�	PROPN
m-806	140	319	�	�	PROPN
m-806	140	320	�	�	PROPN
m-806	140	321	�	�	PROPN
m-806	140	322	�	�	PROPN
m-806	140	323	�	�	PROPN
m-806	140	324	�	�	PROPN
m-806	140	325	�	�	PROPN
m-806	140	326	�	�	PROPN
m-806	140	327	�	�	PROPN
m-806	140	328	�	�	PROPN
m-806	140	329	�	�	PROPN
m-806	140	330	�	�	PROPN
m-806	140	331	�	�	PROPN
m-806	140	332	�	�	PROPN
m-806	140	333	−	−	PROPN
m-806	140	334	�	�	PROPN
m-806	140	335	�	�	PROPN
m-806	140	336	�	�	PROPN
m-806	140	337	�	�	PROPN
m-806	140	338	�	�	PROPN
m-806	140	339	�	�	PROPN
m-806	140	340	�	�	PROPN
m-806	140	341	�	�	PROPN
m-806	140	342	�	�	PROPN
m-806	140	343	�	�	PROPN
m-806	140	344	�	�	PROPN
m-806	140	345	�	�	PROPN
m-806	140	346	�	�	PROPN
m-806	140	347	�	�	PROPN
m-806	140	348	�	�	PROPN
m-806	140	349	�	�	PROPN
m-806	140	350	�	�	PROPN
m-806	140	351	�	�	PROPN
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m-806	140	354	)	)	PUNCT
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m-806	140	358	=	=	SYM
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m-806	140	360	�	�	PROPN
m-806	140	361	�	�	PROPN
m-806	140	362	�	�	PROPN
m-806	140	363	�	�	PROPN
m-806	140	364	�	�	PROPN
m-806	140	365	�	�	PROPN
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m-806	140	380	�	�	PROPN
m-806	140	381	�	�	PROPN
m-806	140	382	�	�	PROPN
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m-806	140	384	−	−	PROPN
m-806	140	385	�	�	PROPN
m-806	140	386	�	�	PROPN
m-806	140	387	�	�	PROPN
m-806	140	388	�	�	PROPN
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m-806	140	391	+	+	CCONJ
m-806	140	392	�	�	PROPN
m-806	140	393	�	�	PROPN
m-806	140	394	�	�	PROPN
m-806	140	395	�	�	PROPN
m-806	140	396	�	�	PROPN
m-806	140	397	�	�	PROPN
m-806	140	398	�	�	PROPN
m-806	140	399	�	�	PROPN
m-806	140	400	�	�	PROPN
m-806	140	401	�	�	PROPN
m-806	140	402	�	�	PROPN
m-806	140	403	�	�	PROPN
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m-806	140	405	�	�	PROPN
m-806	140	406	�	�	PROPN
m-806	140	407	�	�	PROPN
m-806	140	408	�	�	PROPN
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m-806	140	412	+	+	SYM
m-806	140	413	�	�	PROPN
m-806	140	414	�	�	PROPN
m-806	140	415	�	�	PROPN
m-806	140	416	�	�	PROPN
m-806	140	417	�	�	PROPN
m-806	140	418	�	�	PROPN
m-806	140	419	�	�	PROPN
m-806	140	420	�	�	PROPN
m-806	140	421	�	�	PROPN
m-806	140	422	�	�	PROPN
m-806	140	423	�	�	PROPN
m-806	140	424	�	�	PROPN
m-806	140	425	�	�	PROPN
m-806	140	426	�	�	PROPN
m-806	140	427	�	�	PROPN
m-806	140	428	�	�	PROPN
m-806	140	429	�	�	PROPN
m-806	140	430	�	�	PROPN
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m-806	140	433	�	�	PROPN
m-806	140	434	�	�	PROPN
m-806	140	435	�	�	PROPN
m-806	140	436	�	�	PROPN
m-806	140	437	�	�	PROPN
m-806	140	438	�	�	PROPN
m-806	140	439	�	�	PROPN
m-806	140	440	�	�	PROPN
m-806	140	441	�	�	PROPN
m-806	140	442	�	�	PROPN
m-806	140	443	�	�	PROPN
m-806	140	444	�	�	PROPN
m-806	140	445	�	�	PROPN
m-806	140	446	�	�	PROPN
m-806	140	447	�	�	PROPN
m-806	140	448	�	�	PROPN
m-806	140	449	�	�	PROPN
m-806	140	450	�	�	PROPN
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m-806	140	457	=	=	SYM
m-806	140	458	�	�	PROPN
m-806	140	459	�	�	PROPN
m-806	140	460	�	�	PROPN
m-806	140	461	�	�	PROPN
m-806	140	462	�	�	PROPN
m-806	140	463	�	�	PROPN
m-806	140	464	�	�	PROPN
m-806	140	465	�	�	PROPN
m-806	140	466	�	�	PROPN
m-806	140	467	(	(	PUNCT
m-806	140	468	6.67i	6.67i	NUM
m-806	140	469	)	)	PUNCT
m-806	140	470	on	on	ADP
m-806	140	471	solving	solve	VERB
m-806	140	472	(	(	PUNCT
m-806	140	473	6.67a	6.67a	NOUN
m-806	140	474	,	,	PUNCT
m-806	140	475	b	b	NOUN
m-806	140	476	)	)	PUNCT
m-806	140	477	,	,	PUNCT
m-806	140	478	we	we	PRON
m-806	140	479	get	get	VERB
m-806	140	480	u	u	NOUN
m-806	140	481	�	�	PROPN
m-806	140	482	�	�	PROPN
m-806	140	483	(	(	PUNCT
m-806	140	484	�	�	PROPN
m-806	140	485	�	�	PROPN
m-806	140	486	)	)	PUNCT
m-806	140	487	(	(	PUNCT
m-806	140	488	�	�	PROPN
m-806	140	489	̂	̂	NUM
m-806	140	490	,	,	PUNCT
m-806	140	491	�	�	PROPN
m-806	140	492	)	)	PUNCT
m-806	140	493	=	=	SYM
m-806	140	494	�	�	PROPN
m-806	140	495	�	�	PROPN
m-806	140	496	�	�	PROPN
m-806	140	497	cos	cos	PROPN
m-806	140	498	�	�	PROPN
m-806	140	499	�	�	PROPN
m-806	140	500	�	�	PROPN
m-806	140	501	�	�	PROPN
m-806	140	502	̂	̂	VERB
m-806	140	503	+	+	NUM
m-806	140	504	�	�	PROPN
m-806	140	505	�	�	PROPN
m-806	140	506	�	�	PROPN
m-806	140	507	sin	sin	PROPN
m-806	140	508	�	�	PROPN
m-806	140	509	�	�	PROPN
m-806	140	510	�	�	PROPN
m-806	140	511	�	�	PROPN
m-806	140	512	̂	̂	VERB
m-806	140	513	+	+	NUM
m-806	140	514	�	�	PROPN
m-806	140	515	�	�	PROPN
m-806	140	516	�	�	PROPN
m-806	140	517	�	�	PROPN
m-806	140	518	�	�	PROPN
m-806	140	519	�	�	PROPN
m-806	140	520	�	�	PROPN
m-806	140	521	+	+	CCONJ
m-806	140	522	�	�	PROPN
m-806	140	523	1	1	NUM
m-806	140	524	�	�	PROPN
m-806	140	525	�	�	PROPN
m-806	140	526	�	�	PROPN
m-806	140	527	�	�	PROPN
m-806	140	528	−	−	PROPN
m-806	140	529	�	�	PROPN
m-806	140	530	�	�	PROPN
m-806	140	531	�	�	PROPN
m-806	140	532	(	(	PUNCT
m-806	140	533	�	�	PROPN
m-806	140	534	�	�	PROPN
m-806	140	535	�	�	PROPN
m-806	140	536	cos	cos	PROPN
m-806	140	537	�	�	PROPN
m-806	140	538	�	�	PROPN
m-806	140	539	̂	̂	VERB
m-806	140	540	+	+	NUM
m-806	140	541	�	�	PROPN
m-806	140	542	�	�	PROPN
m-806	140	543	�	�	PROPN
m-806	140	544	sin	sin	PROPN
m-806	140	545	�	�	PROPN
m-806	140	546	�	�	PROPN
m-806	140	547	̂	̂	NUM
m-806	140	548	)	)	PUNCT
m-806	141	1	+	+	CCONJ
m-806	141	2	�	�	PROPN
m-806	141	3	�	�	PROPN
m-806	141	4	�	�	PROPN
m-806	141	5	�	�	PROPN
m-806	141	6	�	�	PROPN
m-806	141	7	�	�	PROPN
m-806	141	8	�	�	PROPN
m-806	141	9	�	�	PROPN
m-806	141	10	�	�	PROPN
m-806	141	11	�	�	PROPN
m-806	141	12	�	�	PROPN
m-806	141	13	(	(	PUNCT
m-806	141	14	�	�	PROPN
m-806	141	15	�	�	PROPN
m-806	141	16	�	�	PROPN
m-806	141	17	cos	cos	PROPN
m-806	141	18	2	2	PROPN
m-806	141	19	�	�	PROPN
m-806	141	20	�	�	PROPN
m-806	141	21	̂	̂	VERB
m-806	141	22	+	+	NUM
m-806	141	23	�	�	PROPN
m-806	141	24	�	�	PROPN
m-806	141	25	�	�	PROPN
m-806	141	26	sin	sin	NOUN
m-806	141	27	2	2	NUM
m-806	141	28	�	�	PROPN
m-806	141	29	�	�	NOUN
m-806	141	30	̂	̂	NUM
m-806	141	31	)	)	PUNCT
m-806	142	1	+	+	CCONJ
m-806	142	2	�	�	PROPN
m-806	142	3	�	�	PROPN
m-806	142	4	�	�	PROPN
m-806	142	5	�	�	PROPN
m-806	142	6	�	�	PROPN
m-806	142	7	�	�	PROPN
m-806	142	8	�	�	PROPN
m-806	142	9	�	�	PROPN
m-806	142	10	�	�	PROPN
m-806	142	11	�	�	PROPN
m-806	142	12	�	�	PROPN
m-806	142	13	(	(	PUNCT
m-806	142	14	�	�	PROPN
m-806	142	15	�	�	PROPN
m-806	142	16	�	�	PROPN
m-806	142	17	cos	cos	PROPN
m-806	142	18	3	3	PROPN
m-806	142	19	�	�	PROPN
m-806	142	20	�	�	PROPN
m-806	142	21	̂	̂	VERB
m-806	142	22	+	+	NUM
m-806	142	23	�	�	PROPN
m-806	142	24	�	�	PROPN
m-806	142	25	�	�	PROPN
m-806	142	26	sin	sin	NOUN
m-806	142	27	3	3	NUM
m-806	142	28	�	�	PROPN
m-806	142	29	�	�	NOUN
m-806	142	30	̂	̂	NUM
m-806	142	31	)	)	PUNCT
m-806	142	32	(	(	PUNCT
m-806	142	33	6.68a	6.68a	NOUN
m-806	142	34	)	)	PUNCT
m-806	142	35	we	we	PRON
m-806	142	36	may	may	AUX
m-806	142	37	not	not	PART
m-806	142	38	need	need	VERB
m-806	142	39	�	�	PROPN
m-806	142	40	�	�	PROPN
m-806	142	41	�	�	PROPN
m-806	142	42	(	(	PUNCT
m-806	142	43	0	0	NUM
m-806	142	44	)	)	PUNCT
m-806	142	45	and	and	CCONJ
m-806	142	46	�	�	PROPN
m-806	142	47	�	�	PROPN
m-806	142	48	�	�	PROPN
m-806	142	49	(	(	PUNCT
m-806	142	50	0	0	NUM
m-806	142	51	)	)	PUNCT
m-806	142	52	.	.	PUNCT
m-806	143	1	we	we	PRON
m-806	143	2	next	next	VERB
m-806	143	3	substitute	substitute	VERB
m-806	143	4	into	into	ADP
m-806	143	5	(	(	PUNCT
m-806	143	6	6.62a	6.62a	NOUN
m-806	143	7	)	)	PUNCT
m-806	143	8	and	and	CCONJ
m-806	143	9	to	to	PART
m-806	143	10	ensure	ensure	VERB
m-806	143	11	a	a	DET
m-806	143	12	uniformly	uniformly	ADV
m-806	143	13	valid	valid	ADJ
m-806	143	14	solution	solution	NOUN
m-806	143	15	in	in	ADP
m-806	143	16	�	�	PROPN
m-806	143	17	̂	̂	NUM
m-806	143	18	,	,	PUNCT
m-806	143	19	equate	equate	ADJ
m-806	143	20	to	to	ADP
m-806	143	21	zero	zero	NUM
m-806	143	22	,	,	PUNCT
m-806	143	23	the	the	DET
m-806	143	24	coefficients	coefficient	NOUN
m-806	143	25	of	of	ADP
m-806	143	26	cos	cos	PROPN
m-806	143	27	�	�	PROPN
m-806	143	28	�	�	PROPN
m-806	143	29	�	�	PROPN
m-806	143	30	�	�	PROPN
m-806	143	31	̂	̂	VERB
m-806	143	32	and	and	CCONJ
m-806	143	33	sin	sin	PROPN
m-806	143	34	�	�	PROPN
m-806	143	35	�	�	PROPN
m-806	143	36	�	�	PROPN
m-806	143	37	�	�	PROPN
m-806	143	38	̂	̂	VERB
m-806	143	39	and	and	CCONJ
m-806	143	40	respectively	respectively	ADV
m-806	143	41	get	get	VERB
m-806	143	42	�	�	PROPN
m-806	143	43	�	�	PROPN
m-806	143	44	�	�	PROPN
m-806	143	45	+	+	CCONJ
m-806	143	46	�	�	PROPN
m-806	143	47	�	�	PROPN
m-806	143	48	=	=	SYM
m-806	143	49	�	�	PROPN
m-806	143	50	�	�	PROPN
m-806	143	51	�	�	PROPN
m-806	143	52	�	�	PROPN
m-806	143	53	�	�	PROPN
m-806	143	54	�	�	PROPN
m-806	143	55	(	(	PUNCT
m-806	143	56	�	�	PROPN
m-806	143	57	�	�	PROPN
m-806	143	58	�	�	PROPN
m-806	143	59	�	�	PROPN
m-806	143	60	+	+	CCONJ
m-806	143	61	2	2	NUM
m-806	143	62	�	�	PROPN
m-806	143	63	�	�	PROPN
m-806	143	64	�	�	PROPN
m-806	143	65	)	)	PUNCT
m-806	143	66	(	(	PUNCT
m-806	143	67	6.68b	6.68b	NUM
m-806	143	68	)	)	PUNCT
m-806	143	69	and	and	CCONJ
m-806	143	70	�	�	PROPN
m-806	143	71	�	�	PROPN
m-806	143	72	�	�	PROPN
m-806	143	73	+	+	CCONJ
m-806	143	74	�	�	PROPN
m-806	143	75	�	�	PROPN
m-806	143	76	=	=	SYM
m-806	143	77	�	�	PROPN
m-806	143	78	�	�	PROPN
m-806	143	79	�	�	PROPN
m-806	143	80	�	�	PROPN
m-806	143	81	�	�	PROPN
m-806	143	82	(	(	PUNCT
m-806	143	83	�	�	PROPN
m-806	143	84	�	�	PROPN
m-806	143	85	�	�	PROPN
m-806	143	86	�	�	PROPN
m-806	143	87	+	+	CCONJ
m-806	143	88	2	2	NUM
m-806	143	89	�	�	PROPN
m-806	143	90	�	�	PROPN
m-806	143	91	�	�	PROPN
m-806	143	92	)	)	PUNCT
m-806	143	93	(	(	PUNCT
m-806	143	94	6.68c	6.68c	NOUN
m-806	143	95	)	)	PUNCT
m-806	143	96	on	on	ADP
m-806	143	97	solving	solve	VERB
m-806	143	98	,	,	PUNCT
m-806	143	99	we	we	PRON
m-806	143	100	get	get	VERB
m-806	143	101	�	�	PROPN
m-806	143	102	�	�	PROPN
m-806	143	103	=	=	SYM
m-806	143	104	�	�	PROPN
m-806	143	105	�	�	PROPN
m-806	143	106	�	�	PROPN
m-806	143	107	�	�	PROPN
m-806	143	108	�	�	PROPN
m-806	143	109	�	�	PROPN
m-806	143	110	(	(	PUNCT
m-806	143	111	0	0	NUM
m-806	143	112	)	)	PUNCT
m-806	143	113	−	−	PROPN
m-806	143	114	�	�	PROPN
m-806	143	115	�	�	PROPN
m-806	143	116	�	�	PROPN
m-806	143	117	�	�	PROPN
m-806	143	118	�	�	PROPN
m-806	143	119	∫	∫	PROPN
m-806	143	120	�	�	PROPN
m-806	143	121	�	�	PROPN
m-806	143	122	(	(	PUNCT
m-806	143	123	�	�	PROPN
m-806	143	124	�	�	PROPN
m-806	143	125	�	�	PROPN
m-806	143	126	�	�	PROPN
m-806	143	127	+	+	CCONJ
m-806	143	128	2	2	NUM
m-806	143	129	�	�	PROPN
m-806	143	130	�	�	PROPN
m-806	143	131	�	�	PROPN
m-806	143	132	)	)	PUNCT
m-806	143	133	�	�	PROPN
m-806	143	134	�	�	PROPN
m-806	143	135	�	�	PROPN
m-806	143	136	�	�	PROPN
m-806	143	137	�	�	PROPN
m-806	143	138	(	(	PUNCT
m-806	143	139	6.68d	6.68d	PROPN
m-806	143	140	)	)	PUNCT
m-806	143	141	�	�	PROPN
m-806	143	142	�	�	PROPN
m-806	143	143	=	=	SYM
m-806	143	144	�	�	PROPN
m-806	143	145	�	�	PROPN
m-806	143	146	�	�	PROPN
m-806	143	147	�	�	PROPN
m-806	143	148	�	�	PROPN
m-806	143	149	�	�	PROPN
m-806	143	150	(	(	PUNCT
m-806	143	151	0	0	NUM
m-806	143	152	)	)	PUNCT
m-806	143	153	+	+	CCONJ
m-806	143	154	�	�	PROPN
m-806	143	155	�	�	PROPN
m-806	143	156	�	�	PROPN
m-806	143	157	�	�	PROPN
m-806	143	158	�	�	PROPN
m-806	143	159	�	�	PROPN
m-806	143	160	∫	∫	PROPN
m-806	143	161	�	�	PROPN
m-806	143	162	�	�	PROPN
m-806	143	163	(	(	PUNCT
m-806	143	164	�	�	PROPN
m-806	143	165	�	�	PROPN
m-806	143	166	�	�	PROPN
m-806	143	167	�	�	PROPN
m-806	143	168	+	+	CCONJ
m-806	143	169	2	2	NUM
m-806	143	170	�	�	PROPN
m-806	143	171	�	�	PROPN
m-806	143	172	�	�	PROPN
m-806	143	173	)	)	PUNCT
m-806	143	174	�	�	PROPN
m-806	143	175	�	�	PROPN
m-806	143	176	�	�	PROPN
m-806	143	177	�	�	PROPN
m-806	143	178	�	�	PROPN
m-806	143	179	(	(	PUNCT
m-806	143	180	6.68e	6.68e	NUM
m-806	143	181	)	)	PUNCT
m-806	143	182	the	the	DET
m-806	143	183	remaining	remain	VERB
m-806	143	184	equation	equation	NOUN
m-806	143	185	in	in	ADP
m-806	143	186	the	the	DET
m-806	143	187	substitution	substitution	NOUN
m-806	143	188	into	into	ADP
m-806	143	189	(	(	PUNCT
m-806	143	190	6.62a	6.62a	NOUN
m-806	143	191	)	)	PUNCT
m-806	143	192	is	be	AUX
m-806	143	193	u	u	PRON
m-806	143	194	�	�	PROPN
m-806	143	195	�	�	PROPN
m-806	143	196	,	,	PUNCT
m-806	143	197	�	�	PROPN
m-806	143	198	�	�	PROPN
m-806	143	199	�	�	PROPN
m-806	143	200	�	�	PROPN
m-806	143	201	(	(	PUNCT
m-806	143	202	�	�	PROPN
m-806	143	203	�	�	PROPN
m-806	143	204	)	)	PUNCT
m-806	144	1	+	+	SYM
m-806	144	2	�	�	PROPN
m-806	144	3	�	�	PROPN
m-806	144	4	�	�	PROPN
m-806	144	5	�	�	PROPN
m-806	144	6	u	u	PROPN
m-806	144	7	�	�	PROPN
m-806	144	8	�	�	PROPN
m-806	144	9	(	(	PUNCT
m-806	144	10	�	�	PROPN
m-806	144	11	�	�	PROPN
m-806	144	12	)	)	PUNCT
m-806	144	13	=	=	SYM
m-806	144	14	�	�	PROPN
m-806	144	15	�	�	PROPN
m-806	144	16	�	�	PROPN
m-806	144	17	+	+	CCONJ
m-806	144	18	�	�	PROPN
m-806	144	19	�	�	PROPN
m-806	144	20	�	�	PROPN
m-806	144	21	cos	cos	PROPN
m-806	144	22	�	�	PROPN
m-806	144	23	�	�	PROPN
m-806	144	24	̂	̂	VERB
m-806	144	25	+	+	NUM
m-806	144	26	�	�	PROPN
m-806	144	27	�	�	PROPN
m-806	144	28	�	�	PROPN
m-806	144	29	sin	sin	PROPN
m-806	144	30	�	�	PROPN
m-806	144	31	�	�	PROPN
m-806	144	32	̂	̂	VERB
m-806	144	33	+	+	NUM
m-806	144	34	�	�	PROPN
m-806	144	35	�	�	PROPN
m-806	144	36	�	�	PROPN
m-806	144	37	cos	cos	PROPN
m-806	144	38	2	2	NUM
m-806	144	39	�	�	PROPN
m-806	144	40	�	�	PROPN
m-806	144	41	̂	̂	VERB
m-806	144	42	+	+	NUM
m-806	144	43	�	�	PROPN
m-806	144	44	�	�	PROPN
m-806	144	45	�	�	PROPN
m-806	144	46	sin	sin	NOUN
m-806	144	47	2	2	NUM
m-806	144	48	�	�	PROPN
m-806	144	49	�	�	PROPN
m-806	144	50	̂	̂	VERB
m-806	144	51	+	+	NUM
m-806	144	52	�	�	PROPN
m-806	144	53	�	�	PROPN
m-806	144	54	�	�	PROPN
m-806	144	55	cos	cos	PROPN
m-806	144	56	3	3	NUM
m-806	144	57	�	�	PROPN
m-806	144	58	�	�	PROPN
m-806	144	59	̂	̂	VERB
m-806	144	60	+	+	NUM
m-806	144	61	�	�	PROPN
m-806	144	62	�	�	PROPN
m-806	144	63	�	�	PROPN
m-806	144	64	sin	sin	NOUN
m-806	144	65	3	3	NUM
m-806	144	66	�	�	PROPN
m-806	144	67	�	�	PROPN
m-806	144	68	̂	̂	PUNCT
m-806	144	69	(	(	PUNCT
m-806	144	70	6.69a	6.69a	NUM
m-806	144	71	)	)	PUNCT
m-806	144	72	u	u	PROPN
m-806	144	73	�	�	PROPN
m-806	144	74	�	�	PROPN
m-806	144	75	(	(	PUNCT
m-806	144	76	�	�	PROPN
m-806	144	77	�	�	PROPN
m-806	144	78	)	)	PUNCT
m-806	144	79	(	(	PUNCT
m-806	144	80	0,0	0,0	NUM
m-806	144	81	)	)	PUNCT
m-806	144	82	=	=	SYM
m-806	144	83	0	0	NUM
m-806	144	84	,	,	PUNCT
m-806	144	85	�	�	PROPN
m-806	144	86	�	�	PROPN
m-806	144	87	�	�	PROPN
m-806	144	88	,	,	PUNCT
m-806	144	89	�	�	PROPN
m-806	144	90	�	�	PROPN
m-806	144	91	(	(	PUNCT
m-806	144	92	�	�	PROPN
m-806	144	93	�	�	PROPN
m-806	144	94	)	)	PUNCT
m-806	144	95	(	(	PUNCT
m-806	144	96	0	0	NUM
m-806	144	97	,	,	PUNCT
m-806	144	98	0	0	NUM
m-806	144	99	)	)	PUNCT
m-806	144	100	+	+	CCONJ
m-806	144	101	�	�	PROPN
m-806	144	102	�	�	PROPN
m-806	144	103	�	�	PROPN
m-806	144	104	,	,	PUNCT
m-806	144	105	�	�	PROPN
m-806	144	106	(	(	PUNCT
m-806	144	107	�	�	PROPN
m-806	144	108	�	�	PROPN
m-806	144	109	)	)	PUNCT
m-806	144	110	(	(	PUNCT
m-806	144	111	0	0	NUM
m-806	144	112	,	,	PUNCT
m-806	144	113	0	0	NUM
m-806	144	114	)	)	PUNCT
m-806	144	115	(	(	PUNCT
m-806	144	116	6.69b	6.69b	NUM
m-806	144	117	)	)	PUNCT
m-806	144	118	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	144	119	ijo	ijo	PROPN
m-806	144	120	journals	journal	NOUN
m-806	144	121	volume	volume	NOUN
m-806	144	122	07	07	NUM
m-806	144	123	|	|	ADV
m-806	144	124	issue	issue	NOUN
m-806	144	125	02	02	NUM
m-806	144	126	|	|	CCONJ
m-806	144	127	february	february	PROPN
m-806	144	128	2024	2024	NUM
m-806	145	1	|	|	ADV
m-806	145	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	145	3	19	19	NUM
m-806	145	4	ijo	ijo	PROPN
m-806	145	5	international	international	PROPN
m-806	145	6	journal	journal	PROPN
m-806	145	7	of	of	ADP
m-806	145	8	mathematics	mathematics	PROPN
m-806	145	9	(	(	PUNCT
m-806	145	10	issn	issn	PROPN
m-806	145	11	:	:	PUNCT
m-806	145	12	2992	2992	NUM
m-806	145	13	-	-	SYM
m-806	145	14	4421	4421	NUM
m-806	145	15	)	)	PUNCT
m-806	145	16	i.u	i.u	PROPN
m-806	145	17	.	.	PROPN
m-806	145	18	udo	udo	PROPN
m-806	145	19	-	-	PROPN
m-806	145	20	akpan1	akpan1	ADJ
m-806	145	21	*	*	PUNCT
m-806	145	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	145	23	volume	volume	NOUN
m-806	145	24	07	07	NUM
m-806	145	25	issue	issue	NOUN
m-806	145	26	02	02	NUM
m-806	145	27	||	||	NUM
m-806	145	28	february	february	PROPN
m-806	145	29	,	,	PUNCT
m-806	145	30	2024	2024	NUM
m-806	145	31	||	||	NOUN
m-806	145	32	on	on	ADP
m-806	145	33	a	a	DET
m-806	145	34	-	-	PUNCT
m-806	145	35	two	two	NUM
m-806	145	36	-	-	PUNCT
m-806	145	37	parameter	parameter	NOUN
m-806	145	38	dynamic	dynamic	ADJ
m-806	145	39	buckling	buckling	NOUN
m-806	145	40	of	of	ADP
m-806	145	41	a	a	DET
m-806	145	42	viscously	viscously	ADV
m-806	145	43	damped	damp	VERB
m-806	145	44	but	but	CCONJ
m-806	145	45	clamped	clamp	VERB
m-806	145	46	column	column	NOUN
m-806	145	47	stressed	stress	VERB
m-806	145	48	by	by	ADP
m-806	145	49	a	a	DET
m-806	145	50	step	step	NOUN
m-806	145	51	load	load	NOUN
m-806	145	52	where	where	SCONJ
m-806	145	53	,	,	PUNCT
m-806	145	54	�	�	PROPN
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m-806	145	75	�	�	PROPN
m-806	145	76	�	�	PROPN
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m-806	145	84	�	�	PROPN
m-806	145	85	�	�	PROPN
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m-806	145	91	(	(	PUNCT
m-806	145	92	6.69c	6.69c	PROPN
m-806	145	93	)	)	PUNCT
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m-806	145	107	+	+	CCONJ
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m-806	145	119	+	+	CCONJ
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m-806	145	123	−	−	PROPN
m-806	145	124	�	�	PROPN
m-806	145	125	�	�	PROPN
m-806	145	126	�	�	PROPN
m-806	145	127	�	�	PROPN
m-806	145	128	�	�	PROPN
m-806	145	129	�	�	PROPN
m-806	145	130	�	�	PROPN
m-806	145	131	�	�	PROPN
m-806	145	132	�	�	PROPN
m-806	145	133	�	�	PROPN
m-806	145	134	�	�	PROPN
m-806	145	135	�	�	PROPN
m-806	145	136	�	�	PROPN
m-806	145	137	�	�	PROPN
m-806	145	138	�	�	PROPN
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m-806	145	140	�	�	PROPN
m-806	145	141	�	�	PROPN
m-806	145	142	�	�	PROPN
m-806	145	143	�	�	PROPN
m-806	145	144	�	�	PROPN
m-806	145	145	�	�	PROPN
m-806	145	146	�	�	PROPN
m-806	145	147	�	�	PROPN
m-806	145	148	�	�	PROPN
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m-806	145	152	�	�	PROPN
m-806	145	153	�	�	PROPN
m-806	145	154	�	�	PROPN
m-806	145	155	�	�	PROPN
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m-806	145	157	−	−	PROPN
m-806	145	158	�	�	PROPN
m-806	145	159	�	�	PROPN
m-806	145	160	�	�	PROPN
m-806	145	161	�	�	PROPN
m-806	145	162	�	�	PROPN
m-806	145	163	�	�	PROPN
m-806	145	164	�	�	PROPN
m-806	145	165	�	�	PROPN
m-806	145	166	�	�	PROPN
m-806	145	167	�	�	PROPN
m-806	145	168	�	�	PROPN
m-806	145	169	�	�	PROPN
m-806	145	170	�	�	PROPN
m-806	145	171	�	�	PROPN
m-806	145	172	�	�	PROPN
m-806	145	173	(	(	PUNCT
m-806	145	174	6.69d	6.69d	PROPN
m-806	145	175	)	)	PUNCT
m-806	145	176	�	�	PROPN
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m-806	145	178	�	�	PROPN
m-806	145	179	=	=	SYM
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m-806	145	181	�	�	PROPN
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m-806	145	186	�	�	PROPN
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m-806	145	188	�	�	PROPN
m-806	145	189	�	�	PROPN
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m-806	145	194	6.69e	6.69e	PROPN
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m-806	145	199	=	=	SYM
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m-806	145	204	�	�	PROPN
m-806	145	205	�	�	PROPN
m-806	145	206	�	�	PROPN
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m-806	145	208	+	+	CCONJ
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m-806	145	211	�	�	PROPN
m-806	145	212	�	�	PROPN
m-806	145	213	�	�	PROPN
m-806	145	214	�	�	PROPN
m-806	145	215	�	�	PROPN
m-806	145	216	�	�	PROPN
m-806	145	217	−	−	PROPN
m-806	145	218	�	�	PROPN
m-806	145	219	�	�	PROPN
m-806	145	220	�	�	PROPN
m-806	145	221	�	�	PROPN
m-806	145	222	�	�	PROPN
m-806	145	223	�	�	PROPN
m-806	145	224	�	�	PROPN
m-806	145	225	�	�	PROPN
m-806	145	226	�	�	PROPN
m-806	145	227	�	�	PROPN
m-806	145	228	�	�	PROPN
m-806	145	229	�	�	PROPN
m-806	145	230	�	�	PROPN
m-806	145	231	�	�	PROPN
m-806	145	232	�	�	PROPN
m-806	145	233	�	�	PROPN
m-806	145	234	�	�	PROPN
m-806	145	235	�	�	PROPN
m-806	145	236	�	�	PROPN
m-806	145	237	�	�	PROPN
m-806	145	238	�	�	PROPN
m-806	145	239	−	−	PROPN
m-806	145	240	�	�	PROPN
m-806	145	241	�	�	PROPN
m-806	145	242	�	�	PROPN
m-806	145	243	�	�	PROPN
m-806	145	244	�	�	PROPN
m-806	145	245	�	�	PROPN
m-806	145	246	�	�	PROPN
m-806	145	247	�	�	PROPN
m-806	145	248	�	�	PROPN
m-806	145	249	�	�	PROPN
m-806	145	250	�	�	PROPN
m-806	145	251	�	�	PROPN
m-806	145	252	�	�	PROPN
m-806	145	253	�	�	PROPN
m-806	145	254	�	�	PROPN
m-806	145	255	�	�	PROPN
m-806	145	256	�	�	PROPN
m-806	145	257	−	−	PROPN
m-806	145	258	�	�	PROPN
m-806	145	259	�	�	PROPN
m-806	145	260	�	�	PROPN
m-806	145	261	�	�	PROPN
m-806	145	262	�	�	PROPN
m-806	145	263	�	�	PROPN
m-806	145	264	�	�	PROPN
m-806	145	265	�	�	PROPN
m-806	145	266	�	�	PROPN
m-806	145	267	�	�	PROPN
m-806	145	268	�	�	PROPN
m-806	145	269	�	�	PROPN
m-806	145	270	�	�	PROPN
m-806	145	271	�	�	PROPN
m-806	145	272	�	�	PROPN
m-806	145	273	�	�	PROPN
m-806	145	274	�	�	PROPN
m-806	145	275	�	�	PROPN
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m-806	145	277	6.69f	6.69f	NUM
m-806	145	278	)	)	PUNCT
m-806	145	279	�	�	PROPN
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m-806	145	282	=	=	SYM
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m-806	145	286	�	�	PROPN
m-806	145	287	�	�	PROPN
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m-806	145	289	�	�	PROPN
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m-806	145	292	6.69	6.69	NUM
m-806	145	293	g	g	NOUN
m-806	145	294	)	)	PUNCT
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m-806	145	298	=	=	SYM
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m-806	145	302	�	�	PROPN
m-806	145	303	�	�	PROPN
m-806	145	304	�	�	PROPN
m-806	145	305	�	�	PROPN
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m-806	145	309	+	+	CCONJ
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m-806	145	312	�	�	PROPN
m-806	145	313	�	�	PROPN
m-806	145	314	�	�	PROPN
m-806	145	315	�	�	PROPN
m-806	145	316	�	�	PROPN
m-806	145	317	�	�	PROPN
m-806	145	318	�	�	PROPN
m-806	145	319	−	−	PROPN
m-806	145	320	�	�	PROPN
m-806	145	321	�	�	PROPN
m-806	145	322	�	�	PROPN
m-806	145	323	�	�	PROPN
m-806	145	324	�	�	PROPN
m-806	145	325	�	�	PROPN
m-806	145	326	�	�	PROPN
m-806	145	327	�	�	PROPN
m-806	145	328	�	�	PROPN
m-806	145	329	�	�	PROPN
m-806	145	330	�	�	PROPN
m-806	145	331	�	�	PROPN
m-806	145	332	�	�	PROPN
m-806	145	333	�	�	PROPN
m-806	145	334	�	�	PROPN
m-806	145	335	�	�	PROPN
m-806	145	336	�	�	PROPN
m-806	145	337	�	�	PROPN
m-806	145	338	�	�	PROPN
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m-806	145	340	�	�	PROPN
m-806	145	341	�	�	PROPN
m-806	145	342	�	�	PROPN
m-806	145	343	�	�	PROPN
m-806	145	344	�	�	PROPN
m-806	145	345	�	�	PROPN
m-806	145	346	�	�	PROPN
m-806	145	347	�	�	PROPN
m-806	145	348	�	�	PROPN
m-806	145	349	�	�	PROPN
m-806	145	350	�	�	PROPN
m-806	145	351	�	�	PROPN
m-806	145	352	�	�	PROPN
m-806	145	353	�	�	PROPN
m-806	145	354	�	�	PROPN
m-806	145	355	�	�	PROPN
m-806	145	356	�	�	PROPN
m-806	145	357	�	�	PROPN
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m-806	145	359	�	�	PROPN
m-806	145	360	�	�	PROPN
m-806	145	361	�	�	PROPN
m-806	145	362	�	�	PROPN
m-806	145	363	�	�	PROPN
m-806	145	364	�	�	PROPN
m-806	145	365	�	�	PROPN
m-806	145	366	�	�	PROPN
m-806	145	367	�	�	PROPN
m-806	145	368	�	�	PROPN
m-806	145	369	�	�	PROPN
m-806	145	370	�	�	PROPN
m-806	145	371	�	�	PROPN
m-806	145	372	�	�	PROPN
m-806	145	373	�	�	PROPN
m-806	145	374	�	�	PROPN
m-806	145	375	�	�	PROPN
m-806	145	376	�	�	PROPN
m-806	145	377	�	�	PROPN
m-806	145	378	�	�	PROPN
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m-806	145	380	6.69h	6.69h	NUM
m-806	145	381	)	)	PUNCT
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m-806	145	385	=	=	SYM
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m-806	145	388	�	�	PROPN
m-806	145	389	�	�	PROPN
m-806	145	390	�	�	PROPN
m-806	145	391	�	�	PROPN
m-806	145	392	�	�	PROPN
m-806	145	393	�	�	PROPN
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m-806	145	395	(	(	PUNCT
m-806	145	396	6.69i	6.69i	PROPN
m-806	145	397	)	)	PUNCT
m-806	145	398	�	�	PROPN
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m-806	145	403	)	)	PUNCT
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m-806	145	410	�	�	PROPN
m-806	145	411	�	�	PROPN
m-806	145	412	,	,	PUNCT
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m-806	145	418	)	)	PUNCT
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m-806	145	425	�	�	PROPN
m-806	145	426	�	�	PROPN
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m-806	145	428	6.69j	6.69j	PROPN
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m-806	145	433	=	=	SYM
m-806	145	434	�	�	PROPN
m-806	145	435	�	�	PROPN
m-806	145	436	�	�	PROPN
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m-806	145	440	+	+	SYM
m-806	145	441	�	�	PROPN
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m-806	145	443	�	�	PROPN
m-806	145	444	�	�	PROPN
m-806	145	445	�	�	PROPN
m-806	145	446	�	�	PROPN
m-806	145	447	�	�	PROPN
m-806	145	448	�	�	PROPN
m-806	145	449	�	�	PROPN
m-806	145	450	�	�	PROPN
m-806	145	451	�	�	PROPN
m-806	145	452	�	�	PROPN
m-806	145	453	�	�	PROPN
m-806	145	454	+	+	CCONJ
m-806	145	455	�	�	PROPN
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m-806	145	457	�	�	PROPN
m-806	145	458	�	�	PROPN
m-806	145	459	�	�	PROPN
m-806	145	460	�	�	PROPN
m-806	145	461	�	�	PROPN
m-806	145	462	�	�	PROPN
m-806	145	463	�	�	PROPN
m-806	145	464	�	�	PROPN
m-806	145	465	�	�	PROPN
m-806	145	466	�	�	PROPN
m-806	145	467	�	�	PROPN
m-806	145	468	�	�	PROPN
m-806	145	469	�	�	PROPN
m-806	145	470	�	�	PROPN
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m-806	145	472	+	+	SYM
m-806	145	473	�	�	PROPN
m-806	145	474	�	�	PROPN
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m-806	145	476	�	�	PROPN
m-806	145	477	�	�	PROPN
m-806	145	478	�	�	PROPN
m-806	145	479	�	�	PROPN
m-806	145	480	�	�	PROPN
m-806	145	481	�	�	PROPN
m-806	145	482	�	�	PROPN
m-806	145	483	�	�	PROPN
m-806	145	484	�	�	PROPN
m-806	145	485	�	�	PROPN
m-806	145	486	�	�	PROPN
m-806	145	487	−	−	PROPN
m-806	145	488	�	�	PROPN
m-806	145	489	�	�	PROPN
m-806	145	490	�	�	PROPN
m-806	145	491	�	�	PROPN
m-806	145	492	�	�	PROPN
m-806	145	493	�	�	PROPN
m-806	145	494	�	�	PROPN
m-806	145	495	�	�	PROPN
m-806	145	496	�	�	PROPN
m-806	145	497	�	�	PROPN
m-806	145	498	�	�	PROPN
m-806	145	499	�	�	PROPN
m-806	145	500	(	(	PUNCT
m-806	145	501	6.69k	6.69k	PROPN
m-806	145	502	)	)	PUNCT
m-806	145	503	�	�	PROPN
m-806	145	504	�	�	PROPN
m-806	145	505	�	�	PROPN
m-806	145	506	(	(	PUNCT
m-806	145	507	0	0	NUM
m-806	145	508	)	)	PUNCT
m-806	145	509	=	=	SYM
m-806	145	510	0	0	NUM
m-806	145	511	,	,	PUNCT
m-806	145	512	�	�	PROPN
m-806	145	513	�	�	PROPN
m-806	145	514	�	�	PROPN
m-806	145	515	(	(	PUNCT
m-806	145	516	0	0	NUM
m-806	145	517	)	)	PUNCT
m-806	145	518	=	=	SYM
m-806	145	519	3	3	NUM
m-806	145	520	�	�	PROPN
m-806	145	521	�	�	PROPN
m-806	145	522	�	�	PROPN
m-806	145	523	�	�	PROPN
m-806	145	524	�	�	PROPN
m-806	145	525	�	�	PROPN
m-806	145	526	(	(	PUNCT
m-806	145	527	6.69l	6.69l	NOUN
m-806	145	528	)	)	PUNCT
m-806	145	529	�	�	PROPN
m-806	145	530	�	�	PROPN
m-806	145	531	�	�	PROPN
m-806	145	532	=	=	SYM
m-806	145	533	�	�	PROPN
m-806	145	534	�	�	PROPN
m-806	145	535	�	�	PROPN
m-806	145	536	�	�	PROPN
m-806	145	537	�	�	PROPN
m-806	145	538	−	−	PROPN
m-806	145	539	�	�	PROPN
m-806	145	540	�	�	PROPN
m-806	145	541	�	�	PROPN
m-806	145	542	�	�	PROPN
m-806	145	543	�	�	PROPN
m-806	145	544	�	�	PROPN
m-806	145	545	�	�	PROPN
m-806	145	546	�	�	PROPN
m-806	145	547	�	�	PROPN
m-806	145	548	�	�	PROPN
m-806	145	549	�	�	PROPN
m-806	145	550	−	−	PROPN
m-806	145	551	�	�	PROPN
m-806	145	552	�	�	PROPN
m-806	145	553	�	�	PROPN
m-806	145	554	�	�	PROPN
m-806	145	555	�	�	PROPN
m-806	145	556	�	�	PROPN
m-806	145	557	�	�	PROPN
m-806	145	558	�	�	PROPN
m-806	145	559	�	�	PROPN
m-806	145	560	�	�	PROPN
m-806	145	561	�	�	PROPN
m-806	145	562	�	�	PROPN
m-806	145	563	�	�	PROPN
m-806	145	564	�	�	PROPN
m-806	145	565	�	�	PROPN
m-806	145	566	−	−	PROPN
m-806	145	567	�	�	PROPN
m-806	145	568	�	�	PROPN
m-806	145	569	�	�	PROPN
m-806	145	570	�	�	PROPN
m-806	145	571	�	�	PROPN
m-806	145	572	�	�	PROPN
m-806	145	573	�	�	PROPN
m-806	145	574	�	�	PROPN
m-806	145	575	�	�	PROPN
m-806	145	576	�	�	PROPN
m-806	145	577	+	+	CCONJ
m-806	145	578	�	�	PROPN
m-806	145	579	�	�	PROPN
m-806	145	580	�	�	PROPN
m-806	145	581	�	�	PROPN
m-806	145	582	�	�	PROPN
m-806	145	583	�	�	PROPN
m-806	145	584	�	�	PROPN
m-806	145	585	�	�	PROPN
m-806	145	586	(	(	PUNCT
m-806	145	587	6.69	6.69	NUM
m-806	145	588	m	m	NOUN
m-806	145	589	)	)	PUNCT
m-806	145	590	�	�	PROPN
m-806	145	591	�	�	PROPN
m-806	145	592	�	�	PROPN
m-806	145	593	(	(	PUNCT
m-806	145	594	0	0	NUM
m-806	145	595	)	)	PUNCT
m-806	145	596	=	=	SYM
m-806	145	597	0	0	NUM
m-806	145	598	,	,	PUNCT
m-806	145	599	�	�	PROPN
m-806	145	600	�	�	PROPN
m-806	145	601	�	�	PROPN
m-806	145	602	(	(	PUNCT
m-806	145	603	0	0	NUM
m-806	145	604	)	)	PUNCT
m-806	145	605	=	=	SYM
m-806	145	606	3	3	NUM
m-806	145	607	�	�	PROPN
m-806	145	608	�	�	PROPN
m-806	145	609	�	�	PROPN
m-806	145	610	�	�	PROPN
m-806	145	611	�	�	PROPN
m-806	145	612	�	�	PROPN
m-806	145	613	,	,	PUNCT
m-806	145	614	�	�	PROPN
m-806	145	615	�	�	PROPN
m-806	145	616	�	�	PROPN
m-806	145	617	(	(	PUNCT
m-806	145	618	0	0	NUM
m-806	145	619	)	)	PUNCT
m-806	145	620	=	=	SYM
m-806	145	621	0	0	PUNCT
m-806	145	622	(	(	PUNCT
m-806	145	623	6.69n	6.69n	NUM
m-806	145	624	)	)	PUNCT
m-806	145	625	�	�	PROPN
m-806	145	626	�	�	PROPN
m-806	145	627	�	�	PROPN
m-806	145	628	=	=	SYM
m-806	145	629	�	�	PROPN
m-806	145	630	�	�	PROPN
m-806	145	631	�	�	PROPN
m-806	145	632	�	�	PROPN
m-806	145	633	�	�	PROPN
m-806	145	634	+	+	SYM
m-806	145	635	�	�	PROPN
m-806	145	636	�	�	PROPN
m-806	145	637	�	�	PROPN
m-806	145	638	�	�	PROPN
m-806	145	639	�	�	PROPN
m-806	145	640	�	�	PROPN
m-806	145	641	�	�	PROPN
m-806	145	642	�	�	PROPN
m-806	145	643	�	�	PROPN
m-806	145	644	�	�	PROPN
m-806	145	645	�	�	PROPN
m-806	145	646	�	�	PROPN
m-806	145	647	�	�	PROPN
m-806	145	648	�	�	PROPN
m-806	145	649	(	(	PUNCT
m-806	145	650	6.69o	6.69o	PROPN
m-806	145	651	)	)	PUNCT
m-806	145	652	on	on	ADP
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m-806	145	654	(	(	PUNCT
m-806	145	655	6.69a	6.69a	ADJ
m-806	145	656	,	,	PUNCT
m-806	145	657	b	b	NOUN
m-806	145	658	)	)	PUNCT
m-806	145	659	,	,	PUNCT
m-806	145	660	we	we	PRON
m-806	145	661	get	get	VERB
m-806	145	662	�	�	PROPN
m-806	145	663	�	�	PROPN
m-806	145	664	�	�	PROPN
m-806	145	665	�	�	PROPN
m-806	145	666	�	�	PROPN
m-806	145	667	(	(	PUNCT
m-806	145	668	�	�	PROPN
m-806	145	669	̂	̂	NUM
m-806	145	670	,	,	PUNCT
m-806	145	671	�	�	PROPN
m-806	145	672	)	)	PUNCT
m-806	145	673	=	=	SYM
m-806	145	674	�	�	PROPN
m-806	145	675	�	�	PROPN
m-806	145	676	�	�	PROPN
m-806	145	677	cos	cos	PROPN
m-806	145	678	�	�	PROPN
m-806	145	679	�	�	PROPN
m-806	145	680	�	�	PROPN
m-806	145	681	�	�	PROPN
m-806	145	682	̂	̂	VERB
m-806	145	683	+	+	NUM
m-806	145	684	�	�	PROPN
m-806	145	685	�	�	PROPN
m-806	145	686	�	�	PROPN
m-806	145	687	sin	sin	PROPN
m-806	145	688	�	�	PROPN
m-806	145	689	�	�	PROPN
m-806	145	690	�	�	PROPN
m-806	145	691	�	�	PROPN
m-806	145	692	̂	̂	VERB
m-806	145	693	+	+	NUM
m-806	145	694	�	�	PROPN
m-806	145	695	�	�	PROPN
m-806	145	696	�	�	PROPN
m-806	145	697	�	�	PROPN
m-806	145	698	�	�	PROPN
m-806	145	699	�	�	PROPN
m-806	145	700	�	�	PROPN
m-806	145	701	+	+	CCONJ
m-806	145	702	�	�	PROPN
m-806	145	703	1	1	NUM
m-806	145	704	�	�	PROPN
m-806	145	705	�	�	PROPN
m-806	145	706	�	�	PROPN
m-806	145	707	�	�	PROPN
m-806	145	708	−	−	PROPN
m-806	145	709	�	�	PROPN
m-806	145	710	�	�	PROPN
m-806	145	711	�	�	PROPN
m-806	145	712	(	(	PUNCT
m-806	145	713	�	�	PROPN
m-806	145	714	�	�	PROPN
m-806	145	715	�	�	PROPN
m-806	145	716	cos	cos	PROPN
m-806	145	717	�	�	PROPN
m-806	145	718	�	�	PROPN
m-806	145	719	̂	̂	VERB
m-806	145	720	+	+	NUM
m-806	145	721	�	�	PROPN
m-806	145	722	�	�	PROPN
m-806	145	723	�	�	PROPN
m-806	145	724	sin	sin	PROPN
m-806	145	725	�	�	PROPN
m-806	145	726	�	�	PROPN
m-806	145	727	̂	̂	NUM
m-806	145	728	)	)	PUNCT
m-806	146	1	+	+	CCONJ
m-806	146	2	�	�	PROPN
m-806	146	3	�	�	PROPN
m-806	146	4	�	�	PROPN
m-806	146	5	�	�	PROPN
m-806	146	6	�	�	PROPN
m-806	146	7	�	�	PROPN
m-806	146	8	�	�	PROPN
m-806	146	9	�	�	PROPN
m-806	146	10	�	�	PROPN
m-806	146	11	�	�	PROPN
m-806	146	12	�	�	PROPN
m-806	146	13	(	(	PUNCT
m-806	146	14	�	�	PROPN
m-806	146	15	�	�	PROPN
m-806	146	16	�	�	PROPN
m-806	146	17	cos	cos	PROPN
m-806	146	18	2	2	PROPN
m-806	146	19	�	�	PROPN
m-806	146	20	�	�	PROPN
m-806	146	21	̂	̂	VERB
m-806	146	22	+	+	NUM
m-806	146	23	�	�	PROPN
m-806	146	24	�	�	PROPN
m-806	146	25	�	�	PROPN
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m-806	146	28	�	�	PROPN
m-806	146	29	�	�	NOUN
m-806	146	30	̂	̂	NUM
m-806	146	31	)	)	PUNCT
m-806	147	1	+	+	CCONJ
m-806	147	2	�	�	PROPN
m-806	147	3	�	�	PROPN
m-806	147	4	�	�	PROPN
m-806	147	5	�	�	PROPN
m-806	147	6	�	�	PROPN
m-806	147	7	�	�	PROPN
m-806	147	8	�	�	PROPN
m-806	147	9	�	�	PROPN
m-806	147	10	�	�	PROPN
m-806	147	11	�	�	PROPN
m-806	147	12	�	�	PROPN
m-806	147	13	(	(	PUNCT
m-806	147	14	�	�	PROPN
m-806	147	15	�	�	PROPN
m-806	147	16	�	�	PROPN
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m-806	147	18	3	3	PROPN
m-806	147	19	�	�	PROPN
m-806	147	20	�	�	PROPN
m-806	147	21	̂	̂	VERB
m-806	147	22	+	+	NUM
m-806	147	23	�	�	PROPN
m-806	147	24	�	�	PROPN
m-806	147	25	�	�	PROPN
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m-806	147	27	3	3	NUM
m-806	147	28	�	�	PROPN
m-806	147	29	�	�	NOUN
m-806	147	30	̂	̂	NUM
m-806	147	31	)	)	PUNCT
m-806	147	32	(	(	PUNCT
m-806	147	33	6.70a	6.70a	NUM
m-806	147	34	)	)	PUNCT
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m-806	147	36	,	,	PUNCT
m-806	147	37	�	�	PROPN
m-806	147	38	�	�	PROPN
m-806	147	39	�	�	PROPN
m-806	147	40	(	(	PUNCT
m-806	147	41	0	0	NUM
m-806	147	42	)	)	PUNCT
m-806	147	43	=	=	SYM
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m-806	147	45	�	�	PROPN
m-806	147	46	�	�	PROPN
m-806	147	47	�	�	PROPN
m-806	147	48	�	�	PROPN
m-806	147	49	�	�	PROPN
m-806	147	50	�	�	PROPN
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m-806	147	52	(	(	PUNCT
m-806	148	1	6.70b	6.70b	NUM
m-806	148	2	)	)	PUNCT
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m-806	148	4	�	�	PROPN
m-806	148	5	�	�	PROPN
m-806	148	6	=	=	SYM
m-806	148	7	−	−	PROPN
m-806	148	8	�	�	PROPN
m-806	148	9	�	�	PROPN
m-806	148	10	�	�	PROPN
m-806	148	11	�	�	PROPN
m-806	148	12	�	�	PROPN
m-806	148	13	�	�	PROPN
m-806	148	14	�	�	PROPN
m-806	148	15	�	�	PROPN
m-806	148	16	�	�	PROPN
m-806	148	17	+	+	CCONJ
m-806	148	18	�	�	PROPN
m-806	148	19	�	�	PROPN
m-806	148	20	�	�	PROPN
m-806	148	21	�	�	PROPN
m-806	148	22	�	�	PROPN
m-806	148	23	�	�	PROPN
m-806	148	24	�	�	PROPN
m-806	148	25	�	�	PROPN
m-806	148	26	�	�	PROPN
m-806	148	27	�	�	PROPN
m-806	148	28	+	+	CCONJ
m-806	148	29	�	�	PROPN
m-806	148	30	�	�	PROPN
m-806	148	31	�	�	PROPN
m-806	148	32	�	�	PROPN
m-806	148	33	�	�	PROPN
m-806	148	34	�	�	PROPN
m-806	148	35	�	�	PROPN
m-806	148	36	�	�	PROPN
m-806	148	37	�	�	PROPN
m-806	148	38	�	�	PROPN
m-806	148	39	�	�	PROPN
m-806	148	40	+	+	CCONJ
m-806	148	41	�	�	PROPN
m-806	148	42	�	�	PROPN
m-806	148	43	�	�	PROPN
m-806	148	44	�	�	PROPN
m-806	148	45	�	�	PROPN
m-806	148	46	�	�	PROPN
m-806	148	47	�	�	PROPN
m-806	148	48	�	�	PROPN
m-806	148	49	�	�	PROPN
m-806	148	50	�	�	PROPN
m-806	148	51	�	�	PROPN
m-806	148	52	�	�	PROPN
m-806	148	53	(	(	PUNCT
m-806	148	54	6.70c	6.70c	PROPN
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m-806	148	84	=	=	SYM
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m-806	148	90	�	�	PROPN
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m-806	148	92	)	)	PUNCT
m-806	148	93	+	+	SYM
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m-806	148	97	(	(	PUNCT
m-806	148	98	�	�	PROPN
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m-806	148	101	+	+	SYM
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m-806	148	107	�	�	PROPN
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m-806	148	110	+	+	CCONJ
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m-806	148	121	+	+	PROPN
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m-806	148	125	�	�	PROPN
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m-806	148	127	(	(	PUNCT
m-806	148	128	�	�	PROPN
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m-806	148	130	)	)	PUNCT
m-806	148	131	(	(	PUNCT
m-806	148	132	1	1	NUM
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m-806	148	136	�	�	PROPN
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m-806	148	139	+	+	SYM
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m-806	148	142	�	�	PROPN
m-806	148	143	(	(	PUNCT
m-806	148	144	�	�	PROPN
m-806	148	145	�	�	PROPN
m-806	148	146	)	)	PUNCT
m-806	148	147	(	(	PUNCT
m-806	148	148	1	1	NUM
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m-806	148	155	+	+	SYM
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m-806	148	160	�	�	PROPN
m-806	148	161	�	�	PROPN
m-806	148	162	)	)	PUNCT
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m-806	148	164	1	1	NUM
m-806	148	165	−	−	PROPN
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m-806	148	171	�	�	PROPN
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m-806	148	174	�	�	PROPN
m-806	148	175	�	�	PROPN
m-806	148	176	�	�	PROPN
m-806	148	177	(	(	PUNCT
m-806	148	178	�	�	PROPN
m-806	148	179	�	�	PROPN
m-806	148	180	)	)	PUNCT
m-806	148	181	(	(	PUNCT
m-806	148	182	1	1	NUM
m-806	148	183	−	−	PROPN
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m-806	148	185	2	2	NUM
m-806	148	186	�	�	PROPN
m-806	148	187	�	�	PROPN
m-806	148	188	)	)	PUNCT
m-806	148	189	+	+	SYM
m-806	148	190	�	�	PROPN
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m-806	148	193	(	(	PUNCT
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m-806	148	195	�	�	PROPN
m-806	148	196	)	)	PUNCT
m-806	148	197	(	(	PUNCT
m-806	148	198	1	1	NUM
m-806	148	199	−	−	PROPN
m-806	148	200	cos	cos	PROPN
m-806	148	201	4	4	NUM
m-806	148	202	�	�	PROPN
m-806	148	203	�	�	PROPN
m-806	148	204	)	)	PUNCT
m-806	148	205	+	+	SYM
m-806	148	206	�	�	PROPN
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m-806	148	209	(	(	PUNCT
m-806	148	210	�	�	PROPN
m-806	148	211	�	�	PROPN
m-806	148	212	)	)	PUNCT
m-806	148	213	(	(	PUNCT
m-806	148	214	1	1	NUM
m-806	148	215	−	−	PROPN
m-806	148	216	cos	cos	PROPN
m-806	148	217	6	6	NUM
m-806	148	218	�	�	PROPN
m-806	148	219	�	�	NOUN
m-806	148	220	)	)	PUNCT
m-806	148	221	�	�	PROPN
m-806	148	222	+	+	NOUN
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m-806	148	227	�	�	PROPN
m-806	148	228	(	(	PUNCT
m-806	148	229	�	�	PROPN
m-806	148	230	�	�	PROPN
m-806	148	231	)	)	PUNCT
m-806	148	232	(	(	PUNCT
m-806	148	233	1	1	NUM
m-806	148	234	−	−	PROPN
m-806	148	235	cos	cos	PROPN
m-806	148	236	2	2	NUM
m-806	148	237	�	�	PROPN
m-806	148	238	�	�	PROPN
m-806	148	239	)	)	PUNCT
m-806	148	240	+	+	SYM
m-806	148	241	�	�	PROPN
m-806	148	242	�	�	PROPN
m-806	148	243	�	�	PROPN
m-806	148	244	(	(	PUNCT
m-806	148	245	�	�	PROPN
m-806	148	246	�	�	PROPN
m-806	148	247	)	)	PUNCT
m-806	148	248	(	(	PUNCT
m-806	148	249	1	1	NUM
m-806	148	250	−	−	PROPN
m-806	148	251	cos	cos	PROPN
m-806	148	252	4	4	NUM
m-806	148	253	�	�	PROPN
m-806	148	254	�	�	PROPN
m-806	148	255	)	)	PUNCT
m-806	148	256	+	+	SYM
m-806	148	257	�	�	PROPN
m-806	148	258	�	�	PROPN
m-806	148	259	�	�	PROPN
m-806	148	260	(	(	PUNCT
m-806	148	261	�	�	PROPN
m-806	148	262	�	�	PROPN
m-806	148	263	)	)	PUNCT
m-806	148	264	(	(	PUNCT
m-806	148	265	1	1	NUM
m-806	148	266	−	−	PROPN
m-806	148	267	cos	cos	PROPN
m-806	148	268	6	6	NUM
m-806	148	269	�	�	PROPN
m-806	148	270	�	�	PROPN
m-806	148	271	)	)	PUNCT
m-806	148	272	�	�	PROPN
m-806	148	273	�	�	PROPN
m-806	148	274	+	+	PROPN
m-806	148	275	⋯	⋯	ADP
m-806	148	276	]	]	PUNCT
m-806	148	277	+	+	CCONJ
m-806	148	278	⋯	⋯	PROPN
m-806	148	279	(	(	PUNCT
m-806	148	280	6.71	6.71	NUM
m-806	148	281	)	)	PUNCT
m-806	148	282	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	148	283	ijo	ijo	PROPN
m-806	148	284	journals	journal	NOUN
m-806	148	285	volume	volume	NOUN
m-806	148	286	07	07	NUM
m-806	148	287	|	|	ADV
m-806	148	288	issue	issue	NOUN
m-806	148	289	02	02	NUM
m-806	148	290	|	|	CCONJ
m-806	148	291	february	february	PROPN
m-806	148	292	2024	2024	NUM
m-806	149	1	|	|	ADV
m-806	149	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	149	3	20	20	NUM
m-806	149	4	ijo	ijo	PROPN
m-806	149	5	international	international	ADJ
m-806	149	6	journal	journal	PROPN
m-806	149	7	of	of	ADP
m-806	149	8	mathematics	mathematics	PROPN
m-806	149	9	(	(	PUNCT
m-806	149	10	issn	issn	PROPN
m-806	149	11	:	:	PUNCT
m-806	149	12	2992	2992	NUM
m-806	149	13	-	-	SYM
m-806	149	14	4421	4421	NUM
m-806	149	15	)	)	PUNCT
m-806	149	16	i.u	i.u	PROPN
m-806	149	17	.	.	PROPN
m-806	149	18	udo	udo	PROPN
m-806	149	19	-	-	PROPN
m-806	149	20	akpan1	akpan1	ADJ
m-806	149	21	*	*	PUNCT
m-806	149	22	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	149	23	volume	volume	NOUN
m-806	149	24	07	07	NUM
m-806	149	25	issue	issue	NOUN
m-806	149	26	02	02	NUM
m-806	149	27	||	||	NUM
m-806	149	28	february	february	PROPN
m-806	149	29	,	,	PUNCT
m-806	149	30	2024	2024	NUM
m-806	149	31	||	||	NOUN
m-806	149	32	on	on	ADP
m-806	149	33	a	a	DET
m-806	149	34	-	-	PUNCT
m-806	149	35	two	two	NUM
m-806	149	36	-	-	PUNCT
m-806	149	37	parameter	parameter	NOUN
m-806	149	38	dynamic	dynamic	ADJ
m-806	149	39	buckling	buckling	NOUN
m-806	149	40	of	of	ADP
m-806	149	41	a	a	DET
m-806	149	42	viscously	viscously	ADV
m-806	149	43	damped	damp	VERB
m-806	149	44	but	but	CCONJ
m-806	149	45	clamped	clamp	VERB
m-806	149	46	column	column	NOUN
m-806	149	47	stressed	stress	VERB
m-806	149	48	by	by	ADP
m-806	149	49	a	a	DET
m-806	149	50	step	step	NOUN
m-806	149	51	load	load	NOUN
m-806	149	52	7	7	NUM
m-806	149	53	.	.	PUNCT
m-806	149	54	critical	critical	ADJ
m-806	149	55	values	value	NOUN
m-806	149	56	of	of	ADP
m-806	149	57	the	the	DET
m-806	149	58	dependent	dependent	ADJ
m-806	149	59	variables	variable	NOUN
m-806	149	60	at	at	ADP
m-806	149	61	maximum	maximum	ADJ
m-806	149	62	deflection	deflection	NOUN
m-806	149	63	as	as	ADP
m-806	149	64	in	in	ADP
m-806	149	65	[	[	X
m-806	149	66	18	18	NUM
m-806	149	67	,	,	PUNCT
m-806	149	68	19	19	NUM
m-806	149	69	]	]	PUNCT
m-806	149	70	,	,	PUNCT
m-806	149	71	the	the	DET
m-806	149	72	dynamic	dynamic	ADJ
m-806	149	73	buckling	buckling	NOUN
m-806	149	74	load	load	NOUN
m-806	149	75	�	�	PROPN
m-806	149	76	�	�	PROPN
m-806	149	77	,	,	PUNCT
m-806	149	78	which	which	PRON
m-806	149	79	is	be	AUX
m-806	149	80	defined	define	VERB
m-806	149	81	as	as	ADP
m-806	149	82	the	the	DET
m-806	149	83	largest	large	ADJ
m-806	149	84	load	load	NOUN
m-806	149	85	parameter	parameter	NOUN
m-806	149	86	for	for	ADP
m-806	149	87	the	the	DET
m-806	149	88	solution	solution	NOUN
m-806	149	89	of	of	ADP
m-806	149	90	the	the	DET
m-806	149	91	problem	problem	NOUN
m-806	149	92	to	to	PART
m-806	149	93	be	be	AUX
m-806	149	94	bounded	bound	VERB
m-806	149	95	,	,	PUNCT
m-806	149	96	is	be	AUX
m-806	149	97	obtained	obtain	VERB
m-806	149	98	from	from	ADP
m-806	149	99	the	the	DET
m-806	149	100	maximization	maximization	PROPN
m-806	149	101	�	�	PROPN
m-806	149	102	�	�	PROPN
m-806	149	103	�	�	PROPN
m-806	149	104	�	�	PROPN
m-806	149	105	�	�	PROPN
m-806	149	106	=	=	SYM
m-806	149	107	0	0	NUM
m-806	149	108	(	(	PUNCT
m-806	149	109	7.1	7.1	NUM
m-806	149	110	)	)	PUNCT
m-806	149	111	where	where	SCONJ
m-806	149	112	,	,	PUNCT
m-806	149	113	�	�	PROPN
m-806	149	114	�	�	PROPN
m-806	149	115	is	be	AUX
m-806	149	116	the	the	DET
m-806	149	117	maximum	maximum	ADJ
m-806	149	118	deflection	deflection	NOUN
m-806	149	119	whose	whose	DET
m-806	149	120	maximum	maximum	ADJ
m-806	149	121	values	value	NOUN
m-806	149	122	of	of	ADP
m-806	149	123	the	the	DET
m-806	149	124	dependent	dependent	ADJ
m-806	149	125	variables	variable	NOUN
m-806	149	126	we	we	PRON
m-806	149	127	shall	shall	AUX
m-806	149	128	now	now	ADV
m-806	149	129	determine	determine	VERB
m-806	149	130	.	.	PUNCT
m-806	150	1	let	let	VERB
m-806	150	2	�	�	PROPN
m-806	150	3	�	�	PROPN
m-806	150	4	,	,	PUNCT
m-806	150	5	�	�	PROPN
m-806	150	6	̂	̂	SYM
m-806	150	7	�	�	PROPN
m-806	150	8	,	,	PUNCT
m-806	150	9	�	�	PROPN
m-806	150	10	�	�	PROPN
m-806	150	11	be	be	VERB
m-806	150	12	the	the	DET
m-806	150	13	values	value	NOUN
m-806	150	14	,	,	PUNCT
m-806	150	15	at	at	ADP
m-806	150	16	maximum	maximum	ADJ
m-806	150	17	displacement	displacement	NOUN
m-806	150	18	of	of	ADP
m-806	150	19	�	�	PROPN
m-806	150	20	,	,	PUNCT
m-806	150	21	�	�	PROPN
m-806	150	22	̂and	̂and	PART
m-806	150	23	�	�	PROPN
m-806	150	24	respectively	respectively	ADV
m-806	150	25	and	and	CCONJ
m-806	150	26	let	let	VERB
m-806	150	27	us	we	PRON
m-806	150	28	now	now	ADV
m-806	150	29	assume	assume	VERB
m-806	150	30	the	the	DET
m-806	150	31	following	follow	VERB
m-806	150	32	asymptotic	asymptotic	ADJ
m-806	150	33	series	series	NOUN
m-806	150	34	�	�	PROPN
m-806	150	35	̂	̂	PROPN
m-806	150	36	�	�	PROPN
m-806	150	37	=	=	SYM
m-806	150	38	�	�	PROPN
m-806	150	39	̂	̂	NUM
m-806	150	40	�	�	PROPN
m-806	150	41	+	+	SYM
m-806	150	42	�	�	PROPN
m-806	150	43	�	�	PROPN
m-806	150	44	̂	̂	NOUN
m-806	150	45	�	�	PROPN
m-806	150	46	�	�	PROPN
m-806	150	47	+	+	SYM
m-806	150	48	�	�	PROPN
m-806	150	49	�	�	PROPN
m-806	150	50	�	�	PROPN
m-806	150	51	̂	̂	NOUN
m-806	150	52	�	�	NOUN
m-806	150	53	�	�	PROPN
m-806	150	54	+	+	SYM
m-806	150	55	⋯	⋯	PROPN
m-806	150	56	+	+	SYM
m-806	150	57	�	�	PROPN
m-806	150	58	�	�	PROPN
m-806	150	59	(	(	PUNCT
m-806	150	60	�	�	PROPN
m-806	150	61	̂	̂	SYM
m-806	150	62	�	�	PROPN
m-806	150	63	�	�	PROPN
m-806	150	64	+	+	SYM
m-806	150	65	�	�	PROPN
m-806	150	66	�	�	PROPN
m-806	150	67	̂	̂	NOUN
m-806	150	68	�	�	PROPN
m-806	150	69	�	�	PROPN
m-806	150	70	+	+	SYM
m-806	150	71	�	�	PROPN
m-806	150	72	�	�	PROPN
m-806	150	73	�	�	PROPN
m-806	150	74	̂	̂	NOUN
m-806	150	75	�	�	NOUN
m-806	150	76	�	�	PROPN
m-806	150	77	+	+	CCONJ
m-806	150	78	⋯	⋯	PROPN
m-806	150	79	)	)	PUNCT
m-806	151	1	+	+	CCONJ
m-806	151	2	⋯	⋯	PROPN
m-806	151	3	(	(	PUNCT
m-806	151	4	7.2a	7.2a	PROPN
m-806	151	5	)	)	PUNCT
m-806	151	6	�	�	PROPN
m-806	151	7	�	�	PROPN
m-806	151	8	=	=	SYM
m-806	151	9	�	�	PROPN
m-806	151	10	�	�	PROPN
m-806	151	11	+	+	CCONJ
m-806	151	12	�	�	PROPN
m-806	151	13	�	�	PROPN
m-806	151	14	�	�	PROPN
m-806	151	15	�	�	PROPN
m-806	151	16	+	+	SYM
m-806	151	17	�	�	PROPN
m-806	151	18	�	�	PROPN
m-806	151	19	�	�	PROPN
m-806	151	20	�	�	PROPN
m-806	151	21	�	�	PROPN
m-806	151	22	+	+	CCONJ
m-806	151	23	⋯	⋯	PROPN
m-806	151	24	+	+	SYM
m-806	151	25	�	�	PROPN
m-806	151	26	�	�	PROPN
m-806	151	27	(	(	PUNCT
m-806	151	28	�	�	PROPN
m-806	151	29	�	�	PROPN
m-806	151	30	�	�	PROPN
m-806	151	31	+	+	SYM
m-806	151	32	�	�	PROPN
m-806	151	33	�	�	PROPN
m-806	151	34	�	�	PROPN
m-806	151	35	�	�	PROPN
m-806	151	36	+	+	SYM
m-806	151	37	�	�	PROPN
m-806	151	38	�	�	PROPN
m-806	151	39	�	�	PROPN
m-806	151	40	�	�	PROPN
m-806	151	41	�	�	PROPN
m-806	151	42	+	+	CCONJ
m-806	151	43	⋯	⋯	PROPN
m-806	151	44	)	)	PUNCT
m-806	152	1	+	+	CCONJ
m-806	152	2	⋯	⋯	PROPN
m-806	152	3	�	�	PROPN
m-806	152	4	�	�	PROPN
m-806	152	5	=	=	SYM
m-806	152	6	�	�	PROPN
m-806	152	7	�	�	PROPN
m-806	152	8	�	�	PROPN
m-806	152	9	=	=	SYM
m-806	152	10	�	�	PROPN
m-806	152	11	[	[	NOUN
m-806	152	12	�	�	PROPN
m-806	152	13	�	�	PROPN
m-806	152	14	+	+	SYM
m-806	152	15	�	�	PROPN
m-806	152	16	�	�	PROPN
m-806	152	17	�	�	PROPN
m-806	152	18	�	�	PROPN
m-806	152	19	+	+	SYM
m-806	152	20	�	�	PROPN
m-806	152	21	�	�	PROPN
m-806	152	22	�	�	PROPN
m-806	152	23	�	�	PROPN
m-806	152	24	�	�	PROPN
m-806	152	25	+	+	CCONJ
m-806	152	26	⋯	⋯	PROPN
m-806	152	27	+	+	SYM
m-806	152	28	�	�	PROPN
m-806	152	29	�	�	PROPN
m-806	152	30	(	(	PUNCT
m-806	152	31	�	�	PROPN
m-806	152	32	�	�	PROPN
m-806	152	33	�	�	PROPN
m-806	152	34	+	+	SYM
m-806	152	35	�	�	PROPN
m-806	152	36	�	�	PROPN
m-806	152	37	�	�	PROPN
m-806	152	38	�	�	PROPN
m-806	152	39	+	+	SYM
m-806	152	40	�	�	PROPN
m-806	152	41	�	�	PROPN
m-806	152	42	�	�	PROPN
m-806	152	43	�	�	PROPN
m-806	152	44	�	�	PROPN
m-806	152	45	+	+	CCONJ
m-806	152	46	⋯	⋯	PROPN
m-806	152	47	)	)	PUNCT
m-806	153	1	+	+	CCONJ
m-806	153	2	⋯	⋯	ADP
m-806	153	3	]	]	X
m-806	153	4	(	(	PUNCT
m-806	153	5	7.2b	7.2b	NOUN
m-806	153	6	)	)	PUNCT
m-806	153	7	as	as	ADP
m-806	153	8	a	a	DET
m-806	153	9	function	function	NOUN
m-806	153	10	of	of	ADP
m-806	153	11	�	�	PROPN
m-806	153	12	,	,	PUNCT
m-806	153	13	�	�	PROPN
m-806	153	14	̂	̂	NUM
m-806	153	15	,	,	PUNCT
m-806	153	16	�	�	PROPN
m-806	153	17	,	,	PUNCT
m-806	153	18	the	the	DET
m-806	153	19	conditions	condition	NOUN
m-806	153	20	for	for	ADP
m-806	153	21	�	�	PROPN
m-806	153	22	(	(	PUNCT
m-806	153	23	�	�	PROPN
m-806	153	24	,	,	PUNCT
m-806	153	25	�	�	PROPN
m-806	153	26	̂	̂	NUM
m-806	153	27	,	,	PUNCT
m-806	153	28	�	�	PROPN
m-806	153	29	)	)	PUNCT
m-806	153	30	to	to	PART
m-806	153	31	have	have	VERB
m-806	153	32	a	a	DET
m-806	153	33	maximum	maximum	NOUN
m-806	153	34	are	be	AUX
m-806	153	35	�	�	PROPN
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m-806	153	37	�	�	PROPN
m-806	153	38	=	=	SYM
m-806	153	39	0	0	PROPN
m-806	153	40	,	,	PUNCT
m-806	153	41	(	(	PUNCT
m-806	153	42	1	1	NUM
m-806	153	43	+	+	NUM
m-806	153	44	�	�	PROPN
m-806	153	45	�	�	PROPN
m-806	153	46	�	�	PROPN
m-806	153	47	�	�	PROPN
m-806	153	48	�	�	PROPN
m-806	153	49	+	+	CCONJ
m-806	153	50	�	�	PROPN
m-806	153	51	�	�	PROPN
m-806	153	52	�	�	PROPN
m-806	153	53	�	�	PROPN
m-806	153	54	�	�	PROPN
m-806	153	55	+	+	CCONJ
m-806	153	56	⋯	⋯	PROPN
m-806	153	57	)	)	PUNCT
m-806	153	58	�	�	PROPN
m-806	153	59	,	,	PUNCT
m-806	153	60	�	�	PROPN
m-806	153	61	�	�	PROPN
m-806	153	62	+	+	SYM
m-806	153	63	�	�	PROPN
m-806	153	64	�	�	PROPN
m-806	153	65	,	,	PUNCT
m-806	153	66	�	�	PROPN
m-806	153	67	=	=	SYM
m-806	153	68	0	0	NUM
m-806	153	69	(	(	PUNCT
m-806	153	70	7.3	7.3	NUM
m-806	153	71	)	)	PUNCT
m-806	153	72	on	on	ADP
m-806	153	73	substituting	substitute	VERB
m-806	153	74	(	(	PUNCT
m-806	153	75	6.71	6.71	NUM
m-806	153	76	)	)	PUNCT
m-806	153	77	into	into	ADP
m-806	153	78	the	the	DET
m-806	153	79	first	first	ADJ
m-806	153	80	of	of	ADP
m-806	153	81	(	(	PUNCT
m-806	153	82	7.3	7.3	NUM
m-806	153	83	)	)	PUNCT
m-806	153	84	,	,	PUNCT
m-806	153	85	we	we	PRON
m-806	153	86	get	get	VERB
m-806	153	87	the	the	DET
m-806	153	88	value	value	NOUN
m-806	153	89	of	of	ADP
m-806	153	90	�	�	PROPN
m-806	153	91	at	at	ADP
m-806	153	92	maximum	maximum	ADJ
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m-806	153	94	,	,	PUNCT
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m-806	153	96	�	�	PROPN
m-806	153	97	�	�	PROPN
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m-806	153	100	�	�	PROPN
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m-806	153	102	=	=	SYM
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m-806	153	107	�	�	PROPN
m-806	153	108	=	=	SYM
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m-806	153	110	,	,	PUNCT
m-806	153	111	2	2	NUM
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m-806	153	113	3	3	NUM
m-806	153	114	,	,	PUNCT
m-806	153	115	…	…	PUNCT
m-806	153	116	(	(	PUNCT
m-806	153	117	7.4	7.4	NUM
m-806	153	118	)	)	PUNCT
m-806	153	119	on	on	ADP
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m-806	153	121	(	(	PUNCT
m-806	153	122	6.71	6.71	NUM
m-806	153	123	)	)	PUNCT
m-806	153	124	at	at	ADP
m-806	153	125	�	�	PROPN
m-806	153	126	=	=	SYM
m-806	153	127	�	�	PROPN
m-806	153	128	�	�	PROPN
m-806	153	129	=	=	SYM
m-806	153	130	�	�	PROPN
m-806	153	131	�	�	PROPN
m-806	153	132	�	�	PROPN
m-806	153	133	,	,	PUNCT
m-806	153	134	we	we	PRON
m-806	153	135	get	get	VERB
m-806	153	136	�	�	PROPN
m-806	153	137	=	=	SYM
m-806	153	138	2	2	NUM
m-806	153	139	�	�	PROPN
m-806	153	140	�	�	PROPN
m-806	153	141	�	�	PROPN
m-806	153	142	�	�	PROPN
m-806	153	143	(	(	PUNCT
m-806	153	144	�	�	PROPN
m-806	153	145	�	�	PROPN
m-806	153	146	)	)	PUNCT
m-806	153	147	+	+	SYM
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m-806	153	149	�	�	PROPN
m-806	153	150	�	�	PROPN
m-806	153	151	(	(	PUNCT
m-806	153	152	�	�	PROPN
m-806	153	153	�	�	PROPN
m-806	153	154	)	)	PUNCT
m-806	153	155	+	+	SYM
m-806	153	156	�	�	PROPN
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m-806	153	158	�	�	PROPN
m-806	153	159	�	�	PROPN
m-806	153	160	(	(	PUNCT
m-806	153	161	�	�	PROPN
m-806	153	162	�	�	PROPN
m-806	153	163	)	)	PUNCT
m-806	154	1	+	+	NUM
m-806	154	2	⋯	⋯	PROPN
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m-806	154	4	+	+	CCONJ
m-806	154	5	2	2	NUM
m-806	154	6	�	�	PROPN
m-806	154	7	�	�	PROPN
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m-806	154	11	(	(	PUNCT
m-806	154	12	�	�	PROPN
m-806	154	13	�	�	PROPN
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m-806	154	15	+	+	SYM
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m-806	154	19	(	(	PUNCT
m-806	154	20	�	�	PROPN
m-806	154	21	�	�	PROPN
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m-806	154	23	+	+	SYM
m-806	154	24	�	�	PROPN
m-806	154	25	�	�	PROPN
m-806	154	26	�	�	PROPN
m-806	154	27	�	�	PROPN
m-806	154	28	(	(	PUNCT
m-806	154	29	�	�	PROPN
m-806	154	30	�	�	PROPN
m-806	154	31	)	)	PUNCT
m-806	154	32	+	+	SYM
m-806	154	33	�	�	PROPN
m-806	154	34	�	�	PROPN
m-806	154	35	�	�	PROPN
m-806	154	36	(	(	PUNCT
m-806	154	37	�	�	PROPN
m-806	154	38	�	�	PROPN
m-806	154	39	)	)	PUNCT
m-806	154	40	�	�	PROPN
m-806	154	41	�	�	PROPN
m-806	154	42	+	+	PROPN
m-806	154	43	�	�	PROPN
m-806	154	44	�	�	PROPN
m-806	154	45	�	�	PROPN
m-806	154	46	�	�	PROPN
m-806	154	47	�	�	PROPN
m-806	154	48	�	�	PROPN
m-806	154	49	(	(	PUNCT
m-806	154	50	�	�	PROPN
m-806	154	51	�	�	PROPN
m-806	154	52	)	)	PUNCT
m-806	154	53	+	+	SYM
m-806	154	54	�	�	PROPN
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m-806	154	56	�	�	PROPN
m-806	154	57	(	(	PUNCT
m-806	154	58	�	�	PROPN
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m-806	154	60	)	)	PUNCT
m-806	154	61	�	�	PROPN
m-806	154	62	+	+	CCONJ
m-806	154	63	⋯	⋯	PROPN
m-806	154	64	�	�	PROPN
m-806	154	65	(	(	PUNCT
m-806	154	66	7.5	7.5	NUM
m-806	154	67	)	)	PUNCT
m-806	154	68	we	we	PRON
m-806	154	69	shall	shall	AUX
m-806	154	70	now	now	ADV
m-806	154	71	expand	expand	VERB
m-806	154	72	each	each	PRON
m-806	154	73	of	of	ADP
m-806	154	74	the	the	DET
m-806	154	75	terms	term	NOUN
m-806	154	76	of	of	ADP
m-806	154	77	(	(	PUNCT
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m-806	154	79	)	)	PUNCT
m-806	154	80	,	,	PUNCT
m-806	154	81	(	(	PUNCT
m-806	154	82	which	which	PRON
m-806	154	83	is	be	AUX
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m-806	154	85	at	at	ADP
m-806	154	86	(	(	PUNCT
m-806	154	87	�	�	PROPN
m-806	154	88	�	�	PROPN
m-806	154	89	,	,	PUNCT
m-806	154	90	�	�	PROPN
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m-806	154	92	�	�	PROPN
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m-806	154	94	�	�	PROPN
m-806	154	95	�	�	PROPN
m-806	154	96	)	)	PUNCT
m-806	154	97	)	)	PUNCT
m-806	154	98	by	by	ADP
m-806	154	99	using	use	VERB
m-806	154	100	(	(	PUNCT
m-806	154	101	7.2a	7.2a	PROPN
m-806	154	102	-	-	NOUN
m-806	154	103	c	c	NOUN
m-806	154	104	)	)	PUNCT
m-806	154	105	,	,	PUNCT
m-806	154	106	as	as	ADV
m-806	154	107	well	well	ADV
m-806	154	108	as	as	ADP
m-806	154	109	(	(	PUNCT
m-806	154	110	7.4	7.4	NUM
m-806	154	111	)	)	PUNCT
m-806	154	112	and	and	CCONJ
m-806	154	113	(	(	PUNCT
m-806	154	114	7.5	7.5	NUM
m-806	154	115	)	)	PUNCT
m-806	154	116	.	.	PUNCT
m-806	155	1	thus	thus	ADV
m-806	155	2	,	,	PUNCT
m-806	155	3	we	we	PRON
m-806	155	4	get	get	VERB
m-806	155	5	�	�	PROPN
m-806	155	6	�	�	PROPN
m-806	155	7	�	�	PROPN
m-806	155	8	,	,	PUNCT
m-806	155	9	�	�	PROPN
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m-806	155	12	�	�	PROPN
m-806	155	13	�	�	PROPN
m-806	155	14	)	)	PUNCT
m-806	155	15	=	=	PROPN
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m-806	155	18	�	�	PROPN
m-806	155	19	�	�	PROPN
m-806	155	20	,	,	PUNCT
m-806	155	21	�	�	PROPN
m-806	155	22	�	�	PROPN
m-806	155	23	(	(	PUNCT
m-806	155	24	�	�	PROPN
m-806	155	25	�	�	PROPN
m-806	155	26	)	)	PUNCT
m-806	155	27	+	+	CCONJ
m-806	155	28	{	{	PUNCT
m-806	155	29	�	�	PROPN
m-806	155	30	�	�	PROPN
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m-806	155	32	�	�	PROPN
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m-806	155	34	+	+	SYM
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m-806	155	40	�	�	PROPN
m-806	155	41	+	+	SYM
m-806	155	42	⋯	⋯	PROPN
m-806	155	43	+	+	SYM
m-806	155	44	�	�	PROPN
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m-806	155	47	�	�	PROPN
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m-806	155	49	�	�	PROPN
m-806	155	50	�	�	PROPN
m-806	155	51	+	+	SYM
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m-806	155	55	�	�	PROPN
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m-806	155	57	+	+	SYM
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m-806	155	62	�	�	NOUN
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m-806	155	64	+	+	CCONJ
m-806	155	65	⋯	⋯	PROPN
m-806	155	66	)	)	PUNCT
m-806	156	1	+	+	CCONJ
m-806	156	2	⋯	⋯	VERB
m-806	156	3	}	}	PUNCT
m-806	156	4	�	�	PROPN
m-806	156	5	�	�	PROPN
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m-806	156	7	�	�	PROPN
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m-806	156	12	�	�	PROPN
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m-806	156	15	�	�	PROPN
m-806	156	16	+	+	PROPN
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m-806	156	19	�	�	PROPN
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m-806	156	21	+	+	SYM
m-806	156	22	�	�	PROPN
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m-806	156	25	�	�	PROPN
m-806	156	26	+	+	SYM
m-806	156	27	�	�	PROPN
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m-806	156	29	�	�	PROPN
m-806	156	30	�	�	PROPN
m-806	156	31	�	�	PROPN
m-806	156	32	+	+	CCONJ
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m-806	156	34	+	+	SYM
m-806	156	35	�	�	PROPN
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m-806	156	38	�	�	PROPN
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m-806	156	41	+	+	SYM
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m-806	156	46	+	+	SYM
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m-806	156	52	+	+	CCONJ
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m-806	157	1	+	+	CCONJ
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m-806	157	14	+	+	CCONJ
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m-806	157	31	+	+	SYM
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m-806	157	37	�	�	PROPN
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m-806	157	41	+	+	SYM
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m-806	157	45	�	�	PROPN
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m-806	157	83	+	+	SYM
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m-806	157	85	+	+	SYM
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m-806	157	93	+	+	SYM
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m-806	157	99	+	+	CCONJ
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m-806	158	4	×	×	PROPN
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m-806	158	13	+	+	CCONJ
m-806	158	14	⋯	⋯	PROPN
m-806	158	15	+	+	SYM
m-806	158	16	�	�	PROPN
m-806	158	17	�	�	PROPN
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m-806	158	19	�	�	PROPN
m-806	158	20	�	�	PROPN
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m-806	158	22	+	+	SYM
m-806	158	23	�	�	PROPN
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m-806	158	27	+	+	CCONJ
m-806	158	28	⋯	⋯	PROPN
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m-806	158	31	�	�	PROPN
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m-806	158	36	�	�	PROPN
m-806	158	37	�	�	PROPN
m-806	158	38	�	�	PROPN
m-806	158	39	(	(	PUNCT
m-806	158	40	�	�	PROPN
m-806	158	41	�	�	PROPN
m-806	158	42	)	)	PUNCT
m-806	158	43	+	+	PROPN
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m-806	158	46	{	{	SYM
m-806	158	47	�	�	PROPN
m-806	158	48	�	�	PROPN
m-806	158	49	+	+	SYM
m-806	158	50	�	�	PROPN
m-806	158	51	�	�	PROPN
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m-806	158	53	�	�	PROPN
m-806	158	54	+	+	CCONJ
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m-806	158	56	+	+	SYM
m-806	158	57	�	�	PROPN
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m-806	158	60	�	�	PROPN
m-806	158	61	�	�	PROPN
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m-806	158	64	�	�	PROPN
m-806	158	65	�	�	PROPN
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m-806	158	68	+	+	CCONJ
m-806	158	69	⋯	⋯	PROPN
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m-806	159	1	+	+	CCONJ
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m-806	159	4	�	�	PROPN
m-806	159	5	�	�	PROPN
m-806	159	6	�	�	PROPN
m-806	159	7	�	�	PROPN
m-806	159	8	�	�	PROPN
m-806	159	9	,	,	PUNCT
m-806	159	10	�	�	PROPN
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m-806	159	12	�	�	PROPN
m-806	159	13	�	�	PROPN
m-806	159	14	(	(	PUNCT
m-806	159	15	�	�	PROPN
m-806	159	16	�	�	PROPN
m-806	159	17	)	)	PUNCT
m-806	159	18	�	�	PROPN
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m-806	165	60	�	�	PROPN
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m-806	165	62	�	�	PROPN
m-806	165	63	�	�	PROPN
m-806	165	64	(	(	PUNCT
m-806	165	65	�	�	PROPN
m-806	165	66	�	�	PROPN
m-806	165	67	)	)	PUNCT
m-806	165	68	+	+	SYM
m-806	165	69	�	�	PROPN
m-806	165	70	�	�	PROPN
m-806	165	71	�	�	PROPN
m-806	165	72	,	,	PUNCT
m-806	165	73	�	�	PROPN
m-806	165	74	�	�	PROPN
m-806	165	75	(	(	PUNCT
m-806	165	76	�	�	PROPN
m-806	165	77	�	�	PROPN
m-806	165	78	)	)	PUNCT
m-806	165	79	�	�	PROPN
m-806	165	80	+	+	CCONJ
m-806	165	81	{	{	PUNCT
m-806	165	82	�	�	PROPN
m-806	165	83	�	�	PROPN
m-806	165	84	̂	̂	NOUN
m-806	165	85	�	�	PROPN
m-806	165	86	�	�	PROPN
m-806	165	87	+	+	SYM
m-806	165	88	�	�	PROPN
m-806	165	89	�	�	PROPN
m-806	165	90	�	�	PROPN
m-806	165	91	̂	̂	NOUN
m-806	165	92	�	�	NOUN
m-806	165	93	�	�	PROPN
m-806	165	94	+	+	CCONJ
m-806	165	95	⋯	⋯	PROPN
m-806	165	96	}	}	PUNCT
m-806	165	97	�	�	PROPN
m-806	165	98	�	�	PROPN
m-806	165	99	�	�	PROPN
m-806	165	100	,	,	PUNCT
m-806	165	101	�	�	PROPN
m-806	165	102	�	�	PROPN
m-806	165	103	�	�	PROPN
m-806	165	104	�	�	PROPN
m-806	165	105	(	(	PUNCT
m-806	165	106	�	�	PROPN
m-806	165	107	�	�	PROPN
m-806	165	108	)	)	PUNCT
m-806	165	109	+	+	SYM
m-806	165	110	�	�	PROPN
m-806	165	111	�	�	PROPN
m-806	165	112	�	�	PROPN
m-806	165	113	,	,	PUNCT
m-806	165	114	�	�	PROPN
m-806	165	115	�	�	PROPN
m-806	165	116	�	�	PROPN
m-806	165	117	�	�	PROPN
m-806	165	118	(	(	PUNCT
m-806	165	119	�	�	PROPN
m-806	165	120	�	�	PROPN
m-806	165	121	)	)	PUNCT
m-806	165	122	�	�	PROPN
m-806	165	123	�	�	PROPN
m-806	165	124	+	+	CCONJ
m-806	165	125	�	�	PROPN
m-806	165	126	{	{	PUNCT
m-806	165	127	�	�	PROPN
m-806	165	128	�	�	PROPN
m-806	165	129	+	+	SYM
m-806	165	130	�	�	PROPN
m-806	165	131	�	�	PROPN
m-806	165	132	�	�	PROPN
m-806	165	133	�	�	PROPN
m-806	165	134	+	+	CCONJ
m-806	165	135	⋯	⋯	PROPN
m-806	165	136	}	}	PUNCT
m-806	165	137	�	�	PROPN
m-806	165	138	�	�	PROPN
m-806	165	139	�	�	PROPN
m-806	165	140	�	�	PROPN
m-806	165	141	�	�	PROPN
m-806	165	142	,	,	PUNCT
m-806	165	143	�	�	PROPN
m-806	165	144	�	�	PROPN
m-806	165	145	�	�	PROPN
m-806	165	146	(	(	PUNCT
m-806	165	147	�	�	PROPN
m-806	165	148	�	�	PROPN
m-806	165	149	)	)	PUNCT
m-806	165	150	+	+	CCONJ
m-806	165	151	�	�	PROPN
m-806	165	152	�	�	PROPN
m-806	165	153	�	�	PROPN
m-806	165	154	,	,	PUNCT
m-806	165	155	�	�	PROPN
m-806	165	156	�	�	PROPN
m-806	165	157	�	�	PROPN
m-806	165	158	(	(	PUNCT
m-806	165	159	�	�	PROPN
m-806	165	160	�	�	PROPN
m-806	165	161	)	)	PUNCT
m-806	165	162	�	�	PROPN
m-806	165	163	+	+	CCONJ
m-806	165	164	⋯	⋯	PROPN
m-806	165	165	�	�	PROPN
m-806	165	166	�	�	PROPN
m-806	165	167	(	(	PUNCT
m-806	165	168	�	�	PROPN
m-806	165	169	�	�	PROPN
m-806	165	170	�	�	PROPN
m-806	165	171	,	,	PUNCT
m-806	165	172	�	�	PROPN
m-806	165	173	)	)	PUNCT
m-806	165	174	(	(	PUNCT
m-806	165	175	7.6d	7.6d	NOUN
m-806	165	176	)	)	PUNCT
m-806	165	177	�	�	PROPN
m-806	165	178	�	�	PROPN
m-806	165	179	�	�	PROPN
m-806	165	180	�	�	PROPN
m-806	165	181	�	�	PROPN
m-806	165	182	�	�	PROPN
m-806	165	183	,	,	PUNCT
m-806	165	184	�	�	PROPN
m-806	165	185	�	�	PROPN
m-806	165	186	(	(	PUNCT
m-806	165	187	�	�	PROPN
m-806	165	188	�	�	PROPN
m-806	165	189	)	)	PUNCT
m-806	165	190	+	+	CCONJ
m-806	165	191	�	�	PROPN
m-806	165	192	�	�	PROPN
m-806	165	193	�	�	PROPN
m-806	165	194	,	,	PUNCT
m-806	165	195	�	�	PROPN
m-806	165	196	�	�	PROPN
m-806	165	197	(	(	PUNCT
m-806	165	198	�	�	PROPN
m-806	165	199	�	�	PROPN
m-806	165	200	)	)	PUNCT
m-806	165	201	�	�	PROPN
m-806	165	202	=	=	SYM
m-806	165	203	�	�	PROPN
m-806	165	204	�	�	PROPN
m-806	165	205	�	�	PROPN
m-806	165	206	�	�	PROPN
m-806	165	207	�	�	PROPN
m-806	165	208	�	�	PROPN
m-806	165	209	�	�	PROPN
m-806	165	210	,	,	PUNCT
m-806	165	211	�	�	PROPN
m-806	165	212	�	�	PROPN
m-806	165	213	(	(	PUNCT
m-806	165	214	�	�	PROPN
m-806	165	215	�	�	PROPN
m-806	165	216	)	)	PUNCT
m-806	165	217	+	+	SYM
m-806	165	218	�	�	PROPN
m-806	165	219	�	�	PROPN
m-806	165	220	�	�	PROPN
m-806	165	221	,	,	PUNCT
m-806	165	222	�	�	PROPN
m-806	165	223	�	�	PROPN
m-806	165	224	(	(	PUNCT
m-806	165	225	�	�	PROPN
m-806	165	226	�	�	PROPN
m-806	165	227	)	)	PUNCT
m-806	165	228	�	�	PROPN
m-806	165	229	+	+	CCONJ
m-806	165	230	{	{	PUNCT
m-806	165	231	�	�	PROPN
m-806	165	232	�	�	PROPN
m-806	165	233	̂	̂	NOUN
m-806	165	234	�	�	NOUN
m-806	165	235	�	�	PROPN
m-806	165	236	+	+	CCONJ
m-806	165	237	⋯	⋯	PROPN
m-806	165	238	}	}	PUNCT
m-806	165	239	�	�	PROPN
m-806	165	240	�	�	PROPN
m-806	165	241	�	�	PROPN
m-806	165	242	,	,	PUNCT
m-806	165	243	�	�	PROPN
m-806	165	244	�	�	PROPN
m-806	165	245	�	�	PROPN
m-806	165	246	�	�	PROPN
m-806	165	247	(	(	PUNCT
m-806	165	248	�	�	PROPN
m-806	165	249	�	�	PROPN
m-806	165	250	)	)	PUNCT
m-806	165	251	+	+	SYM
m-806	165	252	�	�	PROPN
m-806	165	253	�	�	PROPN
m-806	165	254	�	�	PROPN
m-806	165	255	,	,	PUNCT
m-806	165	256	�	�	PROPN
m-806	165	257	�	�	PROPN
m-806	165	258	�	�	PROPN
m-806	165	259	�	�	PROPN
m-806	165	260	(	(	PUNCT
m-806	165	261	�	�	PROPN
m-806	165	262	�	�	PROPN
m-806	165	263	)	)	PUNCT
m-806	165	264	�	�	PROPN
m-806	165	265	�	�	PROPN
m-806	165	266	+	+	CCONJ
m-806	165	267	�	�	PROPN
m-806	165	268	{	{	PUNCT
m-806	165	269	�	�	PROPN
m-806	165	270	�	�	PROPN
m-806	165	271	+	+	SYM
m-806	165	272	�	�	PROPN
m-806	165	273	�	�	PROPN
m-806	165	274	�	�	PROPN
m-806	165	275	�	�	PROPN
m-806	165	276	+	+	CCONJ
m-806	165	277	⋯	⋯	PROPN
m-806	165	278	}	}	PUNCT
m-806	165	279	�	�	PROPN
m-806	165	280	�	�	PROPN
m-806	165	281	�	�	PROPN
m-806	165	282	�	�	PROPN
m-806	165	283	�	�	PROPN
m-806	165	284	,	,	PUNCT
m-806	165	285	�	�	PROPN
m-806	165	286	�	�	PROPN
m-806	165	287	�	�	PROPN
m-806	165	288	(	(	PUNCT
m-806	165	289	�	�	PROPN
m-806	165	290	�	�	PROPN
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m-806	165	292	+	+	CCONJ
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m-806	165	294	�	�	PROPN
m-806	165	295	�	�	PROPN
m-806	165	296	,	,	PUNCT
m-806	165	297	�	�	PROPN
m-806	165	298	�	�	PROPN
m-806	165	299	�	�	PROPN
m-806	165	300	(	(	PUNCT
m-806	165	301	�	�	PROPN
m-806	165	302	�	�	PROPN
m-806	165	303	)	)	PUNCT
m-806	165	304	�	�	PROPN
m-806	165	305	+	+	CCONJ
m-806	165	306	⋯	⋯	PROPN
m-806	165	307	�	�	PROPN
m-806	165	308	�	�	PROPN
m-806	165	309	(	(	PUNCT
m-806	165	310	�	�	PROPN
m-806	165	311	�	�	PROPN
m-806	165	312	�	�	PROPN
m-806	165	313	,	,	PUNCT
m-806	165	314	�	�	PROPN
m-806	165	315	)	)	PUNCT
m-806	165	316	(	(	PUNCT
m-806	165	317	7.6e	7.6e	NUM
m-806	165	318	)	)	PUNCT
m-806	165	319	�	�	PROPN
m-806	165	320	�	�	PROPN
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m-806	165	322	�	�	PROPN
m-806	165	323	�	�	PROPN
m-806	165	324	�	�	PROPN
m-806	165	325	�	�	PROPN
m-806	165	326	,	,	PUNCT
m-806	165	327	�	�	PROPN
m-806	165	328	�	�	PROPN
m-806	165	329	(	(	PUNCT
m-806	165	330	�	�	PROPN
m-806	165	331	�	�	PROPN
m-806	165	332	)	)	PUNCT
m-806	165	333	+	+	CCONJ
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m-806	165	338	�	�	PROPN
m-806	165	339	�	�	PROPN
m-806	165	340	(	(	PUNCT
m-806	165	341	�	�	PROPN
m-806	165	342	�	�	PROPN
m-806	165	343	)	)	PUNCT
m-806	165	344	�	�	PROPN
m-806	165	345	=	=	SYM
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m-806	165	347	�	�	PROPN
m-806	165	348	�	�	PROPN
m-806	165	349	�	�	PROPN
m-806	165	350	�	�	PROPN
m-806	165	351	�	�	PROPN
m-806	165	352	�	�	PROPN
m-806	165	353	�	�	PROPN
m-806	165	354	�	�	PROPN
m-806	165	355	,	,	PUNCT
m-806	165	356	�	�	PROPN
m-806	165	357	�	�	PROPN
m-806	165	358	(	(	PUNCT
m-806	165	359	�	�	PROPN
m-806	165	360	�	�	PROPN
m-806	165	361	)	)	PUNCT
m-806	165	362	+	+	CCONJ
m-806	165	363	�	�	PROPN
m-806	165	364	�	�	PROPN
m-806	165	365	�	�	PROPN
m-806	165	366	,	,	PUNCT
m-806	165	367	�	�	PROPN
m-806	165	368	�	�	PROPN
m-806	165	369	(	(	PUNCT
m-806	165	370	�	�	PROPN
m-806	165	371	�	�	PROPN
m-806	165	372	)	)	PUNCT
m-806	165	373	�	�	PROPN
m-806	165	374	+	+	CCONJ
m-806	165	375	⋯	⋯	PROPN
m-806	165	376	�	�	PROPN
m-806	165	377	�	�	PROPN
m-806	165	378	(	(	PUNCT
m-806	165	379	�	�	PROPN
m-806	165	380	�	�	PROPN
m-806	165	381	�	�	PROPN
m-806	165	382	,	,	PUNCT
m-806	165	383	�	�	PROPN
m-806	165	384	)	)	PUNCT
m-806	165	385	(	(	PUNCT
m-806	165	386	7.6f	7.6f	X
m-806	165	387	)	)	PUNCT
m-806	165	388	�	�	PROPN
m-806	165	389	�	�	PROPN
m-806	165	390	�	�	PROPN
m-806	165	391	�	�	PROPN
m-806	165	392	�	�	PROPN
m-806	165	393	�	�	PROPN
m-806	165	394	�	�	PROPN
m-806	165	395	,	,	PUNCT
m-806	165	396	�	�	PROPN
m-806	165	397	�	�	PROPN
m-806	165	398	(	(	PUNCT
m-806	165	399	�	�	PROPN
m-806	165	400	�	�	PROPN
m-806	165	401	)	)	PUNCT
m-806	165	402	=	=	SYM
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m-806	165	404	�	�	PROPN
m-806	165	405	�	�	PROPN
m-806	165	406	�	�	PROPN
m-806	165	407	�	�	PROPN
m-806	165	408	�	�	PROPN
m-806	165	409	�	�	PROPN
m-806	165	410	�	�	PROPN
m-806	165	411	,	,	PUNCT
m-806	165	412	�	�	PROPN
m-806	165	413	�	�	PROPN
m-806	165	414	(	(	PUNCT
m-806	165	415	�	�	PROPN
m-806	165	416	�	�	PROPN
m-806	165	417	)	)	PUNCT
m-806	166	1	+	+	SYM
m-806	166	2	�	�	PROPN
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m-806	166	4	�	�	PROPN
m-806	166	5	{	{	PUNCT
m-806	166	6	�	�	PROPN
m-806	166	7	�	�	PROPN
m-806	166	8	̂	̂	NOUN
m-806	166	9	�	�	PROPN
m-806	166	10	�	�	PROPN
m-806	166	11	+	+	SYM
m-806	166	12	�	�	PROPN
m-806	166	13	�	�	PROPN
m-806	166	14	�	�	PROPN
m-806	166	15	̂	̂	NOUN
m-806	166	16	�	�	NOUN
m-806	166	17	�	�	PROPN
m-806	166	18	+	+	CCONJ
m-806	166	19	⋯	⋯	PROPN
m-806	166	20	}	}	SYM
m-806	166	21	�	�	PROPN
m-806	166	22	�	�	PROPN
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m-806	166	24	�	�	PROPN
m-806	166	25	�	�	PROPN
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m-806	166	27	�	�	PROPN
m-806	166	28	(	(	PUNCT
m-806	166	29	�	�	PROPN
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m-806	166	32	+	+	SYM
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m-806	166	35	�	�	PROPN
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m-806	166	38	�	�	PROPN
m-806	166	39	�	�	PROPN
m-806	166	40	�	�	PROPN
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m-806	166	42	+	+	CCONJ
m-806	166	43	⋯	⋯	PROPN
m-806	166	44	}	}	PUNCT
m-806	166	45	�	�	PROPN
m-806	166	46	�	�	PROPN
m-806	166	47	�	�	PROPN
m-806	166	48	�	�	PROPN
m-806	166	49	�	�	PROPN
m-806	166	50	�	�	PROPN
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m-806	166	52	�	�	PROPN
m-806	166	53	�	�	PROPN
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m-806	166	70	+	+	SYM
m-806	166	71	⋯	⋯	PROPN
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m-806	166	84	(	(	PUNCT
m-806	166	85	�	�	PROPN
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m-806	166	88	+	+	SYM
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m-806	166	90	{	{	PUNCT
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m-806	166	93	+	+	SYM
m-806	166	94	�	�	PROPN
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m-806	166	96	�	�	PROPN
m-806	166	97	�	�	PROPN
m-806	166	98	+	+	CCONJ
m-806	166	99	⋯	⋯	PROPN
m-806	166	100	}	}	PUNCT
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m-806	166	110	�	�	PROPN
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m-806	166	112	�	�	NOUN
m-806	166	113	�	�	PROPN
m-806	166	114	+	+	SYM
m-806	166	115	⋯	⋯	PROPN
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m-806	166	117	�	�	PROPN
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m-806	166	119	�	�	PROPN
m-806	166	120	�	�	PROPN
m-806	166	121	�	�	PROPN
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m-806	166	123	,	,	PUNCT
m-806	166	124	�	�	PROPN
m-806	166	125	�	�	PROPN
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m-806	166	127	�	�	PROPN
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m-806	166	129	�	�	PROPN
m-806	166	130	�	�	PROPN
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m-806	166	134	�	�	PROPN
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m-806	166	136	�	�	PROPN
m-806	166	137	�	�	PROPN
m-806	166	138	�	�	PROPN
m-806	166	139	�	�	PROPN
m-806	166	140	(	(	PUNCT
m-806	166	141	�	�	PROPN
m-806	166	142	�	�	PROPN
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m-806	166	144	⋯	⋯	PROPN
m-806	166	145	)	)	PUNCT
m-806	166	146	�	�	PROPN
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m-806	166	154	�	�	PROPN
m-806	166	155	,	,	PUNCT
m-806	166	156	�	�	PROPN
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m-806	166	159	�	�	PROPN
m-806	166	160	�	�	PROPN
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m-806	166	162	�	�	PROPN
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m-806	166	164	�	�	PROPN
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m-806	166	166	+	+	CCONJ
m-806	166	167	⋯	⋯	PROPN
m-806	166	168	�	�	PROPN
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m-806	166	170	(	(	PUNCT
m-806	166	171	�	�	PROPN
m-806	166	172	�	�	PROPN
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m-806	166	175	�	�	PROPN
m-806	166	176	)	)	PUNCT
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m-806	166	178	7.6	7.6	NUM
m-806	166	179	g	g	NOUN
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m-806	166	181	�	�	PROPN
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m-806	166	187	�	�	PROPN
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m-806	166	189	,	,	PUNCT
m-806	166	190	�	�	PROPN
m-806	166	191	�	�	PROPN
m-806	166	192	(	(	PUNCT
m-806	166	193	�	�	PROPN
m-806	166	194	�	�	PROPN
m-806	166	195	)	)	PUNCT
m-806	166	196	=	=	SYM
m-806	166	197	�	�	PROPN
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m-806	166	200	�	�	PROPN
m-806	166	201	�	�	PROPN
m-806	166	202	�	�	PROPN
m-806	166	203	�	�	PROPN
m-806	166	204	�	�	PROPN
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m-806	166	207	�	�	PROPN
m-806	166	208	�	�	PROPN
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m-806	166	210	�	�	PROPN
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m-806	166	212	)	)	PUNCT
m-806	166	213	+	+	CCONJ
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m-806	166	215	�	�	PROPN
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m-806	166	220	+	+	SYM
m-806	166	221	⋯	⋯	PROPN
m-806	166	222	)	)	PUNCT
m-806	166	223	�	�	PROPN
m-806	166	224	�	�	PROPN
m-806	166	225	�	�	PROPN
m-806	166	226	�	�	PROPN
m-806	166	227	�	�	PROPN
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m-806	166	229	�	�	PROPN
m-806	166	230	�	�	PROPN
m-806	166	231	�	�	PROPN
m-806	166	232	�	�	PROPN
m-806	166	233	(	(	PUNCT
m-806	166	234	�	�	PROPN
m-806	166	235	�	�	PROPN
m-806	166	236	)	)	PUNCT
m-806	166	237	�	�	PROPN
m-806	166	238	+	+	SYM
m-806	166	239	�	�	PROPN
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m-806	166	242	(	(	PUNCT
m-806	166	243	�	�	PROPN
m-806	166	244	�	�	PROPN
m-806	166	245	+	+	CCONJ
m-806	166	246	⋯	⋯	PROPN
m-806	166	247	)	)	PUNCT
m-806	166	248	�	�	PROPN
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m-806	166	254	,	,	PUNCT
m-806	166	255	�	�	PROPN
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m-806	166	260	�	�	PROPN
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m-806	166	263	�	�	PROPN
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m-806	166	265	�	�	PROPN
m-806	166	266	+	+	CCONJ
m-806	166	267	⋯	⋯	PROPN
m-806	166	268	�	�	PROPN
m-806	166	269	�	�	PROPN
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m-806	166	271	�	�	PROPN
m-806	166	272	�	�	PROPN
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m-806	166	275	�	�	PROPN
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m-806	166	278	7.6h	7.6h	NUM
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m-806	166	280	�	�	PROPN
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m-806	166	287	�	�	PROPN
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m-806	166	290	�	�	PROPN
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m-806	166	296	=	=	SYM
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m-806	166	301	�	�	PROPN
m-806	166	302	�	�	PROPN
m-806	166	303	�	�	PROPN
m-806	166	304	�	�	PROPN
m-806	166	305	�	�	PROPN
m-806	166	306	�	�	PROPN
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m-806	166	309	�	�	PROPN
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m-806	166	312	�	�	PROPN
m-806	166	313	�	�	PROPN
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m-806	166	315	+	+	CCONJ
m-806	166	316	⋯	⋯	PROPN
m-806	166	317	�	�	PROPN
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m-806	166	320	�	�	PROPN
m-806	166	321	�	�	PROPN
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m-806	166	324	�	�	PROPN
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m-806	166	327	7.6i	7.6i	X
m-806	166	328	)	)	PUNCT
m-806	166	329	�	�	PROPN
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m-806	166	333	,	,	PUNCT
m-806	166	334	�	�	PROPN
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m-806	166	339	=	=	SYM
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m-806	166	346	�	�	PROPN
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m-806	166	351	+	+	CCONJ
m-806	166	352	{	{	PUNCT
m-806	166	353	�	�	PROPN
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m-806	166	358	+	+	SYM
m-806	166	359	⋯	⋯	PROPN
m-806	166	360	+	+	SYM
m-806	166	361	�	�	PROPN
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m-806	166	364	�	�	PROPN
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m-806	166	368	+	+	SYM
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m-806	166	375	…	…	PUNCT
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m-806	166	394	�	�	PROPN
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m-806	166	399	+	+	CCONJ
m-806	166	400	…	…	PUNCT
m-806	166	401	+	+	CCONJ
m-806	166	402	�	�	PROPN
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m-806	166	409	+	+	SYM
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m-806	166	415	+	+	CCONJ
m-806	166	416	⋯	⋯	PROPN
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m-806	167	2	⋯	⋯	VERB
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m-806	167	17	�	�	PROPN
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m-806	167	26	+	+	SYM
m-806	167	27	⋯	⋯	PROPN
m-806	167	28	+	+	SYM
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m-806	168	45	+	+	CCONJ
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m-806	168	152	+	+	SYM
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m-806	168	184	�	�	PROPN
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m-806	169	12	|	|	ADV
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m-806	169	15	|	|	CCONJ
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m-806	169	18	|	|	ADV
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m-806	170	12	||	||	NUM
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m-806	171	5	-	-	PUNCT
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m-806	172	184	�	�	PROPN
m-806	172	185	,	,	PUNCT
m-806	172	186	�	�	PROPN
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m-806	172	188	�	�	PROPN
m-806	172	189	�	�	PROPN
m-806	172	190	(	(	PUNCT
m-806	172	191	�	�	PROPN
m-806	172	192	�	�	PROPN
m-806	172	193	)	)	PUNCT
m-806	172	194	+	+	SYM
m-806	172	195	�	�	PROPN
m-806	172	196	�	�	PROPN
m-806	172	197	�	�	PROPN
m-806	172	198	,	,	PUNCT
m-806	172	199	�	�	PROPN
m-806	172	200	�	�	PROPN
m-806	172	201	�	�	PROPN
m-806	172	202	�	�	PROPN
m-806	172	203	(	(	PUNCT
m-806	172	204	�	�	PROPN
m-806	172	205	�	�	PROPN
m-806	172	206	)	)	PUNCT
m-806	172	207	+	+	CCONJ
m-806	172	208	�	�	PROPN
m-806	172	209	�	�	PROPN
m-806	172	210	�	�	PROPN
m-806	172	211	,	,	PUNCT
m-806	172	212	�	�	PROPN
m-806	172	213	�	�	PROPN
m-806	172	214	�	�	PROPN
m-806	172	215	�	�	PROPN
m-806	172	216	(	(	PUNCT
m-806	172	217	�	�	PROPN
m-806	172	218	�	�	PROPN
m-806	172	219	)	)	PUNCT
m-806	172	220	�	�	PROPN
m-806	172	221	+	+	SYM
m-806	172	222	�	�	PROPN
m-806	172	223	�	�	PROPN
m-806	172	224	�	�	PROPN
m-806	172	225	(	(	PUNCT
m-806	172	226	0	0	NUM
m-806	172	227	)	)	PUNCT
m-806	172	228	�	�	PROPN
m-806	172	229	�	�	PROPN
m-806	172	230	,	,	PUNCT
m-806	172	231	�	�	PROPN
m-806	172	232	�	�	PROPN
m-806	172	233	(	(	PUNCT
m-806	172	234	�	�	PROPN
m-806	172	235	�	�	PROPN
m-806	172	236	)	)	PUNCT
m-806	172	237	=	=	SYM
m-806	172	238	0	0	NUM
m-806	172	239	(	(	PUNCT
m-806	172	240	7.7d	7.7d	NUM
m-806	172	241	)	)	PUNCT
m-806	172	242	�	�	PROPN
m-806	172	243	(	(	PUNCT
m-806	172	244	�	�	PROPN
m-806	172	245	�	�	PROPN
m-806	172	246	�	�	PROPN
m-806	172	247	):	):	PUNCT
m-806	172	248	�	�	PROPN
m-806	172	249	̂	̂	SYM
m-806	172	250	�	�	PROPN
m-806	172	251	�	�	PROPN
m-806	172	252	�	�	PROPN
m-806	172	253	�	�	PROPN
m-806	172	254	,	,	PUNCT
m-806	172	255	�	�	PROPN
m-806	172	256	�	�	PROPN
m-806	172	257	�	�	PROPN
m-806	172	258	�	�	PROPN
m-806	172	259	(	(	PUNCT
m-806	172	260	�	�	PROPN
m-806	172	261	�	�	PROPN
m-806	172	262	)	)	PUNCT
m-806	172	263	+	+	SYM
m-806	172	264	�	�	PROPN
m-806	172	265	�	�	PROPN
m-806	172	266	�	�	PROPN
m-806	172	267	�	�	PROPN
m-806	172	268	�	�	PROPN
m-806	172	269	,	,	PUNCT
m-806	172	270	�	�	PROPN
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m-806	172	272	�	�	PROPN
m-806	172	273	(	(	PUNCT
m-806	172	274	�	�	PROPN
m-806	172	275	�	�	PROPN
m-806	172	276	)	)	PUNCT
m-806	172	277	+	+	CCONJ
m-806	172	278	1	1	NUM
m-806	172	279	2	2	NUM
m-806	172	280	�	�	PROPN
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m-806	172	282	�	�	PROPN
m-806	172	283	̂	̂	SYM
m-806	172	284	�	�	PROPN
m-806	172	285	�	�	PROPN
m-806	172	286	�	�	PROPN
m-806	172	287	̂	̂	PROPN
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m-806	172	289	�	�	PROPN
m-806	172	290	�	�	PROPN
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m-806	172	292	,	,	PUNCT
m-806	172	293	�	�	PROPN
m-806	172	294	�	�	PROPN
m-806	172	295	�	�	PROPN
m-806	172	296	�	�	PROPN
m-806	172	297	�	�	PROPN
m-806	172	298	�	�	PROPN
m-806	172	299	(	(	PUNCT
m-806	172	300	�	�	PROPN
m-806	172	301	�	�	PROPN
m-806	172	302	)	)	PUNCT
m-806	172	303	+	+	CCONJ
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m-806	172	313	,	,	PUNCT
m-806	172	314	�	�	PROPN
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m-806	172	318	�	�	PROPN
m-806	172	319	(	(	PUNCT
m-806	172	320	�	�	PROPN
m-806	172	321	�	�	PROPN
m-806	172	322	)	)	PUNCT
m-806	172	323	�	�	PROPN
m-806	172	324	+	+	SYM
m-806	172	325	�	�	PROPN
m-806	172	326	̂	̂	SYM
m-806	172	327	�	�	PROPN
m-806	172	328	�	�	PROPN
m-806	172	329	�	�	PROPN
m-806	172	330	�	�	PROPN
m-806	172	331	,	,	PUNCT
m-806	172	332	�	�	PROPN
m-806	172	333	�	�	PROPN
m-806	172	334	�	�	PROPN
m-806	172	335	�	�	PROPN
m-806	172	336	(	(	PUNCT
m-806	172	337	�	�	PROPN
m-806	172	338	�	�	PROPN
m-806	172	339	)	)	PUNCT
m-806	172	340	+	+	NUM
m-806	172	341	�	�	PROPN
m-806	172	342	̂	̂	SYM
m-806	172	343	�	�	PROPN
m-806	172	344	�	�	PROPN
m-806	172	345	�	�	PROPN
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m-806	172	348	,	,	PUNCT
m-806	172	349	�	�	PROPN
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m-806	172	353	(	(	PUNCT
m-806	172	354	�	�	PROPN
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m-806	172	356	)	)	PUNCT
m-806	172	357	+	+	SYM
m-806	172	358	�	�	PROPN
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m-806	172	362	�	�	PROPN
m-806	172	363	�	�	PROPN
m-806	172	364	�	�	PROPN
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m-806	172	366	(	(	PUNCT
m-806	172	367	�	�	PROPN
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m-806	172	369	)	)	PUNCT
m-806	172	370	�	�	PROPN
m-806	172	371	+	+	SYM
m-806	172	372	�	�	PROPN
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m-806	172	381	(	(	PUNCT
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m-806	172	385	+	+	SYM
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m-806	172	393	(	(	PUNCT
m-806	172	394	�	�	PROPN
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m-806	172	398	+	+	SYM
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m-806	172	402	,	,	PUNCT
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m-806	172	405	(	(	PUNCT
m-806	172	406	�	�	PROPN
m-806	172	407	�	�	PROPN
m-806	172	408	)	)	PUNCT
m-806	172	409	+	+	SYM
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m-806	172	413	,	,	PUNCT
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m-806	172	416	(	(	PUNCT
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m-806	172	419	)	)	PUNCT
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m-806	172	421	+	+	SYM
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m-806	172	432	(	(	PUNCT
m-806	172	433	�	�	PROPN
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m-806	172	435	)	)	PUNCT
m-806	172	436	+	+	SYM
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m-806	172	440	,	,	PUNCT
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m-806	172	442	(	(	PUNCT
m-806	172	443	�	�	PROPN
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m-806	172	445	)	)	PUNCT
m-806	172	446	+	+	SYM
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m-806	172	450	,	,	PUNCT
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m-806	172	452	(	(	PUNCT
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m-806	172	457	=	=	SYM
m-806	172	458	0	0	PUNCT
m-806	172	459	(	(	PUNCT
m-806	172	460	7.7e	7.7e	NOUN
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m-806	172	467	(	(	PUNCT
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m-806	172	469	)	)	PUNCT
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m-806	172	472	7.7e	7.7e	NOUN
m-806	172	473	)	)	PUNCT
m-806	172	474	are	be	AUX
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m-806	173	4	)	)	PUNCT
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m-806	173	17	=	=	SYM
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m-806	173	24	…	…	PUNCT
m-806	173	25	∴	∴	PROPN
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m-806	173	39	7.8a	7.8a	NOUN
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m-806	173	46	=	=	SYM
m-806	173	47	1	1	X
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m-806	174	3	(	(	PUNCT
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m-806	174	5	)	)	PUNCT
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m-806	174	8	7.7b	7.7b	NUM
m-806	174	9	)	)	PUNCT
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m-806	174	14	get	get	VERB
m-806	174	15	�	�	PROPN
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m-806	174	18	�	�	PROPN
m-806	174	19	=	=	SYM
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m-806	174	22	�	�	PROPN
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m-806	174	25	,	,	PUNCT
m-806	174	26	�	�	PROPN
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m-806	174	29	�	�	PROPN
m-806	174	30	�	�	PROPN
m-806	174	31	)	)	PUNCT
m-806	174	32	�	�	PROPN
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m-806	174	35	,	,	PUNCT
m-806	174	36	�	�	PROPN
m-806	174	37	(	(	PUNCT
m-806	174	38	�	�	PROPN
m-806	174	39	�	�	PROPN
m-806	174	40	)	)	PUNCT
m-806	174	41	�	�	PROPN
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m-806	174	44	,	,	PUNCT
m-806	174	45	�	�	PROPN
m-806	174	46	�	�	PROPN
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m-806	174	51	)	)	PUNCT
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m-806	174	72	=	=	SYM
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m-806	175	2	7.8b	7.8b	NOUN
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m-806	175	10	7.7c	7.7c	NOUN
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m-806	175	17	�	�	PROPN
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m-806	175	20	�	�	PROPN
m-806	175	21	=	=	SYM
m-806	175	22	�	�	PROPN
m-806	175	23	�	�	PROPN
m-806	175	24	�	�	PROPN
m-806	175	25	�	�	PROPN
m-806	175	26	�	�	PROPN
m-806	175	27	�	�	PROPN
m-806	175	28	�	�	PROPN
m-806	175	29	,	,	PUNCT
m-806	175	30	�	�	PROPN
m-806	175	31	�	�	PROPN
m-806	175	32	(	(	PUNCT
m-806	175	33	�	�	PROPN
m-806	175	34	�	�	PROPN
m-806	175	35	)	)	PUNCT
m-806	175	36	�	�	PROPN
m-806	175	37	�	�	PROPN
m-806	175	38	,	,	PUNCT
m-806	175	39	�	�	PROPN
m-806	175	40	�	�	PROPN
m-806	175	41	�	�	PROPN
m-806	175	42	�	�	PROPN
m-806	175	43	(	(	PUNCT
m-806	175	44	�	�	PROPN
m-806	175	45	�	�	PROPN
m-806	175	46	)	)	PUNCT
m-806	175	47	�	�	PROPN
m-806	175	48	(	(	PUNCT
m-806	175	49	�	�	PROPN
m-806	175	50	�	�	PROPN
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m-806	175	52	,	,	PUNCT
m-806	175	53	�	�	PROPN
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m-806	175	55	=	=	SYM
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m-806	175	57	�	�	PROPN
m-806	175	58	�	�	PROPN
m-806	175	59	�	�	PROPN
m-806	175	60	�	�	PROPN
m-806	175	61	=	=	SYM
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m-806	175	64	�	�	PROPN
m-806	175	65	(	(	PUNCT
m-806	175	66	7.8c	7.8c	NUM
m-806	175	67	)	)	PUNCT
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m-806	175	72	(	(	PUNCT
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m-806	175	74	)	)	PUNCT
m-806	175	75	and	and	CCONJ
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m-806	175	78	̂	̂	SYM
m-806	175	79	�	�	NOUN
m-806	175	80	�	�	PROPN
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m-806	175	87	,	,	PUNCT
m-806	175	88	�	�	PROPN
m-806	175	89	�	�	PROPN
m-806	175	90	�	�	PROPN
m-806	175	91	�	�	PROPN
m-806	175	92	(	(	PUNCT
m-806	175	93	�	�	PROPN
m-806	175	94	�	�	PROPN
m-806	175	95	)	)	PUNCT
m-806	175	96	�	�	PROPN
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m-806	175	98	�	�	PROPN
m-806	175	99	�	�	PROPN
m-806	175	100	,	,	PUNCT
m-806	175	101	�	�	PROPN
m-806	175	102	�	�	PROPN
m-806	175	103	�	�	PROPN
m-806	175	104	�	�	PROPN
m-806	175	105	(	(	PUNCT
m-806	175	106	�	�	PROPN
m-806	175	107	�	�	PROPN
m-806	175	108	)	)	PUNCT
m-806	175	109	�	�	PROPN
m-806	175	110	�	�	PROPN
m-806	175	111	�	�	PROPN
m-806	175	112	,	,	PUNCT
m-806	175	113	�	�	PROPN
m-806	175	114	�	�	PROPN
m-806	175	115	�	�	PROPN
m-806	175	116	�	�	PROPN
m-806	175	117	(	(	PUNCT
m-806	175	118	�	�	PROPN
m-806	175	119	�	�	PROPN
m-806	175	120	)	)	PUNCT
m-806	175	121	�	�	PROPN
m-806	175	122	(	(	PUNCT
m-806	175	123	�	�	PROPN
m-806	175	124	�	�	PROPN
m-806	175	125	�	�	PROPN
m-806	175	126	,	,	PUNCT
m-806	175	127	�	�	PROPN
m-806	175	128	)	)	PUNCT
m-806	175	129	(	(	PUNCT
m-806	175	130	7.8d	7.8d	X
m-806	175	131	)	)	PUNCT
m-806	175	132	now	now	ADV
m-806	175	133	,	,	PUNCT
m-806	175	134	�	�	PROPN
m-806	175	135	�	�	PROPN
m-806	175	136	,	,	PUNCT
m-806	175	137	�	�	PROPN
m-806	175	138	�	�	PROPN
m-806	175	139	�	�	PROPN
m-806	175	140	�	�	PROPN
m-806	175	141	(	(	PUNCT
m-806	175	142	�	�	PROPN
m-806	175	143	�	�	PROPN
m-806	175	144	)	)	PUNCT
m-806	175	145	(	(	PUNCT
m-806	175	146	�	�	NOUN
m-806	175	147	̂	̂	SYM
m-806	175	148	�	�	PROPN
m-806	175	149	,	,	PUNCT
m-806	175	150	0	0	NUM
m-806	175	151	)	)	PUNCT
m-806	175	152	=	=	SYM
m-806	175	153	�	�	PROPN
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m-806	175	155	�	�	PROPN
m-806	175	156	�	�	PROPN
m-806	175	157	�	�	PROPN
m-806	175	158	�	�	PROPN
m-806	175	159	�	�	PROPN
m-806	175	160	,	,	PUNCT
m-806	175	161	�	�	PROPN
m-806	175	162	�	�	PROPN
m-806	175	163	�	�	PROPN
m-806	175	164	,	,	PUNCT
m-806	175	165	�	�	PROPN
m-806	175	166	�	�	PROPN
m-806	175	167	�	�	PROPN
m-806	175	168	�	�	PROPN
m-806	175	169	(	(	PUNCT
m-806	175	170	�	�	PROPN
m-806	175	171	�	�	PROPN
m-806	175	172	)	)	PUNCT
m-806	175	173	(	(	PUNCT
m-806	175	174	�	�	NOUN
m-806	175	175	̂	̂	SYM
m-806	175	176	�	�	PROPN
m-806	175	177	,	,	PUNCT
m-806	175	178	0	0	NUM
m-806	175	179	)	)	PUNCT
m-806	175	180	=	=	SYM
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m-806	175	184	�	�	PROPN
m-806	175	185	�	�	PROPN
m-806	175	186	�	�	PROPN
m-806	175	187	,	,	PUNCT
m-806	175	188	(	(	PUNCT
m-806	175	189	7.8e	7.8e	NOUN
m-806	175	190	)	)	PUNCT
m-806	176	1	�	�	PROPN
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m-806	176	4	=	=	SYM
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m-806	176	7	�	�	PROPN
m-806	176	8	�	�	PROPN
m-806	176	9	�	�	PROPN
m-806	176	10	�	�	PROPN
m-806	176	11	�	�	PROPN
m-806	176	12	�	�	PROPN
m-806	176	13	�	�	PROPN
m-806	176	14	�	�	PROPN
m-806	176	15	−	−	PROPN
m-806	176	16	�	�	PROPN
m-806	176	17	�	�	PROPN
m-806	176	18	�	�	PROPN
m-806	176	19	�	�	PROPN
m-806	176	20	�	�	PROPN
m-806	176	21	�	�	PROPN
m-806	176	22	�	�	PROPN
m-806	176	23	�	�	PROPN
m-806	176	24	�	�	PROPN
m-806	176	25	�	�	PROPN
m-806	176	26	�	�	PROPN
m-806	176	27	�	�	PROPN
m-806	176	28	+	+	CCONJ
m-806	176	29	�	�	PROPN
m-806	176	30	�	�	PROPN
m-806	176	31	�	�	PROPN
m-806	176	32	�	�	PROPN
m-806	176	33	�	�	PROPN
m-806	176	34	�	�	PROPN
m-806	176	35	�	�	PROPN
m-806	176	36	�	�	PROPN
m-806	176	37	�	�	PROPN
m-806	176	38	�	�	PROPN
m-806	176	39	�	�	PROPN
m-806	176	40	�	�	PROPN
m-806	176	41	−	−	PROPN
m-806	176	42	�	�	PROPN
m-806	176	43	�	�	PROPN
m-806	176	44	�	�	PROPN
m-806	176	45	�	�	PROPN
m-806	176	46	�	�	PROPN
m-806	176	47	�	�	PROPN
m-806	176	48	�	�	PROPN
m-806	176	49	�	�	PROPN
m-806	176	50	�	�	PROPN
m-806	176	51	�	�	PROPN
m-806	176	52	�	�	PROPN
m-806	176	53	�	�	PROPN
m-806	176	54	�	�	PROPN
m-806	176	55	�	�	PROPN
m-806	176	56	−	−	PROPN
m-806	176	57	�	�	PROPN
m-806	176	58	�	�	PROPN
m-806	176	59	�	�	PROPN
m-806	176	60	�	�	PROPN
m-806	176	61	�	�	PROPN
m-806	176	62	�	�	PROPN
m-806	176	63	�	�	PROPN
m-806	176	64	�	�	PROPN
m-806	176	65	�	�	PROPN
m-806	176	66	�	�	PROPN
m-806	176	67	�	�	PROPN
m-806	176	68	�	�	PROPN
m-806	176	69	�	�	PROPN
m-806	176	70	�	�	PROPN
m-806	176	71	�	�	PROPN
m-806	176	72	�	�	PROPN
m-806	176	73	+	+	SYM
m-806	176	74	�	�	PROPN
m-806	176	75	�	�	PROPN
m-806	176	76	�	�	PROPN
m-806	176	77	�	�	PROPN
m-806	176	78	�	�	PROPN
m-806	176	79	�	�	PROPN
m-806	176	80	�	�	PROPN
m-806	176	81	�	�	PROPN
m-806	176	82	�	�	PROPN
m-806	176	83	�	�	PROPN
m-806	176	84	�	�	PROPN
m-806	176	85	�	�	PROPN
m-806	176	86	�	�	PROPN
m-806	176	87	�	�	PROPN
m-806	176	88	−	−	PROPN
m-806	176	89	�	�	PROPN
m-806	176	90	�	�	PROPN
m-806	176	91	�	�	PROPN
m-806	176	92	�	�	PROPN
m-806	176	93	�	�	PROPN
m-806	176	94	�	�	PROPN
m-806	176	95	�	�	PROPN
m-806	176	96	�	�	PROPN
m-806	176	97	�	�	PROPN
m-806	176	98	�	�	PROPN
m-806	176	99	�	�	PROPN
m-806	176	100	�	�	PROPN
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m-806	176	104	�	�	PROPN
m-806	176	105	(	(	PUNCT
m-806	176	106	7.8f	7.8f	PROPN
m-806	176	107	)	)	PUNCT
m-806	176	108	�	�	PROPN
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m-806	176	111	�	�	PROPN
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m-806	176	113	�	�	PROPN
m-806	176	114	�	�	PROPN
m-806	176	115	(	(	PUNCT
m-806	176	116	�	�	PROPN
m-806	176	117	�	�	PROPN
m-806	176	118	)	)	PUNCT
m-806	176	119	(	(	PUNCT
m-806	176	120	�	�	PROPN
m-806	176	121	̂	̂	SYM
m-806	176	122	�	�	PROPN
m-806	176	123	,	,	PUNCT
m-806	176	124	0	0	NUM
m-806	176	125	)	)	PUNCT
m-806	176	126	=	=	SYM
m-806	177	1	−	−	NUM
m-806	177	2	�	�	PROPN
m-806	177	3	�	�	PROPN
m-806	177	4	�	�	PROPN
m-806	177	5	(	(	PUNCT
m-806	177	6	7.8	7.8	NUM
m-806	177	7	g	g	NOUN
m-806	177	8	)	)	PUNCT
m-806	177	9	on	on	ADP
m-806	177	10	substituting	substitute	VERB
m-806	177	11	for	for	ADP
m-806	177	12	terms	term	NOUN
m-806	177	13	in	in	ADP
m-806	177	14	(	(	PUNCT
m-806	177	15	7.8d	7.8d	NOUN
m-806	177	16	)	)	PUNCT
m-806	177	17	,	,	PUNCT
m-806	177	18	we	we	PRON
m-806	177	19	get	get	VERB
m-806	177	20	�	�	PROPN
m-806	177	21	̂	̂	SYM
m-806	177	22	�	�	NOUN
m-806	177	23	�	�	PROPN
m-806	177	24	=	=	SYM
m-806	177	25	�	�	PROPN
m-806	177	26	�	�	PROPN
m-806	177	27	�	�	PROPN
m-806	177	28	�	�	PROPN
m-806	177	29	�	�	PROPN
m-806	177	30	�	�	PROPN
m-806	177	31	,	,	PUNCT
m-806	177	32	�	�	PROPN
m-806	177	33	�	�	PROPN
m-806	177	34	�	�	PROPN
m-806	177	35	=	=	SYM
m-806	177	36	�	�	PROPN
m-806	177	37	�	�	PROPN
m-806	177	38	�	�	PROPN
m-806	177	39	�	�	PROPN
m-806	177	40	+	+	SYM
m-806	177	41	�	�	PROPN
m-806	177	42	�	�	PROPN
m-806	177	43	�	�	PROPN
m-806	177	44	�	�	PROPN
m-806	177	45	�	�	PROPN
m-806	177	46	(	(	PUNCT
m-806	177	47	7.8h	7.8h	PROPN
m-806	177	48	)	)	PUNCT
m-806	177	49	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	NOUN
m-806	177	50	ijo	ijo	PROPN
m-806	177	51	journals	journal	NOUN
m-806	177	52	volume	volume	NOUN
m-806	177	53	07	07	NUM
m-806	177	54	|	|	ADV
m-806	177	55	issue	issue	NOUN
m-806	177	56	02	02	NUM
m-806	177	57	|	|	CCONJ
m-806	177	58	february	february	PROPN
m-806	177	59	2024	2024	NUM
m-806	178	1	|	|	ADV
m-806	178	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	178	3	23	23	NUM
m-806	178	4	ijo	ijo	PROPN
m-806	178	5	international	international	ADJ
m-806	178	6	journal	journal	PROPN
m-806	178	7	of	of	ADP
m-806	178	8	mathematics	mathematics	PROPN
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m-806	178	10	issn	issn	PROPN
m-806	178	11	:	:	PUNCT
m-806	178	12	2992	2992	NUM
m-806	178	13	-	-	SYM
m-806	178	14	4421	4421	NUM
m-806	178	15	)	)	PUNCT
m-806	178	16	i.u	i.u	PROPN
m-806	178	17	.	.	PROPN
m-806	178	18	udo	udo	PROPN
m-806	178	19	-	-	PROPN
m-806	178	20	akpan1	akpan1	ADJ
m-806	178	21	*	*	PUNCT
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m-806	178	23	volume	volume	NOUN
m-806	178	24	07	07	NUM
m-806	178	25	issue	issue	NOUN
m-806	178	26	02	02	NUM
m-806	178	27	||	||	NUM
m-806	178	28	february	february	PROPN
m-806	178	29	,	,	PUNCT
m-806	178	30	2024	2024	NUM
m-806	178	31	||	||	NOUN
m-806	178	32	on	on	ADP
m-806	178	33	a	a	DET
m-806	178	34	-	-	PUNCT
m-806	178	35	two	two	NUM
m-806	178	36	-	-	PUNCT
m-806	178	37	parameter	parameter	NOUN
m-806	178	38	dynamic	dynamic	ADJ
m-806	178	39	buckling	buckling	NOUN
m-806	178	40	of	of	ADP
m-806	178	41	a	a	DET
m-806	178	42	viscously	viscously	ADV
m-806	178	43	damped	damp	VERB
m-806	178	44	but	but	CCONJ
m-806	178	45	clamped	clamp	VERB
m-806	178	46	column	column	NOUN
m-806	178	47	stressed	stress	VERB
m-806	178	48	by	by	ADP
m-806	178	49	a	a	DET
m-806	178	50	step	step	NOUN
m-806	178	51	load	load	NOUN
m-806	178	52	after	after	ADP
m-806	178	53	substituting	substitute	VERB
m-806	178	54	for	for	ADP
m-806	178	55	terms	term	NOUN
m-806	178	56	in	in	ADP
m-806	178	57	(	(	PUNCT
m-806	178	58	7.7e	7.7e	NOUN
m-806	178	59	)	)	PUNCT
m-806	178	60	and	and	CCONJ
m-806	178	61	simplifying	simplify	VERB
m-806	178	62	,	,	PUNCT
m-806	178	63	many	many	ADJ
m-806	178	64	terms	term	NOUN
m-806	178	65	vanish	vanish	VERB
m-806	178	66	and	and	CCONJ
m-806	178	67	the	the	DET
m-806	178	68	remaining	remain	VERB
m-806	178	69	terms	term	NOUN
m-806	178	70	give	give	VERB
m-806	178	71	�	�	PROPN
m-806	178	72	̂	̂	NOUN
m-806	178	73	�	�	NOUN
m-806	178	74	�	�	PROPN
m-806	178	75	=	=	SYM
m-806	178	76	�	�	PROPN
m-806	178	77	�	�	PROPN
m-806	178	78	�	�	PROPN
m-806	178	79	�	�	PROPN
m-806	178	80	�	�	PROPN
m-806	178	81	�	�	PROPN
m-806	178	82	,	,	PUNCT
m-806	178	83	�	�	PROPN
m-806	178	84	�	�	PROPN
m-806	178	85	�	�	PROPN
m-806	178	86	�	�	PROPN
m-806	178	87	(	(	PUNCT
m-806	178	88	�	�	PROPN
m-806	178	89	�	�	PROPN
m-806	178	90	)	)	PUNCT
m-806	179	1	�	�	PROPN
m-806	179	2	�	�	PROPN
m-806	179	3	̂	̂	PROPN
m-806	179	4	�	�	PROPN
m-806	179	5	�	�	PROPN
m-806	179	6	�	�	PROPN
m-806	179	7	�	�	PROPN
m-806	179	8	+	+	CCONJ
m-806	179	9	�	�	PROPN
m-806	179	10	�	�	PROPN
m-806	179	11	,	,	PUNCT
m-806	179	12	�	�	PROPN
m-806	179	13	�	�	PROPN
m-806	179	14	�	�	PROPN
m-806	179	15	�	�	PROPN
m-806	179	16	�	�	PROPN
m-806	179	17	(	(	PUNCT
m-806	179	18	�	�	PROPN
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m-806	179	21	+	+	CCONJ
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m-806	179	25	�	�	PROPN
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m-806	179	27	(	(	PUNCT
m-806	179	28	�	�	PROPN
m-806	179	29	�	�	PROPN
m-806	179	30	)	)	PUNCT
m-806	179	31	+	+	CCONJ
m-806	179	32	�	�	PROPN
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m-806	179	34	�	�	PROPN
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m-806	179	36	�	�	PROPN
m-806	179	37	�	�	PROPN
m-806	179	38	(	(	PUNCT
m-806	179	39	�	�	PROPN
m-806	179	40	�	�	PROPN
m-806	179	41	)	)	PUNCT
m-806	179	42	+	+	SYM
m-806	179	43	�	�	PROPN
m-806	179	44	�	�	PROPN
m-806	179	45	,	,	PUNCT
m-806	179	46	�	�	PROPN
m-806	179	47	(	(	PUNCT
m-806	179	48	�	�	PROPN
m-806	179	49	�	�	PROPN
m-806	179	50	)	)	PUNCT
m-806	179	51	+	+	SYM
m-806	179	52	�	�	PROPN
m-806	179	53	�	�	PROPN
m-806	179	54	�	�	PROPN
m-806	179	55	,	,	PUNCT
m-806	179	56	�	�	PROPN
m-806	179	57	(	(	PUNCT
m-806	179	58	�	�	PROPN
m-806	179	59	�	�	PROPN
m-806	179	60	)	)	PUNCT
m-806	179	61	�	�	PROPN
m-806	179	62	�	�	PROPN
m-806	179	63	�	�	PROPN
m-806	179	64	(	(	PUNCT
m-806	179	65	�	�	PROPN
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m-806	179	69	�	�	PROPN
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m-806	179	71	(	(	PUNCT
m-806	179	72	7.8i	7.8i	X
m-806	179	73	)	)	PUNCT
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m-806	179	76	evaluate	evaluate	VERB
m-806	179	77	each	each	PRON
m-806	179	78	of	of	ADP
m-806	179	79	the	the	DET
m-806	179	80	terms	term	NOUN
m-806	179	81	in	in	ADP
m-806	179	82	(	(	PUNCT
m-806	179	83	7.8i	7.8i	NUM
m-806	179	84	)	)	PUNCT
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m-806	179	87	:	:	PUNCT
m-806	179	88	�	�	PROPN
m-806	179	89	�	�	PROPN
m-806	179	90	,	,	PUNCT
m-806	179	91	�	�	PROPN
m-806	179	92	�	�	PROPN
m-806	179	93	(	(	PUNCT
m-806	179	94	�	�	PROPN
m-806	179	95	�	�	PROPN
m-806	179	96	)	)	PUNCT
m-806	179	97	(	(	PUNCT
m-806	179	98	�	�	NOUN
m-806	179	99	̂	̂	SYM
m-806	179	100	�	�	PROPN
m-806	179	101	,	,	PUNCT
m-806	179	102	0	0	NUM
m-806	179	103	)	)	PUNCT
m-806	179	104	=	=	SYM
m-806	179	105	�	�	PROPN
m-806	179	106	�	�	PROPN
m-806	179	107	�	�	PROPN
m-806	179	108	�	�	PROPN
m-806	179	109	�	�	PROPN
m-806	179	110	�	�	PROPN
m-806	179	111	�	�	PROPN
m-806	179	112	�	�	PROPN
m-806	179	113	�	�	PROPN
m-806	179	114	�	�	PROPN
m-806	179	115	(	(	PUNCT
m-806	179	116	7.9a	7.9a	PROPN
m-806	179	117	)	)	PUNCT
m-806	179	118	�	�	PROPN
m-806	179	119	�	�	PROPN
m-806	179	120	�	�	PROPN
m-806	179	121	,	,	PUNCT
m-806	179	122	�	�	PROPN
m-806	179	123	�	�	PROPN
m-806	179	124	(	(	PUNCT
m-806	179	125	�	�	PROPN
m-806	179	126	�	�	PROPN
m-806	179	127	)	)	PUNCT
m-806	179	128	(	(	PUNCT
m-806	179	129	�	�	NOUN
m-806	179	130	̂	̂	SYM
m-806	179	131	�	�	PROPN
m-806	179	132	,	,	PUNCT
m-806	179	133	0	0	NUM
m-806	179	134	)	)	PUNCT
m-806	179	135	=	=	SYM
m-806	179	136	�	�	PROPN
m-806	179	137	�	�	PROPN
m-806	179	138	�	�	PROPN
m-806	179	139	�	�	PROPN
m-806	179	140	�	�	PROPN
m-806	179	141	�	�	PROPN
m-806	179	142	(	(	PUNCT
m-806	179	143	7.9b	7.9b	NUM
m-806	179	144	)	)	PUNCT
m-806	179	145	�	�	PROPN
m-806	179	146	�	�	PROPN
m-806	179	147	�	�	PROPN
m-806	179	148	=	=	SYM
m-806	179	149	�	�	PROPN
m-806	179	150	�	�	PROPN
m-806	179	151	cos	cos	PROPN
m-806	179	152	�	�	PROPN
m-806	179	153	�	�	PROPN
m-806	179	154	�	�	PROPN
m-806	179	155	�	�	PROPN
m-806	179	156	̂	̂	PROPN
m-806	179	157	�	�	PROPN
m-806	179	158	−	−	PROPN
m-806	179	159	�	�	PROPN
m-806	179	160	�	�	PROPN
m-806	179	161	�	�	PROPN
m-806	179	162	�	�	PROPN
m-806	179	163	�	�	PROPN
m-806	179	164	�	�	PROPN
m-806	179	165	�	�	PROPN
m-806	179	166	�	�	PROPN
m-806	179	167	�	�	PROPN
m-806	179	168	�	�	PROPN
m-806	179	169	�	�	PROPN
m-806	179	170	�	�	PROPN
m-806	179	171	�	�	PROPN
m-806	179	172	−	−	PROPN
m-806	179	173	�	�	PROPN
m-806	179	174	�	�	PROPN
m-806	179	175	�	�	PROPN
m-806	179	176	�	�	PROPN
m-806	179	177	�	�	PROPN
m-806	179	178	�	�	PROPN
m-806	179	179	�	�	PROPN
m-806	179	180	�	�	PROPN
m-806	179	181	�	�	PROPN
m-806	179	182	�	�	PROPN
m-806	179	183	�	�	PROPN
m-806	179	184	�	�	PROPN
m-806	179	185	�	�	PROPN
m-806	179	186	−	−	PROPN
m-806	179	187	�	�	PROPN
m-806	179	188	�	�	PROPN
m-806	179	189	�	�	PROPN
m-806	179	190	�	�	PROPN
m-806	179	191	�	�	PROPN
m-806	179	192	�	�	PROPN
m-806	179	193	�	�	PROPN
m-806	179	194	�	�	PROPN
m-806	179	195	�	�	PROPN
m-806	179	196	�	�	PROPN
m-806	179	197	�	�	PROPN
m-806	179	198	�	�	PROPN
m-806	179	199	�	�	PROPN
m-806	179	200	(	(	PUNCT
m-806	179	201	7.9c	7.9c	NUM
m-806	179	202	)	)	PUNCT
m-806	179	203	�	�	PROPN
m-806	179	204	�	�	PROPN
m-806	179	205	,	,	PUNCT
m-806	179	206	�	�	PROPN
m-806	179	207	(	(	PUNCT
m-806	179	208	�	�	PROPN
m-806	179	209	�	�	PROPN
m-806	179	210	)	)	PUNCT
m-806	179	211	(	(	PUNCT
m-806	179	212	�	�	PROPN
m-806	179	213	̂	̂	SYM
m-806	179	214	�	�	PROPN
m-806	179	215	,	,	PUNCT
m-806	179	216	0	0	NUM
m-806	179	217	)	)	PUNCT
m-806	179	218	=	=	SYM
m-806	179	219	�	�	PROPN
m-806	179	220	�	�	PROPN
m-806	179	221	�	�	PROPN
m-806	179	222	�	�	PROPN
m-806	179	223	�	�	PROPN
m-806	179	224	�	�	PROPN
m-806	179	225	�	�	PROPN
m-806	179	226	�	�	PROPN
m-806	179	227	�	�	PROPN
m-806	179	228	�	�	PROPN
m-806	179	229	(	(	PUNCT
m-806	179	230	7.9d	7.9d	NOUN
m-806	179	231	)	)	PUNCT
m-806	179	232	�	�	PROPN
m-806	179	233	�	�	PROPN
m-806	179	234	�	�	PROPN
m-806	179	235	,	,	PUNCT
m-806	179	236	�	�	PROPN
m-806	179	237	(	(	PUNCT
m-806	179	238	�	�	PROPN
m-806	179	239	�	�	PROPN
m-806	179	240	)	)	PUNCT
m-806	179	241	(	(	PUNCT
m-806	179	242	�	�	NOUN
m-806	179	243	̂	̂	SYM
m-806	179	244	�	�	PROPN
m-806	179	245	,	,	PUNCT
m-806	179	246	0	0	NUM
m-806	179	247	)	)	PUNCT
m-806	179	248	=	=	SYM
m-806	179	249	�	�	PROPN
m-806	179	250	�	�	PROPN
m-806	179	251	�	�	PROPN
m-806	179	252	�	�	PROPN
m-806	179	253	�	�	PROPN
m-806	179	254	�	�	PROPN
m-806	179	255	(	(	PUNCT
m-806	179	256	7.9e	7.9e	PROPN
m-806	179	257	)	)	PUNCT
m-806	179	258	�	�	PROPN
m-806	179	259	�	�	PROPN
m-806	179	260	�	�	PROPN
m-806	179	261	=	=	SYM
m-806	179	262	−	−	PROPN
m-806	179	263	�	�	PROPN
m-806	179	264	�	�	PROPN
m-806	179	265	�	�	PROPN
m-806	179	266	�	�	PROPN
m-806	179	267	�	�	PROPN
m-806	179	268	�	�	PROPN
m-806	179	269	�	�	PROPN
m-806	179	270	�	�	PROPN
m-806	179	271	�	�	PROPN
m-806	179	272	�	�	PROPN
m-806	179	273	�	�	PROPN
m-806	179	274	�	�	PROPN
m-806	179	275	−	−	PROPN
m-806	179	276	�	�	PROPN
m-806	179	277	�	�	PROPN
m-806	179	278	�	�	PROPN
m-806	179	279	�	�	PROPN
m-806	179	280	�	�	PROPN
m-806	179	281	�	�	PROPN
m-806	179	282	�	�	PROPN
m-806	179	283	�	�	PROPN
m-806	179	284	+	+	CCONJ
m-806	179	285	�	�	PROPN
m-806	179	286	�	�	PROPN
m-806	179	287	�	�	PROPN
m-806	179	288	�	�	PROPN
m-806	179	289	�	�	PROPN
m-806	179	290	�	�	PROPN
m-806	179	291	�	�	PROPN
m-806	179	292	�	�	PROPN
m-806	179	293	�	�	PROPN
m-806	179	294	�	�	PROPN
m-806	179	295	�	�	PROPN
m-806	179	296	�	�	PROPN
m-806	179	297	+	+	CCONJ
m-806	179	298	�	�	PROPN
m-806	179	299	�	�	PROPN
m-806	179	300	�	�	PROPN
m-806	179	301	�	�	PROPN
m-806	179	302	�	�	PROPN
m-806	179	303	�	�	PROPN
m-806	179	304	�	�	PROPN
m-806	179	305	�	�	PROPN
m-806	179	306	�	�	PROPN
m-806	179	307	�	�	PROPN
m-806	179	308	�	�	PROPN
m-806	179	309	�	�	PROPN
m-806	179	310	�	�	PROPN
m-806	179	311	+	+	CCONJ
m-806	179	312	�	�	PROPN
m-806	179	313	�	�	PROPN
m-806	179	314	�	�	PROPN
m-806	179	315	�	�	PROPN
m-806	179	316	�	�	PROPN
m-806	179	317	�	�	PROPN
m-806	179	318	�	�	PROPN
m-806	179	319	�	�	PROPN
m-806	179	320	�	�	PROPN
m-806	179	321	�	�	PROPN
m-806	179	322	�	�	PROPN
m-806	179	323	�	�	PROPN
m-806	179	324	�	�	PROPN
m-806	179	325	�	�	PROPN
m-806	179	326	(	(	PUNCT
m-806	179	327	7.9f	7.9f	PROPN
m-806	179	328	)	)	PUNCT
m-806	179	329	�	�	PROPN
m-806	179	330	�	�	PROPN
m-806	179	331	,	,	PUNCT
m-806	179	332	�	�	PROPN
m-806	179	333	�	�	PROPN
m-806	179	334	�	�	PROPN
m-806	179	335	�	�	PROPN
m-806	179	336	�	�	PROPN
m-806	179	337	(	(	PUNCT
m-806	179	338	�	�	PROPN
m-806	179	339	�	�	PROPN
m-806	179	340	)	)	PUNCT
m-806	179	341	(	(	PUNCT
m-806	179	342	�	�	NOUN
m-806	179	343	̂	̂	SYM
m-806	179	344	�	�	PROPN
m-806	179	345	,	,	PUNCT
m-806	179	346	0	0	NUM
m-806	179	347	)	)	PUNCT
m-806	179	348	=	=	SYM
m-806	179	349	�	�	PROPN
m-806	179	350	�	�	PROPN
m-806	179	351	�	�	PROPN
m-806	179	352	�	�	PROPN
m-806	179	353	�	�	PROPN
m-806	179	354	(	(	PUNCT
m-806	179	355	0	0	NUM
m-806	179	356	)	)	PUNCT
m-806	179	357	=	=	SYM
m-806	179	358	�	�	PROPN
m-806	179	359	�	�	PROPN
m-806	179	360	�	�	PROPN
m-806	179	361	(	(	PUNCT
m-806	179	362	7.9	7.9	NUM
m-806	179	363	g	g	NOUN
m-806	179	364	)	)	PUNCT
m-806	179	365	on	on	ADP
m-806	179	366	substituting	substitute	VERB
m-806	179	367	for	for	ADP
m-806	179	368	terms	term	NOUN
m-806	179	369	in	in	ADP
m-806	179	370	(	(	PUNCT
m-806	179	371	7.8i	7.8i	NUM
m-806	179	372	)	)	PUNCT
m-806	180	1	,	,	PUNCT
m-806	180	2	we	we	PRON
m-806	180	3	get	get	VERB
m-806	180	4	�	�	PROPN
m-806	180	5	̂	̂	SYM
m-806	180	6	�	�	NOUN
m-806	180	7	�	�	PROPN
m-806	180	8	=	=	SYM
m-806	180	9	�	�	PROPN
m-806	180	10	�	�	PROPN
m-806	180	11	�	�	PROPN
m-806	180	12	�	�	PROPN
m-806	180	13	�	�	PROPN
m-806	180	14	�	�	PROPN
m-806	180	15	,	,	PUNCT
m-806	180	16	�	�	PROPN
m-806	180	17	�	�	PROPN
m-806	180	18	�	�	PROPN
m-806	180	19	=	=	SYM
m-806	180	20	�	�	PROPN
m-806	180	21	�	�	PROPN
m-806	180	22	�	�	PROPN
m-806	180	23	�	�	PROPN
m-806	180	24	�	�	PROPN
m-806	180	25	�	�	PROPN
m-806	180	26	�	�	PROPN
m-806	180	27	�	�	PROPN
m-806	180	28	�	�	PROPN
m-806	180	29	�	�	PROPN
m-806	180	30	�	�	PROPN
m-806	180	31	+	+	SYM
m-806	180	32	�	�	PROPN
m-806	180	33	�	�	PROPN
m-806	180	34	�	�	PROPN
m-806	180	35	�	�	PROPN
m-806	180	36	�	�	PROPN
m-806	180	37	�	�	PROPN
m-806	180	38	�	�	PROPN
m-806	180	39	+	+	CCONJ
m-806	180	40	�	�	PROPN
m-806	180	41	�	�	PROPN
m-806	180	42	�	�	PROPN
m-806	180	43	−	−	PROPN
m-806	180	44	�	�	PROPN
m-806	180	45	�	�	PROPN
m-806	180	46	�	�	PROPN
m-806	180	47	�	�	PROPN
m-806	180	48	�	�	PROPN
m-806	180	49	�	�	PROPN
m-806	180	50	�	�	PROPN
m-806	180	51	�	�	PROPN
m-806	180	52	�	�	PROPN
m-806	180	53	�	�	PROPN
m-806	180	54	+	+	SYM
m-806	180	55	�	�	PROPN
m-806	180	56	�	�	PROPN
m-806	180	57	�	�	PROPN
m-806	180	58	�	�	PROPN
m-806	180	59	(	(	PUNCT
m-806	180	60	7.10	7.10	NUM
m-806	180	61	)	)	PUNCT
m-806	180	62	later	later	ADV
m-806	180	63	,	,	PUNCT
m-806	180	64	we	we	PRON
m-806	180	65	shall	shall	AUX
m-806	180	66	also	also	ADV
m-806	180	67	need	need	VERB
m-806	180	68	terms	term	NOUN
m-806	180	69	like	like	ADP
m-806	180	70	�	�	PROPN
m-806	180	71	�	�	PROPN
m-806	180	72	,	,	PUNCT
m-806	180	73	�	�	PROPN
m-806	180	74	�	�	PROPN
m-806	180	75	�	�	PROPN
m-806	180	76	,	,	PUNCT
m-806	180	77	�	�	PROPN
m-806	180	78	�	�	PROPN
m-806	180	79	�	�	PROPN
m-806	180	80	,	,	PUNCT
m-806	180	81	�	�	PROPN
m-806	180	82	�	�	PROPN
m-806	180	83	�	�	PROPN
m-806	180	84	�	�	PROPN
m-806	180	85	�	�	PROPN
m-806	180	86	�	�	PROPN
m-806	180	87	�	�	PROPN
m-806	180	88	�	�	PROPN
m-806	180	89	�	�	PROPN
m-806	180	90	which	which	PRON
m-806	180	91	we	we	PRON
m-806	180	92	now	now	ADV
m-806	180	93	evaluate	evaluate	VERB
m-806	180	94	directly	directly	ADV
m-806	180	95	from	from	ADP
m-806	180	96	(	(	PUNCT
m-806	180	97	6.2b	6.2b	NOUN
m-806	180	98	)	)	PUNCT
m-806	180	99	(	(	PUNCT
m-806	180	100	evaluated	evaluate	VERB
m-806	180	101	at	at	ADP
m-806	180	102	maximum	maximum	ADJ
m-806	180	103	values	value	NOUN
m-806	180	104	of	of	ADP
m-806	180	105	the	the	DET
m-806	180	106	variables	variable	NOUN
m-806	180	107	)	)	PUNCT
m-806	180	108	.	.	PUNCT
m-806	181	1	thus	thus	ADV
m-806	181	2	,	,	PUNCT
m-806	181	3	at	at	ADP
m-806	181	4	maximum	maximum	ADJ
m-806	181	5	deflection	deflection	NOUN
m-806	181	6	,	,	PUNCT
m-806	181	7	(	(	PUNCT
m-806	181	8	6.2b	6.2b	NOUN
m-806	181	9	)	)	PUNCT
m-806	181	10	becomes	become	VERB
m-806	181	11	�	�	NOUN
m-806	181	12	̂	̂	SYM
m-806	181	13	�	�	PROPN
m-806	181	14	=	=	SYM
m-806	181	15	�	�	PROPN
m-806	181	16	�	�	PROPN
m-806	181	17	+	+	CCONJ
m-806	181	18	�	�	PROPN
m-806	181	19	�	�	PROPN
m-806	181	20	�	�	PROPN
m-806	181	21	(	(	PUNCT
m-806	181	22	�	�	PROPN
m-806	181	23	�	�	PROPN
m-806	181	24	)	)	PUNCT
m-806	181	25	�	�	PROPN
m-806	181	26	�	�	PROPN
m-806	181	27	�	�	PROPN
m-806	181	28	�	�	PROPN
m-806	181	29	�	�	PROPN
m-806	181	30	(	(	PUNCT
m-806	181	31	�	�	PROPN
m-806	181	32	�	�	PROPN
m-806	181	33	)	)	PUNCT
m-806	181	34	�	�	PROPN
m-806	181	35	�	�	PROPN
m-806	181	36	�	�	PROPN
m-806	181	37	⋯	⋯	PROPN
m-806	181	38	�	�	PROPN
m-806	181	39	�	�	PROPN
m-806	181	40	(	(	PUNCT
m-806	181	41	7.11	7.11	NUM
m-806	181	42	)	)	PUNCT
m-806	181	43	by	by	ADP
m-806	181	44	using	use	VERB
m-806	181	45	(	(	PUNCT
m-806	181	46	7.2a	7.2a	NUM
m-806	181	47	–	–	PUNCT
m-806	181	48	c	c	NOUN
m-806	181	49	)	)	PUNCT
m-806	181	50	,	,	PUNCT
m-806	181	51	we	we	PRON
m-806	181	52	can	can	AUX
m-806	181	53	write	write	VERB
m-806	181	54	(	(	PUNCT
m-806	181	55	7.11	7.11	NUM
m-806	181	56	)	)	PUNCT
m-806	181	57	as	as	ADP
m-806	181	58	�	�	PROPN
m-806	181	59	̂	̂	NUM
m-806	181	60	�	�	PROPN
m-806	181	61	+	+	SYM
m-806	181	62	�	�	PROPN
m-806	181	63	�	�	PROPN
m-806	181	64	̂	̂	NOUN
m-806	181	65	�	�	PROPN
m-806	181	66	�	�	PROPN
m-806	181	67	+	+	SYM
m-806	181	68	�	�	PROPN
m-806	181	69	�	�	PROPN
m-806	181	70	�	�	PROPN
m-806	181	71	̂	̂	NOUN
m-806	181	72	�	�	NOUN
m-806	181	73	�	�	PROPN
m-806	181	74	+	+	SYM
m-806	181	75	⋯	⋯	PROPN
m-806	181	76	+	+	SYM
m-806	181	77	�	�	PROPN
m-806	181	78	�	�	PROPN
m-806	181	79	(	(	PUNCT
m-806	181	80	�	�	PROPN
m-806	181	81	̂	̂	SYM
m-806	181	82	�	�	PROPN
m-806	181	83	�	�	PROPN
m-806	181	84	+	+	SYM
m-806	181	85	�	�	PROPN
m-806	181	86	�	�	PROPN
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m-806	181	88	�	�	PROPN
m-806	181	89	�	�	PROPN
m-806	181	90	+	+	SYM
m-806	181	91	�	�	PROPN
m-806	181	92	�	�	PROPN
m-806	181	93	�	�	PROPN
m-806	181	94	̂	̂	NOUN
m-806	181	95	�	�	NOUN
m-806	181	96	�	�	PROPN
m-806	181	97	+	+	CCONJ
m-806	181	98	⋯	⋯	PROPN
m-806	181	99	)	)	PUNCT
m-806	182	1	+	+	CCONJ
m-806	182	2	⋯	⋯	PROPN
m-806	182	3	=	=	SYM
m-806	182	4	�	�	PROPN
m-806	182	5	�	�	PROPN
m-806	182	6	+	+	CCONJ
m-806	182	7	�	�	PROPN
m-806	182	8	�	�	PROPN
m-806	182	9	�	�	PROPN
m-806	182	10	�	�	PROPN
m-806	182	11	+	+	SYM
m-806	182	12	�	�	PROPN
m-806	182	13	�	�	PROPN
m-806	182	14	�	�	PROPN
m-806	182	15	�	�	PROPN
m-806	182	16	�	�	PROPN
m-806	182	17	+	+	CCONJ
m-806	182	18	⋯	⋯	PROPN
m-806	182	19	+	+	SYM
m-806	182	20	�	�	PROPN
m-806	182	21	�	�	PROPN
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m-806	183	1	+	+	CCONJ
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m-806	183	14	|	|	ADV
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m-806	183	17	|	|	CCONJ
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m-806	183	20	|	|	ADV
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m-806	183	34	)	)	PUNCT
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m-806	184	12	||	||	NUM
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m-806	185	30	)	)	PUNCT
m-806	185	31	=	=	SYM
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m-806	185	44	7.2b	7.2b	NOUN
m-806	185	45	)	)	PUNCT
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m-806	186	12	)	)	PUNCT
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m-806	187	191	�	�	PROPN
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m-806	187	194	(	(	PUNCT
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m-806	187	207	(	(	PUNCT
m-806	187	208	7.15a	7.15a	NUM
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m-806	187	214	�	�	PROPN
m-806	187	215	)	)	PUNCT
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m-806	187	220	−	−	PROPN
m-806	187	221	�	�	PROPN
m-806	187	222	�	�	PROPN
m-806	187	223	�	�	PROPN
m-806	187	224	�	�	PROPN
m-806	187	225	�	�	PROPN
m-806	187	226	�	�	PROPN
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m-806	187	229	(	(	PUNCT
m-806	187	230	7.15b	7.15b	NOUN
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m-806	188	10	deflection	deflection	PROPN
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m-806	188	16	(	(	PUNCT
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m-806	188	24	�	�	PROPN
m-806	188	25	�	�	PROPN
m-806	188	26	�	�	PROPN
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m-806	188	31	.	.	PUNCT
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m-806	189	14	(	(	PUNCT
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m-806	189	18	+	+	SYM
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m-806	189	23	(	(	PUNCT
m-806	189	24	�	�	PROPN
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m-806	189	27	+	+	SYM
m-806	189	28	�	�	PROPN
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m-806	189	33	(	(	PUNCT
m-806	189	34	�	�	PROPN
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m-806	189	47	(	(	PUNCT
m-806	189	48	�	�	PROPN
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m-806	190	1	+	+	SYM
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m-806	190	7	�	�	PROPN
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m-806	190	11	+	+	SYM
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m-806	190	17	(	(	PUNCT
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m-806	190	21	+	+	SYM
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m-806	190	26	(	(	PUNCT
m-806	190	27	�	�	PROPN
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m-806	190	30	�	�	PROPN
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m-806	190	32	+	+	SYM
m-806	190	33	�	�	PROPN
m-806	190	34	�	�	PROPN
m-806	190	35	�	�	PROPN
m-806	190	36	�	�	PROPN
m-806	190	37	�	�	PROPN
m-806	190	38	�	�	PROPN
m-806	190	39	�	�	PROPN
m-806	190	40	(	(	PUNCT
m-806	190	41	�	�	PROPN
m-806	190	42	�	�	PROPN
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m-806	190	44	+	+	SYM
m-806	190	45	�	�	PROPN
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m-806	190	48	�	�	PROPN
m-806	190	49	(	(	PUNCT
m-806	190	50	�	�	PROPN
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m-806	190	54	+	+	CCONJ
m-806	190	55	⋯	⋯	PROPN
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m-806	190	59	(	(	PUNCT
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m-806	190	71	=	=	SYM
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m-806	190	76	�	�	PROPN
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m-806	191	7	(	(	PUNCT
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m-806	191	9	)	)	PUNCT
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m-806	191	12	7.2a	7.2a	NUM
m-806	191	13	–	–	PUNCT
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m-806	191	15	)	)	PUNCT
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m-806	192	4	have	have	VERB
m-806	192	5	�	�	PROPN
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m-806	192	13	=	=	SYM
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m-806	195	350	�	�	PROPN
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m-806	195	355	+	+	SYM
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m-806	195	360	+	+	CCONJ
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m-806	195	362	)	)	PUNCT
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m-806	195	366	,	,	PUNCT
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m-806	195	368	(	(	PUNCT
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m-806	195	372	+	+	SYM
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m-806	195	376	,	,	PUNCT
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m-806	195	378	(	(	PUNCT
m-806	195	379	�	�	PROPN
m-806	195	380	�	�	PROPN
m-806	195	381	)	)	PUNCT
m-806	195	382	�	�	PROPN
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m-806	195	385	(	(	PUNCT
m-806	195	386	�	�	PROPN
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m-806	195	389	,	,	PUNCT
m-806	195	390	�	�	PROPN
m-806	195	391	)	)	PUNCT
m-806	195	392	(	(	PUNCT
m-806	195	393	8.6	8.6	NUM
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m-806	195	395	�	�	PROPN
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m-806	195	397	�	�	PROPN
m-806	195	398	�	�	PROPN
m-806	195	399	�	�	PROPN
m-806	195	400	�	�	PROPN
m-806	195	401	�	�	PROPN
m-806	195	402	(	(	PUNCT
m-806	195	403	�	�	PROPN
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m-806	195	405	)	)	PUNCT
m-806	195	406	+	+	SYM
m-806	195	407	�	�	PROPN
m-806	195	408	�	�	PROPN
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m-806	195	410	(	(	PUNCT
m-806	195	411	�	�	PROPN
m-806	195	412	�	�	PROPN
m-806	195	413	)	)	PUNCT
m-806	195	414	�	�	PROPN
m-806	195	415	=	=	SYM
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m-806	195	420	�	�	PROPN
m-806	195	421	�	�	PROPN
m-806	195	422	�	�	PROPN
m-806	195	423	�	�	PROPN
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m-806	195	425	,	,	PUNCT
m-806	195	426	�	�	PROPN
m-806	195	427	(	(	PUNCT
m-806	195	428	�	�	PROPN
m-806	195	429	�	�	PROPN
m-806	195	430	)	)	PUNCT
m-806	195	431	+	+	SYM
m-806	195	432	�	�	PROPN
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m-806	195	435	,	,	PUNCT
m-806	195	436	�	�	PROPN
m-806	195	437	(	(	PUNCT
m-806	195	438	�	�	PROPN
m-806	195	439	�	�	PROPN
m-806	195	440	)	)	PUNCT
m-806	195	441	�	�	PROPN
m-806	195	442	�	�	PROPN
m-806	195	443	�	�	PROPN
m-806	195	444	(	(	PUNCT
m-806	195	445	�	�	PROPN
m-806	195	446	�	�	PROPN
m-806	195	447	�	�	PROPN
m-806	195	448	,	,	PUNCT
m-806	195	449	�	�	PROPN
m-806	195	450	)	)	PUNCT
m-806	195	451	(	(	PUNCT
m-806	195	452	8.7	8.7	NUM
m-806	195	453	)	)	PUNCT
m-806	195	454	on	on	ADP
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m-806	195	456	(	(	PUNCT
m-806	195	457	8.2	8.2	NUM
m-806	195	458	)	)	PUNCT
m-806	195	459	–	–	PUNCT
m-806	195	460	(	(	PUNCT
m-806	195	461	8.7	8.7	NUM
m-806	195	462	)	)	PUNCT
m-806	195	463	into	into	ADP
m-806	195	464	(	(	PUNCT
m-806	195	465	8.1	8.1	NUM
m-806	195	466	)	)	PUNCT
m-806	195	467	,	,	PUNCT
m-806	195	468	we	we	PRON
m-806	195	469	observe	observe	VERB
m-806	195	470	that	that	SCONJ
m-806	195	471	most	most	ADJ
m-806	195	472	terms	term	NOUN
m-806	195	473	vanish	vanish	VERB
m-806	195	474	and	and	CCONJ
m-806	195	475	the	the	DET
m-806	195	476	remaining	remain	VERB
m-806	195	477	ones	one	NOUN
m-806	195	478	are	be	AUX
m-806	195	479	given	give	VERB
m-806	195	480	as	as	ADP
m-806	195	481	w	w	PROPN
m-806	195	482	�	�	PROPN
m-806	195	483	=	=	SYM
m-806	195	484	2	2	NUM
m-806	195	485	�	�	PROPN
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m-806	195	487	�	�	PROPN
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m-806	195	489	�	�	PROPN
m-806	195	490	�	�	PROPN
m-806	195	491	(	(	PUNCT
m-806	195	492	�	�	PROPN
m-806	195	493	�	�	PROPN
m-806	195	494	)	)	PUNCT
m-806	195	495	+	+	SYM
m-806	195	496	�	�	PROPN
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m-806	195	499	�	�	PROPN
m-806	195	500	�	�	PROPN
m-806	195	501	,	,	PUNCT
m-806	195	502	�	�	PROPN
m-806	195	503	(	(	PUNCT
m-806	195	504	�	�	PROPN
m-806	195	505	�	�	PROPN
m-806	195	506	)	)	PUNCT
m-806	195	507	+	+	SYM
m-806	195	508	�	�	PROPN
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m-806	195	510	�	�	PROPN
m-806	195	511	�	�	PROPN
m-806	195	512	�	�	PROPN
m-806	195	513	2	2	NUM
m-806	195	514	�	�	PROPN
m-806	195	515	�	�	PROPN
m-806	195	516	,	,	PUNCT
m-806	195	517	�	�	PROPN
m-806	195	518	�	�	PROPN
m-806	195	519	(	(	PUNCT
m-806	195	520	�	�	PROPN
m-806	195	521	�	�	PROPN
m-806	195	522	)	)	PUNCT
m-806	195	523	�	�	PROPN
m-806	195	524	�	�	PROPN
m-806	195	525	�	�	PROPN
m-806	195	526	(	(	PUNCT
m-806	195	527	�	�	PROPN
m-806	195	528	�	�	PROPN
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m-806	195	530	,	,	PUNCT
m-806	195	531	�	�	PROPN
m-806	195	532	)	)	PUNCT
m-806	196	1	+2	+2	PROPN
m-806	196	2	�	�	PROPN
m-806	196	3	�	�	PROPN
m-806	196	4	�	�	PROPN
m-806	196	5	�	�	PROPN
m-806	196	6	�	�	PROPN
m-806	196	7	�	�	PROPN
m-806	196	8	(	(	PUNCT
m-806	196	9	�	�	PROPN
m-806	196	10	�	�	PROPN
m-806	196	11	)	)	PUNCT
m-806	196	12	+	+	SYM
m-806	196	13	�	�	PROPN
m-806	196	14	�	�	PROPN
m-806	196	15	�	�	PROPN
m-806	196	16	(	(	PUNCT
m-806	196	17	�	�	PROPN
m-806	196	18	�	�	PROPN
m-806	196	19	)	)	PUNCT
m-806	196	20	�	�	PROPN
m-806	196	21	+	+	CCONJ
m-806	196	22	�	�	PROPN
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m-806	196	24	�	�	PROPN
m-806	196	25	�	�	PROPN
m-806	196	26	�	�	PROPN
m-806	196	27	�	�	PROPN
m-806	196	28	�	�	PROPN
m-806	196	29	,	,	PUNCT
m-806	196	30	�	�	PROPN
m-806	196	31	(	(	PUNCT
m-806	196	32	�	�	PROPN
m-806	196	33	�	�	PROPN
m-806	196	34	)	)	PUNCT
m-806	196	35	+	+	NUM
m-806	196	36	�	�	PROPN
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m-806	196	38	�	�	PROPN
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m-806	196	41	�	�	PROPN
m-806	196	42	,	,	PUNCT
m-806	196	43	�	�	PROPN
m-806	196	44	�	�	PROPN
m-806	196	45	(	(	PUNCT
m-806	196	46	�	�	PROPN
m-806	196	47	�	�	PROPN
m-806	196	48	)	)	PUNCT
m-806	196	49	+	+	SYM
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m-806	196	51	�	�	PROPN
m-806	196	52	�	�	PROPN
m-806	196	53	�	�	PROPN
m-806	196	54	�	�	PROPN
m-806	196	55	,	,	PUNCT
m-806	196	56	�	�	PROPN
m-806	196	57	(	(	PUNCT
m-806	196	58	�	�	PROPN
m-806	196	59	�	�	PROPN
m-806	196	60	)	)	PUNCT
m-806	196	61	+	+	SYM
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m-806	196	66	�	�	PROPN
m-806	196	67	(	(	PUNCT
m-806	196	68	�	�	PROPN
m-806	196	69	�	�	PROPN
m-806	196	70	)	)	PUNCT
m-806	196	71	�	�	PROPN
m-806	196	72	�	�	PROPN
m-806	196	73	�	�	PROPN
m-806	196	74	+	+	PROPN
m-806	196	75	�	�	PROPN
m-806	196	76	�	�	PROPN
m-806	196	77	�	�	PROPN
m-806	196	78	�	�	PROPN
m-806	196	79	�	�	PROPN
m-806	196	80	�	�	PROPN
m-806	196	81	�	�	PROPN
m-806	196	82	�	�	PROPN
m-806	196	83	,	,	PUNCT
m-806	196	84	�	�	PROPN
m-806	196	85	(	(	PUNCT
m-806	196	86	�	�	PROPN
m-806	196	87	�	�	PROPN
m-806	196	88	)	)	PUNCT
m-806	196	89	+	+	NUM
m-806	196	90	�	�	PROPN
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m-806	196	92	�	�	PROPN
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m-806	196	94	�	�	PROPN
m-806	196	95	̂	̂	PROPN
m-806	196	96	�	�	PROPN
m-806	196	97	�	�	PROPN
m-806	196	98	�	�	PROPN
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m-806	196	100	,	,	PUNCT
m-806	196	101	�	�	PROPN
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m-806	196	104	�	�	PROPN
m-806	196	105	(	(	PUNCT
m-806	196	106	�	�	PROPN
m-806	196	107	�	�	PROPN
m-806	196	108	)	)	PUNCT
m-806	196	109	+	+	SYM
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m-806	196	113	�	�	PROPN
m-806	196	114	�	�	PROPN
m-806	196	115	�	�	PROPN
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m-806	196	118	�	�	PROPN
m-806	196	119	�	�	PROPN
m-806	196	120	(	(	PUNCT
m-806	196	121	�	�	PROPN
m-806	196	122	�	�	PROPN
m-806	196	123	)	)	PUNCT
m-806	196	124	+	+	NUM
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m-806	196	127	�	�	PROPN
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m-806	196	133	�	�	PROPN
m-806	196	134	(	(	PUNCT
m-806	196	135	�	�	PROPN
m-806	196	136	�	�	PROPN
m-806	196	137	)	)	PUNCT
m-806	196	138	+	+	SYM
m-806	196	139	�	�	PROPN
m-806	196	140	�	�	PROPN
m-806	196	141	�	�	PROPN
m-806	196	142	̂	̂	PROPN
m-806	196	143	�	�	PROPN
m-806	196	144	�	�	PROPN
m-806	196	145	�	�	PROPN
m-806	196	146	�	�	PROPN
m-806	196	147	,	,	PUNCT
m-806	196	148	�	�	PROPN
m-806	196	149	�	�	PROPN
m-806	196	150	�	�	PROPN
m-806	196	151	(	(	PUNCT
m-806	196	152	�	�	PROPN
m-806	196	153	�	�	PROPN
m-806	196	154	)	)	PUNCT
m-806	196	155	�	�	PROPN
m-806	196	156	�	�	PROPN
m-806	196	157	�	�	PROPN
m-806	196	158	�	�	PROPN
m-806	196	159	+	+	SYM
m-806	196	160	�	�	PROPN
m-806	196	161	�	�	PROPN
m-806	196	162	�	�	PROPN
m-806	196	163	�	�	PROPN
m-806	196	164	�	�	PROPN
m-806	196	165	�	�	PROPN
m-806	196	166	�	�	PROPN
m-806	196	167	,	,	PUNCT
m-806	196	168	�	�	PROPN
m-806	196	169	(	(	PUNCT
m-806	196	170	�	�	PROPN
m-806	196	171	�	�	PROPN
m-806	196	172	)	)	PUNCT
m-806	196	173	+	+	SYM
m-806	196	174	�	�	PROPN
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m-806	196	178	�	�	PROPN
m-806	196	179	(	(	PUNCT
m-806	196	180	�	�	PROPN
m-806	196	181	�	�	PROPN
m-806	196	182	)	)	PUNCT
m-806	196	183	�	�	PROPN
m-806	196	184	+	+	SYM
m-806	196	185	�	�	PROPN
m-806	196	186	�	�	PROPN
m-806	196	187	�	�	PROPN
m-806	196	188	(	(	PUNCT
m-806	196	189	�	�	PROPN
m-806	196	190	�	�	PROPN
m-806	196	191	)	)	PUNCT
m-806	196	192	+	+	SYM
m-806	196	193	�	�	PROPN
m-806	196	194	�	�	PROPN
m-806	196	195	�	�	PROPN
m-806	196	196	(	(	PUNCT
m-806	196	197	�	�	PROPN
m-806	196	198	�	�	PROPN
m-806	196	199	)	)	PUNCT
m-806	196	200	�	�	PROPN
m-806	196	201	�	�	PROPN
m-806	196	202	�	�	PROPN
m-806	196	203	�	�	PROPN
m-806	196	204	(	(	PUNCT
m-806	196	205	�	�	PROPN
m-806	196	206	�	�	PROPN
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m-806	196	208	,	,	PUNCT
m-806	196	209	�	�	PROPN
m-806	196	210	)	)	PUNCT
m-806	196	211	+	+	CCONJ
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m-806	196	213	(	(	PUNCT
m-806	196	214	8.8	8.8	NUM
m-806	196	215	)	)	PUNCT
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m-806	196	219	that	that	SCONJ
m-806	196	220	�	�	PROPN
m-806	196	221	�	�	PROPN
m-806	196	222	(	(	PUNCT
m-806	196	223	�	�	PROPN
m-806	196	224	�	�	PROPN
m-806	196	225	)	)	PUNCT
m-806	196	226	(	(	PUNCT
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m-806	196	232	)	)	PUNCT
m-806	196	233	=	=	SYM
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m-806	196	237	�	�	PROPN
m-806	196	238	�	�	PROPN
m-806	196	239	�	�	PROPN
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m-806	196	241	,	,	PUNCT
m-806	196	242	(	(	PUNCT
m-806	196	243	8.9a	8.9a	NOUN
m-806	196	244	)	)	PUNCT
m-806	196	245	�	�	PROPN
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m-806	196	247	�	�	PROPN
m-806	196	248	(	(	PUNCT
m-806	196	249	�	�	PROPN
m-806	196	250	�	�	PROPN
m-806	196	251	)	)	PUNCT
m-806	196	252	(	(	PUNCT
m-806	196	253	�	�	PROPN
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m-806	196	259	=	=	SYM
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m-806	196	263	�	�	PROPN
m-806	196	264	�	�	PROPN
m-806	196	265	(	(	PUNCT
m-806	196	266	8.9b	8.9b	PROPN
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m-806	196	270	=	=	SYM
m-806	196	271	�	�	PROPN
m-806	196	272	�	�	PROPN
m-806	196	273	�	�	PROPN
m-806	196	274	�	�	PROPN
m-806	196	275	(	(	PUNCT
m-806	196	276	�	�	PROPN
m-806	196	277	�	�	PROPN
m-806	196	278	�	�	PROPN
m-806	196	279	�	�	PROPN
m-806	196	280	�	�	PROPN
m-806	196	281	�	�	PROPN
m-806	196	282	�	�	PROPN
m-806	196	283	�	�	PROPN
m-806	196	284	�	�	PROPN
m-806	196	285	�	�	PROPN
m-806	196	286	�	�	PROPN
m-806	196	287	)	)	PUNCT
m-806	197	1	�	�	PROPN
m-806	197	2	�	�	PROPN
m-806	197	3	�	�	PROPN
m-806	197	4	+	+	SYM
m-806	197	5	�	�	PROPN
m-806	197	6	(	(	PUNCT
m-806	197	7	�	�	PROPN
m-806	197	8	�	�	PROPN
m-806	197	9	�	�	PROPN
m-806	197	10	�	�	PROPN
m-806	197	11	�	�	PROPN
m-806	197	12	�	�	PROPN
m-806	197	13	�	�	PROPN
m-806	197	14	�	�	PROPN
m-806	197	15	�	�	PROPN
m-806	197	16	�	�	PROPN
m-806	197	17	�	�	PROPN
m-806	197	18	)	)	PUNCT
m-806	197	19	�	�	PROPN
m-806	197	20	�	�	PROPN
m-806	197	21	�	�	PROPN
m-806	197	22	�	�	PROPN
m-806	197	23	�	�	PROPN
m-806	197	24	�	�	PROPN
m-806	197	25	�	�	PROPN
m-806	197	26	�	�	PROPN
m-806	197	27	�	�	PROPN
m-806	197	28	�	�	PROPN
m-806	197	29	+	+	SYM
m-806	197	30	�	�	PROPN
m-806	197	31	(	(	PUNCT
m-806	197	32	�	�	PROPN
m-806	197	33	�	�	PROPN
m-806	197	34	�	�	PROPN
m-806	197	35	�	�	PROPN
m-806	197	36	�	�	PROPN
m-806	197	37	�	�	PROPN
m-806	197	38	�	�	PROPN
m-806	197	39	�	�	PROPN
m-806	197	40	�	�	PROPN
m-806	197	41	�	�	PROPN
m-806	197	42	�	�	PROPN
m-806	197	43	)	)	PUNCT
m-806	197	44	�	�	PROPN
m-806	197	45	�	�	PROPN
m-806	197	46	�	�	PROPN
m-806	197	47	�	�	PROPN
m-806	197	48	�	�	PROPN
m-806	197	49	�	�	PROPN
m-806	197	50	�	�	PROPN
m-806	197	51	�	�	PROPN
m-806	197	52	�	�	PROPN
m-806	197	53	�	�	PROPN
m-806	197	54	�	�	PROPN
m-806	197	55	+	+	CCONJ
m-806	197	56	(	(	PUNCT
m-806	197	57	�	�	PROPN
m-806	197	58	�	�	PROPN
m-806	197	59	�	�	PROPN
m-806	197	60	�	�	PROPN
m-806	197	61	�	�	PROPN
m-806	197	62	�	�	PROPN
m-806	197	63	�	�	PROPN
m-806	197	64	�	�	PROPN
m-806	197	65	�	�	PROPN
m-806	197	66	�	�	PROPN
m-806	197	67	�	�	PROPN
m-806	197	68	)	)	PUNCT
m-806	197	69	�	�	PROPN
m-806	197	70	�	�	PROPN
m-806	197	71	�	�	PROPN
m-806	197	72	�	�	PROPN
m-806	197	73	�	�	PROPN
m-806	197	74	�	�	PROPN
m-806	197	75	�	�	PROPN
m-806	197	76	�	�	PROPN
m-806	197	77	�	�	PROPN
m-806	197	78	�	�	PROPN
m-806	197	79	�	�	PROPN
m-806	197	80	�	�	PROPN
m-806	197	81	(	(	PUNCT
m-806	197	82	8.9c	8.9c	NUM
m-806	197	83	)	)	PUNCT
m-806	197	84	�	�	PROPN
m-806	197	85	�	�	PROPN
m-806	197	86	(	(	PUNCT
m-806	197	87	�	�	PROPN
m-806	197	88	�	�	PROPN
m-806	197	89	)	)	PUNCT
m-806	197	90	(	(	PUNCT
m-806	197	91	�	�	PROPN
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m-806	197	93	�	�	PROPN
m-806	197	94	,	,	PUNCT
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m-806	197	96	)	)	PUNCT
m-806	197	97	=	=	SYM
m-806	197	98	�	�	PROPN
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m-806	197	100	�	�	PROPN
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m-806	197	102	�	�	PROPN
m-806	197	103	�	�	PROPN
m-806	197	104	�	�	PROPN
m-806	197	105	�	�	PROPN
m-806	197	106	�	�	PROPN
m-806	197	107	,	,	PUNCT
m-806	197	108	(	(	PUNCT
m-806	197	109	8.10a	8.10a	NOUN
m-806	197	110	)	)	PUNCT
m-806	197	111	�	�	PROPN
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m-806	197	114	(	(	PUNCT
m-806	197	115	�	�	PROPN
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m-806	197	117	)	)	PUNCT
m-806	197	118	(	(	PUNCT
m-806	197	119	�	�	PROPN
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m-806	197	122	,	,	PUNCT
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m-806	197	124	)	)	PUNCT
m-806	197	125	=	=	SYM
m-806	197	126	�	�	PROPN
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m-806	197	128	�	�	PROPN
m-806	197	129	�	�	PROPN
m-806	197	130	�	�	PROPN
m-806	197	131	�	�	PROPN
m-806	197	132	(	(	PUNCT
m-806	197	133	8.10b	8.10b	NUM
m-806	197	134	)	)	PUNCT
m-806	197	135	�	�	PROPN
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m-806	197	138	=	=	SYM
m-806	197	139	�	�	PROPN
m-806	197	140	�	�	PROPN
m-806	197	141	(	(	PUNCT
m-806	197	142	�	�	PROPN
m-806	197	143	�	�	PROPN
m-806	197	144	�	�	PROPN
m-806	197	145	�	�	PROPN
m-806	197	146	�	�	PROPN
m-806	197	147	�	�	PROPN
m-806	197	148	�	�	PROPN
m-806	197	149	�	�	PROPN
m-806	197	150	�	�	PROPN
m-806	197	151	�	�	PROPN
m-806	197	152	�	�	PROPN
m-806	197	153	)	)	PUNCT
m-806	197	154	�	�	PROPN
m-806	197	155	�	�	PROPN
m-806	197	156	�	�	PROPN
m-806	197	157	�	�	PROPN
m-806	197	158	�	�	PROPN
m-806	197	159	�	�	PROPN
m-806	197	160	�	�	PROPN
m-806	197	161	−	−	PROPN
m-806	197	162	�	�	PROPN
m-806	197	163	�	�	PROPN
m-806	197	164	�	�	PROPN
m-806	197	165	(	(	PUNCT
m-806	197	166	�	�	PROPN
m-806	197	167	�	�	PROPN
m-806	197	168	�	�	PROPN
m-806	197	169	�	�	PROPN
m-806	197	170	�	�	PROPN
m-806	197	171	�	�	PROPN
m-806	197	172	�	�	PROPN
m-806	197	173	�	�	PROPN
m-806	197	174	�	�	PROPN
m-806	197	175	�	�	PROPN
m-806	197	176	�	�	PROPN
m-806	197	177	)	)	PUNCT
m-806	197	178	�	�	PROPN
m-806	197	179	�	�	PROPN
m-806	197	180	�	�	PROPN
m-806	197	181	�	�	PROPN
m-806	197	182	�	�	PROPN
m-806	197	183	�	�	PROPN
m-806	197	184	�	�	PROPN
m-806	197	185	+	+	SYM
m-806	197	186	�	�	PROPN
m-806	197	187	�	�	PROPN
m-806	197	188	�	�	PROPN
m-806	197	189	(	(	PUNCT
m-806	197	190	�	�	PROPN
m-806	197	191	�	�	PROPN
m-806	197	192	�	�	PROPN
m-806	197	193	�	�	PROPN
m-806	197	194	�	�	PROPN
m-806	197	195	�	�	PROPN
m-806	197	196	�	�	PROPN
m-806	197	197	�	�	PROPN
m-806	197	198	�	�	PROPN
m-806	197	199	�	�	PROPN
m-806	197	200	�	�	PROPN
m-806	197	201	)	)	PUNCT
m-806	197	202	�	�	PROPN
m-806	197	203	�	�	PROPN
m-806	197	204	�	�	PROPN
m-806	197	205	�	�	PROPN
m-806	197	206	�	�	PROPN
m-806	197	207	�	�	PROPN
m-806	197	208	�	�	PROPN
m-806	197	209	�	�	PROPN
m-806	197	210	−	−	PROPN
m-806	197	211	�	�	PROPN
m-806	197	212	�	�	PROPN
m-806	197	213	�	�	PROPN
m-806	197	214	(	(	PUNCT
m-806	197	215	�	�	PROPN
m-806	197	216	�	�	PROPN
m-806	197	217	�	�	PROPN
m-806	197	218	�	�	PROPN
m-806	197	219	�	�	PROPN
m-806	197	220	�	�	PROPN
m-806	197	221	�	�	PROPN
m-806	197	222	�	�	PROPN
m-806	197	223	�	�	PROPN
m-806	197	224	�	�	PROPN
m-806	197	225	�	�	PROPN
m-806	197	226	)	)	PUNCT
m-806	197	227	�	�	PROPN
m-806	197	228	�	�	PROPN
m-806	197	229	�	�	PROPN
m-806	197	230	�	�	PROPN
m-806	197	231	�	�	PROPN
m-806	197	232	�	�	PROPN
m-806	197	233	�	�	PROPN
m-806	197	234	�	�	PROPN
m-806	197	235	�	�	PROPN
m-806	197	236	�	�	PROPN
m-806	197	237	�	�	PROPN
m-806	197	238	�	�	PROPN
m-806	197	239	(	(	PUNCT
m-806	197	240	8.10c	8.10c	NUM
m-806	197	241	)	)	PUNCT
m-806	197	242	on	on	ADP
m-806	197	243	substituting	substitute	VERB
m-806	197	244	(	(	PUNCT
m-806	197	245	8.9a	8.9a	NOUN
m-806	197	246	)	)	PUNCT
m-806	197	247	–	–	PUNCT
m-806	197	248	(	(	PUNCT
m-806	197	249	8.10c	8.10c	NUM
m-806	197	250	)	)	PUNCT
m-806	197	251	into	into	ADP
m-806	197	252	(	(	PUNCT
m-806	197	253	8.8	8.8	NUM
m-806	197	254	)	)	PUNCT
m-806	197	255	and	and	CCONJ
m-806	197	256	simplifying	simplify	VERB
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m-806	197	259	get	get	VERB
m-806	197	260	w	w	NOUN
m-806	197	261	�	�	NOUN
m-806	197	262	=	=	SYM
m-806	197	263	4	4	NUM
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m-806	197	266	�	�	PROPN
m-806	197	267	1	1	NUM
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m-806	197	269	�	�	PROPN
m-806	197	270	�	�	PROPN
m-806	197	271	�	�	PROPN
m-806	197	272	�	�	PROPN
m-806	197	273	+	+	CCONJ
m-806	197	274	�	�	PROPN
m-806	197	275	�	�	PROPN
m-806	197	276	�	�	PROPN
m-806	197	277	�	�	PROPN
m-806	197	278	�	�	PROPN
m-806	197	279	�	�	PROPN
m-806	197	280	�	�	PROPN
m-806	197	281	�	�	PROPN
m-806	197	282	�	�	PROPN
m-806	197	283	+	+	CCONJ
m-806	197	284	�	�	PROPN
m-806	197	285	�	�	PROPN
m-806	197	286	�	�	PROPN
m-806	197	287	�	�	PROPN
m-806	197	288	�	�	PROPN
m-806	197	289	�	�	PROPN
m-806	197	290	�	�	PROPN
m-806	197	291	�	�	PROPN
m-806	197	292	�	�	PROPN
m-806	197	293	�	�	PROPN
m-806	197	294	�	�	PROPN
m-806	197	295	1	1	NUM
m-806	197	296	+	+	NUM
m-806	197	297	�	�	PROPN
m-806	197	298	�	�	PROPN
m-806	197	299	�	�	PROPN
m-806	197	300	�	�	PROPN
m-806	197	301	�	�	PROPN
m-806	197	302	�	�	PROPN
m-806	197	303	�	�	PROPN
m-806	197	304	+	+	CCONJ
m-806	197	305	�	�	PROPN
m-806	197	306	�	�	PROPN
m-806	197	307	�	�	PROPN
m-806	197	308	�	�	PROPN
m-806	197	309	+	+	SYM
m-806	197	310	�	�	PROPN
m-806	197	311	�	�	PROPN
m-806	197	312	�	�	PROPN
m-806	197	313	�	�	PROPN
m-806	197	314	�	�	PROPN
m-806	197	315	�	�	PROPN
m-806	197	316	+	+	CCONJ
m-806	197	317	⋯	⋯	PROPN
m-806	197	318	(	(	PUNCT
m-806	197	319	8.11a	8.11a	NUM
m-806	197	320	)	)	PUNCT
m-806	197	321	where	where	SCONJ
m-806	197	322	,	,	PUNCT
m-806	197	323	�	�	PROPN
m-806	197	324	�	�	PROPN
m-806	197	325	�	�	PROPN
m-806	197	326	=	=	SYM
m-806	197	327	�	�	PROPN
m-806	197	328	�	�	PROPN
m-806	197	329	�	�	PROPN
m-806	197	330	�	�	PROPN
m-806	197	331	�	�	PROPN
m-806	197	332	�	�	PROPN
m-806	197	333	�	�	PROPN
m-806	197	334	�	�	PROPN
m-806	197	335	�	�	PROPN
m-806	197	336	�	�	PROPN
m-806	197	337	�	�	PROPN
m-806	197	338	�	�	PROPN
m-806	197	339	�	�	PROPN
m-806	197	340	�	�	PROPN
m-806	197	341	�	�	PROPN
m-806	197	342	+	+	SYM
m-806	197	343	�	�	PROPN
m-806	197	344	�	�	PROPN
m-806	197	345	�	�	PROPN
m-806	197	346	�	�	PROPN
m-806	197	347	−	−	PROPN
m-806	197	348	�	�	PROPN
m-806	197	349	�	�	PROPN
m-806	197	350	�	�	PROPN
m-806	197	351	(	(	PUNCT
m-806	197	352	�	�	PROPN
m-806	197	353	)	)	PUNCT
m-806	197	354	−	−	PROPN
m-806	197	355	�	�	PROPN
m-806	197	356	�	�	PROPN
m-806	197	357	�	�	PROPN
m-806	197	358	�	�	PROPN
m-806	197	359	(	(	PUNCT
m-806	197	360	8.11b	8.11b	PROPN
m-806	197	361	)	)	PUNCT
m-806	197	362	�	�	PROPN
m-806	197	363	�	�	PROPN
m-806	197	364	�	�	PROPN
m-806	197	365	=	=	SYM
m-806	197	366	�	�	PROPN
m-806	197	367	�	�	PROPN
m-806	197	368	�	�	PROPN
m-806	197	369	�	�	PROPN
m-806	197	370	�	�	PROPN
m-806	197	371	�	�	PROPN
m-806	197	372	�	�	PROPN
m-806	197	373	�	�	PROPN
m-806	197	374	�	�	PROPN
m-806	197	375	�	�	PROPN
m-806	197	376	�	�	PROPN
m-806	197	377	�	�	PROPN
m-806	197	378	(	(	PUNCT
m-806	197	379	�	�	PROPN
m-806	197	380	)	)	PUNCT
m-806	197	381	−	−	PROPN
m-806	197	382	�	�	PROPN
m-806	197	383	�	�	PROPN
m-806	197	384	�	�	PROPN
m-806	197	385	(	(	PUNCT
m-806	197	386	�	�	PROPN
m-806	197	387	)	)	PUNCT
m-806	197	388	−	−	PROPN
m-806	197	389	�	�	PROPN
m-806	197	390	�	�	PROPN
m-806	197	391	�	�	PROPN
m-806	197	392	�	�	PROPN
m-806	197	393	�	�	PROPN
m-806	197	394	�	�	PROPN
m-806	197	395	�	�	PROPN
m-806	197	396	−	−	PROPN
m-806	197	397	�	�	PROPN
m-806	197	398	�	�	PROPN
m-806	197	399	�	�	PROPN
m-806	197	400	+	+	CCONJ
m-806	197	401	�	�	PROPN
m-806	197	402	�	�	PROPN
m-806	197	403	�	�	PROPN
m-806	197	404	�	�	PROPN
m-806	197	405	�	�	PROPN
m-806	197	406	�	�	PROPN
m-806	197	407	�	�	PROPN
m-806	197	408	�	�	PROPN
m-806	197	409	�	�	PROPN
m-806	197	410	�	�	PROPN
m-806	197	411	�	�	PROPN
m-806	197	412	�	�	PROPN
m-806	197	413	�	�	PROPN
m-806	197	414	�	�	PROPN
m-806	197	415	�	�	PROPN
m-806	197	416	+	+	SYM
m-806	197	417	�	�	PROPN
m-806	197	418	�	�	PROPN
m-806	197	419	�	�	PROPN
m-806	197	420	�	�	PROPN
m-806	197	421	−	−	PROPN
m-806	197	422	�	�	PROPN
m-806	197	423	�	�	PROPN
m-806	197	424	�	�	PROPN
m-806	197	425	�	�	PROPN
m-806	197	426	�	�	PROPN
m-806	197	427	+	+	SYM
m-806	197	428	�	�	PROPN
m-806	197	429	�	�	PROPN
m-806	197	430	�	�	PROPN
m-806	197	431	�	�	PROPN
m-806	197	432	(	(	PUNCT
m-806	197	433	8.11c	8.11c	NUM
m-806	197	434	)	)	PUNCT
m-806	197	435	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
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m-806	197	438	volume	volume	NOUN
m-806	197	439	07	07	NUM
m-806	197	440	|	|	ADV
m-806	197	441	issue	issue	NOUN
m-806	197	442	02	02	NUM
m-806	197	443	|	|	CCONJ
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m-806	197	445	2024	2024	NUM
m-806	197	446	|	|	ADV
m-806	197	447	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	197	448	26	26	NUM
m-806	197	449	ijo	ijo	PROPN
m-806	197	450	international	international	PROPN
m-806	197	451	journal	journal	PROPN
m-806	197	452	of	of	ADP
m-806	197	453	mathematics	mathematics	PROPN
m-806	197	454	(	(	PUNCT
m-806	197	455	issn	issn	PROPN
m-806	197	456	:	:	PUNCT
m-806	197	457	2992	2992	NUM
m-806	197	458	-	-	SYM
m-806	197	459	4421	4421	NUM
m-806	197	460	)	)	PUNCT
m-806	198	1	i.u	i.u	PROPN
m-806	198	2	.	.	PROPN
m-806	198	3	udo	udo	PROPN
m-806	198	4	-	-	PROPN
m-806	198	5	akpan1	akpan1	ADJ
m-806	198	6	*	*	PUNCT
m-806	198	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	198	8	volume	volume	NOUN
m-806	198	9	07	07	NUM
m-806	198	10	issue	issue	NOUN
m-806	198	11	02	02	NUM
m-806	198	12	||	||	NUM
m-806	198	13	february	february	PROPN
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m-806	198	15	2024	2024	NUM
m-806	198	16	||	||	NOUN
m-806	199	1	on	on	ADP
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m-806	199	5	-	-	PUNCT
m-806	199	6	parameter	parameter	NOUN
m-806	199	7	dynamic	dynamic	ADJ
m-806	199	8	buckling	buckling	NOUN
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m-806	199	10	a	a	DET
m-806	199	11	viscously	viscously	ADV
m-806	199	12	damped	damp	VERB
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m-806	199	14	clamped	clamp	VERB
m-806	199	15	column	column	NOUN
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m-806	199	20	load	load	NOUN
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m-806	199	23	dynamic	dynamic	ADJ
m-806	199	24	buckling	buckling	NOUN
m-806	199	25	load	load	NOUN
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m-806	199	27	�	�	PROPN
m-806	199	28	�	�	PROPN
m-806	199	29	having	having	AUX
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m-806	199	32	maximum	maximum	ADJ
m-806	199	33	deflection	deflection	NOUN
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m-806	199	35	w	w	PROPN
m-806	199	36	�	�	PROPN
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m-806	199	38	in	in	ADP
m-806	199	39	(	(	PUNCT
m-806	199	40	8.11a	8.11a	NUM
m-806	199	41	–	–	PUNCT
m-806	199	42	c	c	NOUN
m-806	199	43	)	)	PUNCT
m-806	199	44	,	,	PUNCT
m-806	199	45	we	we	PRON
m-806	199	46	shall	shall	AUX
m-806	199	47	now	now	ADV
m-806	199	48	determine	determine	VERB
m-806	199	49	the	the	DET
m-806	199	50	dynamic	dynamic	ADJ
m-806	199	51	buckling	buckling	NOUN
m-806	199	52	load	load	NOUN
m-806	199	53	�	�	NOUN
m-806	199	54	�	�	PROPN
m-806	199	55	from	from	ADP
m-806	199	56	the	the	DET
m-806	199	57	maximization	maximization	NOUN
m-806	199	58	(	(	PUNCT
m-806	199	59	7.1	7.1	NUM
m-806	199	60	)	)	PUNCT
m-806	199	61	.	.	PUNCT
m-806	200	1	we	we	PRON
m-806	200	2	shall	shall	AUX
m-806	200	3	first	first	ADV
m-806	200	4	reverse	reverse	VERB
m-806	200	5	the	the	DET
m-806	200	6	series	series	NOUN
m-806	200	7	(	(	PUNCT
m-806	200	8	8.10a	8.10a	PROPN
m-806	200	9	)	)	PUNCT
m-806	200	10	which	which	PRON
m-806	200	11	we	we	PRON
m-806	200	12	now	now	ADV
m-806	200	13	write	write	VERB
m-806	200	14	as	as	ADP
m-806	200	15	w	w	PROPN
m-806	200	16	�	�	PROPN
m-806	200	17	=	=	SYM
m-806	200	18	�	�	PROPN
m-806	200	19	�	�	PROPN
m-806	200	20	�	�	PROPN
m-806	200	21	+	+	SYM
m-806	200	22	�	�	PROPN
m-806	200	23	�	�	PROPN
m-806	200	24	�	�	PROPN
m-806	200	25	�	�	PROPN
m-806	200	26	+	+	CCONJ
m-806	200	27	⋯	⋯	PROPN
m-806	200	28	(	(	PUNCT
m-806	200	29	9.1a	9.1a	NOUN
m-806	200	30	)	)	PUNCT
m-806	201	1	where	where	SCONJ
m-806	201	2	,	,	PUNCT
m-806	201	3	�	�	PROPN
m-806	201	4	�	�	PROPN
m-806	201	5	=	=	SYM
m-806	201	6	4	4	NUM
m-806	201	7	�	�	NOUN
m-806	201	8	1	1	NUM
m-806	201	9	−	−	PROPN
m-806	201	10	�	�	PROPN
m-806	201	11	�	�	PROPN
m-806	201	12	�	�	PROPN
m-806	201	13	�	�	PROPN
m-806	201	14	+	+	CCONJ
m-806	201	15	�	�	PROPN
m-806	201	16	�	�	PROPN
m-806	201	17	�	�	PROPN
m-806	201	18	�	�	PROPN
m-806	201	19	�	�	PROPN
m-806	201	20	�	�	PROPN
m-806	201	21	�	�	PROPN
m-806	201	22	�	�	PROPN
m-806	201	23	�	�	PROPN
m-806	201	24	(	(	PUNCT
m-806	201	25	9.1b	9.1b	PROPN
m-806	201	26	)	)	PUNCT
m-806	201	27	�	�	PROPN
m-806	201	28	�	�	PROPN
m-806	201	29	=	=	SYM
m-806	201	30	�	�	PROPN
m-806	201	31	�	�	PROPN
m-806	201	32	�	�	PROPN
m-806	201	33	�	�	PROPN
m-806	201	34	�	�	PROPN
m-806	201	35	�	�	PROPN
m-806	201	36	�	�	PROPN
m-806	201	37	�	�	PROPN
m-806	201	38	�	�	PROPN
m-806	201	39	1	1	NUM
m-806	201	40	+	+	NUM
m-806	201	41	�	�	PROPN
m-806	201	42	�	�	PROPN
m-806	201	43	�	�	PROPN
m-806	201	44	�	�	PROPN
m-806	201	45	�	�	PROPN
m-806	201	46	�	�	PROPN
m-806	201	47	�	�	PROPN
m-806	201	48	+	+	CCONJ
m-806	201	49	�	�	PROPN
m-806	201	50	�	�	PROPN
m-806	201	51	�	�	PROPN
m-806	201	52	�	�	PROPN
m-806	201	53	+	+	SYM
m-806	201	54	�	�	PROPN
m-806	201	55	�	�	PROPN
m-806	201	56	�	�	PROPN
m-806	201	57	�	�	PROPN
m-806	201	58	�	�	PROPN
m-806	201	59	�	�	PROPN
m-806	201	60	(	(	PUNCT
m-806	201	61	9.1c	9.1c	PROPN
m-806	201	62	)	)	PUNCT
m-806	201	63	thus	thus	ADV
m-806	201	64	,	,	PUNCT
m-806	201	65	for	for	ADP
m-806	201	66	the	the	DET
m-806	201	67	reversal	reversal	NOUN
m-806	201	68	,	,	PUNCT
m-806	201	69	we	we	PRON
m-806	201	70	write	write	VERB
m-806	201	71	�	�	PROPN
m-806	201	72	=	=	SYM
m-806	201	73	�	�	PROPN
m-806	201	74	�	�	PROPN
m-806	201	75	w	w	PROPN
m-806	201	76	�	�	PROPN
m-806	201	77	+	+	NUM
m-806	201	78	�	�	PROPN
m-806	201	79	�	�	PROPN
m-806	201	80	�	�	PROPN
m-806	201	81	�	�	PROPN
m-806	201	82	�	�	PROPN
m-806	201	83	+	+	CCONJ
m-806	201	84	⋯	⋯	PROPN
m-806	201	85	(	(	PUNCT
m-806	201	86	9.2	9.2	NUM
m-806	201	87	)	)	PUNCT
m-806	201	88	upon	upon	SCONJ
m-806	201	89	substituting	substitute	VERB
m-806	201	90	in	in	ADP
m-806	201	91	(	(	PUNCT
m-806	201	92	8.13	8.13	NUM
m-806	201	93	)	)	PUNCT
m-806	201	94	for	for	ADP
m-806	201	95	w	w	PROPN
m-806	201	96	�	�	PROPN
m-806	201	97	from	from	ADP
m-806	201	98	(	(	PUNCT
m-806	201	99	8.12a	8.12a	NUM
m-806	201	100	)	)	PUNCT
m-806	201	101	,	,	PUNCT
m-806	201	102	and	and	CCONJ
m-806	201	103	equating	equate	VERB
m-806	201	104	the	the	DET
m-806	201	105	coefficients	coefficient	NOUN
m-806	201	106	of	of	ADP
m-806	201	107	�	�	PROPN
m-806	201	108	,	,	PUNCT
m-806	201	109	we	we	PRON
m-806	201	110	get	get	VERB
m-806	201	111	�	�	NOUN
m-806	201	112	�	�	PROPN
m-806	201	113	=	=	SYM
m-806	201	114	�	�	PROPN
m-806	201	115	�	�	PROPN
m-806	201	116	�	�	PROPN
m-806	201	117	,	,	PUNCT
m-806	201	118	�	�	PROPN
m-806	201	119	�	�	PROPN
m-806	201	120	=	=	SYM
m-806	201	121	−	−	PROPN
m-806	201	122	�	�	PROPN
m-806	201	123	�	�	PROPN
m-806	201	124	�	�	PROPN
m-806	201	125	�	�	PROPN
m-806	201	126	�	�	PROPN
m-806	201	127	�	�	PROPN
m-806	201	128	�	�	PROPN
m-806	201	129	(	(	PUNCT
m-806	201	130	9.3a	9.3a	NUM
m-806	201	131	)	)	PUNCT
m-806	201	132	the	the	DET
m-806	201	133	maximization	maximization	NOUN
m-806	201	134	(	(	PUNCT
m-806	201	135	7.1	7.1	NUM
m-806	201	136	)	)	PUNCT
m-806	201	137	is	be	AUX
m-806	201	138	now	now	ADV
m-806	201	139	easily	easily	ADV
m-806	201	140	executed	execute	VERB
m-806	201	141	from	from	ADP
m-806	201	142	(	(	PUNCT
m-806	201	143	9.2	9.2	NUM
m-806	201	144	)	)	PUNCT
m-806	201	145	to	to	PART
m-806	201	146	yield	yield	VERB
m-806	201	147	�	�	PROPN
m-806	201	148	�	�	PROPN
m-806	201	149	+	+	CCONJ
m-806	201	150	3	3	NUM
m-806	201	151	�	�	PROPN
m-806	201	152	�	�	PROPN
m-806	201	153	�	�	PROPN
m-806	201	154	�	�	PROPN
m-806	201	155	�	�	PROPN
m-806	201	156	�	�	PROPN
m-806	201	157	=	=	SYM
m-806	201	158	0	0	PROPN
m-806	201	159	,	,	PUNCT
m-806	201	160	(	(	PUNCT
m-806	201	161	9.3b	9.3b	NUM
m-806	201	162	)	)	PUNCT
m-806	201	163	where	where	SCONJ
m-806	201	164	w	w	PROPN
m-806	201	165	�	�	PROPN
m-806	201	166	�	�	PROPN
m-806	201	167	is	be	AUX
m-806	201	168	the	the	DET
m-806	201	169	maximum	maximum	ADJ
m-806	201	170	value	value	NOUN
m-806	201	171	of	of	ADP
m-806	201	172	the	the	DET
m-806	201	173	deflection	deflection	NOUN
m-806	201	174	at	at	ADP
m-806	201	175	dynamic	dynamic	ADJ
m-806	201	176	buckling	buckling	NOUN
m-806	201	177	.	.	PUNCT
m-806	202	1	thus	thus	ADV
m-806	202	2	,	,	PUNCT
m-806	202	3	we	we	PRON
m-806	202	4	have	have	VERB
m-806	202	5	w	w	PROPN
m-806	202	6	�	�	PROPN
m-806	202	7	�	�	PROPN
m-806	202	8	=	=	SYM
m-806	202	9	�	�	PROPN
m-806	202	10	�	�	PROPN
m-806	202	11	�	�	PROPN
m-806	202	12	�	�	PROPN
m-806	202	13	�	�	PROPN
m-806	202	14	�	�	PROPN
m-806	202	15	�	�	PROPN
m-806	202	16	(	(	PUNCT
m-806	202	17	9.4	9.4	NUM
m-806	202	18	)	)	PUNCT
m-806	202	19	on	on	ADP
m-806	202	20	substituting	substitute	VERB
m-806	202	21	from	from	ADP
m-806	202	22	(	(	PUNCT
m-806	202	23	9.3a	9.3a	NOUN
m-806	202	24	)	)	PUNCT
m-806	202	25	in	in	ADP
m-806	202	26	(	(	PUNCT
m-806	202	27	9.4	9.4	NUM
m-806	202	28	)	)	PUNCT
m-806	202	29	we	we	PRON
m-806	202	30	get	get	VERB
m-806	202	31	w	w	PROPN
m-806	202	32	�	�	PROPN
m-806	202	33	�	�	PROPN
m-806	202	34	=	=	SYM
m-806	202	35	�	�	PROPN
m-806	202	36	√	√	NUM
m-806	202	37	�	�	PROPN
m-806	202	38	�	�	PROPN
m-806	202	39	�	�	PROPN
m-806	202	40	�	�	PROPN
m-806	202	41	�	�	PROPN
m-806	202	42	�	�	PROPN
m-806	202	43	�	�	PROPN
m-806	202	44	�	�	PROPN
m-806	202	45	(	(	PUNCT
m-806	202	46	9.5	9.5	NUM
m-806	202	47	)	)	PUNCT
m-806	202	48	if	if	SCONJ
m-806	202	49	we	we	PRON
m-806	202	50	next	next	VERB
m-806	202	51	evaluate	evaluate	VERB
m-806	202	52	(	(	PUNCT
m-806	202	53	9.2	9.2	NUM
m-806	202	54	)	)	PUNCT
m-806	202	55	at	at	ADP
m-806	202	56	dynamic	dynamic	ADJ
m-806	202	57	buckling	buckling	NOUN
m-806	202	58	,	,	PUNCT
m-806	202	59	we	we	PRON
m-806	202	60	get	get	VERB
m-806	202	61	�	�	PROPN
m-806	202	62	=	=	SYM
m-806	202	63	�	�	PROPN
m-806	202	64	�	�	PROPN
m-806	202	65	w	w	PROPN
m-806	202	66	�	�	PROPN
m-806	202	67	�	�	PROPN
m-806	202	68	+	+	SYM
m-806	202	69	�	�	PROPN
m-806	202	70	�	�	PROPN
m-806	202	71	�	�	PROPN
m-806	202	72	�	�	PROPN
m-806	202	73	�	�	PROPN
m-806	202	74	�	�	PROPN
m-806	202	75	+	+	CCONJ
m-806	202	76	⋯	⋯	PROPN
m-806	202	77	=	=	SYM
m-806	202	78	w	w	PROPN
m-806	202	79	�	�	PROPN
m-806	202	80	�	�	PROPN
m-806	202	81	(	(	PUNCT
m-806	202	82	�	�	PROPN
m-806	202	83	�	�	PROPN
m-806	202	84	+	+	CCONJ
m-806	202	85	3	3	NUM
m-806	202	86	�	�	PROPN
m-806	202	87	�	�	PROPN
m-806	202	88	�	�	PROPN
m-806	202	89	�	�	PROPN
m-806	202	90	�	�	PROPN
m-806	202	91	�	�	PROPN
m-806	202	92	)	)	PUNCT
m-806	202	93	(	(	PUNCT
m-806	202	94	9.6	9.6	NUM
m-806	202	95	)	)	PUNCT
m-806	202	96	on	on	ADP
m-806	202	97	substituting	substitute	VERB
m-806	202	98	in	in	ADP
m-806	202	99	(	(	PUNCT
m-806	202	100	9.6	9.6	NUM
m-806	202	101	)	)	PUNCT
m-806	202	102	for	for	ADP
m-806	202	103	�	�	PROPN
m-806	202	104	�	�	PROPN
m-806	202	105	,	,	PUNCT
m-806	202	106	�	�	PROPN
m-806	202	107	�	�	PROPN
m-806	202	108	�	�	PROPN
m-806	202	109	�	�	PROPN
m-806	202	110	�	�	PROPN
m-806	202	111	w	w	PROPN
m-806	202	112	�	�	PROPN
m-806	202	113	�	�	PROPN
m-806	202	114	,	,	PUNCT
m-806	202	115	we	we	PRON
m-806	202	116	get	get	VERB
m-806	202	117	�	�	PROPN
m-806	202	118	=	=	SYM
m-806	202	119	�	�	PROPN
m-806	202	120	�	�	PROPN
m-806	202	121	√	√	NUM
m-806	202	122	�	�	PROPN
m-806	202	123	�	�	PROPN
m-806	202	124	�	�	PROPN
m-806	202	125	�	�	PROPN
m-806	202	126	�	�	PROPN
m-806	202	127	�	�	PROPN
m-806	202	128	�	�	PROPN
m-806	202	129	�	�	PROPN
m-806	202	130	�	�	PROPN
m-806	202	131	(	(	PUNCT
m-806	202	132	9.7	9.7	NUM
m-806	202	133	)	)	PUNCT
m-806	202	134	on	on	ADP
m-806	202	135	substituting	substitute	VERB
m-806	202	136	in	in	ADP
m-806	202	137	(	(	PUNCT
m-806	202	138	9.7	9.7	NUM
m-806	202	139	)	)	PUNCT
m-806	202	140	,	,	PUNCT
m-806	202	141	we	we	PRON
m-806	202	142	get	get	VERB
m-806	202	143	the	the	DET
m-806	202	144	equation	equation	NOUN
m-806	202	145	for	for	ADP
m-806	202	146	determining	determine	VERB
m-806	202	147	the	the	DET
m-806	202	148	dynamic	dynamic	ADJ
m-806	202	149	buckling	buckling	NOUN
m-806	202	150	load	load	NOUN
m-806	202	151	λ	λ	NOUN
m-806	202	152	�	�	PROPN
m-806	202	153	as	as	ADP
m-806	202	154	(	(	PUNCT
m-806	202	155	16	16	NUM
m-806	202	156	�	�	PROPN
m-806	202	157	�	�	PROPN
m-806	202	158	−	−	PROPN
m-806	202	159	8	8	NUM
m-806	202	160	�	�	PROPN
m-806	202	161	�	�	PROPN
m-806	202	162	λ	λ	NOUN
m-806	202	163	�	�	NOUN
m-806	202	164	+	+	CCONJ
m-806	202	165	1	1	NUM
m-806	202	166	)	)	PUNCT
m-806	202	167	�	�	PROPN
m-806	202	168	�	�	PROPN
m-806	202	169	=	=	SYM
m-806	202	170	18√10(	18√10(	NUM
m-806	202	171	�	�	PROPN
m-806	202	172	�	�	PROPN
m-806	202	173	�	�	PROPN
m-806	202	174	�	�	PROPN
m-806	202	175	)	)	PUNCT
m-806	202	176	�	�	PROPN
m-806	202	177	�	�	PROPN
m-806	202	178	λ	λ	SYM
m-806	202	179	�	�	PROPN
m-806	202	180	�	�	PROPN
m-806	202	181	�	�	PROPN
m-806	202	182	�	�	PROPN
m-806	202	183	�	�	PROPN
m-806	202	184	�	�	PROPN
m-806	202	185	�	�	PROPN
m-806	202	186	�	�	PROPN
m-806	202	187	�	�	PROPN
m-806	202	188	�	�	PROPN
m-806	202	189	�	�	PROPN
m-806	202	190	�	�	PROPN
m-806	202	191	�	�	PROPN
m-806	202	192	�	�	PROPN
m-806	202	193	�	�	PROPN
m-806	202	194	�	�	PROPN
m-806	202	195	�	�	PROPN
m-806	202	196	�	�	PROPN
m-806	202	197	�	�	PROPN
m-806	202	198	�	�	PROPN
m-806	202	199	�	�	PROPN
m-806	202	200	�	�	PROPN
m-806	202	201	�	�	PROPN
m-806	202	202	�	�	PROPN
m-806	202	203	�	�	PROPN
m-806	202	204	�	�	PROPN
m-806	202	205	�	�	PROPN
m-806	202	206	�	�	PROPN
m-806	202	207	�	�	PROPN
m-806	202	208	�	�	PROPN
m-806	202	209	�	�	PROPN
m-806	202	210	�	�	PROPN
m-806	202	211	�	�	PROPN
m-806	202	212	�	�	PROPN
m-806	202	213	�	�	PROPN
m-806	202	214	�	�	PROPN
m-806	202	215	�	�	PROPN
m-806	202	216	�	�	PROPN
m-806	202	217	�	�	PROPN
m-806	202	218	�	�	PROPN
m-806	202	219	�	�	PROPN
m-806	202	220	�	�	PROPN
m-806	202	221	�	�	PROPN
m-806	202	222	�	�	PROPN
m-806	202	223	�	�	PROPN
m-806	202	224	�	�	PROPN
m-806	202	225	(	(	PUNCT
m-806	202	226	9.9	9.9	NUM
m-806	202	227	)	)	PUNCT
m-806	202	228	equation	equation	NOUN
m-806	202	229	(	(	PUNCT
m-806	202	230	9.9	9.9	NUM
m-806	202	231	)	)	PUNCT
m-806	202	232	gives	give	VERB
m-806	202	233	an	an	DET
m-806	202	234	implicit	implicit	ADJ
m-806	202	235	formula	formula	NOUN
m-806	202	236	for	for	ADP
m-806	202	237	determining	determine	VERB
m-806	202	238	the	the	DET
m-806	202	239	dynamic	dynamic	ADJ
m-806	202	240	buckling	buckling	NOUN
m-806	202	241	load	load	NOUN
m-806	202	242	λ	λ	NOUN
m-806	202	243	�	�	PROPN
m-806	202	244	.	.	PUNCT
m-806	203	1	by	by	ADP
m-806	203	2	using	use	VERB
m-806	203	3	equation	equation	NOUN
m-806	203	4	(	(	PUNCT
m-806	203	5	5.25	5.25	NUM
m-806	203	6	)	)	PUNCT
m-806	203	7	,	,	PUNCT
m-806	203	8	we	we	PRON
m-806	203	9	can	can	AUX
m-806	203	10	eliminate	eliminate	VERB
m-806	203	11	the	the	DET
m-806	203	12	imperfection	imperfection	NOUN
m-806	203	13	parameter	parameter	NOUN
m-806	203	14	ϵ	ϵ	PROPN
m-806	203	15	and	and	CCONJ
m-806	203	16	hence	hence	ADV
m-806	203	17	relate	relate	VERB
m-806	203	18	λ	λ	X
m-806	203	19	�	�	PROPN
m-806	203	20	to	to	ADP
m-806	203	21	λ	λ	PROPN
m-806	203	22	�	�	PROPN
m-806	203	23	.	.	PUNCT
m-806	204	1	this	this	PRON
m-806	204	2	gives	give	VERB
m-806	204	3	�	�	PROPN
m-806	204	4	�	�	PROPN
m-806	204	5	�	�	PROPN
m-806	204	6	�	�	PROPN
m-806	204	7	�	�	PROPN
m-806	204	8	�	�	PROPN
m-806	204	9	�	�	PROPN
m-806	204	10	�	�	PROPN
m-806	204	11	�	�	PROPN
m-806	204	12	�	�	PROPN
m-806	204	13	�	�	PROPN
m-806	204	14	�	�	PROPN
m-806	204	15	�	�	PROPN
m-806	204	16	�	�	PROPN
m-806	204	17	�	�	PROPN
m-806	204	18	�	�	PROPN
m-806	204	19	�	�	PROPN
m-806	204	20	�	�	PROPN
m-806	204	21	�	�	PROPN
m-806	204	22	�	�	PROPN
m-806	204	23	�	�	PROPN
m-806	204	24	�	�	PROPN
m-806	204	25	�	�	PROPN
m-806	204	26	�	�	PROPN
m-806	204	27	�	�	PROPN
m-806	204	28	�	�	PROPN
m-806	204	29	�	�	PROPN
m-806	204	30	�	�	PROPN
m-806	204	31	=	=	SYM
m-806	204	32	√2	√2	PROPN
m-806	204	33	�	�	PROPN
m-806	204	34	�	�	PROPN
m-806	204	35	�	�	PROPN
m-806	204	36	�	�	PROPN
m-806	204	37	�	�	PROPN
m-806	204	38	�	�	PROPN
m-806	204	39	⎣	⎣	PROPN
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m-806	204	42	⎢	⎢	NOUN
m-806	204	43	⎢	⎢	NOUN
m-806	204	44	⎡	⎡	NUM
m-806	204	45	�	�	PROPN
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m-806	204	47	�	�	PROPN
m-806	204	48	�	�	PROPN
m-806	204	49	�	�	PROPN
m-806	204	50	�	�	PROPN
m-806	204	51	�	�	PROPN
m-806	204	52	�	�	PROPN
m-806	204	53	�	�	PROPN
m-806	204	54	�	�	PROPN
m-806	204	55	�	�	PROPN
m-806	204	56	�	�	PROPN
m-806	204	57	�	�	PROPN
m-806	204	58	�	�	PROPN
m-806	204	59	�	�	PROPN
m-806	204	60	�	�	PROPN
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m-806	204	62	�	�	PROPN
m-806	204	63	�	�	PROPN
m-806	204	64	�	�	PROPN
m-806	204	65	�	�	PROPN
m-806	204	66	�	�	PROPN
m-806	204	67	�	�	PROPN
m-806	204	68	�	�	PROPN
m-806	204	69	�	�	PROPN
m-806	204	70	�	�	PROPN
m-806	204	71	�	�	PROPN
m-806	204	72	�	�	PROPN
m-806	204	73	�	�	PROPN
m-806	204	74	�	�	PROPN
m-806	204	75	�	�	PROPN
m-806	204	76	�	�	PROPN
m-806	204	77	�	�	PROPN
m-806	204	78	�	�	PROPN
m-806	204	79	�	�	PROPN
m-806	204	80	�	�	PROPN
m-806	204	81	�	�	PROPN
m-806	204	82	�	�	PROPN
m-806	204	83	�	�	PROPN
m-806	204	84	�	�	PROPN
m-806	204	85	�	�	PROPN
m-806	204	86	�	�	PROPN
m-806	204	87	�	�	PROPN
m-806	204	88	�	�	PROPN
m-806	204	89	�	�	PROPN
m-806	204	90	�	�	PROPN
m-806	204	91	�	�	PROPN
m-806	204	92	�	�	PROPN
m-806	204	93	�	�	PROPN
m-806	204	94	�	�	PROPN
m-806	204	95	�	�	PROPN
m-806	204	96	�	�	PROPN
m-806	204	97	�	�	PROPN
m-806	204	98	�	�	PROPN
m-806	204	99	�	�	PROPN
m-806	204	100	�	�	PROPN
m-806	204	101	�	�	PROPN
m-806	204	102	�	�	PROPN
m-806	204	103	�	�	PROPN
m-806	204	104	�	�	PROPN
m-806	204	105	�	�	PROPN
m-806	204	106	�	�	PROPN
m-806	204	107	�	�	PROPN
m-806	204	108	�	�	PROPN
m-806	204	109	�	�	PROPN
m-806	204	110	�	�	PROPN
m-806	204	111	�	�	PROPN
m-806	204	112	�	�	PROPN
m-806	204	113	�	�	PROPN
m-806	204	114	�	�	PROPN
m-806	204	115	�	�	PROPN
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m-806	204	117	⎦	⎦	NOUN
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m-806	204	119	⎥	⎥	PROPN
m-806	204	120	⎥	⎥	PROPN
m-806	204	121	⎥	⎥	PROPN
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m-806	204	124	�	�	PROPN
m-806	204	125	(	(	PUNCT
m-806	204	126	9.10	9.10	NUM
m-806	204	127	)	)	PUNCT
m-806	204	128	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	204	129	ijo	ijo	PROPN
m-806	204	130	journals	journal	NOUN
m-806	204	131	volume	volume	NOUN
m-806	204	132	07	07	NUM
m-806	204	133	|	|	ADV
m-806	204	134	issue	issue	NOUN
m-806	204	135	02	02	NUM
m-806	204	136	|	|	CCONJ
m-806	204	137	february	february	PROPN
m-806	204	138	2024	2024	NUM
m-806	205	1	|	|	ADV
m-806	205	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	205	3	27	27	NUM
m-806	205	4	ijo	ijo	PROPN
m-806	205	5	international	international	ADJ
m-806	205	6	journal	journal	PROPN
m-806	205	7	of	of	ADP
m-806	205	8	mathematics	mathematics	PROPN
m-806	205	9	(	(	PUNCT
m-806	205	10	issn	issn	PROPN
m-806	205	11	:	:	PUNCT
m-806	205	12	2992	2992	NUM
m-806	205	13	-	-	SYM
m-806	205	14	4421	4421	NUM
m-806	205	15	)	)	PUNCT
m-806	205	16	i.u	i.u	PROPN
m-806	205	17	.	.	PROPN
m-806	205	18	udo	udo	PROPN
m-806	205	19	-	-	PROPN
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m-806	205	21	*	*	PUNCT
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m-806	205	23	volume	volume	NOUN
m-806	205	24	07	07	NUM
m-806	205	25	issue	issue	NOUN
m-806	205	26	02	02	NUM
m-806	205	27	||	||	NUM
m-806	205	28	february	february	PROPN
m-806	205	29	,	,	PUNCT
m-806	205	30	2024	2024	NUM
m-806	205	31	||	||	NOUN
m-806	205	32	on	on	ADP
m-806	205	33	a	a	DET
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m-806	205	35	two	two	NUM
m-806	205	36	-	-	PUNCT
m-806	205	37	parameter	parameter	NOUN
m-806	205	38	dynamic	dynamic	ADJ
m-806	205	39	buckling	buckling	NOUN
m-806	205	40	of	of	ADP
m-806	205	41	a	a	DET
m-806	205	42	viscously	viscously	ADV
m-806	205	43	damped	damp	VERB
m-806	205	44	but	but	CCONJ
m-806	205	45	clamped	clamp	VERB
m-806	205	46	column	column	NOUN
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m-806	205	51	load	load	NOUN
m-806	205	52	the	the	DET
m-806	205	53	least	least	ADJ
m-806	205	54	value	value	NOUN
m-806	205	55	of	of	ADP
m-806	205	56	the	the	DET
m-806	205	57	dynamic	dynamic	ADJ
m-806	205	58	buckling	buckling	NOUN
m-806	205	59	load	load	NOUN
m-806	205	60	λ	λ	PROPN
m-806	205	61	�	�	PROPN
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m-806	205	63	obtained	obtain	VERB
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m-806	205	65	�	�	PROPN
m-806	205	66	=	=	PROPN
m-806	205	67	1	1	NUM
m-806	205	68	and	and	CCONJ
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m-806	205	70	this	this	DET
m-806	205	71	value	value	NOUN
m-806	205	72	,	,	PUNCT
m-806	205	73	equations	equation	NOUN
m-806	205	74	(	(	PUNCT
m-806	205	75	9.9	9.9	NUM
m-806	205	76	)	)	PUNCT
m-806	205	77	and	and	CCONJ
m-806	205	78	(	(	PUNCT
m-806	205	79	9.10	9.10	NUM
m-806	205	80	)	)	PUNCT
m-806	205	81	respectively	respectively	ADV
m-806	205	82	become	become	VERB
m-806	205	83	(	(	PUNCT
m-806	205	84	17	17	NUM
m-806	205	85	−	−	PROPN
m-806	205	86	8λ	8λ	NUM
m-806	205	87	�	�	SYM
m-806	205	88	)	)	PUNCT
m-806	205	89	�	�	PROPN
m-806	205	90	�	�	PROPN
m-806	205	91	=	=	SYM
m-806	205	92	18√10(	18√10(	NUM
m-806	205	93	�	�	PROPN
m-806	205	94	�	�	PROPN
m-806	205	95	�	�	PROPN
m-806	205	96	�	�	PROPN
m-806	205	97	)λ	)λ	PROPN
m-806	205	98	�	�	PROPN
m-806	205	99	�	�	PROPN
m-806	205	100	�	�	PROPN
m-806	205	101	�	�	PROPN
m-806	205	102	�	�	PROPN
m-806	205	103	�	�	PROPN
m-806	205	104	�	�	PROPN
m-806	205	105	�	�	PROPN
m-806	205	106	�	�	PROPN
m-806	205	107	�	�	PROPN
m-806	205	108	�	�	PROPN
m-806	205	109	�	�	PROPN
m-806	205	110	�	�	PROPN
m-806	205	111	�	�	PROPN
m-806	205	112	�	�	PROPN
m-806	205	113	�	�	PROPN
m-806	205	114	�	�	PROPN
m-806	205	115	�	�	PROPN
m-806	205	116	�	�	PROPN
m-806	205	117	�	�	PROPN
m-806	205	118	�	�	PROPN
m-806	205	119	�	�	PROPN
m-806	205	120	�	�	PROPN
m-806	205	121	�	�	PROPN
m-806	205	122	�	�	PROPN
m-806	205	123	�	�	PROPN
m-806	205	124	�	�	PROPN
m-806	205	125	�	�	PROPN
m-806	205	126	�	�	PROPN
m-806	205	127	�	�	PROPN
m-806	205	128	�	�	PROPN
m-806	205	129	�	�	PROPN
m-806	205	130	�	�	PROPN
m-806	205	131	�	�	PROPN
m-806	205	132	�	�	PROPN
m-806	205	133	�	�	PROPN
m-806	205	134	�	�	PROPN
m-806	205	135	�	�	PROPN
m-806	205	136	�	�	PROPN
m-806	205	137	�	�	PROPN
m-806	205	138	�	�	PROPN
m-806	205	139	�	�	PROPN
m-806	205	140	�	�	PROPN
m-806	205	141	�	�	PROPN
m-806	205	142	�	�	PROPN
m-806	205	143	�	�	PROPN
m-806	205	144	(	(	PUNCT
m-806	205	145	9.11	9.11	NUM
m-806	205	146	)	)	PUNCT
m-806	205	147	and	and	CCONJ
m-806	205	148	�	�	PROPN
m-806	205	149	�	�	PROPN
m-806	205	150	�	�	PROPN
m-806	205	151	�	�	PROPN
m-806	205	152	�	�	PROPN
m-806	205	153	�	�	PROPN
m-806	205	154	�	�	PROPN
m-806	205	155	�	�	PROPN
m-806	205	156	�	�	PROPN
m-806	205	157	�	�	PROPN
m-806	205	158	�	�	PROPN
m-806	205	159	�	�	PROPN
m-806	205	160	�	�	PROPN
m-806	205	161	�	�	PROPN
m-806	205	162	�	�	PROPN
m-806	205	163	�	�	PROPN
m-806	205	164	=	=	SYM
m-806	205	165	√2	√2	PROPN
m-806	205	166	�	�	PROPN
m-806	205	167	�	�	PROPN
m-806	205	168	�	�	PROPN
m-806	205	169	�	�	PROPN
m-806	205	170	�	�	PROPN
m-806	205	171	�	�	PROPN
m-806	206	1	⎣	⎣	PROPN
m-806	206	2	⎢	⎢	NOUN
m-806	206	3	⎢	⎢	NOUN
m-806	206	4	⎢	⎢	NOUN
m-806	206	5	⎢	⎢	NOUN
m-806	206	6	⎡	⎡	NUM
m-806	206	7	�	�	PROPN
m-806	206	8	�	�	PROPN
m-806	206	9	�	�	PROPN
m-806	206	10	�	�	PROPN
m-806	206	11	�	�	PROPN
m-806	206	12	�	�	PROPN
m-806	206	13	�	�	PROPN
m-806	206	14	�	�	PROPN
m-806	206	15	�	�	PROPN
m-806	206	16	�	�	PROPN
m-806	206	17	�	�	PROPN
m-806	206	18	�	�	PROPN
m-806	206	19	�	�	PROPN
m-806	206	20	�	�	PROPN
m-806	206	21	�	�	PROPN
m-806	206	22	�	�	PROPN
m-806	206	23	�	�	PROPN
m-806	206	24	�	�	PROPN
m-806	206	25	�	�	PROPN
m-806	206	26	�	�	PROPN
m-806	206	27	�	�	PROPN
m-806	206	28	�	�	PROPN
m-806	206	29	�	�	PROPN
m-806	206	30	�	�	PROPN
m-806	206	31	�	�	PROPN
m-806	206	32	�	�	PROPN
m-806	206	33	�	�	PROPN
m-806	206	34	�	�	PROPN
m-806	206	35	�	�	PROPN
m-806	206	36	�	�	PROPN
m-806	206	37	�	�	PROPN
m-806	206	38	�	�	PROPN
m-806	206	39	�	�	PROPN
m-806	206	40	�	�	PROPN
m-806	206	41	�	�	PROPN
m-806	206	42	�	�	PROPN
m-806	206	43	�	�	PROPN
m-806	206	44	�	�	PROPN
m-806	206	45	�	�	PROPN
m-806	206	46	�	�	PROPN
m-806	206	47	�	�	PROPN
m-806	206	48	�	�	PROPN
m-806	206	49	�	�	PROPN
m-806	206	50	�	�	PROPN
m-806	206	51	�	�	PROPN
m-806	206	52	�	�	PROPN
m-806	206	53	�	�	PROPN
m-806	206	54	�	�	PROPN
m-806	206	55	�	�	PROPN
m-806	206	56	�	�	PROPN
m-806	206	57	�	�	PROPN
m-806	206	58	�	�	PROPN
m-806	206	59	�	�	PROPN
m-806	206	60	�	�	PROPN
m-806	206	61	�	�	PROPN
m-806	206	62	�	�	PROPN
m-806	206	63	�	�	PROPN
m-806	206	64	�	�	PROPN
m-806	206	65	�	�	PROPN
m-806	206	66	�	�	PROPN
m-806	206	67	⎦	⎦	NOUN
m-806	206	68	⎥	⎥	PROPN
m-806	206	69	⎥	⎥	PROPN
m-806	206	70	⎥	⎥	PROPN
m-806	206	71	⎥	⎥	PROPN
m-806	206	72	⎤	⎤	PROPN
m-806	206	73	�	�	PROPN
m-806	206	74	�	�	PROPN
m-806	206	75	(	(	PUNCT
m-806	206	76	9.12	9.12	NUM
m-806	206	77	)	)	PUNCT
m-806	206	78	where	where	SCONJ
m-806	206	79	the	the	DET
m-806	206	80	right	right	ADJ
m-806	206	81	hand	hand	NOUN
m-806	206	82	sides	side	NOUN
m-806	206	83	of	of	ADP
m-806	206	84	(	(	PUNCT
m-806	206	85	9.11	9.11	NUM
m-806	206	86	)	)	PUNCT
m-806	206	87	and	and	CCONJ
m-806	206	88	(	(	PUNCT
m-806	206	89	9.12	9.12	NUM
m-806	206	90	)	)	PUNCT
m-806	206	91	are	be	AUX
m-806	206	92	to	to	PART
m-806	206	93	be	be	AUX
m-806	206	94	evaluated	evaluate	VERB
m-806	206	95	at	at	ADP
m-806	206	96	�	�	PROPN
m-806	206	97	=	=	SYM
m-806	206	98	1	1	NUM
m-806	206	99	.	.	NOUN
m-806	206	100	10	10	NUM
m-806	206	101	.	.	PUNCT
m-806	207	1	analysis	analysis	NOUN
m-806	207	2	of	of	ADP
m-806	207	3	results	result	NOUN
m-806	207	4	the	the	DET
m-806	207	5	graphical	graphical	ADJ
m-806	207	6	plots	plot	NOUN
m-806	207	7	of	of	ADP
m-806	207	8	the	the	DET
m-806	207	9	results	result	NOUN
m-806	207	10	were	be	AUX
m-806	207	11	done	do	VERB
m-806	207	12	using	use	VERB
m-806	207	13	q	q	ADJ
m-806	207	14	-	-	ADJ
m-806	207	15	basic	basic	ADJ
m-806	207	16	codes	code	NOUN
m-806	207	17	and	and	CCONJ
m-806	207	18	the	the	DET
m-806	207	19	results	result	NOUN
m-806	207	20	are	be	AUX
m-806	207	21	hereby	hereby	ADV
m-806	207	22	presented	present	VERB
m-806	207	23	in	in	ADP
m-806	207	24	fig	fig	NOUN
m-806	207	25	.	.	PUNCT
m-806	208	1	1	1	NUM
m-806	208	2	,	,	PUNCT
m-806	208	3	fig	fig	NOUN
m-806	208	4	.	.	NOUN
m-806	208	5	2	2	NUM
m-806	208	6	and	and	CCONJ
m-806	208	7	fig	fig	NOUN
m-806	208	8	.	.	PUNCT
m-806	209	1	3	3	X
m-806	209	2	.	.	X
m-806	209	3	fig	fig	NOUN
m-806	209	4	.	.	PUNCT
m-806	210	1	1	1	NUM
m-806	210	2	:	:	PUNCT
m-806	210	3	relationship	relationship	NOUN
m-806	210	4	between	between	ADP
m-806	210	5	the	the	DET
m-806	210	6	static	static	ADJ
m-806	210	7	buckling	buckling	NOUN
m-806	210	8	load	load	NOUN
m-806	210	9	,	,	PUNCT
m-806	210	10	�	�	PROPN
m-806	210	11	�	�	PROPN
m-806	210	12	and	and	CCONJ
m-806	210	13	imperfection	imperfection	NOUN
m-806	210	14	factor	factor	NOUN
m-806	210	15	,	,	PUNCT
m-806	210	16	ϵ	ϵ	X
m-806	210	17	using	use	VERB
m-806	210	18	eqn	eqn	NOUN
m-806	210	19	.	.	PUNCT
m-806	211	1	(	(	PUNCT
m-806	211	2	5.26	5.26	NUM
m-806	211	3	)	)	PUNCT
m-806	211	4	,	,	PUNCT
m-806	211	5	eqn.(5.28	eqn.(5.28	NOUN
m-806	211	6	)	)	PUNCT
m-806	211	7	,	,	PUNCT
m-806	211	8	eqn.(5.30	eqn.(5.30	NOUN
m-806	211	9	)	)	PUNCT
m-806	211	10	and	and	CCONJ
m-806	211	11	eqn.(5.32	eqn.(5.32	NOUN
m-806	211	12	)	)	PUNCT
m-806	211	13	.	.	PUNCT
m-806	212	1	0	0	NUM
m-806	212	2	0.5	0.5	NUM
m-806	212	3	1	1	NUM
m-806	212	4	1.5	1.5	NUM
m-806	212	5	2	2	NUM
m-806	212	6	2.5	2.5	NUM
m-806	212	7	0.01	0.01	NUM
m-806	212	8	0.02	0.02	NUM
m-806	212	9	0.03	0.03	NUM
m-806	212	10	0.04	0.04	NUM
m-806	212	11	0.05	0.05	NUM
m-806	212	12	0.06	0.06	NUM
m-806	212	13	0.07	0.07	NUM
m-806	212	14	0.08	0.08	NUM
m-806	212	15	0.09	0.09	NUM
m-806	212	16	0.1	0.1	NUM
m-806	212	17	0.2	0.2	NUM
m-806	212	18	st	st	PROPN
m-806	212	19	a	a	DET
m-806	212	20	ti	ti	NOUN
m-806	212	21	c	c	PROPN
m-806	212	22	b	b	SYM
m-806	212	23	u	u	X
m-806	212	24	c	c	PROPN
m-806	212	25	k	k	PROPN
m-806	212	26	li	li	PROPN
m-806	212	27	n	n	CCONJ
m-806	212	28	g	g	PROPN
m-806	212	29	l	l	NOUN
m-806	212	30	o	o	X
m-806	213	1	a	a	DET
m-806	213	2	d	d	NOUN
m-806	213	3	imperfection	imperfection	NOUN
m-806	213	4	factor	factor	NOUN
m-806	213	5	static	static	ADJ
m-806	213	6	buckling	buckling	NOUN
m-806	213	7	load	load	NOUN
m-806	213	8	(	(	PUNCT
m-806	213	9	eqn	eqn	NOUN
m-806	213	10	5.28	5.28	NUM
m-806	213	11	)	)	PUNCT
m-806	213	12	static	static	ADJ
m-806	213	13	buckling	buckling	NOUN
m-806	213	14	load	load	NOUN
m-806	213	15	(	(	PUNCT
m-806	213	16	eqn	eqn	NOUN
m-806	213	17	5.30	5.30	NUM
m-806	213	18	)	)	PUNCT
m-806	213	19	static	static	ADJ
m-806	213	20	buckling	buckling	NOUN
m-806	213	21	load	load	NOUN
m-806	213	22	(	(	PUNCT
m-806	213	23	eqn	eqn	NOUN
m-806	213	24	5.32	5.32	NUM
m-806	213	25	)	)	PUNCT
m-806	213	26	static	static	ADJ
m-806	213	27	buckling	buckling	NOUN
m-806	213	28	load	load	NOUN
m-806	213	29	(	(	PUNCT
m-806	213	30	eqn	eqn	NOUN
m-806	213	31	.	.	PUNCT
m-806	213	32	5.26	5.26	NUM
m-806	213	33	)	)	PUNCT
m-806	213	34	〖λ	〖λ	PRON
m-806	213	35	�	�	X
m-806	213	36	〗^	〗^	VERB
m-806	213	37	ϵ	ϵ	X
m-806	213	38	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	213	39	ijo	ijo	PROPN
m-806	213	40	journals	journal	NOUN
m-806	213	41	volume	volume	NOUN
m-806	213	42	07	07	NUM
m-806	213	43	|	|	ADV
m-806	213	44	issue	issue	NOUN
m-806	213	45	02	02	NUM
m-806	213	46	|	|	CCONJ
m-806	213	47	february	february	PROPN
m-806	213	48	2024	2024	NUM
m-806	213	49	|	|	ADV
m-806	213	50	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	213	51	28	28	NUM
m-806	213	52	ijo	ijo	PROPN
m-806	213	53	international	international	PROPN
m-806	213	54	journal	journal	PROPN
m-806	213	55	of	of	ADP
m-806	213	56	mathematics	mathematics	PROPN
m-806	213	57	(	(	PUNCT
m-806	213	58	issn	issn	PROPN
m-806	213	59	:	:	PUNCT
m-806	213	60	2992	2992	NUM
m-806	213	61	-	-	SYM
m-806	213	62	4421	4421	NUM
m-806	213	63	)	)	PUNCT
m-806	214	1	i.u	i.u	PROPN
m-806	214	2	.	.	PROPN
m-806	214	3	udo	udo	PROPN
m-806	214	4	-	-	PROPN
m-806	214	5	akpan1	akpan1	ADJ
m-806	214	6	*	*	PUNCT
m-806	214	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	214	8	volume	volume	NOUN
m-806	214	9	07	07	NUM
m-806	214	10	issue	issue	NOUN
m-806	214	11	02	02	NUM
m-806	214	12	||	||	NUM
m-806	214	13	february	february	PROPN
m-806	214	14	,	,	PUNCT
m-806	214	15	2024	2024	NUM
m-806	214	16	||	||	NOUN
m-806	215	1	on	on	ADP
m-806	215	2	a	a	DET
m-806	215	3	-	-	PUNCT
m-806	215	4	two	two	NUM
m-806	215	5	-	-	PUNCT
m-806	215	6	parameter	parameter	NOUN
m-806	215	7	dynamic	dynamic	ADJ
m-806	215	8	buckling	buckling	NOUN
m-806	215	9	of	of	ADP
m-806	215	10	a	a	DET
m-806	215	11	viscously	viscously	ADV
m-806	215	12	damped	damp	VERB
m-806	215	13	but	but	CCONJ
m-806	215	14	clamped	clamp	VERB
m-806	215	15	column	column	NOUN
m-806	215	16	stressed	stress	VERB
m-806	215	17	by	by	ADP
m-806	215	18	a	a	DET
m-806	215	19	step	step	NOUN
m-806	215	20	load	load	NOUN
m-806	215	21	fig	fig	NOUN
m-806	215	22	.	.	PUNCT
m-806	216	1	2	2	NUM
m-806	216	2	:	:	PUNCT
m-806	216	3	relationship	relationship	NOUN
m-806	216	4	between	between	ADP
m-806	216	5	the	the	DET
m-806	216	6	dynamic	dynamic	ADJ
m-806	216	7	buckling	buckling	NOUN
m-806	216	8	loads	load	NOUN
m-806	216	9	and	and	CCONJ
m-806	216	10	imperfection	imperfection	NOUN
m-806	216	11	parameters	parameter	NOUN
m-806	216	12	at	at	ADP
m-806	216	13	some	some	DET
m-806	216	14	fixed	fix	VERB
m-806	216	15	values	value	NOUN
m-806	216	16	of	of	ADP
m-806	216	17	the	the	DET
m-806	216	18	damping	damp	VERB
m-806	216	19	factor	factor	NOUN
m-806	216	20	,	,	PUNCT
m-806	216	21	δ	δ	PROPN
m-806	216	22	,	,	PUNCT
m-806	216	23	using	use	VERB
m-806	216	24	eqn	eqn	PRON
m-806	216	25	.	.	PUNCT
m-806	217	1	(	(	PUNCT
m-806	217	2	9.11	9.11	NUM
m-806	217	3	)	)	PUNCT
m-806	217	4	.	.	PUNCT
m-806	218	1	fig	fig	NOUN
m-806	218	2	.	.	PUNCT
m-806	219	1	3	3	NUM
m-806	219	2	:	:	PUNCT
m-806	219	3	relationship	relationship	NOUN
m-806	219	4	between	between	ADP
m-806	219	5	the	the	DET
m-806	219	6	dynamic	dynamic	ADJ
m-806	219	7	buckling	buckling	NOUN
m-806	219	8	loads	load	NOUN
m-806	219	9	and	and	CCONJ
m-806	219	10	the	the	DET
m-806	219	11	static	static	ADJ
m-806	219	12	buckling	buckling	NOUN
m-806	219	13	loads	load	NOUN
m-806	219	14	at	at	ADP
m-806	219	15	some	some	DET
m-806	219	16	fixed	fix	VERB
m-806	219	17	values	value	NOUN
m-806	219	18	of	of	ADP
m-806	219	19	the	the	DET
m-806	219	20	damping	damp	VERB
m-806	219	21	factor	factor	NOUN
m-806	219	22	,	,	PUNCT
m-806	219	23	δ	δ	PROPN
m-806	219	24	,	,	PUNCT
m-806	219	25	using	use	VERB
m-806	219	26	eqn	eqn	PRON
m-806	219	27	.	.	PUNCT
m-806	220	1	(	(	PUNCT
m-806	220	2	9.12	9.12	NUM
m-806	220	3	)	)	PUNCT
m-806	220	4	.	.	PUNCT
m-806	221	1	from	from	ADP
m-806	221	2	fig	fig	NOUN
m-806	221	3	.	.	PUNCT
m-806	222	1	1	1	NUM
m-806	222	2	,	,	PUNCT
m-806	222	3	we	we	PRON
m-806	222	4	observe	observe	VERB
m-806	222	5	that	that	SCONJ
m-806	222	6	the	the	DET
m-806	222	7	static	static	ADJ
m-806	222	8	buckling	buckling	NOUN
m-806	222	9	load	load	NOUN
m-806	222	10	of	of	ADP
m-806	222	11	a	a	DET
m-806	222	12	clamped	clamp	VERB
m-806	222	13	column	column	NOUN
m-806	222	14	is	be	AUX
m-806	222	15	always	always	ADV
m-806	222	16	higher	high	ADJ
m-806	222	17	than	than	ADP
m-806	222	18	that	that	PRON
m-806	222	19	of	of	ADP
m-806	222	20	the	the	DET
m-806	222	21	same	same	ADJ
m-806	222	22	column	column	NOUN
m-806	222	23	with	with	ADP
m-806	222	24	simply	simply	ADV
m-806	222	25	–	–	PUNCT
m-806	222	26	supported	support	VERB
m-806	222	27	boundary	boundary	ADJ
m-806	222	28	conditions	condition	NOUN
m-806	222	29	.	.	PUNCT
m-806	223	1	in	in	ADP
m-806	223	2	general	general	ADJ
m-806	223	3	,	,	PUNCT
m-806	223	4	the	the	DET
m-806	223	5	static	static	ADJ
m-806	223	6	buckling	buckling	NOUN
m-806	223	7	load	load	NOUN
m-806	223	8	of	of	ADP
m-806	223	9	a	a	DET
m-806	223	10	column	column	NOUN
m-806	223	11	with	with	ADP
m-806	223	12	either	either	CCONJ
m-806	223	13	clamped	clamp	VERB
m-806	223	14	or	or	CCONJ
m-806	223	15	simply	simply	ADV
m-806	223	16	-	-	PUNCT
m-806	223	17	supported	support	VERB
m-806	223	18	boundary	boundary	ADJ
m-806	223	19	conditions	condition	NOUN
m-806	223	20	and	and	CCONJ
m-806	223	21	whose	whose	DET
m-806	223	22	deflections	deflection	NOUN
m-806	223	23	are	be	AUX
m-806	223	24	strictly	strictly	ADV
m-806	223	25	in	in	ADP
m-806	223	26	the	the	DET
m-806	223	27	shape	shape	NOUN
m-806	223	28	of	of	ADP
m-806	223	29	imperfection	imperfection	NOUN
m-806	223	30	always	always	ADV
m-806	223	31	has	have	VERB
m-806	223	32	the	the	DET
m-806	223	33	least	least	ADJ
m-806	223	34	static	static	ADJ
m-806	223	35	buckling	buckling	NOUN
m-806	223	36	load	load	NOUN
m-806	223	37	.	.	PUNCT
m-806	224	1	however	however	ADV
m-806	224	2	,	,	PUNCT
m-806	224	3	while	while	SCONJ
m-806	224	4	the	the	DET
m-806	224	5	static	static	ADJ
m-806	224	6	buckling	buckling	NOUN
m-806	224	7	load	load	NOUN
m-806	224	8	of	of	ADP
m-806	224	9	a	a	DET
m-806	224	10	clamped	clamp	VERB
m-806	224	11	column	column	NOUN
m-806	224	12	satisfies	satisfy	VERB
m-806	224	13	the	the	DET
m-806	224	14	inequality	inequality	NOUN
m-806	224	15	,	,	PUNCT
m-806	224	16	1	1	NUM
m-806	224	17	<	<	X
m-806	224	18	�	�	PROPN
m-806	224	19	�	�	PROPN
m-806	224	20	<	<	X
m-806	224	21	2.125	2.125	NUM
m-806	224	22	,	,	PUNCT
m-806	224	23	a	a	DET
m-806	224	24	similar	similar	ADJ
m-806	224	25	column	column	NOUN
m-806	224	26	with	with	ADP
m-806	224	27	simply	simply	ADV
m-806	224	28	–	–	PUNCT
m-806	224	29	supported	support	VERB
m-806	224	30	boundary	boundary	ADJ
m-806	224	31	supports	support	NOUN
m-806	224	32	satisfies	satisfy	VERB
m-806	224	33	the	the	DET
m-806	224	34	inequality	inequality	NOUN
m-806	224	35	0	0	PUNCT
m-806	224	36	<	<	X
m-806	224	37	�	�	PROPN
m-806	224	38	�	�	PROPN
m-806	224	39	<	<	X
m-806	224	40	1	1	PROPN
m-806	224	41	.	.	PUNCT
m-806	224	42	fig	fig	NOUN
m-806	224	43	.	.	PUNCT
m-806	225	1	2	2	NUM
m-806	225	2	shows	show	VERB
m-806	225	3	that	that	SCONJ
m-806	225	4	the	the	DET
m-806	225	5	dynamic	dynamic	ADJ
m-806	225	6	buckling	buckling	NOUN
m-806	225	7	load	load	NOUN
m-806	225	8	�	�	PROPN
m-806	225	9	�	�	PROPN
m-806	225	10	decreases	decrease	VERB
m-806	225	11	with	with	ADP
m-806	225	12	increased	increase	VERB
m-806	225	13	imperfection	imperfection	NOUN
m-806	225	14	for	for	ADP
m-806	225	15	any	any	DET
m-806	225	16	value	value	NOUN
m-806	225	17	of	of	ADP
m-806	225	18	the	the	DET
m-806	225	19	damping	damp	VERB
m-806	225	20	parameter	parameter	NOUN
m-806	225	21	.	.	PUNCT
m-806	226	1	from	from	ADP
m-806	226	2	fig	fig	NOUN
m-806	226	3	.	.	PUNCT
m-806	227	1	3	3	NUM
m-806	227	2	,	,	PUNCT
m-806	227	3	we	we	PRON
m-806	227	4	observe	observe	VERB
m-806	227	5	that	that	SCONJ
m-806	227	6	at	at	ADP
m-806	227	7	low	low	ADJ
m-806	227	8	values	value	NOUN
m-806	227	9	of	of	ADP
m-806	227	10	the	the	DET
m-806	227	11	static	static	ADJ
m-806	227	12	buckling	buckling	NOUN
m-806	227	13	load	load	NOUN
m-806	227	14	�	�	PROPN
m-806	227	15	�	�	PROPN
m-806	227	16	(	(	PUNCT
m-806	227	17	precisely	precisely	ADV
m-806	227	18	for	for	ADP
m-806	227	19	1	1	NUM
m-806	227	20	<	<	X
m-806	227	21	�	�	PROPN
m-806	227	22	�	�	PROPN
m-806	227	23	<	<	X
m-806	227	24	1.45	1.45	NUM
m-806	227	25	)	)	PUNCT
m-806	227	26	,	,	PUNCT
m-806	227	27	there	there	PRON
m-806	227	28	is	be	VERB
m-806	227	29	no	no	DET
m-806	227	30	significant	significant	ADJ
m-806	227	31	difference	difference	NOUN
m-806	227	32	in	in	ADP
m-806	227	33	the	the	DET
m-806	227	34	value	value	NOUN
m-806	227	35	of	of	ADP
m-806	227	36	the	the	DET
m-806	227	37	dynamic	dynamic	ADJ
m-806	227	38	buckling	buckling	NOUN
m-806	227	39	load	load	NOUN
m-806	227	40	�	�	NOUN
m-806	227	41	�	�	PROPN
m-806	227	42	of	of	ADP
m-806	227	43	the	the	DET
m-806	227	44	column	column	NOUN
m-806	227	45	,	,	PUNCT
m-806	227	46	whether	whether	SCONJ
m-806	227	47	damped	damped	ADJ
m-806	227	48	or	or	CCONJ
m-806	227	49	undamped	undampe	VERB
m-806	227	50	.	.	PUNCT
m-806	228	1	however	however	ADV
m-806	228	2	,	,	PUNCT
m-806	228	3	at	at	ADP
m-806	228	4	higher	high	ADJ
m-806	228	5	values	value	NOUN
m-806	228	6	of	of	ADP
m-806	228	7	�	�	PROPN
m-806	228	8	�	�	PROPN
m-806	228	9	(	(	PUNCT
m-806	228	10	i.e	i.e	PROPN
m-806	228	11	,	,	PUNCT
m-806	228	12	1.45	1.45	NUM
m-806	228	13	<	<	X
m-806	228	14	�	�	PROPN
m-806	228	15	�	�	PROPN
m-806	228	16	<	<	X
m-806	228	17	2.125	2.125	NUM
m-806	228	18	)	)	PUNCT
m-806	228	19	,	,	PUNCT
m-806	228	20	the	the	DET
m-806	228	21	dynamic	dynamic	ADJ
m-806	228	22	buckling	buckling	NOUN
m-806	228	23	load	load	NOUN
m-806	228	24	�	�	PROPN
m-806	228	25	�	�	PROPN
m-806	228	26	rises	rise	VERB
m-806	228	27	with	with	ADP
m-806	228	28	�	�	PROPN
m-806	228	29	�	�	PROPN
m-806	228	30	and	and	CCONJ
m-806	228	31	the	the	DET
m-806	228	32	highest	high	ADJ
m-806	228	33	of	of	ADP
m-806	228	34	0	0	NUM
m-806	228	35	0.2	0.2	NUM
m-806	228	36	0.4	0.4	NUM
m-806	228	37	0.6	0.6	NUM
m-806	228	38	0.8	0.8	NUM
m-806	228	39	1	1	NUM
m-806	228	40	1.2	1.2	NUM
m-806	228	41	0.01	0.01	NUM
m-806	228	42	0.02	0.02	NUM
m-806	228	43	0.03	0.03	NUM
m-806	228	44	0.04	0.04	NUM
m-806	228	45	0.05	0.05	NUM
m-806	228	46	0.06	0.06	NUM
m-806	228	47	0.07	0.07	NUM
m-806	228	48	0.08	0.08	NUM
m-806	228	49	0.09	0.09	NUM
m-806	228	50	0.1	0.1	NUM
m-806	228	51	0.2	0.2	NUM
m-806	228	52	d	d	SYM
m-806	228	53	y	y	PROPN
m-806	228	54	n	n	PROPN
m-806	228	55	a	a	PROPN
m-806	228	56	m	m	NOUN
m-806	228	57	ic	ic	PROPN
m-806	228	58	b	b	NUM
m-806	228	59	u	u	X
m-806	228	60	c	c	PROPN
m-806	228	61	k	k	PROPN
m-806	228	62	li	li	PROPN
m-806	228	63	n	n	CCONJ
m-806	228	64	g	g	PROPN
m-806	228	65	l	l	NOUN
m-806	228	66	o	o	X
m-806	228	67	a	a	DET
m-806	228	68	d	d	NOUN
m-806	228	69	imperfection	imperfection	NOUN
m-806	228	70	factor	factor	NOUN
m-806	228	71	dynamic	dynamic	ADJ
m-806	228	72	buckling	buckling	NOUN
m-806	228	73	load	load	NOUN
m-806	228	74	,	,	PUNCT
m-806	228	75	δ	δ	X
m-806	228	76	=	=	SYM
m-806	228	77	0	0	NUM
m-806	228	78	dynamic	dynamic	ADJ
m-806	228	79	buckling	buckling	NOUN
m-806	228	80	load	load	NOUN
m-806	228	81	,	,	PUNCT
m-806	228	82	δ	δ	X
m-806	228	83	=	=	NOUN
m-806	228	84	0.01	0.01	NUM
m-806	228	85	dynamic	dynamic	ADJ
m-806	228	86	buckling	buckling	NOUN
m-806	228	87	load	load	NOUN
m-806	228	88	,	,	PUNCT
m-806	228	89	δ	δ	X
m-806	228	90	=	=	NOUN
m-806	228	91	0.02	0.02	NUM
m-806	228	92	dynamic	dynamic	ADJ
m-806	228	93	buckling	buckling	NOUN
m-806	228	94	load	load	NOUN
m-806	228	95	,	,	PUNCT
m-806	228	96	δ	δ	X
m-806	228	97	=	=	PUNCT
m-806	228	98	0.03	0.03	NUM
m-806	228	99	λd	λd	NOUN
m-806	228	100	ϵ	ϵ	X
m-806	228	101	0	0	NUM
m-806	228	102	0.5	0.5	NUM
m-806	228	103	1	1	NUM
m-806	228	104	1.5	1.5	NUM
m-806	228	105	2	2	NUM
m-806	228	106	2.5	2.5	NUM
m-806	228	107	1.2	1.2	NUM
m-806	228	108	1.3	1.3	NUM
m-806	228	109	1.4	1.4	NUM
m-806	228	110	1.5	1.5	NUM
m-806	228	111	1.6	1.6	NUM
m-806	228	112	1.7	1.7	NUM
m-806	228	113	1.8	1.8	NUM
m-806	228	114	1.9	1.9	NUM
m-806	228	115	2	2	NUM
m-806	228	116	2.1d	2.1d	NUM
m-806	228	117	y	y	PROPN
m-806	228	118	n	n	DET
m-806	228	119	a	a	PROPN
m-806	228	120	m	m	NOUN
m-806	228	121	ic	ic	PROPN
m-806	228	122	b	b	NUM
m-806	228	123	u	u	X
m-806	228	124	c	c	PROPN
m-806	228	125	k	k	PROPN
m-806	228	126	li	li	PROPN
m-806	228	127	n	n	CCONJ
m-806	228	128	g	g	PROPN
m-806	228	129	l	l	NOUN
m-806	228	130	o	o	NOUN
m-806	229	1	a	a	DET
m-806	229	2	d	d	X
m-806	229	3	static	static	ADJ
m-806	229	4	buckling	buckling	NOUN
m-806	229	5	load	load	NOUN
m-806	229	6	dynamic	dynamic	ADJ
m-806	229	7	buckling	buckling	NOUN
m-806	229	8	load	load	NOUN
m-806	229	9	,	,	PUNCT
m-806	229	10	δ	δ	PROPN
m-806	229	11	=	=	SYM
m-806	229	12	0	0	NUM
m-806	229	13	dynamic	dynamic	ADJ
m-806	229	14	buckling	buckling	NOUN
m-806	229	15	load	load	NOUN
m-806	229	16	,	,	PUNCT
m-806	229	17	δ	δ	X
m-806	229	18	=	=	NOUN
m-806	229	19	0.01	0.01	NUM
m-806	229	20	dynamic	dynamic	ADJ
m-806	229	21	buckling	buckling	NOUN
m-806	229	22	load	load	NOUN
m-806	229	23	,	,	PUNCT
m-806	229	24	δ	δ	PROPN
m-806	229	25	=	=	NOUN
m-806	229	26	0.02	0.02	NUM
m-806	229	27	dynamic	dynamic	ADJ
m-806	229	28	buckling	buckling	NOUN
m-806	229	29	load	load	NOUN
m-806	229	30	,	,	PUNCT
m-806	229	31	δ	δ	X
m-806	229	32	=	=	PUNCT
m-806	229	33	0.03	0.03	NUM
m-806	229	34	λd	λd	NOUN
m-806	229	35	λs	λs	ADP
m-806	229	36	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	229	37	ijo	ijo	PROPN
m-806	229	38	journals	journal	NOUN
m-806	229	39	volume	volume	NOUN
m-806	229	40	07	07	NUM
m-806	229	41	|	|	ADV
m-806	229	42	issue	issue	NOUN
m-806	229	43	02	02	NUM
m-806	229	44	|	|	CCONJ
m-806	229	45	february	february	PROPN
m-806	229	46	2024	2024	NUM
m-806	229	47	|	|	ADV
m-806	229	48	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	229	49	29	29	NUM
m-806	229	50	ijo	ijo	PROPN
m-806	229	51	international	international	PROPN
m-806	229	52	journal	journal	PROPN
m-806	229	53	of	of	ADP
m-806	229	54	mathematics	mathematics	PROPN
m-806	229	55	(	(	PUNCT
m-806	229	56	issn	issn	PROPN
m-806	229	57	:	:	PUNCT
m-806	229	58	2992	2992	NUM
m-806	229	59	-	-	SYM
m-806	229	60	4421	4421	NUM
m-806	229	61	)	)	PUNCT
m-806	230	1	i.u	i.u	PROPN
m-806	230	2	.	.	PROPN
m-806	230	3	udo	udo	PROPN
m-806	230	4	-	-	PROPN
m-806	230	5	akpan1	akpan1	ADJ
m-806	230	6	*	*	PUNCT
m-806	230	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	230	8	volume	volume	NOUN
m-806	230	9	07	07	NUM
m-806	230	10	issue	issue	NOUN
m-806	230	11	02	02	NUM
m-806	230	12	||	||	NUM
m-806	230	13	february	february	PROPN
m-806	230	14	,	,	PUNCT
m-806	230	15	2024	2024	NUM
m-806	230	16	||	||	NOUN
m-806	231	1	on	on	ADP
m-806	231	2	a	a	DET
m-806	231	3	-	-	PUNCT
m-806	231	4	two	two	NUM
m-806	231	5	-	-	PUNCT
m-806	231	6	parameter	parameter	NOUN
m-806	231	7	dynamic	dynamic	ADJ
m-806	231	8	buckling	buckling	NOUN
m-806	231	9	of	of	ADP
m-806	231	10	a	a	DET
m-806	231	11	viscously	viscously	ADV
m-806	231	12	damped	damp	VERB
m-806	231	13	but	but	CCONJ
m-806	231	14	clamped	clamp	VERB
m-806	231	15	column	column	NOUN
m-806	231	16	stressed	stress	VERB
m-806	231	17	by	by	ADP
m-806	231	18	a	a	DET
m-806	231	19	step	step	NOUN
m-806	231	20	load	load	NOUN
m-806	231	21	such	such	ADJ
m-806	231	22	rise	rise	NOUN
m-806	231	23	is	be	AUX
m-806	231	24	the	the	DET
m-806	231	25	undamped	undampe	VERB
m-806	231	26	case	case	NOUN
m-806	231	27	.	.	PUNCT
m-806	232	1	it	it	PRON
m-806	232	2	is	be	AUX
m-806	232	3	not	not	PART
m-806	232	4	clear	clear	ADJ
m-806	232	5	whether	whether	SCONJ
m-806	232	6	such	such	DET
m-806	232	7	a	a	DET
m-806	232	8	result	result	NOUN
m-806	232	9	is	be	AUX
m-806	232	10	specific	specific	ADJ
m-806	232	11	to	to	PART
m-806	232	12	clamped	clamp	VERB
m-806	232	13	boundary	boundary	ADJ
m-806	232	14	conditions	condition	NOUN
m-806	232	15	or	or	CCONJ
m-806	232	16	whether	whether	SCONJ
m-806	232	17	it	it	PRON
m-806	232	18	is	be	AUX
m-806	232	19	general	general	ADJ
m-806	232	20	.	.	PUNCT
m-806	233	1	as	as	ADP
m-806	233	2	in	in	ADP
m-806	233	3	the	the	DET
m-806	233	4	static	static	ADJ
m-806	233	5	loading	loading	NOUN
m-806	233	6	case	case	NOUN
m-806	233	7	,	,	PUNCT
m-806	233	8	the	the	DET
m-806	233	9	inequality	inequality	NOUN
m-806	233	10	satisfied	satisfy	VERB
m-806	233	11	by	by	ADP
m-806	233	12	the	the	DET
m-806	233	13	clamped	clamp	VERB
m-806	233	14	column	column	NOUN
m-806	233	15	is	be	AUX
m-806	233	16	1	1	NUM
m-806	233	17	<	<	X
m-806	233	18	�	�	PROPN
m-806	233	19	�	�	PROPN
m-806	233	20	<	<	X
m-806	233	21	2.125	2.125	NUM
m-806	233	22	.	.	PUNCT
m-806	234	1	we	we	PRON
m-806	234	2	thus	thus	ADV
m-806	234	3	observe	observe	VERB
m-806	234	4	that	that	SCONJ
m-806	234	5	generally	generally	ADV
m-806	234	6	,	,	PUNCT
m-806	234	7	whether	whether	SCONJ
m-806	234	8	in	in	ADP
m-806	234	9	the	the	DET
m-806	234	10	static	static	ADJ
m-806	234	11	or	or	CCONJ
m-806	234	12	dynamic	dynamic	ADJ
m-806	234	13	loading	loading	NOUN
m-806	234	14	cases	case	NOUN
m-806	234	15	,	,	PUNCT
m-806	234	16	clamped	clamp	VERB
m-806	234	17	columns	column	NOUN
m-806	234	18	buckle	buckle	VERB
m-806	234	19	at	at	ADP
m-806	234	20	much	much	ADV
m-806	234	21	more	more	ADV
m-806	234	22	higher	high	ADJ
m-806	234	23	loads	load	NOUN
m-806	234	24	than	than	ADP
m-806	234	25	similar	similar	ADJ
m-806	234	26	columns	column	NOUN
m-806	234	27	with	with	ADP
m-806	234	28	simply	simply	ADV
m-806	234	29	–	–	PUNCT
m-806	234	30	supported	support	VERB
m-806	234	31	boundary	boundary	ADJ
m-806	234	32	supports	support	NOUN
m-806	234	33	.	.	PUNCT
m-806	235	1	for	for	ADP
m-806	235	2	reasons	reason	NOUN
m-806	235	3	attributed	attribute	VERB
m-806	235	4	to	to	ADP
m-806	235	5	nonlinearity	nonlinearity	NOUN
m-806	235	6	and	and	CCONJ
m-806	235	7	imperfection	imperfection	NOUN
m-806	235	8	,	,	PUNCT
m-806	235	9	clamped	clamp	VERB
m-806	235	10	columns	column	NOUN
m-806	235	11	on	on	ADP
m-806	235	12	nonlinear	nonlinear	ADJ
m-806	235	13	elastic	elastic	ADJ
m-806	235	14	foundations	foundation	NOUN
m-806	235	15	buckle	buckle	NOUN
m-806	235	16	at	at	ADP
m-806	235	17	lower	low	ADJ
m-806	235	18	values	value	NOUN
m-806	235	19	of	of	ADP
m-806	235	20	buckling	buckle	VERB
m-806	235	21	loads	load	NOUN
m-806	235	22	than	than	ADP
m-806	235	23	the	the	DET
m-806	235	24	corresponding	corresponding	ADJ
m-806	235	25	classical	classical	ADJ
m-806	235	26	buckling	buckling	NOUN
m-806	235	27	load	load	NOUN
m-806	235	28	of	of	ADP
m-806	235	29	the	the	DET
m-806	235	30	column	column	NOUN
m-806	235	31	.	.	PUNCT
m-806	236	1	we	we	PRON
m-806	236	2	observe	observe	VERB
m-806	236	3	that	that	SCONJ
m-806	236	4	while	while	SCONJ
m-806	236	5	the	the	DET
m-806	236	6	buckling	buckle	VERB
m-806	236	7	modes	mode	NOUN
m-806	236	8	split	split	VERB
m-806	236	9	into	into	ADP
m-806	236	10	three	three	NUM
m-806	236	11	distinct	distinct	ADJ
m-806	236	12	modes	mode	NOUN
m-806	236	13	proportional	proportional	ADJ
m-806	236	14	to	to	ADP
m-806	236	15	(	(	PUNCT
m-806	236	16	1	1	NUM
m-806	236	17	−	−	PROPN
m-806	236	18	cos	cos	PROPN
m-806	236	19	2	2	NUM
m-806	236	20	�	�	PROPN
m-806	236	21	�	�	PROPN
m-806	236	22	)	)	PUNCT
m-806	236	23	,	,	PUNCT
m-806	236	24	(	(	PUNCT
m-806	236	25	1	1	NUM
m-806	236	26	−	−	PROPN
m-806	236	27	cos	cos	PROPN
m-806	236	28	4	4	NUM
m-806	236	29	�	�	PROPN
m-806	236	30	�	�	PROPN
m-806	236	31	)	)	PUNCT
m-806	236	32	and	and	CCONJ
m-806	236	33	(	(	PUNCT
m-806	236	34	1	1	NUM
m-806	236	35	−	−	PROPN
m-806	236	36	cos	cos	PROPN
m-806	236	37	6	6	NUM
m-806	236	38	�	�	PROPN
m-806	236	39	�	�	PROPN
m-806	236	40	)	)	PUNCT
m-806	236	41	,	,	PUNCT
m-806	236	42	it	it	PRON
m-806	236	43	is	be	AUX
m-806	236	44	only	only	ADV
m-806	236	45	the	the	DET
m-806	236	46	buckling	buckle	VERB
m-806	236	47	modes	mode	NOUN
m-806	236	48	in	in	ADP
m-806	236	49	the	the	DET
m-806	236	50	shapes	shape	NOUN
m-806	236	51	of	of	ADP
m-806	236	52	(	(	PUNCT
m-806	236	53	1	1	NUM
m-806	236	54	−	−	PROPN
m-806	236	55	cos	cos	PROPN
m-806	236	56	2	2	NUM
m-806	236	57	�	�	PROPN
m-806	236	58	�	�	PROPN
m-806	236	59	)	)	PUNCT
m-806	236	60	and	and	CCONJ
m-806	236	61	(	(	PUNCT
m-806	236	62	1	1	NUM
m-806	236	63	−	−	PROPN
m-806	236	64	cos	cos	PROPN
m-806	236	65	6	6	NUM
m-806	236	66	�	�	PROPN
m-806	236	67	�	�	PROPN
m-806	236	68	)	)	PUNCT
m-806	236	69	that	that	PRON
m-806	236	70	eventually	eventually	ADV
m-806	236	71	contribute	contribute	VERB
m-806	236	72	to	to	ADP
m-806	236	73	dynamic	dynamic	ADJ
m-806	236	74	buckling	buckling	NOUN
m-806	236	75	.	.	PUNCT
m-806	237	1	the	the	DET
m-806	237	2	mode	mode	NOUN
m-806	237	3	in	in	ADP
m-806	237	4	the	the	DET
m-806	237	5	shape	shape	NOUN
m-806	237	6	of	of	ADP
m-806	237	7	(	(	PUNCT
m-806	237	8	1	1	NUM
m-806	237	9	−	−	PROPN
m-806	237	10	cos	cos	PROPN
m-806	237	11	4	4	NUM
m-806	237	12	�	�	PROPN
m-806	237	13	�	�	PROPN
m-806	237	14	)	)	PUNCT
m-806	237	15	does	do	AUX
m-806	237	16	not	not	PART
m-806	237	17	contribute	contribute	VERB
m-806	237	18	.	.	PUNCT
m-806	238	1	lastly	lastly	ADV
m-806	238	2	,	,	PUNCT
m-806	238	3	as	as	SCONJ
m-806	238	4	seen	see	VERB
m-806	238	5	in	in	ADP
m-806	238	6	equations	equation	NOUN
m-806	238	7	(	(	PUNCT
m-806	238	8	8.20	8.20	NUM
m-806	238	9	)	)	PUNCT
m-806	238	10	and	and	CCONJ
m-806	238	11	(	(	PUNCT
m-806	238	12	8.22	8.22	NUM
m-806	238	13	)	)	PUNCT
m-806	238	14	,	,	PUNCT
m-806	238	15	we	we	PRON
m-806	238	16	are	be	AUX
m-806	238	17	able	able	ADJ
m-806	238	18	to	to	PART
m-806	238	19	directly	directly	ADV
m-806	238	20	relate	relate	VERB
m-806	238	21	�	�	PROPN
m-806	238	22	�	�	PROPN
m-806	238	23	to	to	PART
m-806	238	24	�	�	VERB
m-806	238	25	�	�	PROPN
m-806	238	26	even	even	ADV
m-806	238	27	without	without	ADP
m-806	238	28	the	the	DET
m-806	238	29	knowledge	knowledge	NOUN
m-806	238	30	of	of	ADP
m-806	238	31	the	the	DET
m-806	238	32	size	size	NOUN
m-806	238	33	of	of	ADP
m-806	238	34	the	the	DET
m-806	238	35	associated	associated	ADJ
m-806	238	36	imperfection	imperfection	NOUN
m-806	238	37	.	.	PUNCT
m-806	239	1	in	in	ADP
m-806	239	2	this	this	DET
m-806	239	3	way	way	NOUN
m-806	239	4	,	,	PUNCT
m-806	239	5	we	we	PRON
m-806	239	6	have	have	AUX
m-806	239	7	circumvented	circumvent	VERB
m-806	239	8	the	the	DET
m-806	239	9	process	process	NOUN
m-806	239	10	of	of	ADP
m-806	239	11	repeating	repeat	VERB
m-806	239	12	the	the	DET
m-806	239	13	arduous	arduous	ADJ
m-806	239	14	manipulations	manipulation	NOUN
m-806	239	15	for	for	ADP
m-806	239	16	different	different	ADJ
m-806	239	17	imperfection	imperfection	NOUN
m-806	239	18	parameters	parameter	NOUN
m-806	239	19	.	.	PUNCT
m-806	240	1	11	11	NUM
m-806	240	2	.	.	PUNCT
m-806	241	1	conclusion	conclusion	NOUN
m-806	241	2	we	we	PRON
m-806	241	3	have	have	AUX
m-806	241	4	carried	carry	VERB
m-806	241	5	out	out	ADP
m-806	241	6	an	an	DET
m-806	241	7	analytical	analytical	ADJ
m-806	241	8	investigation	investigation	NOUN
m-806	241	9	of	of	ADP
m-806	241	10	the	the	DET
m-806	241	11	buckling	buckling	NOUN
m-806	241	12	of	of	ADP
m-806	241	13	an	an	DET
m-806	241	14	imperfect	imperfect	ADJ
m-806	241	15	clamped	clamp	VERB
m-806	241	16	column	column	NOUN
m-806	241	17	lying	lie	VERB
m-806	241	18	on	on	ADP
m-806	241	19	a	a	DET
m-806	241	20	nonlinear	nonlinear	ADJ
m-806	241	21	elastic	elastic	ADJ
m-806	241	22	foundation	foundation	NOUN
m-806	241	23	but	but	CCONJ
m-806	241	24	struck	strike	VERB
m-806	241	25	axially	axially	ADV
m-806	241	26	by	by	ADP
m-806	241	27	a	a	DET
m-806	241	28	step	step	NOUN
m-806	241	29	load	load	NOUN
m-806	241	30	.	.	PUNCT
m-806	242	1	it	it	PRON
m-806	242	2	is	be	AUX
m-806	242	3	our	our	PRON
m-806	242	4	contention	contention	NOUN
m-806	242	5	that	that	SCONJ
m-806	242	6	similar	similar	ADJ
m-806	242	7	enquiries	enquiry	NOUN
m-806	242	8	can	can	AUX
m-806	242	9	be	be	AUX
m-806	242	10	extended	extend	VERB
m-806	242	11	to	to	ADP
m-806	242	12	other	other	ADJ
m-806	242	13	loading	loading	NOUN
m-806	242	14	conditions	condition	NOUN
m-806	242	15	apart	apart	ADV
m-806	242	16	from	from	ADP
m-806	242	17	step	step	NOUN
m-806	242	18	load	load	NOUN
m-806	242	19	and	and	CCONJ
m-806	242	20	to	to	ADP
m-806	242	21	other	other	ADJ
m-806	242	22	structures	structure	NOUN
m-806	242	23	apart	apart	ADV
m-806	242	24	from	from	ADP
m-806	242	25	columns	column	NOUN
m-806	242	26	.	.	PUNCT
m-806	243	1	acknowledgements	acknowledgement	NOUN
m-806	243	2	:	:	PUNCT
m-806	244	1	authors	author	NOUN
m-806	244	2	acknowledge	acknowledge	VERB
m-806	244	3	the	the	DET
m-806	244	4	valuable	valuable	ADJ
m-806	244	5	contribution	contribution	NOUN
m-806	244	6	their	their	PRON
m-806	244	7	mentor	mentor	NOUN
m-806	244	8	,	,	PUNCT
m-806	244	9	prof	prof	PROPN
m-806	244	10	.	.	PUNCT
m-806	244	11	a.m.	a.m.	PROPN
m-806	245	1	ette	ette	PROPN
m-806	245	2	(	(	PUNCT
m-806	245	3	fnms	fnms	NOUN
m-806	245	4	)	)	PUNCT
m-806	245	5	,	,	PUNCT
m-806	245	6	for	for	ADP
m-806	245	7	his	his	PRON
m-806	245	8	guardian	guardian	NOUN
m-806	245	9	and	and	CCONJ
m-806	245	10	support	support	NOUN
m-806	245	11	on	on	ADP
m-806	245	12	this	this	DET
m-806	245	13	work	work	NOUN
m-806	245	14	.	.	PUNCT
m-806	246	1	references	reference	NOUN
m-806	246	2	[	[	X
m-806	246	3	1	1	NUM
m-806	246	4	]	]	PUNCT
m-806	246	5	timoshenko	timoshenko	NOUN
m-806	246	6	,	,	PUNCT
m-806	246	7	s.p	s.p	PROPN
m-806	246	8	.	.	PROPN
m-806	246	9	and	and	CCONJ
m-806	246	10	gere	gere	PROPN
m-806	246	11	,	,	PUNCT
m-806	246	12	j.m	j.m	PROPN
m-806	246	13	.	.	PROPN
m-806	246	14	,	,	PUNCT
m-806	246	15	theory	theory	NOUN
m-806	246	16	of	of	ADP
m-806	246	17	elastic	elastic	ADJ
m-806	246	18	stability	stability	NOUN
m-806	246	19	,	,	PUNCT
m-806	246	20	dover	dover	PROPN
m-806	246	21	publications	publication	NOUN
m-806	246	22	,	,	PUNCT
m-806	246	23	london	london	PROPN
m-806	246	24	.	.	PUNCT
m-806	246	25	2012	2012	NUM
m-806	246	26	.	.	PUNCT
m-806	247	1	[	[	X
m-806	247	2	2	2	NUM
m-806	247	3	]	]	X
m-806	247	4	thompson	thompson	PROPN
m-806	247	5	,	,	PUNCT
m-806	247	6	j.	j.	PROPN
m-806	247	7	m.	m.	PROPN
m-806	247	8	t.	t.	PROPN
m-806	247	9	and	and	CCONJ
m-806	247	10	hunt	hunt	PROPN
m-806	247	11	,	,	PUNCT
m-806	247	12	g.	g.	PROPN
m-806	247	13	w.	w.	PROPN
m-806	247	14	,a	,a	PUNCT
m-806	247	15	general	general	ADJ
m-806	247	16	theory	theory	NOUN
m-806	247	17	of	of	ADP
m-806	247	18	elastic	elastic	ADJ
m-806	247	19	stability	stability	NOUN
m-806	247	20	,	,	PUNCT
m-806	247	21	john	john	PROPN
m-806	247	22	wiley	wiley	PROPN
m-806	247	23	and	and	CCONJ
m-806	247	24	sons	sons	PROPN
m-806	247	25	ltd	ltd	PROPN
m-806	247	26	.	.	PROPN
m-806	247	27	,	,	PUNCT
m-806	247	28	london	london	PROPN
m-806	247	29	.	.	PUNCT
m-806	248	1	1973	1973	NUM
m-806	248	2	.	.	PUNCT
m-806	249	1	[	[	X
m-806	249	2	3	3	NUM
m-806	249	3	]	]	SYM
m-806	249	4	hu	hu	PROPN
m-806	249	5	,	,	PUNCT
m-806	249	6	n.	n.	NOUN
m-806	249	7	and	and	CCONJ
m-806	249	8	burgue	burgue	PROPN
m-806	249	9	�	�	PROPN
m-806	249	10	�	�	PROPN
m-806	249	11	o	o	PROPN
m-806	249	12	,	,	PUNCT
m-806	249	13	r.	r.	PROPN
m-806	249	14	,elastic	,elastic	PUNCT
m-806	249	15	postbuckling	postbuckle	VERB
m-806	249	16	response	response	NOUN
m-806	249	17	of	of	ADP
m-806	249	18	axially	axially	ADV
m-806	249	19	–	–	PUNCT
m-806	249	20	loaded	load	VERB
m-806	249	21	cylindrical	cylindrical	ADJ
m-806	249	22	shells	shell	NOUN
m-806	249	23	with	with	ADP
m-806	249	24	seeded	seeded	ADJ
m-806	249	25	geometric	geometric	ADJ
m-806	249	26	imperfection	imperfection	NOUN
m-806	249	27	design	design	NOUN
m-806	249	28	;	;	PUNCT
m-806	249	29	thin	thin	ADJ
m-806	249	30	–	–	PUNCT
m-806	249	31	walled	walled	ADJ
m-806	249	32	structures	structure	NOUN
m-806	249	33	,	,	PUNCT
m-806	249	34	96	96	NUM
m-806	249	35	,	,	PUNCT
m-806	249	36	256	256	NUM
m-806	249	37	–	–	PUNCT
m-806	249	38	268	268	NUM
m-806	249	39	,	,	PUNCT
m-806	249	40	2015	2015	NUM
m-806	249	41	.	.	PUNCT
m-806	250	1	[	[	X
m-806	250	2	4	4	NUM
m-806	250	3	]	]	X
m-806	250	4	amazigo	amazigo	PROPN
m-806	250	5	,	,	PUNCT
m-806	250	6	j.	j.	PROPN
m-806	250	7	c.	c.	PROPN
m-806	250	8	,	,	PUNCT
m-806	250	9	budiansky	budiansky	NOUN
m-806	250	10	,	,	PUNCT
m-806	250	11	b.	b.	PROPN
m-806	250	12	and	and	CCONJ
m-806	250	13	carrier	carrier	NOUN
m-806	250	14	,	,	PUNCT
m-806	250	15	g.	g.	PROPN
m-806	250	16	f.	f.	PROPN
m-806	250	17	,asymptotic	,asymptotic	PUNCT
m-806	250	18	analyses	analysis	NOUN
m-806	250	19	of	of	ADP
m-806	250	20	the	the	DET
m-806	250	21	buckling	buckling	NOUN
m-806	250	22	of	of	ADP
m-806	250	23	imperfect	imperfect	ADJ
m-806	250	24	columns	column	NOUN
m-806	250	25	on	on	ADP
m-806	250	26	nonlinear	nonlinear	ADJ
m-806	250	27	elastic	elastic	ADJ
m-806	250	28	foundations	foundation	NOUN
m-806	250	29	,	,	PUNCT
m-806	250	30	int	int	NOUN
m-806	250	31	.	.	PUNCT
m-806	251	1	j.	j.	PROPN
m-806	251	2	solids	solids	PROPN
m-806	251	3	structures	structure	NOUN
m-806	251	4	,	,	PUNCT
m-806	251	5	10	10	NUM
m-806	251	6	,	,	PUNCT
m-806	251	7	1342	1342	NUM
m-806	251	8	–	–	PUNCT
m-806	251	9	1356	1356	NUM
m-806	251	10	,	,	PUNCT
m-806	251	11	1970	1970	NUM
m-806	251	12	.	.	PUNCT
m-806	252	1	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	252	2	ijo	ijo	PROPN
m-806	252	3	journals	journal	NOUN
m-806	252	4	volume	volume	NOUN
m-806	252	5	07	07	NUM
m-806	252	6	|	|	ADV
m-806	252	7	issue	issue	NOUN
m-806	252	8	02	02	NUM
m-806	252	9	|	|	CCONJ
m-806	252	10	february	february	PROPN
m-806	252	11	2024	2024	NUM
m-806	252	12	|	|	ADV
m-806	252	13	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	252	14	30	30	NUM
m-806	252	15	ijo	ijo	PROPN
m-806	252	16	international	international	PROPN
m-806	252	17	journal	journal	PROPN
m-806	252	18	of	of	ADP
m-806	252	19	mathematics	mathematics	PROPN
m-806	252	20	(	(	PUNCT
m-806	252	21	issn	issn	PROPN
m-806	252	22	:	:	PUNCT
m-806	252	23	2992	2992	NUM
m-806	252	24	-	-	SYM
m-806	252	25	4421	4421	NUM
m-806	252	26	)	)	PUNCT
m-806	253	1	i.u	i.u	PROPN
m-806	253	2	.	.	PROPN
m-806	253	3	udo	udo	PROPN
m-806	253	4	-	-	PROPN
m-806	253	5	akpan1	akpan1	ADJ
m-806	253	6	*	*	PUNCT
m-806	253	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	253	8	volume	volume	NOUN
m-806	253	9	07	07	NUM
m-806	253	10	issue	issue	NOUN
m-806	253	11	02	02	NUM
m-806	253	12	||	||	NUM
m-806	253	13	february	february	PROPN
m-806	253	14	,	,	PUNCT
m-806	253	15	2024	2024	NUM
m-806	253	16	||	||	NOUN
m-806	254	1	on	on	ADP
m-806	254	2	a	a	DET
m-806	254	3	-	-	PUNCT
m-806	254	4	two	two	NUM
m-806	254	5	-	-	PUNCT
m-806	254	6	parameter	parameter	NOUN
m-806	254	7	dynamic	dynamic	ADJ
m-806	254	8	buckling	buckling	NOUN
m-806	254	9	of	of	ADP
m-806	254	10	a	a	DET
m-806	254	11	viscously	viscously	ADV
m-806	254	12	damped	damp	VERB
m-806	254	13	but	but	CCONJ
m-806	254	14	clamped	clamp	VERB
m-806	254	15	column	column	NOUN
m-806	254	16	stressed	stress	VERB
m-806	254	17	by	by	ADP
m-806	254	18	a	a	DET
m-806	254	19	step	step	NOUN
m-806	254	20	load	load	NOUN
m-806	255	1	[	[	X
m-806	255	2	5	5	NUM
m-806	255	3	]	]	X
m-806	255	4	qiang	qiang	PROPN
m-806	255	5	,	,	PUNCT
m-806	255	6	h.	h.	PROPN
m-806	255	7	,	,	PUNCT
m-806	255	8	zhang	zhang	PROPN
m-806	255	9	,	,	PUNCT
m-806	255	10	s.	s.	PROPN
m-806	255	11	and	and	CCONJ
m-806	255	12	yang	yang	PROPN
m-806	255	13	,	,	PUNCT
m-806	255	14	g.	g.	PROPN
m-806	255	15	,the	,the	PUNCT
m-806	255	16	asymptotic	asymptotic	ADJ
m-806	255	17	solution	solution	NOUN
m-806	255	18	of	of	ADP
m-806	255	19	a	a	DET
m-806	255	20	dynamic	dynamic	ADJ
m-806	255	21	buckling	buckling	NOUN
m-806	255	22	problem	problem	NOUN
m-806	255	23	in	in	ADP
m-806	255	24	elastic	elastic	ADJ
m-806	255	25	column	column	NOUN
m-806	255	26	,	,	PUNCT
m-806	255	27	appl	appl	PROPN
m-806	255	28	.	.	PUNCT
m-806	255	29	maths	maths	PROPN
m-806	255	30	.	.	PUNCT
m-806	256	1	and	and	CCONJ
m-806	256	2	mech	mech	NOUN
m-806	256	3	.	.	PUNCT
m-806	257	1	(	(	PUNCT
m-806	257	2	english	english	PROPN
m-806	257	3	edition)20(8	edition)20(8	PROPN
m-806	257	4	)	)	PUNCT
m-806	257	5	,	,	PUNCT
m-806	257	6	867	867	NUM
m-806	257	7	–	–	PUNCT
m-806	257	8	872	872	NUM
m-806	257	9	,	,	PUNCT
m-806	257	10	1999	1999	NUM
m-806	257	11	.	.	PUNCT
m-806	258	1	[	[	X
m-806	258	2	6	6	NUM
m-806	258	3	]	]	SYM
m-806	258	4	amazigo	amazigo	PROPN
m-806	258	5	,	,	PUNCT
m-806	258	6	j.	j.	PROPN
m-806	258	7	c.	c.	PROPN
m-806	258	8	and	and	CCONJ
m-806	258	9	frank	frank	PROPN
m-806	258	10	,	,	PUNCT
m-806	258	11	d.	d.	PROPN
m-806	258	12	,dynamic	,dynamic	PUNCT
m-806	258	13	buckling	buckle	VERB
m-806	258	14	of	of	ADP
m-806	258	15	an	an	DET
m-806	258	16	imperfect	imperfect	ADJ
m-806	258	17	column	column	NOUN
m-806	258	18	on	on	ADP
m-806	258	19	a	a	DET
m-806	258	20	nonlinear	nonlinear	ADJ
m-806	258	21	foundation	foundation	NOUN
m-806	258	22	,	,	PUNCT
m-806	258	23	quart	quart	NOUN
m-806	258	24	.	.	PUNCT
m-806	259	1	appl	appl	PROPN
m-806	259	2	.	.	PROPN
m-806	259	3	math	math	PROPN
m-806	259	4	.	.	PUNCT
m-806	259	5	,	,	PUNCT
m-806	259	6	31(6	31(6	NUM
m-806	259	7	)	)	PUNCT
m-806	259	8	,	,	PUNCT
m-806	259	9	1	1	NUM
m-806	259	10	–	–	PUNCT
m-806	259	11	9	9	NUM
m-806	259	12	,	,	PUNCT
m-806	259	13	1973	1973	NUM
m-806	259	14	.	.	PUNCT
m-806	260	1	[	[	X
m-806	260	2	7	7	NUM
m-806	260	3	]	]	X
m-806	260	4	artem	artem	PROPN
m-806	260	5	,	,	PUNCT
m-806	260	6	h.	h.	PROPN
m-806	260	7	s.	s.	PROPN
m-806	260	8	and	and	CCONJ
m-806	260	9	aydin	aydin	PROPN
m-806	260	10	,	,	PUNCT
m-806	260	11	l.	l.	NOUN
m-806	260	12	,exact	,exact	PUNCT
m-806	260	13	solution	solution	NOUN
m-806	260	14	and	and	CCONJ
m-806	260	15	dynamic	dynamic	ADJ
m-806	260	16	buckling	buckling	NOUN
m-806	260	17	analysis	analysis	NOUN
m-806	260	18	of	of	ADP
m-806	260	19	a	a	DET
m-806	260	20	beam	beam	NOUN
m-806	260	21	–	–	PUNCT
m-806	260	22	column	column	NOUN
m-806	260	23	loading	loading	NOUN
m-806	260	24	.	.	PUNCT
m-806	261	1	appl	appl	PROPN
m-806	261	2	.	.	PROPN
m-806	261	3	math	math	PROPN
m-806	261	4	.	.	PUNCT
m-806	262	1	and	and	CCONJ
m-806	262	2	mech	mech	NOUN
m-806	262	3	.	.	PUNCT
m-806	263	1	31(10	31(10	NUM
m-806	263	2	)	)	PUNCT
m-806	263	3	,	,	PUNCT
m-806	263	4	1317	1317	NUM
m-806	263	5	–	–	PUNCT
m-806	263	6	1324	1324	NUM
m-806	263	7	,	,	PUNCT
m-806	263	8	2010	2010	NUM
m-806	263	9	.	.	PUNCT
m-806	264	1	[	[	X
m-806	264	2	8	8	NUM
m-806	264	3	]	]	X
m-806	264	4	ette	ette	NOUN
m-806	264	5	,	,	PUNCT
m-806	264	6	a.	a.	NOUN
m-806	264	7	m.	m.	NOUN
m-806	264	8	,	,	PUNCT
m-806	264	9	chukwuchekwa	chukwuchekwa	PROPN
m-806	264	10	,	,	PUNCT
m-806	264	11	j.	j.	PROPN
m-806	264	12	u.	u.	PROPN
m-806	264	13	and	and	CCONJ
m-806	264	14	udo	udo	PROPN
m-806	264	15	–	–	PUNCT
m-806	264	16	akpan	akpan	ADJ
m-806	264	17	,	,	PUNCT
m-806	264	18	i.	i.	PROPN
m-806	264	19	u.	u.	PROPN
m-806	264	20	,on	,on	PUNCT
m-806	264	21	the	the	DET
m-806	264	22	buckling	buckling	NOUN
m-806	264	23	of	of	ADP
m-806	264	24	a	a	DET
m-806	264	25	clamped	clamp	VERB
m-806	264	26	viscously	viscously	ADV
m-806	264	27	damped	damp	VERB
m-806	264	28	column	column	NOUN
m-806	264	29	trapped	trap	VERB
m-806	264	30	by	by	ADP
m-806	264	31	a	a	DET
m-806	264	32	step	step	NOUN
m-806	264	33	load	load	NOUN
m-806	264	34	.	.	PUNCT
m-806	265	1	int	int	NOUN
m-806	265	2	.	.	PUNCT
m-806	266	1	j.	j.	PROPN
m-806	266	2	of	of	ADP
m-806	266	3	appl	appl	PROPN
m-806	266	4	.	.	PUNCT
m-806	267	1	sciences	science	NOUN
m-806	267	2	and	and	CCONJ
m-806	267	3	mathematics	mathematic	NOUN
m-806	267	4	,	,	PUNCT
m-806	267	5	3	3	NUM
m-806	267	6	(	(	PUNCT
m-806	267	7	2	2	NUM
m-806	267	8	)	)	PUNCT
m-806	267	9	,	,	PUNCT
m-806	267	10	117	117	NUM
m-806	267	11	–	–	SYM
m-806	267	12	123	123	NUM
m-806	267	13	,	,	PUNCT
m-806	267	14	2016	2016	NUM
m-806	267	15	.	.	PUNCT
m-806	268	1	[	[	X
m-806	268	2	9	9	NUM
m-806	268	3	]	]	PUNCT
m-806	268	4	udo	udo	NOUN
m-806	268	5	-	-	PUNCT
m-806	268	6	akpan	akpan	NOUN
m-806	268	7	,	,	PUNCT
m-806	268	8	i.u	i.u	PROPN
m-806	268	9	.	.	PROPN
m-806	268	10	and	and	CCONJ
m-806	268	11	ette	ette	NOUN
m-806	268	12	,	,	PUNCT
m-806	268	13	a.m.	a.m.	ADV
m-806	268	14	,on	,on	PUNCT
m-806	268	15	the	the	DET
m-806	268	16	dynamic	dynamic	ADJ
m-806	268	17	buckling	buckling	NOUN
m-806	268	18	of	of	ADP
m-806	268	19	a	a	DET
m-806	268	20	model	model	NOUN
m-806	268	21	structure	structure	NOUN
m-806	268	22	with	with	ADP
m-806	268	23	quadratic	quadratic	ADJ
m-806	268	24	nonlinearity	nonlinearity	NOUN
m-806	268	25	struck	strike	VERB
m-806	268	26	by	by	ADP
m-806	268	27	a	a	DET
m-806	268	28	step	step	NOUN
m-806	268	29	load	load	NOUN
m-806	268	30	superposed	superpose	VERB
m-806	268	31	on	on	ADP
m-806	268	32	a	a	DET
m-806	268	33	quasi	quasi	NOUN
m-806	268	34	–	–	PUNCT
m-806	268	35	static	static	ADJ
m-806	268	36	load	load	NOUN
m-806	268	37	,	,	PUNCT
m-806	268	38	j.	j.	PROPN
m-806	268	39	of	of	ADP
m-806	268	40	the	the	DET
m-806	268	41	nigerian	nigerian	PROPN
m-806	268	42	assoc	assoc	PROPN
m-806	268	43	.	.	PUNCT
m-806	269	1	of	of	ADP
m-806	269	2	math	math	NOUN
m-806	269	3	.	.	PUNCT
m-806	270	1	physics	physics	NOUN
m-806	270	2	,	,	PUNCT
m-806	270	3	35	35	NUM
m-806	270	4	,	,	PUNCT
m-806	270	5	461	461	NUM
m-806	270	6	-	-	SYM
m-806	270	7	472	472	NUM
m-806	270	8	,	,	PUNCT
m-806	270	9	2016	2016	NUM
m-806	270	10	.	.	PUNCT
m-806	271	1	[	[	X
m-806	271	2	10	10	NUM
m-806	271	3	]	]	X
m-806	271	4	ette	ette	NOUN
m-806	271	5	,	,	PUNCT
m-806	271	6	a.m.	a.m.	NOUN
m-806	271	7	and	and	CCONJ
m-806	271	8	udo	udo	NOUN
m-806	271	9	-	-	PUNCT
m-806	271	10	akpan	akpan	NOUN
m-806	271	11	,	,	PUNCT
m-806	271	12	i.u	i.u	PROPN
m-806	271	13	.	.	PROPN
m-806	271	14	,on	,on	PUNCT
m-806	271	15	the	the	DET
m-806	271	16	buckling	buckling	NOUN
m-806	271	17	of	of	ADP
m-806	271	18	a	a	DET
m-806	271	19	pre	pre	ADJ
m-806	271	20	-	-	ADJ
m-806	271	21	statically	statically	ADV
m-806	271	22	loaded	load	VERB
m-806	271	23	but	but	CCONJ
m-806	271	24	viscously	viscously	ADV
m-806	271	25	damped	damp	VERB
m-806	271	26	quadratic	quadratic	ADJ
m-806	271	27	model	model	NOUN
m-806	271	28	structure	structure	NOUN
m-806	271	29	trapped	trap	VERB
m-806	271	30	by	by	ADP
m-806	271	31	a	a	DET
m-806	271	32	step	step	NOUN
m-806	271	33	load	load	NOUN
m-806	271	34	,	,	PUNCT
m-806	271	35	global	global	ADJ
m-806	271	36	j.	j.	PROPN
m-806	271	37	of	of	ADP
m-806	271	38	mathematics	mathematic	NOUN
m-806	271	39	,	,	PUNCT
m-806	271	40	7	7	NUM
m-806	271	41	(	(	PUNCT
m-806	271	42	2	2	NUM
m-806	271	43	)	)	PUNCT
m-806	271	44	,	,	PUNCT
m-806	271	45	761	761	NUM
m-806	271	46	–	–	PUNCT
m-806	271	47	770	770	NUM
m-806	271	48	,	,	PUNCT
m-806	271	49	2016	2016	NUM
m-806	271	50	.	.	PUNCT
m-806	272	1	[	[	X
m-806	272	2	11	11	NUM
m-806	272	3	]	]	X
m-806	272	4	chukwuchekwa	chukwuchekwa	PROPN
m-806	272	5	,	,	PUNCT
m-806	272	6	j.	j.	PROPN
m-806	272	7	u.	u.	PROPN
m-806	272	8	and	and	CCONJ
m-806	272	9	ette	ette	PROPN
m-806	272	10	,	,	PUNCT
m-806	272	11	a.	a.	NOUN
m-806	272	12	m.	m.	NOUN
m-806	272	13	,asymptotic	,asymptotic	PUNCT
m-806	272	14	analysis	analysis	NOUN
m-806	272	15	of	of	ADP
m-806	272	16	an	an	DET
m-806	272	17	improved	improved	ADJ
m-806	272	18	quadratic	quadratic	ADJ
m-806	272	19	model	model	NOUN
m-806	272	20	structures	structure	NOUN
m-806	272	21	subjected	subject	VERB
m-806	272	22	to	to	ADP
m-806	272	23	static	static	ADJ
m-806	272	24	loading	loading	NOUN
m-806	272	25	.	.	PUNCT
m-806	273	1	j.	j.	PROPN
m-806	273	2	of	of	ADP
m-806	273	3	nigerian	nigerian	PROPN
m-806	273	4	assoc	assoc	PROPN
m-806	273	5	.	.	PUNCT
m-806	274	1	of	of	ADP
m-806	274	2	math	math	NOUN
m-806	274	3	.	.	PUNCT
m-806	275	1	physics	physics	NOUN
m-806	275	2	,	,	PUNCT
m-806	275	3	32	32	NUM
m-806	275	4	,	,	PUNCT
m-806	275	5	237	237	NUM
m-806	275	6	-	-	SYM
m-806	275	7	244	244	NUM
m-806	275	8	,	,	PUNCT
m-806	275	9	2015	2015	NUM
m-806	275	10	.	.	PUNCT
m-806	276	1	[	[	X
m-806	276	2	12	12	NUM
m-806	276	3	]	]	X
m-806	276	4	chukwuchekwa	chukwuchekwa	PROPN
m-806	276	5	,	,	PUNCT
m-806	276	6	j.	j.	PROPN
m-806	276	7	u.	u.	PROPN
m-806	276	8	and	and	CCONJ
m-806	276	9	ette	ette	PROPN
m-806	276	10	,	,	PUNCT
m-806	276	11	a.	a.	NOUN
m-806	276	12	m.	m.	NOUN
m-806	276	13	,perturbation	,perturbation	PUNCT
m-806	276	14	technique	technique	NOUN
m-806	276	15	in	in	ADP
m-806	276	16	the	the	DET
m-806	276	17	buckling	buckling	NOUN
m-806	276	18	of	of	ADP
m-806	276	19	a	a	DET
m-806	276	20	viscously	viscously	ADV
m-806	276	21	damped	damp	VERB
m-806	276	22	elastic	elastic	ADJ
m-806	276	23	model	model	NOUN
m-806	276	24	structure	structure	NOUN
m-806	276	25	pre	pre	VERB
m-806	276	26	–	–	PUNCT
m-806	276	27	statically	statically	ADV
m-806	276	28	loaded	load	VERB
m-806	276	29	but	but	CCONJ
m-806	276	30	struck	strike	VERB
m-806	276	31	by	by	ADP
m-806	276	32	a	a	DET
m-806	276	33	step	step	NOUN
m-806	276	34	load	load	NOUN
m-806	276	35	,	,	PUNCT
m-806	276	36	j.	j.	PROPN
m-806	276	37	of	of	ADP
m-806	276	38	nigerian	nigerian	PROPN
m-806	276	39	assoc	assoc	PROPN
m-806	276	40	.	.	PUNCT
m-806	277	1	of	of	ADP
m-806	277	2	math	math	NOUN
m-806	277	3	.	.	PUNCT
m-806	278	1	physics	physics	NOUN
m-806	278	2	,	,	PUNCT
m-806	278	3	37	37	NUM
m-806	278	4	–	–	SYM
m-806	278	5	70	70	NUM
m-806	278	6	,	,	PUNCT
m-806	278	7	2016	2016	NUM
m-806	278	8	.	.	PUNCT
m-806	279	1	[	[	X
m-806	279	2	13	13	NUM
m-806	279	3	]	]	X
m-806	279	4	kolakowski	kolakowski	PROPN
m-806	279	5	,	,	PUNCT
m-806	279	6	z.	z.	PROPN
m-806	279	7	,static	,static	PUNCT
m-806	279	8	and	and	CCONJ
m-806	279	9	dynamic	dynamic	ADJ
m-806	279	10	interactive	interactive	ADJ
m-806	279	11	buckling	buckling	NOUN
m-806	279	12	regarding	regard	VERB
m-806	279	13	axial	axial	ADJ
m-806	279	14	extension	extension	NOUN
m-806	279	15	mode	mode	NOUN
m-806	279	16	of	of	ADP
m-806	279	17	thin	thin	ADJ
m-806	279	18	–	–	PUNCT
m-806	279	19	walled	walled	ADJ
m-806	279	20	channels	channel	NOUN
m-806	279	21	,	,	PUNCT
m-806	279	22	j.	j.	PROPN
m-806	279	23	of	of	ADP
m-806	279	24	theoritical	theoritical	ADJ
m-806	279	25	and	and	CCONJ
m-806	279	26	appl	appl	PROPN
m-806	279	27	.	.	PROPN
m-806	279	28	mech	mech	PROPN
m-806	279	29	.	.	PUNCT
m-806	280	1	48	48	NUM
m-806	280	2	(	(	PUNCT
m-806	280	3	3	3	NUM
m-806	280	4	)	)	PUNCT
m-806	280	5	,	,	PUNCT
m-806	280	6	703	703	NUM
m-806	280	7	–	–	PUNCT
m-806	280	8	714	714	NUM
m-806	280	9	,	,	PUNCT
m-806	280	10	2010	2010	NUM
m-806	280	11	.	.	PUNCT
m-806	281	1	[	[	X
m-806	281	2	14	14	NUM
m-806	281	3	]	]	X
m-806	281	4	kowal	kowal	PROPN
m-806	281	5	–	–	PUNCT
m-806	281	6	michalska	michalska	PROPN
m-806	281	7	,	,	PUNCT
m-806	281	8	k.	k.	PROPN
m-806	281	9	,about	,about	PUNCT
m-806	281	10	some	some	DET
m-806	281	11	important	important	ADJ
m-806	281	12	parameters	parameter	NOUN
m-806	281	13	in	in	ADP
m-806	281	14	dynamic	dynamic	ADJ
m-806	281	15	buckling	buckling	NOUN
m-806	281	16	analysis	analysis	NOUN
m-806	281	17	of	of	ADP
m-806	281	18	plate	plate	NOUN
m-806	281	19	structures	structure	NOUN
m-806	281	20	subjected	subject	VERB
m-806	281	21	to	to	ADP
m-806	281	22	pulse	pulse	NOUN
m-806	281	23	loading	loading	NOUN
m-806	281	24	,	,	PUNCT
m-806	281	25	j.	j.	PROPN
m-806	281	26	of	of	ADP
m-806	281	27	mech	mech	PROPN
m-806	281	28	.	.	PUNCT
m-806	282	1	and	and	CCONJ
m-806	282	2	mechanical	mechanical	ADJ
m-806	282	3	engng	engng	NOUN
m-806	282	4	.	.	PUNCT
m-806	283	1	,	,	PUNCT
m-806	283	2	14	14	NUM
m-806	283	3	(	(	PUNCT
m-806	283	4	2	2	NUM
m-806	283	5	)	)	PUNCT
m-806	283	6	,	,	PUNCT
m-806	283	7	259	259	NUM
m-806	283	8	–	–	SYM
m-806	283	9	279	279	NUM
m-806	283	10	,	,	PUNCT
m-806	283	11	2010	2010	NUM
m-806	283	12	.	.	PUNCT
m-806	284	1	[	[	X
m-806	284	2	15	15	NUM
m-806	284	3	]	]	X
m-806	284	4	mcshane	mcshane	PROPN
m-806	284	5	,	,	PUNCT
m-806	284	6	g.j	g.j	PROPN
m-806	284	7	.	.	PROPN
m-806	284	8	,	,	PUNCT
m-806	284	9	pingle	pingle	PROPN
m-806	284	10	,	,	PUNCT
m-806	284	11	s.	s.	PROPN
m-806	284	12	m.	m.	PROPN
m-806	284	13	,	,	PUNCT
m-806	284	14	deshpande	deshpande	PROPN
m-806	284	15	,	,	PUNCT
m-806	284	16	v.s.	v.s.	ADJ
m-806	284	17	and	and	CCONJ
m-806	284	18	flock	flock	NOUN
m-806	284	19	,	,	PUNCT
m-806	285	1	n.a	n.a	PROPN
m-806	285	2	.	.	PROPN
m-806	285	3	,dynamic	,dynamic	PUNCT
m-806	285	4	buckling	buckling	NOUN
m-806	285	5	of	of	ADP
m-806	285	6	inclined	inclined	ADJ
m-806	285	7	structures	structure	NOUN
m-806	285	8	,	,	PUNCT
m-806	285	9	int	int	NOUN
m-806	285	10	.	.	PUNCT
m-806	286	1	j.	j.	PROPN
m-806	286	2	of	of	ADP
m-806	286	3	solids	solid	NOUN
m-806	286	4	and	and	CCONJ
m-806	286	5	struct	struct	NOUN
m-806	286	6	.	.	PUNCT
m-806	286	7	,	,	PUNCT
m-806	286	8	49	49	NUM
m-806	286	9	,	,	PUNCT
m-806	286	10	2830	2830	NUM
m-806	286	11	–	–	PUNCT
m-806	286	12	2838	2838	NUM
m-806	286	13	,	,	PUNCT
m-806	286	14	2012	2012	NUM
m-806	286	15	.	.	PUNCT
m-806	287	1	[	[	X
m-806	287	2	16	16	NUM
m-806	287	3	]	]	X
m-806	287	4	belyaev	belyaev	NOUN
m-806	287	5	,	,	PUNCT
m-806	287	6	a.	a.	PROPN
m-806	287	7	k.	k.	PROPN
m-806	287	8	and	and	CCONJ
m-806	287	9	glim	glim	PROPN
m-806	287	10	,	,	PUNCT
m-806	287	11	d.	d.	PROPN
m-806	287	12	n.	n.	PROPN
m-806	287	13	,stability	,stability	PUNCT
m-806	287	14	of	of	ADP
m-806	287	15	transverse	transverse	NOUN
m-806	287	16	vibration	vibration	NOUN
m-806	287	17	of	of	ADP
m-806	287	18	rod	rod	NOUN
m-806	287	19	under	under	ADP
m-806	287	20	longitudinal	longitudinal	ADJ
m-806	287	21	step	step	NOUN
m-806	287	22	–	–	PUNCT
m-806	287	23	wise	wise	ADJ
m-806	287	24	loading	loading	NOUN
m-806	287	25	,	,	PUNCT
m-806	287	26	j.	j.	PROPN
m-806	287	27	of	of	ADP
m-806	287	28	physics	physics	PROPN
m-806	287	29	,	,	PUNCT
m-806	287	30	conference	conference	NOUN
m-806	287	31	series	series	NOUN
m-806	287	32	,	,	PUNCT
m-806	287	33	451	451	NUM
m-806	287	34	,	,	PUNCT
m-806	287	35	1	1	NUM
m-806	287	36	–	–	SYM
m-806	287	37	6	6	NUM
m-806	287	38	,	,	PUNCT
m-806	287	39	2012	2012	NUM
m-806	287	40	.	.	PUNCT
m-806	288	1	[	[	X
m-806	288	2	17	17	NUM
m-806	288	3	]	]	PUNCT
m-806	288	4	priyadarsini	priyadarsini	NOUN
m-806	288	5	,	,	PUNCT
m-806	288	6	r.s	r.s	PROPN
m-806	288	7	.	.	PROPN
m-806	288	8	,	,	PUNCT
m-806	288	9	kalyanaraman	kalyanaraman	PROPN
m-806	288	10	,	,	PUNCT
m-806	288	11	v.	v.	PROPN
m-806	288	12	and	and	CCONJ
m-806	288	13	srinvasan	srinvasan	PROPN
m-806	288	14	,	,	PUNCT
m-806	288	15	s.m	s.m	PROPN
m-806	288	16	.	.	PROPN
m-806	288	17	,numerical	,numerical	PUNCT
m-806	288	18	and	and	CCONJ
m-806	288	19	experimental	experimental	ADJ
m-806	288	20	study	study	NOUN
m-806	288	21	of	of	ADP
m-806	288	22	buckling	buckling	NOUN
m-806	288	23	of	of	ADP
m-806	288	24	advanced	advanced	ADJ
m-806	288	25	fibre	fibre	NOUN
m-806	288	26	composite	composite	ADJ
m-806	288	27	cylinder	cylinder	NOUN
m-806	288	28	under	under	ADP
m-806	288	29	axial	axial	ADJ
m-806	288	30	compression	compression	NOUN
m-806	288	31	,	,	PUNCT
m-806	288	32	int	int	NOUN
m-806	288	33	.	.	PUNCT
m-806	289	1	j.	j.	PROPN
m-806	289	2	of	of	ADP
m-806	289	3	structural	structural	ADJ
m-806	289	4	stability	stability	NOUN
m-806	289	5	and	and	CCONJ
m-806	289	6	dynamics	dynamic	NOUN
m-806	289	7	,	,	PUNCT
m-806	289	8	12	12	NUM
m-806	289	9	(	(	PUNCT
m-806	289	10	4	4	NUM
m-806	289	11	)	)	PUNCT
m-806	289	12	,	,	PUNCT
m-806	289	13	1	1	NUM
m-806	289	14	–	–	PUNCT
m-806	289	15	24	24	NUM
m-806	289	16	,	,	PUNCT
m-806	289	17	2012	2012	NUM
m-806	289	18	.	.	PUNCT
m-806	290	1	[	[	X
m-806	290	2	18	18	NUM
m-806	290	3	]	]	PUNCT
m-806	290	4	budiansky	budiansky	NOUN
m-806	290	5	,	,	PUNCT
m-806	290	6	b.	b.	PROPN
m-806	290	7	and	and	CCONJ
m-806	290	8	hutchinson	hutchinson	PROPN
m-806	290	9	,	,	PUNCT
m-806	290	10	j.w	j.w	PROPN
m-806	290	11	.	.	PROPN
m-806	290	12	,dynamic	,dynamic	PUNCT
m-806	290	13	buckling	buckling	NOUN
m-806	290	14	of	of	ADP
m-806	290	15	imperfection	imperfection	NOUN
m-806	290	16	–	–	PUNCT
m-806	290	17	sensitive	sensitive	ADJ
m-806	290	18	structures	structure	NOUN
m-806	290	19	,	,	PUNCT
m-806	290	20	proceedings	proceeding	NOUN
m-806	290	21	of	of	ADP
m-806	290	22	xi	xi	PROPN
m-806	290	23	international	international	ADJ
m-806	290	24	congr	congr	NOUN
m-806	290	25	.	.	PUNCT
m-806	291	1	applied	apply	VERB
m-806	291	2	mechanics	mechanic	NOUN
m-806	291	3	.	.	PUNCT
m-806	292	1	springer	springer	NOUN
m-806	292	2	–	–	PUNCT
m-806	292	3	verlag	verlag	PROPN
m-806	292	4	,	,	PUNCT
m-806	292	5	berlin	berlin	PROPN
m-806	292	6	.	.	PUNCT
m-806	293	1	1966	1966	NUM
m-806	293	2	.	.	PUNCT
m-806	294	1	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	294	2	ijo	ijo	PROPN
m-806	294	3	journals	journal	NOUN
m-806	294	4	volume	volume	NOUN
m-806	294	5	07	07	NUM
m-806	294	6	|	|	ADV
m-806	294	7	issue	issue	NOUN
m-806	294	8	02	02	NUM
m-806	294	9	|	|	CCONJ
m-806	294	10	february	february	PROPN
m-806	294	11	2024	2024	NUM
m-806	294	12	|	|	ADV
m-806	294	13	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	PROPN
m-806	294	14	31	31	NUM
m-806	294	15	ijo	ijo	PROPN
m-806	294	16	international	international	PROPN
m-806	294	17	journal	journal	PROPN
m-806	294	18	of	of	ADP
m-806	294	19	mathematics	mathematics	PROPN
m-806	294	20	(	(	PUNCT
m-806	294	21	issn	issn	PROPN
m-806	294	22	:	:	PUNCT
m-806	294	23	2992	2992	NUM
m-806	294	24	-	-	SYM
m-806	294	25	4421	4421	NUM
m-806	294	26	)	)	PUNCT
m-806	295	1	i.u	i.u	PROPN
m-806	295	2	.	.	PROPN
m-806	295	3	udo	udo	PROPN
m-806	295	4	-	-	PROPN
m-806	295	5	akpan1	akpan1	ADJ
m-806	295	6	*	*	PUNCT
m-806	295	7	https://ijojournals.com/	https://ijojournals.com/	NOUN
m-806	295	8	volume	volume	NOUN
m-806	295	9	07	07	NUM
m-806	295	10	issue	issue	NOUN
m-806	295	11	02	02	NUM
m-806	295	12	||	||	NUM
m-806	295	13	february	february	PROPN
m-806	295	14	,	,	PUNCT
m-806	295	15	2024	2024	NUM
m-806	295	16	||	||	NOUN
m-806	296	1	on	on	ADP
m-806	296	2	a	a	DET
m-806	296	3	-	-	PUNCT
m-806	296	4	two	two	NUM
m-806	296	5	-	-	PUNCT
m-806	296	6	parameter	parameter	NOUN
m-806	296	7	dynamic	dynamic	ADJ
m-806	296	8	buckling	buckling	NOUN
m-806	296	9	of	of	ADP
m-806	296	10	a	a	DET
m-806	296	11	viscously	viscously	ADV
m-806	296	12	damped	damp	VERB
m-806	296	13	but	but	CCONJ
m-806	296	14	clamped	clamp	VERB
m-806	296	15	column	column	NOUN
m-806	296	16	stressed	stress	VERB
m-806	296	17	by	by	ADP
m-806	296	18	a	a	DET
m-806	296	19	step	step	NOUN
m-806	296	20	load	load	NOUN
m-806	296	21	[	[	X
m-806	296	22	19	19	NUM
m-806	296	23	]	]	X
m-806	296	24	ette	ette	NOUN
m-806	296	25	,	,	PUNCT
m-806	296	26	a.	a.	NOUN
m-806	296	27	m.	m.	NOUN
m-806	296	28	and	and	CCONJ
m-806	296	29	chukwuchekwa	chukwuchekwa	PROPN
m-806	296	30	,	,	PUNCT
m-806	296	31	j.	j.	PROPN
m-806	296	32	u.	u.	PROPN
m-806	296	33	,	,	PUNCT
m-806	296	34	on	on	ADP
m-806	296	35	the	the	DET
m-806	296	36	static	static	ADJ
m-806	296	37	buckling	buckling	NOUN
m-806	296	38	of	of	ADP
m-806	296	39	an	an	DET
m-806	296	40	externally	externally	ADV
m-806	296	41	pressurized	pressurize	VERB
m-806	296	42	finite	finite	ADJ
m-806	296	43	circular	circular	ADJ
m-806	296	44	cylindrical	cylindrical	ADJ
m-806	296	45	shell	shell	NOUN
m-806	296	46	,	,	PUNCT
m-806	296	47	j.	j.	PROPN
m-806	296	48	of	of	ADP
m-806	296	49	nigerian	nigerian	PROPN
m-806	296	50	assoc	assoc	PROPN
m-806	296	51	.	.	PUNCT
m-806	297	1	of	of	ADP
m-806	297	2	math	math	NOUN
m-806	297	3	.	.	PUNCT
m-806	298	1	physics	physics	NOUN
m-806	298	2	,	,	PUNCT
m-806	298	3	11	11	NUM
m-806	298	4	,	,	PUNCT
m-806	298	5	323	323	NUM
m-806	298	6	–	–	PUNCT
m-806	298	7	332	332	NUM
m-806	298	8	,	,	PUNCT
m-806	298	9	2007	2007	NUM
m-806	298	10	.	.	PUNCT
m-806	299	1	[	[	X
m-806	299	2	20	20	NUM
m-806	299	3	]	]	PUNCT
m-806	299	4	a.	a.	NOUN
m-806	299	5	m.	m.	PROPN
m-806	299	6	ette	ette	PROPN
m-806	299	7	,	,	PUNCT
m-806	299	8	j.	j.	PROPN
m-806	299	9	u.	u.	PROPN
m-806	299	10	chukwuchekwa	chukwuchekwa	PROPN
m-806	299	11	,	,	PUNCT
m-806	299	12	i.	i.	PROPN
m-806	299	13	u.	u.	PROPN
m-806	299	14	udo	udo	PROPN
m-806	299	15	-	-	PUNCT
m-806	299	16	akpan	akpan	NOUN
m-806	299	17	and	and	CCONJ
m-806	299	18	onuoha	onuoha	PROPN
m-806	299	19	,	,	PUNCT
m-806	299	20	n.o	n.o	PROPN
m-806	299	21	.	.	PROPN
m-806	299	22	(	(	PUNCT
m-806	299	23	2020	2020	NUM
m-806	299	24	)	)	PUNCT
m-806	299	25	;	;	PUNCT
m-806	299	26	a	a	DET
m-806	299	27	multitiming	multitime	VERB
m-806	299	28	perturbation	perturbation	NOUN
m-806	299	29	analysis	analysis	NOUN
m-806	299	30	of	of	ADP
m-806	299	31	the	the	DET
m-806	299	32	deformation	deformation	NOUN
m-806	299	33	and	and	CCONJ
m-806	299	34	dynamic	dynamic	ADJ
m-806	299	35	buckling	buckling	NOUN
m-806	299	36	of	of	ADP
m-806	299	37	a	a	DET
m-806	299	38	viscously	viscously	ADV
m-806	299	39	damped	damp	VERB
m-806	299	40	toroidal	toroidal	ADJ
m-806	299	41	shell	shell	NOUN
m-806	299	42	segment	segment	NOUN
m-806	299	43	stressed	stress	VERB
m-806	299	44	by	by	ADP
m-806	299	45	a	a	DET
m-806	299	46	step	step	NOUN
m-806	299	47	load	load	NOUN
m-806	299	48	,	,	PUNCT
m-806	299	49	iosr	iosr	ADJ
m-806	299	50	journal	journal	NOUN
m-806	299	51	of	of	ADP
m-806	299	52	mathematics	mathematics	PROPN
m-806	299	53	(	(	PUNCT
m-806	299	54	iosr	iosr	PROPN
m-806	299	55	-	-	PUNCT
m-806	299	56	jm	jm	NOUN
m-806	299	57	)	)	PUNCT
m-806	299	58	,	,	PUNCT
m-806	299	59	16(4	16(4	NUM
m-806	299	60	)	)	PUNCT
m-806	299	61	,	,	PUNCT
m-806	299	62	40	40	NUM
m-806	299	63	-	-	SYM
m-806	299	64	59	59	NUM
m-806	299	65	.	.	PUNCT
m-806	300	1	[	[	X
m-806	300	2	21	21	NUM
m-806	300	3	]	]	PUNCT
m-806	300	4	a.	a.	NOUN
m-806	300	5	m.	m.	PROPN
m-806	300	6	ette	ette	PROPN
m-806	300	7	,	,	PUNCT
m-806	300	8	j.	j.	PROPN
m-806	300	9	u.	u.	PROPN
m-806	300	10	chukwuchekwa	chukwuchekwa	PROPN
m-806	300	11	,	,	PUNCT
m-806	300	12	n.o	n.o	PROPN
m-806	300	13	.	.	PROPN
m-806	300	14	onuoha	onuoha	PROPN
m-806	300	15	,	,	PUNCT
m-806	300	16	and	and	CCONJ
m-806	300	17	i.	i.	PROPN
m-806	300	18	u.	u.	PROPN
m-806	300	19	udo	udo	PROPN
m-806	300	20	-	-	PUNCT
m-806	300	21	akpan	akpan	NOUN
m-806	300	22	(	(	PUNCT
m-806	300	23	2020	2020	NUM
m-806	300	24	)	)	PUNCT
m-806	300	25	;	;	PUNCT
m-806	300	26	on	on	ADP
m-806	300	27	the	the	DET
m-806	300	28	deformation	deformation	NOUN
m-806	300	29	and	and	CCONJ
m-806	300	30	static	static	ADJ
m-806	300	31	buckling	buckling	NOUN
m-806	300	32	of	of	ADP
m-806	300	33	a	a	DET
m-806	300	34	toroidal	toroidal	ADJ
m-806	300	35	shell	shell	NOUN
m-806	300	36	segment	segment	NOUN
m-806	300	37	using	use	VERB
m-806	300	38	a	a	DET
m-806	300	39	two	two	NUM
m-806	300	40	-	-	PUNCT
m-806	300	41	term	term	NOUN
m-806	300	42	fourier	fourier	NOUN
m-806	300	43	series	series	PROPN
m-806	300	44	imperfections	imperfection	NOUN
m-806	300	45	,	,	PUNCT
m-806	300	46	international	international	ADJ
m-806	300	47	journal	journal	NOUN
m-806	300	48	of	of	ADP
m-806	300	49	mathematics	mathematics	NOUN
m-806	300	50	trends	trend	NOUN
m-806	300	51	and	and	CCONJ
m-806	300	52	technology	technology	NOUN
m-806	300	53	(	(	PUNCT
m-806	300	54	ijmtt	ijmtt	ADJ
m-806	300	55	)	)	PUNCT
m-806	300	56	,	,	PUNCT
m-806	300	57	66(8	66(8	NOUN
m-806	300	58	)	)	PUNCT
m-806	300	59	,	,	PUNCT
m-806	300	60	100	100	NUM
m-806	300	61	-	-	SYM
m-806	300	62	114	114	NUM
m-806	300	63	[	[	SYM
m-806	300	64	22	22	NUM
m-806	300	65	]	]	X
m-806	300	66	g.	g.	PROPN
m-806	300	67	ozoigbo	ozoigbo	PROPN
m-806	300	68	,	,	PUNCT
m-806	300	69	a.m.	a.m.	PROPN
m-806	300	70	ette	ette	PROPN
m-806	300	71	,	,	PUNCT
m-806	300	72	j.	j.	PROPN
m-806	300	73	chukwuchekwa	chukwuchekwa	PROPN
m-806	300	74	,	,	PUNCT
m-806	300	75	w.	w.	PROPN
m-806	300	76	osuji	osuji	PROPN
m-806	300	77	,	,	PUNCT
m-806	300	78	i.u	i.u	PROPN
m-806	300	79	.	.	PROPN
m-806	300	80	udo	udo	PROPN
m-806	300	81	-	-	PUNCT
m-806	300	82	akpan	akpan	NOUN
m-806	300	83	(	(	PUNCT
m-806	300	84	2022	2022	NUM
m-806	300	85	)	)	PUNCT
m-806	300	86	;	;	PUNCT
m-806	300	87	on	on	ADP
m-806	300	88	the	the	DET
m-806	300	89	analysis	analysis	NOUN
m-806	300	90	of	of	ADP
m-806	300	91	a	a	DET
m-806	300	92	pre	pre	ADJ
m-806	300	93	-	-	ADJ
m-806	300	94	statically	statically	ADV
m-806	300	95	loaded	load	VERB
m-806	300	96	nonlinear	nonlinear	ADJ
m-806	300	97	cubic	cubic	ADJ
m-806	300	98	structure	structure	NOUN
m-806	300	99	pressurized	pressurize	VERB
m-806	300	100	by	by	ADP
m-806	300	101	an	an	DET
m-806	300	102	explicitly	explicitly	ADV
m-806	300	103	time	time	NOUN
m-806	300	104	dependent	dependent	ADJ
m-806	300	105	slowlyvarying	slowlyvarying	NOUN
m-806	300	106	load	load	NOUN
m-806	300	107	,	,	PUNCT
m-806	300	108	american	american	PROPN
m-806	300	109	journal	journal	PROPN
m-806	300	110	of	of	ADP
m-806	300	111	mechanics	mechanic	NOUN
m-806	300	112	and	and	CCONJ
m-806	300	113	applications	application	NOUN
m-806	300	114	,	,	PUNCT
m-806	300	115	10(1	10(1	NUM
m-806	300	116	)	)	PUNCT
m-806	300	117	,	,	PUNCT
m-806	300	118	1	1	NUM
m-806	300	119	-	-	SYM
m-806	300	120	15	15	NUM
m-806	300	121	[	[	X
m-806	300	122	23	23	NUM
m-806	300	123	]	]	X
m-806	300	124	g.e	g.e	PROPN
m-806	300	125	.	.	PROPN
m-806	300	126	ozoigbo	ozoigbo	PROPN
m-806	300	127	,	,	PUNCT
m-806	300	128	a.m.	a.m.	PROPN
m-806	300	129	ette	ette	PROPN
m-806	300	130	,	,	PUNCT
m-806	300	131	j.u	j.u	PROPN
m-806	300	132	.	.	PROPN
m-806	300	133	chukwuchekwa	chukwuchekwa	PROPN
m-806	300	134	,	,	PUNCT
m-806	300	135	w.i	w.i	PROPN
m-806	300	136	.	.	PROPN
m-806	300	137	osuji	osuji	PROPN
m-806	300	138	,	,	PUNCT
m-806	300	139	i.u	i.u	PROPN
m-806	300	140	.	.	PROPN
m-806	300	141	udo	udo	PROPN
m-806	300	142	-	-	PUNCT
m-806	300	143	akpan	akpan	NOUN
m-806	300	144	(	(	PUNCT
m-806	300	145	2023	2023	NUM
m-806	300	146	)	)	PUNCT
m-806	300	147	;	;	PUNCT
m-806	300	148	nonlinear	nonlinear	ADJ
m-806	300	149	analytical	analytical	ADJ
m-806	300	150	investigation	investigation	NOUN
m-806	300	151	of	of	ADP
m-806	300	152	dynamic	dynamic	ADJ
m-806	300	153	buckling	buckling	NOUN
m-806	300	154	of	of	ADP
m-806	300	155	spherical	spherical	ADJ
m-806	300	156	shell	shell	NOUN
m-806	300	157	trapped	trap	VERB
m-806	300	158	under	under	ADP
m-806	300	159	a	a	DET
m-806	300	160	periodic	periodic	ADJ
m-806	300	161	load	load	NOUN
m-806	300	162	,	,	PUNCT
m-806	300	163	mechanics	mechanic	NOUN
m-806	300	164	of	of	ADP
m-806	300	165	solids	solid	NOUN
m-806	300	166	,	,	PUNCT
m-806	300	167	springer	springer	NOUN
m-806	300	168	link	link	NOUN
m-806	300	169	,	,	PUNCT
m-806	300	170	58	58	NUM
m-806	300	171	,	,	PUNCT
m-806	300	172	202	202	NUM
m-806	300	173	-	-	SYM
m-806	300	174	215	215	NUM
m-806	300	175	.	.	PUNCT
m-806	301	1	[	[	X
m-806	301	2	24	24	NUM
m-806	301	3	]	]	SYM
m-806	301	4	obong	obong	PROPN
m-806	301	5	,	,	PUNCT
m-806	301	6	h.p	h.p	PROPN
m-806	301	7	.	.	PROPN
m-806	301	8	and	and	CCONJ
m-806	301	9	udoakpan	udoakpan	NOUN
m-806	301	10	,	,	PUNCT
m-806	301	11	i.u	i.u	PROPN
m-806	301	12	.	.	PROPN
m-806	301	13	(	(	PUNCT
m-806	301	14	2023	2023	NUM
m-806	301	15	)	)	PUNCT
m-806	301	16	;	;	PUNCT
m-806	301	17	a	a	DET
m-806	301	18	review	review	NOUN
m-806	301	19	of	of	ADP
m-806	301	20	tensor	tensor	NOUN
m-806	301	21	interaction	interaction	NOUN
m-806	301	22	in	in	ADP
m-806	301	23	the	the	DET
m-806	301	24	theory	theory	NOUN
m-806	301	25	of	of	ADP
m-806	301	26	potential	potential	ADJ
m-806	301	27	models	model	NOUN
m-806	301	28	,	,	PUNCT
m-806	301	29	scientia	scientia	PROPN
m-806	301	30	africana	africana	PROPN
m-806	301	31	,	,	PUNCT
m-806	301	32	22(3	22(3	NUM
m-806	301	33	)	)	PUNCT
m-806	301	34	,	,	PUNCT
m-806	301	35	11	11	NUM
m-806	301	36	-	-	SYM
m-806	301	37	22	22	NUM
m-806	301	38	.	.	PUNCT
m-806	302	1	[	[	X
m-806	302	2	25	25	NUM
m-806	302	3	]	]	X
m-806	302	4	o.g	o.g	PROPN
m-806	302	5	.	.	PROPN
m-806	302	6	udoaka	udoaka	PROPN
m-806	302	7	,	,	PUNCT
m-806	302	8	u.j	u.j	PROPN
m-806	302	9	.	.	PROPN
m-806	302	10	etim	etim	PROPN
m-806	302	11	and	and	CCONJ
m-806	302	12	i.u	i.u	PROPN
m-806	302	13	.	.	PROPN
m-806	302	14	udoakpan	udoakpan	NOUN
m-806	302	15	,	,	PUNCT
m-806	302	16	(	(	PUNCT
m-806	302	17	2024	2024	NUM
m-806	302	18	)	)	PUNCT
m-806	302	19	efficient	efficient	ADJ
m-806	302	20	solution	solution	NOUN
m-806	302	21	of	of	ADP
m-806	302	22	nonhomogeneous	nonhomogeneous	ADJ
m-806	302	23	linear	linear	PROPN
m-806	302	24	differential	differential	NOUN
m-806	302	25	equations	equation	NOUN
m-806	302	26	with	with	ADP
m-806	302	27	constant	constant	ADJ
m-806	302	28	coefficients	coefficient	NOUN
m-806	302	29	:	:	PUNCT
m-806	302	30	the	the	DET
m-806	302	31	method	method	NOUN
m-806	302	32	of	of	ADP
m-806	302	33	undetermined	undetermined	ADJ
m-806	302	34	coefficient	coefficient	NOUN
m-806	302	35	approach	approach	NOUN
m-806	302	36	,	,	PUNCT
m-806	302	37	ieee	ieee	NOUN
m-806	302	38	-	-	PUNCT
m-806	302	39	sem	sem	NOUN
m-806	302	40	,	,	PUNCT
m-806	302	41	12(1	12(1	NUM
m-806	302	42	)	)	PUNCT
m-806	302	43	,	,	PUNCT
m-806	302	44	21	21	NUM
m-806	302	45	-	-	SYM
m-806	302	46	36	36	NUM
m-806	302	47	https://zenodo.org/doi/10.5281/zenodo.10726874	https://zenodo.org/doi/10.5281/zenodo.10726874	PROPN
m-806	302	48	ijo	ijo	PROPN
m-806	302	49	journals	journal	NOUN
m-806	302	50	volume	volume	NOUN
m-806	302	51	07	07	NUM
m-806	302	52	|	|	ADV
m-806	302	53	issue	issue	NOUN
m-806	302	54	02	02	NUM
m-806	302	55	|	|	CCONJ
m-806	302	56	february	february	PROPN
m-806	302	57	2024	2024	NUM
m-806	302	58	|	|	ADV
m-806	302	59	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-806	302	60	32	32	NUM