id	sid	tid	token	lemma	pos
iajs-3928	1	1	381	381	NUM
iajs-3928	1	2	©	©	PROPN
iajs-3928	1	3	2024	2024	NUM
iajs-3928	1	4	the	the	DET
iajs-3928	1	5	author(s	author(s	NOUN
iajs-3928	1	6	)	)	PUNCT
iajs-3928	1	7	.	.	PUNCT
iajs-3928	2	1	published	publish	VERB
iajs-3928	2	2	by	by	ADP
iajs-3928	2	3	college	college	NOUN
iajs-3928	2	4	of	of	ADP
iajs-3928	2	5	education	education	NOUN
iajs-3928	2	6	for	for	ADP
iajs-3928	2	7	pure	pure	ADJ
iajs-3928	2	8	science	science	NOUN
iajs-3928	2	9	(	(	PUNCT
iajs-3928	2	10	ibn	ibn	PROPN
iajs-3928	2	11	al	al	PROPN
iajs-3928	2	12	-	-	PUNCT
iajs-3928	2	13	haitham	haitham	PROPN
iajs-3928	2	14	)	)	PUNCT
iajs-3928	2	15	,	,	PUNCT
iajs-3928	2	16	university	university	NOUN
iajs-3928	2	17	of	of	ADP
iajs-3928	2	18	baghdad	baghdad	PROPN
iajs-3928	2	19	.	.	PUNCT
iajs-3928	3	1	this	this	PRON
iajs-3928	3	2	is	be	AUX
iajs-3928	3	3	an	an	DET
iajs-3928	3	4	open	open	ADJ
iajs-3928	3	5	-	-	PUNCT
iajs-3928	3	6	access	access	NOUN
iajs-3928	3	7	article	article	NOUN
iajs-3928	3	8	distributed	distribute	VERB
iajs-3928	3	9	under	under	ADP
iajs-3928	3	10	the	the	DET
iajs-3928	3	11	terms	term	NOUN
iajs-3928	3	12	of	of	ADP
iajs-3928	3	13	the	the	DET
iajs-3928	3	14	creative	creative	ADJ
iajs-3928	3	15	commons	common	NOUN
iajs-3928	3	16	attribution	attribution	NOUN
iajs-3928	3	17	4.0	4.0	NUM
iajs-3928	3	18	international	international	ADJ
iajs-3928	3	19	license	license	NOUN
iajs-3928	3	20	ibn	ibn	PROPN
iajs-3928	3	21	al	al	PROPN
iajs-3928	3	22	-	-	PUNCT
iajs-3928	3	23	haitham	haitham	PROPN
iajs-3928	3	24	journal	journal	PROPN
iajs-3928	3	25	for	for	ADP
iajs-3928	3	26	pure	pure	ADJ
iajs-3928	3	27	and	and	CCONJ
iajs-3928	3	28	applied	applied	ADJ
iajs-3928	3	29	sciences	sciences	PROPN
iajs-3928	3	30	journal	journal	PROPN
iajs-3928	3	31	homepage	homepage	NOUN
iajs-3928	3	32	:	:	PUNCT
iajs-3928	3	33	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3928	3	34	pissn	pissn	ADJ
iajs-3928	3	35	:	:	PUNCT
iajs-3928	3	36	1609	1609	NUM
iajs-3928	3	37	-	-	SYM
iajs-3928	3	38	4042	4042	NUM
iajs-3928	3	39	,	,	PUNCT
iajs-3928	3	40	eissn	eissn	NOUN
iajs-3928	3	41	:	:	PUNCT
iajs-3928	3	42	2521	2521	NUM
iajs-3928	3	43	-	-	SYM
iajs-3928	3	44	3407	3407	NUM
iajs-3928	3	45	ihjpas	ihjpa	NOUN
iajs-3928	3	46	.	.	PUNCT
iajs-3928	4	1	2024	2024	NUM
iajs-3928	4	2	,	,	PUNCT
iajs-3928	4	3	37(4	37(4	X
iajs-3928	4	4	)	)	PUNCT
iajs-3928	4	5	analysis	analysis	NOUN
iajs-3928	4	6	of	of	ADP
iajs-3928	4	7	loaded	loaded	ADJ
iajs-3928	4	8	beam	beam	NOUN
iajs-3928	4	9	,	,	PUNCT
iajs-3928	4	10	cantilever	cantilever	NOUN
iajs-3928	4	11	,	,	PUNCT
iajs-3928	4	12	and	and	CCONJ
iajs-3928	4	13	elongated	elongate	VERB
iajs-3928	4	14	vertical	vertical	ADJ
iajs-3928	4	15	column	column	NOUN
iajs-3928	4	16	via	via	ADP
iajs-3928	4	17	integral	integral	ADJ
iajs-3928	4	18	rohit	rohit	PROPN
iajs-3928	4	19	transform	transform	NOUN
iajs-3928	4	20	rohit	rohit	NOUN
iajs-3928	4	21	gupta1	gupta1	PROPN
iajs-3928	4	22	,	,	PUNCT
iajs-3928	4	23	*	*	PUNCT
iajs-3928	4	24	,	,	PUNCT
iajs-3928	4	25	shivam	shivam	PROPN
iajs-3928	4	26	sharma2	sharma2	PROPN
iajs-3928	4	27	and	and	CCONJ
iajs-3928	4	28	anikait	anikait	ADJ
iajs-3928	4	29	gupta3	gupta3	PROPN
iajs-3928	4	30	1applied	1applied	NUM
iajs-3928	4	31	sciences	science	NOUN
iajs-3928	4	32	,	,	PUNCT
iajs-3928	4	33	faculty	faculty	NOUN
iajs-3928	4	34	of	of	ADP
iajs-3928	4	35	physics	physics	PROPN
iajs-3928	4	36	,	,	PUNCT
iajs-3928	4	37	yogananda	yogananda	PROPN
iajs-3928	4	38	college	college	PROPN
iajs-3928	4	39	of	of	ADP
iajs-3928	4	40	engineering	engineering	NOUN
iajs-3928	4	41	and	and	CCONJ
iajs-3928	4	42	technology	technology	NOUN
iajs-3928	4	43	(	(	PUNCT
iajs-3928	4	44	ycet	ycet	PROPN
iajs-3928	4	45	)	)	PUNCT
iajs-3928	4	46	,	,	PUNCT
iajs-3928	4	47	jammu	jammu	PROPN
iajs-3928	4	48	,	,	PUNCT
iajs-3928	4	49	india	india	PROPN
iajs-3928	4	50	.	.	PROPN
iajs-3928	5	1	2	2	NUM
iajs-3928	5	2	,	,	PUNCT
iajs-3928	5	3	3civil	3civil	NUM
iajs-3928	5	4	engineering	engineering	NOUN
iajs-3928	5	5	,	,	PUNCT
iajs-3928	5	6	yogananda	yogananda	PROPN
iajs-3928	5	7	college	college	PROPN
iajs-3928	5	8	of	of	ADP
iajs-3928	5	9	engineering	engineering	NOUN
iajs-3928	5	10	and	and	CCONJ
iajs-3928	5	11	technology	technology	NOUN
iajs-3928	5	12	(	(	PUNCT
iajs-3928	5	13	ycet	ycet	PROPN
iajs-3928	5	14	)	)	PUNCT
iajs-3928	5	15	,	,	PUNCT
iajs-3928	5	16	jammu	jammu	PROPN
iajs-3928	5	17	,	,	PUNCT
iajs-3928	5	18	india	india	PROPN
iajs-3928	5	19	.	.	PUNCT
iajs-3928	6	1	*	*	PUNCT
iajs-3928	6	2	corresponding	correspond	VERB
iajs-3928	6	3	author	author	NOUN
iajs-3928	6	4	.	.	PUNCT
iajs-3928	7	1	received	receive	VERB
iajs-3928	7	2	:	:	PUNCT
iajs-3928	7	3	9	9	NUM
iajs-3928	7	4	february	february	NOUN
iajs-3928	7	5	2024	2024	NUM
iajs-3928	7	6	accepted	accept	VERB
iajs-3928	7	7	:	:	PUNCT
iajs-3928	7	8	21	21	NUM
iajs-3928	7	9	april	april	PROPN
iajs-3928	7	10	2024	2024	NUM
iajs-3928	7	11	published	publish	VERB
iajs-3928	7	12	:	:	PUNCT
iajs-3928	7	13	20	20	NUM
iajs-3928	7	14	october	october	NOUN
iajs-3928	7	15	2024	2024	NUM
iajs-3928	7	16	doi.org/10.30526/37.4.3928	doi.org/10.30526/37.4.3928	X
iajs-3928	7	17	abstract	abstract	ADJ
iajs-3928	7	18	structural	structural	ADJ
iajs-3928	7	19	analysis	analysis	NOUN
iajs-3928	7	20	is	be	AUX
iajs-3928	7	21	a	a	DET
iajs-3928	7	22	branch	branch	NOUN
iajs-3928	7	23	of	of	ADP
iajs-3928	7	24	solid	solid	ADJ
iajs-3928	7	25	mechanics	mechanic	NOUN
iajs-3928	7	26	which	which	PRON
iajs-3928	7	27	utilizes	utilize	VERB
iajs-3928	7	28	straight	straight	ADJ
iajs-3928	7	29	forward	forward	ADJ
iajs-3928	7	30	models	model	NOUN
iajs-3928	7	31	for	for	ADP
iajs-3928	7	32	solids	solid	NOUN
iajs-3928	7	33	.	.	PUNCT
iajs-3928	8	1	the	the	DET
iajs-3928	8	2	main	main	ADJ
iajs-3928	8	3	objective	objective	NOUN
iajs-3928	8	4	of	of	ADP
iajs-3928	8	5	structural	structural	ADJ
iajs-3928	8	6	analysis	analysis	NOUN
iajs-3928	8	7	is	be	AUX
iajs-3928	8	8	to	to	PART
iajs-3928	8	9	find	find	VERB
iajs-3928	8	10	out	out	ADP
iajs-3928	8	11	the	the	DET
iajs-3928	8	12	effect	effect	NOUN
iajs-3928	8	13	of	of	ADP
iajs-3928	8	14	loads	load	NOUN
iajs-3928	8	15	on	on	ADP
iajs-3928	8	16	the	the	DET
iajs-3928	8	17	physical	physical	ADJ
iajs-3928	8	18	structures	structure	NOUN
iajs-3928	8	19	and	and	CCONJ
iajs-3928	8	20	their	their	PRON
iajs-3928	8	21	components	component	NOUN
iajs-3928	8	22	.	.	PUNCT
iajs-3928	9	1	a	a	DET
iajs-3928	9	2	beam	beam	NOUN
iajs-3928	9	3	is	be	AUX
iajs-3928	9	4	a	a	DET
iajs-3928	9	5	structure	structure	NOUN
iajs-3928	9	6	with	with	ADP
iajs-3928	9	7	a	a	DET
iajs-3928	9	8	constant	constant	ADJ
iajs-3928	9	9	cross	cross	NOUN
iajs-3928	9	10	-	-	NOUN
iajs-3928	9	11	section	section	NOUN
iajs-3928	9	12	and	and	CCONJ
iajs-3928	9	13	is	be	AUX
iajs-3928	9	14	described	describe	VERB
iajs-3928	9	15	by	by	ADP
iajs-3928	9	16	its	its	PRON
iajs-3928	9	17	significant	significant	ADJ
iajs-3928	9	18	length	length	NOUN
iajs-3928	9	19	in	in	ADP
iajs-3928	9	20	comparison	comparison	NOUN
iajs-3928	9	21	to	to	ADP
iajs-3928	9	22	its	its	PRON
iajs-3928	9	23	thickness	thickness	NOUN
iajs-3928	9	24	and	and	CCONJ
iajs-3928	9	25	width	width	NOUN
iajs-3928	9	26	.	.	PUNCT
iajs-3928	10	1	a	a	DET
iajs-3928	10	2	cantilever	cantilever	NOUN
iajs-3928	10	3	,	,	PUNCT
iajs-3928	10	4	on	on	ADP
iajs-3928	10	5	the	the	DET
iajs-3928	10	6	other	other	ADJ
iajs-3928	10	7	hand	hand	NOUN
iajs-3928	10	8	,	,	PUNCT
iajs-3928	10	9	is	be	AUX
iajs-3928	10	10	a	a	DET
iajs-3928	10	11	slender	slender	ADJ
iajs-3928	10	12	beam	beam	NOUN
iajs-3928	10	13	with	with	ADP
iajs-3928	10	14	a	a	DET
iajs-3928	10	15	uniform	uniform	ADJ
iajs-3928	10	16	cross	cross	ADJ
iajs-3928	10	17	-	-	ADJ
iajs-3928	10	18	sectional	sectional	ADJ
iajs-3928	10	19	shape	shape	NOUN
iajs-3928	10	20	that	that	PRON
iajs-3928	10	21	is	be	AUX
iajs-3928	10	22	fixed	fix	VERB
iajs-3928	10	23	horizontally	horizontally	ADV
iajs-3928	10	24	at	at	ADP
iajs-3928	10	25	one	one	NUM
iajs-3928	10	26	end	end	NOUN
iajs-3928	10	27	and	and	CCONJ
iajs-3928	10	28	subjected	subject	VERB
iajs-3928	10	29	to	to	ADP
iajs-3928	10	30	a	a	DET
iajs-3928	10	31	load	load	NOUN
iajs-3928	10	32	at	at	ADP
iajs-3928	10	33	the	the	DET
iajs-3928	10	34	other	other	ADJ
iajs-3928	10	35	end	end	NOUN
iajs-3928	10	36	.	.	PUNCT
iajs-3928	11	1	columns	column	NOUN
iajs-3928	11	2	,	,	PUNCT
iajs-3928	11	3	which	which	PRON
iajs-3928	11	4	serve	serve	VERB
iajs-3928	11	5	as	as	ADP
iajs-3928	11	6	vertical	vertical	ADJ
iajs-3928	11	7	compression	compression	NOUN
iajs-3928	11	8	members	member	NOUN
iajs-3928	11	9	in	in	ADP
iajs-3928	11	10	building	building	NOUN
iajs-3928	11	11	frames	frame	NOUN
iajs-3928	11	12	,	,	PUNCT
iajs-3928	11	13	are	be	AUX
iajs-3928	11	14	susceptible	susceptible	ADJ
iajs-3928	11	15	to	to	ADP
iajs-3928	11	16	buckling	buckling	NOUN
iajs-3928	11	17	and	and	CCONJ
iajs-3928	11	18	failure	failure	NOUN
iajs-3928	11	19	when	when	SCONJ
iajs-3928	11	20	subjected	subject	VERB
iajs-3928	11	21	to	to	ADP
iajs-3928	11	22	relatively	relatively	ADV
iajs-3928	11	23	small	small	ADJ
iajs-3928	11	24	axial	axial	ADJ
iajs-3928	11	25	loads	load	NOUN
iajs-3928	11	26	.	.	PUNCT
iajs-3928	12	1	the	the	DET
iajs-3928	12	2	analysis	analysis	NOUN
iajs-3928	12	3	of	of	ADP
iajs-3928	12	4	loaded	load	VERB
iajs-3928	12	5	beams	beam	NOUN
iajs-3928	12	6	,	,	PUNCT
iajs-3928	12	7	cantilevers	cantilever	NOUN
iajs-3928	12	8	,	,	PUNCT
iajs-3928	12	9	and	and	CCONJ
iajs-3928	12	10	elongated	elongate	VERB
iajs-3928	12	11	vertical	vertical	ADJ
iajs-3928	12	12	columns	column	NOUN
iajs-3928	12	13	is	be	AUX
iajs-3928	12	14	typically	typically	ADV
iajs-3928	12	15	carried	carry	VERB
iajs-3928	12	16	out	out	ADP
iajs-3928	12	17	using	use	VERB
iajs-3928	12	18	the	the	DET
iajs-3928	12	19	principles	principle	NOUN
iajs-3928	12	20	of	of	ADP
iajs-3928	12	21	calculus	calculus	NOUN
iajs-3928	12	22	.	.	PUNCT
iajs-3928	13	1	however	however	ADV
iajs-3928	13	2	,	,	PUNCT
iajs-3928	13	3	this	this	DET
iajs-3928	13	4	paper	paper	NOUN
iajs-3928	13	5	introduces	introduce	VERB
iajs-3928	13	6	the	the	DET
iajs-3928	13	7	integral	integral	ADJ
iajs-3928	13	8	rohit	rohit	NOUN
iajs-3928	13	9	transform	transform	NOUN
iajs-3928	13	10	for	for	ADP
iajs-3928	13	11	the	the	DET
iajs-3928	13	12	analysis	analysis	NOUN
iajs-3928	13	13	of	of	ADP
iajs-3928	13	14	loaded	load	VERB
iajs-3928	13	15	beam	beam	NOUN
iajs-3928	13	16	supported	support	VERB
iajs-3928	13	17	at	at	ADP
iajs-3928	13	18	ends	end	NOUN
iajs-3928	13	19	,	,	PUNCT
iajs-3928	13	20	cantilever	cantilever	NOUN
iajs-3928	13	21	,	,	PUNCT
iajs-3928	13	22	and	and	CCONJ
iajs-3928	13	23	elongated	elongate	VERB
iajs-3928	13	24	columns	column	NOUN
iajs-3928	13	25	with	with	ADP
iajs-3928	13	26	low	low	ADJ
iajs-3928	13	27	buckling	buckle	VERB
iajs-3928	13	28	axial	axial	ADJ
iajs-3928	13	29	loads	load	NOUN
iajs-3928	13	30	.	.	PUNCT
iajs-3928	14	1	it	it	PRON
iajs-3928	14	2	is	be	AUX
iajs-3928	14	3	found	find	VERB
iajs-3928	14	4	that	that	SCONJ
iajs-3928	14	5	the	the	DET
iajs-3928	14	6	depression	depression	NOUN
iajs-3928	14	7	grows	grow	VERB
iajs-3928	14	8	as	as	ADP
iajs-3928	14	9	the	the	DET
iajs-3928	14	10	cantilever	cantilever	NOUN
iajs-3928	14	11	and	and	CCONJ
iajs-3928	14	12	beam	beam	NOUN
iajs-3928	14	13	lengths	length	NOUN
iajs-3928	14	14	that	that	PRON
iajs-3928	14	15	are	be	AUX
iajs-3928	14	16	loaded	load	VERB
iajs-3928	14	17	in	in	ADP
iajs-3928	14	18	the	the	DET
iajs-3928	14	19	middle	middle	NOUN
iajs-3928	14	20	and	and	CCONJ
iajs-3928	14	21	supported	support	VERB
iajs-3928	14	22	at	at	ADP
iajs-3928	14	23	both	both	DET
iajs-3928	14	24	ends	end	NOUN
iajs-3928	14	25	rise	rise	NOUN
iajs-3928	14	26	.	.	PUNCT
iajs-3928	15	1	an	an	DET
iajs-3928	15	2	attempt	attempt	NOUN
iajs-3928	15	3	has	have	AUX
iajs-3928	15	4	been	be	AUX
iajs-3928	15	5	made	make	VERB
iajs-3928	15	6	to	to	PART
iajs-3928	15	7	analyze	analyze	VERB
iajs-3928	15	8	the	the	DET
iajs-3928	15	9	elongated	elongate	VERB
iajs-3928	15	10	column	column	NOUN
iajs-3928	15	11	with	with	ADP
iajs-3928	15	12	low	low	ADJ
iajs-3928	15	13	axial	axial	ADJ
iajs-3928	15	14	buckling	buckling	NOUN
iajs-3928	15	15	loads	load	NOUN
iajs-3928	15	16	and	and	CCONJ
iajs-3928	15	17	derive	derive	VERB
iajs-3928	15	18	the	the	DET
iajs-3928	15	19	euler	euler	NOUN
iajs-3928	15	20	's	's	PART
iajs-3928	15	21	formula	formula	NOUN
iajs-3928	15	22	for	for	ADP
iajs-3928	15	23	buckling	buckle	VERB
iajs-3928	15	24	load	load	NOUN
iajs-3928	15	25	.	.	PUNCT
iajs-3928	16	1	the	the	DET
iajs-3928	16	2	obtained	obtain	VERB
iajs-3928	16	3	solutions	solution	NOUN
iajs-3928	16	4	are	be	AUX
iajs-3928	16	5	graphically	graphically	ADV
iajs-3928	16	6	represented	represent	VERB
iajs-3928	16	7	,	,	PUNCT
iajs-3928	16	8	and	and	CCONJ
iajs-3928	16	9	the	the	DET
iajs-3928	16	10	results	result	NOUN
iajs-3928	16	11	demonstrate	demonstrate	VERB
iajs-3928	16	12	accuracy	accuracy	NOUN
iajs-3928	16	13	,	,	PUNCT
iajs-3928	16	14	capability	capability	NOUN
iajs-3928	16	15	and	and	CCONJ
iajs-3928	16	16	effectiveness	effectiveness	NOUN
iajs-3928	16	17	of	of	ADP
iajs-3928	16	18	the	the	DET
iajs-3928	16	19	integral	integral	ADJ
iajs-3928	16	20	rohit	rohit	NOUN
iajs-3928	16	21	transform	transform	NOUN
iajs-3928	16	22	technique	technique	NOUN
iajs-3928	16	23	when	when	SCONJ
iajs-3928	16	24	compared	compare	VERB
iajs-3928	16	25	to	to	ADP
iajs-3928	16	26	existing	exist	VERB
iajs-3928	16	27	methods	method	NOUN
iajs-3928	16	28	in	in	ADP
iajs-3928	16	29	the	the	DET
iajs-3928	16	30	literature	literature	NOUN
iajs-3928	16	31	.	.	PUNCT
iajs-3928	17	1	the	the	DET
iajs-3928	17	2	rohit	rohit	PROPN
iajs-3928	17	3	transform	transform	NOUN
iajs-3928	17	4	involves	involve	VERB
iajs-3928	17	5	simple	simple	ADJ
iajs-3928	17	6	formulation	formulation	NOUN
iajs-3928	17	7	and	and	CCONJ
iajs-3928	17	8	less	less	ADV
iajs-3928	17	9	computational	computational	ADJ
iajs-3928	17	10	work	work	NOUN
iajs-3928	17	11	compared	compare	VERB
iajs-3928	17	12	to	to	ADP
iajs-3928	17	13	other	other	ADJ
iajs-3928	17	14	methods	method	NOUN
iajs-3928	17	15	available	available	ADJ
iajs-3928	17	16	in	in	ADP
iajs-3928	17	17	the	the	DET
iajs-3928	17	18	literature	literature	NOUN
iajs-3928	17	19	.	.	PUNCT
iajs-3928	18	1	keywords	keyword	NOUN
iajs-3928	18	2	:	:	PUNCT
iajs-3928	18	3	loaded	loaded	ADJ
iajs-3928	18	4	beam	beam	NOUN
iajs-3928	18	5	,	,	PUNCT
iajs-3928	18	6	cantilever	cantilever	NOUN
iajs-3928	18	7	,	,	PUNCT
iajs-3928	18	8	elongated	elongate	VERB
iajs-3928	18	9	columns	column	NOUN
iajs-3928	18	10	,	,	PUNCT
iajs-3928	18	11	integral	integral	ADJ
iajs-3928	18	12	rohit	rohit	NOUN
iajs-3928	18	13	transform	transform	NOUN
iajs-3928	18	14	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3928	18	15	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3928	18	16	https://orcid.org/0000-0002-9744-5131	https://orcid.org/0000-0002-9744-5131	PROPN
iajs-3928	18	17	mailto:guptarohit565@gmail.com	mailto:guptarohit565@gmail.com	PROPN
iajs-3928	18	18	https://orcid.org/0009-0004-6302-6096	https://orcid.org/0009-0004-6302-6096	PROPN
iajs-3928	18	19	mailto:srsharma.sharma001@gmail.com	mailto:srsharma.sharma001@gmail.com	X
iajs-3928	19	1	https://orcid.org/0000-0003-2250-8588	https://orcid.org/0000-0003-2250-8588	PROPN
iajs-3928	19	2	mailto:aniketgupta321@gmail.com	mailto:aniketgupta321@gmail.com	PROPN
iajs-3928	19	3	ihjpas	ihjpas	PROPN
iajs-3928	19	4	.	.	PUNCT
iajs-3928	20	1	2024	2024	NUM
iajs-3928	20	2	,	,	PUNCT
iajs-3928	20	3	37(4	37(4	PRON
iajs-3928	20	4	)	)	PUNCT
iajs-3928	20	5	382	382	NUM
iajs-3928	20	6	1	1	NUM
iajs-3928	20	7	.	.	PUNCT
iajs-3928	20	8	introduction	introduction	NOUN
iajs-3928	20	9	a	a	DET
iajs-3928	20	10	beam	beam	NOUN
iajs-3928	20	11	is	be	AUX
iajs-3928	20	12	a	a	DET
iajs-3928	20	13	structural	structural	ADJ
iajs-3928	20	14	element	element	NOUN
iajs-3928	20	15	with	with	ADP
iajs-3928	20	16	a	a	DET
iajs-3928	20	17	uniform	uniform	ADJ
iajs-3928	20	18	cross	cross	NOUN
iajs-3928	20	19	-	-	NOUN
iajs-3928	20	20	section	section	NOUN
iajs-3928	20	21	.	.	PUNCT
iajs-3928	21	1	it	it	PRON
iajs-3928	21	2	is	be	AUX
iajs-3928	21	3	described	describe	VERB
iajs-3928	21	4	by	by	ADP
iajs-3928	21	5	its	its	PRON
iajs-3928	21	6	significant	significant	ADJ
iajs-3928	21	7	length	length	NOUN
iajs-3928	21	8	compared	compare	VERB
iajs-3928	21	9	to	to	ADP
iajs-3928	21	10	its	its	PRON
iajs-3928	21	11	width	width	NOUN
iajs-3928	21	12	and	and	CCONJ
iajs-3928	21	13	thickness	thickness	NOUN
iajs-3928	21	14	.	.	PUNCT
iajs-3928	22	1	in	in	ADP
iajs-3928	22	2	such	such	ADJ
iajs-3928	22	3	structures	structure	NOUN
iajs-3928	22	4	,	,	PUNCT
iajs-3928	22	5	the	the	DET
iajs-3928	22	6	shearing	shearing	NOUN
iajs-3928	22	7	stress	stress	NOUN
iajs-3928	22	8	across	across	ADP
iajs-3928	22	9	any	any	DET
iajs-3928	22	10	cross	cross	NOUN
iajs-3928	22	11	-	-	NOUN
iajs-3928	22	12	section	section	NOUN
iajs-3928	22	13	is	be	AUX
iajs-3928	22	14	considered	consider	VERB
iajs-3928	22	15	to	to	PART
iajs-3928	22	16	be	be	AUX
iajs-3928	22	17	negligibly	negligibly	ADV
iajs-3928	22	18	small	small	ADJ
iajs-3928	22	19	[	[	X
iajs-3928	22	20	1	1	NUM
iajs-3928	22	21	]	]	PUNCT
iajs-3928	22	22	.	.	PUNCT
iajs-3928	23	1	a	a	DET
iajs-3928	23	2	cantilever	cantilever	NOUN
iajs-3928	23	3	,	,	PUNCT
iajs-3928	23	4	on	on	ADP
iajs-3928	23	5	the	the	DET
iajs-3928	23	6	other	other	ADJ
iajs-3928	23	7	hand	hand	NOUN
iajs-3928	23	8	,	,	PUNCT
iajs-3928	23	9	refers	refer	VERB
iajs-3928	23	10	to	to	ADP
iajs-3928	23	11	a	a	DET
iajs-3928	23	12	slender	slender	NOUN
iajs-3928	23	13	and	and	CCONJ
iajs-3928	23	14	uniform	uniform	ADJ
iajs-3928	23	15	beam	beam	NOUN
iajs-3928	23	16	that	that	PRON
iajs-3928	23	17	is	be	AUX
iajs-3928	23	18	horizontally	horizontally	ADV
iajs-3928	23	19	fixed	fix	VERB
iajs-3928	23	20	at	at	ADP
iajs-3928	23	21	one	one	NUM
iajs-3928	23	22	end	end	NOUN
iajs-3928	23	23	and	and	CCONJ
iajs-3928	23	24	subjected	subject	VERB
iajs-3928	23	25	to	to	ADP
iajs-3928	23	26	loading	load	VERB
iajs-3928	23	27	at	at	ADP
iajs-3928	23	28	the	the	DET
iajs-3928	23	29	opposite	opposite	ADJ
iajs-3928	23	30	end	end	NOUN
iajs-3928	23	31	.	.	PUNCT
iajs-3928	24	1	beams	beam	NOUN
iajs-3928	24	2	are	be	AUX
iajs-3928	24	3	commonly	commonly	ADV
iajs-3928	24	4	employed	employ	VERB
iajs-3928	24	5	in	in	ADP
iajs-3928	24	6	the	the	DET
iajs-3928	24	7	construction	construction	NOUN
iajs-3928	24	8	of	of	ADP
iajs-3928	24	9	bridges	bridge	NOUN
iajs-3928	24	10	or	or	CCONJ
iajs-3928	24	11	for	for	ADP
iajs-3928	24	12	the	the	DET
iajs-3928	24	13	purpose	purpose	NOUN
iajs-3928	24	14	of	of	ADP
iajs-3928	24	15	supporting	support	VERB
iajs-3928	24	16	heavy	heavy	ADJ
iajs-3928	24	17	loads	load	NOUN
iajs-3928	24	18	,	,	PUNCT
iajs-3928	24	19	often	often	ADV
iajs-3928	24	20	found	find	VERB
iajs-3928	24	21	in	in	ADP
iajs-3928	24	22	the	the	DET
iajs-3928	24	23	structure	structure	NOUN
iajs-3928	24	24	of	of	ADP
iajs-3928	24	25	multistoried	multistorie	VERB
iajs-3928	24	26	buildings	building	NOUN
iajs-3928	25	1	[	[	X
iajs-3928	25	2	2	2	NUM
iajs-3928	25	3	]	]	PUNCT
iajs-3928	25	4	.	.	PUNCT
iajs-3928	26	1	in	in	ADP
iajs-3928	26	2	engineering	engineering	NOUN
iajs-3928	26	3	design	design	NOUN
iajs-3928	26	4	,	,	PUNCT
iajs-3928	26	5	the	the	DET
iajs-3928	26	6	elastic	elastic	ADJ
iajs-3928	26	7	behavior	behavior	NOUN
iajs-3928	26	8	of	of	ADP
iajs-3928	26	9	materials	material	NOUN
iajs-3928	26	10	assumes	assume	VERB
iajs-3928	26	11	a	a	DET
iajs-3928	26	12	critical	critical	ADJ
iajs-3928	26	13	role	role	NOUN
iajs-3928	26	14	in	in	ADP
iajs-3928	26	15	various	various	ADJ
iajs-3928	26	16	applications	application	NOUN
iajs-3928	26	17	such	such	ADJ
iajs-3928	26	18	as	as	ADP
iajs-3928	26	19	the	the	DET
iajs-3928	26	20	construction	construction	NOUN
iajs-3928	26	21	of	of	ADP
iajs-3928	26	22	buildings	building	NOUN
iajs-3928	26	23	,	,	PUNCT
iajs-3928	26	24	bridges	bridge	NOUN
iajs-3928	26	25	,	,	PUNCT
iajs-3928	26	26	automobiles	automobile	NOUN
iajs-3928	26	27	,	,	PUNCT
iajs-3928	26	28	and	and	CCONJ
iajs-3928	26	29	rope	rope	NOUN
iajs-3928	26	30	-	-	PUNCT
iajs-3928	26	31	ways	way	NOUN
iajs-3928	26	32	.	.	PUNCT
iajs-3928	27	1	the	the	DET
iajs-3928	27	2	property	property	NOUN
iajs-3928	27	3	of	of	ADP
iajs-3928	27	4	elasticity	elasticity	NOUN
iajs-3928	27	5	in	in	ADP
iajs-3928	27	6	beam	beam	NOUN
iajs-3928	27	7	materials	material	NOUN
iajs-3928	27	8	leads	lead	VERB
iajs-3928	27	9	to	to	ADP
iajs-3928	27	10	the	the	DET
iajs-3928	27	11	generation	generation	NOUN
iajs-3928	27	12	of	of	ADP
iajs-3928	27	13	a	a	DET
iajs-3928	27	14	restoring	restore	VERB
iajs-3928	27	15	couple	couple	NOUN
iajs-3928	27	16	when	when	SCONJ
iajs-3928	27	17	subjected	subject	VERB
iajs-3928	27	18	to	to	ADP
iajs-3928	27	19	deforming	deform	VERB
iajs-3928	27	20	forces	force	NOUN
iajs-3928	27	21	,	,	PUNCT
iajs-3928	27	22	which	which	PRON
iajs-3928	27	23	acts	act	VERB
iajs-3928	27	24	in	in	ADP
iajs-3928	27	25	equilibrium	equilibrium	NOUN
iajs-3928	27	26	and	and	CCONJ
iajs-3928	27	27	is	be	AUX
iajs-3928	27	28	equal	equal	ADJ
iajs-3928	27	29	in	in	ADP
iajs-3928	27	30	magnitude	magnitude	NOUN
iajs-3928	27	31	but	but	CCONJ
iajs-3928	27	32	opposite	opposite	ADJ
iajs-3928	27	33	in	in	ADP
iajs-3928	27	34	direction	direction	NOUN
iajs-3928	27	35	to	to	ADP
iajs-3928	27	36	the	the	DET
iajs-3928	27	37	bending	bend	VERB
iajs-3928	27	38	couple	couple	NOUN
iajs-3928	27	39	.	.	PUNCT
iajs-3928	28	1	this	this	DET
iajs-3928	28	2	restoring	restore	VERB
iajs-3928	28	3	moment	moment	NOUN
iajs-3928	28	4	is	be	AUX
iajs-3928	28	5	known	know	VERB
iajs-3928	28	6	as	as	ADP
iajs-3928	28	7	the	the	DET
iajs-3928	28	8	bending	bend	VERB
iajs-3928	28	9	moment	moment	NOUN
iajs-3928	28	10	[	[	X
iajs-3928	28	11	3	3	NUM
iajs-3928	28	12	]	]	PUNCT
iajs-3928	28	13	.	.	PUNCT
iajs-3928	29	1	building	building	NOUN
iajs-3928	29	2	frames	frame	NOUN
iajs-3928	29	3	employ	employ	VERB
iajs-3928	29	4	columns	column	NOUN
iajs-3928	29	5	as	as	ADP
iajs-3928	29	6	one	one	NUM
iajs-3928	29	7	of	of	ADP
iajs-3928	29	8	their	their	PRON
iajs-3928	29	9	vertical	vertical	ADJ
iajs-3928	29	10	compression	compression	NOUN
iajs-3928	29	11	components	component	NOUN
iajs-3928	29	12	,	,	PUNCT
iajs-3928	29	13	and	and	CCONJ
iajs-3928	29	14	they	they	PRON
iajs-3928	29	15	are	be	AUX
iajs-3928	29	16	susceptible	susceptible	ADJ
iajs-3928	29	17	to	to	ADP
iajs-3928	29	18	buckling	buckle	VERB
iajs-3928	29	19	and	and	CCONJ
iajs-3928	29	20	failing	fail	VERB
iajs-3928	29	21	at	at	ADP
iajs-3928	29	22	mild	mild	ADJ
iajs-3928	29	23	axial	axial	ADJ
iajs-3928	29	24	stresses	stress	NOUN
iajs-3928	29	25	.	.	PUNCT
iajs-3928	30	1	these	these	DET
iajs-3928	30	2	buckles	buckle	NOUN
iajs-3928	30	3	when	when	SCONJ
iajs-3928	30	4	the	the	DET
iajs-3928	30	5	axial	axial	ADJ
iajs-3928	30	6	load	load	NOUN
iajs-3928	30	7	reaches	reach	VERB
iajs-3928	30	8	a	a	DET
iajs-3928	30	9	threshold	threshold	NOUN
iajs-3928	30	10	value	value	NOUN
iajs-3928	30	11	known	know	VERB
iajs-3928	30	12	as	as	ADP
iajs-3928	30	13	the	the	DET
iajs-3928	30	14	critical	critical	ADJ
iajs-3928	30	15	buckling	buckling	NOUN
iajs-3928	30	16	load	load	NOUN
iajs-3928	30	17	because	because	SCONJ
iajs-3928	30	18	they	they	PRON
iajs-3928	30	19	are	be	AUX
iajs-3928	30	20	significantly	significantly	ADV
iajs-3928	30	21	longer	long	ADJ
iajs-3928	30	22	than	than	ADP
iajs-3928	30	23	their	their	PRON
iajs-3928	30	24	lateral	lateral	ADJ
iajs-3928	30	25	dimensions	dimension	NOUN
iajs-3928	30	26	[	[	X
iajs-3928	30	27	4	4	NUM
iajs-3928	30	28	]	]	PUNCT
iajs-3928	30	29	.	.	PUNCT
iajs-3928	31	1	one	one	NUM
iajs-3928	31	2	of	of	ADP
iajs-3928	31	3	the	the	DET
iajs-3928	31	4	failures	failure	NOUN
iajs-3928	31	5	of	of	ADP
iajs-3928	31	6	a	a	DET
iajs-3928	31	7	structure	structure	NOUN
iajs-3928	31	8	supporting	support	VERB
iajs-3928	31	9	a	a	DET
iajs-3928	31	10	load	load	NOUN
iajs-3928	31	11	is	be	AUX
iajs-3928	31	12	buckling	buckle	VERB
iajs-3928	31	13	.	.	PUNCT
iajs-3928	32	1	because	because	SCONJ
iajs-3928	32	2	they	they	PRON
iajs-3928	32	3	are	be	AUX
iajs-3928	32	4	thin	thin	ADJ
iajs-3928	32	5	,	,	PUNCT
iajs-3928	32	6	columns	column	NOUN
iajs-3928	32	7	buckle	buckle	VERB
iajs-3928	32	8	when	when	SCONJ
iajs-3928	32	9	the	the	DET
iajs-3928	32	10	axial	axial	ADJ
iajs-3928	32	11	load	load	NOUN
iajs-3928	32	12	reaches	reach	VERB
iajs-3928	32	13	a	a	DET
iajs-3928	32	14	threshold	threshold	NOUN
iajs-3928	32	15	amount	amount	NOUN
iajs-3928	32	16	called	call	VERB
iajs-3928	32	17	the	the	DET
iajs-3928	32	18	critical	critical	ADJ
iajs-3928	32	19	buckling	buckling	NOUN
iajs-3928	32	20	load	load	NOUN
iajs-3928	32	21	.	.	PUNCT
iajs-3928	33	1	they	they	PRON
iajs-3928	33	2	also	also	ADV
iajs-3928	33	3	deflect	deflect	VERB
iajs-3928	33	4	laterally	laterally	ADV
iajs-3928	33	5	when	when	SCONJ
iajs-3928	33	6	compressed	compress	VERB
iajs-3928	33	7	.	.	PUNCT
iajs-3928	34	1	it	it	PRON
iajs-3928	34	2	has	have	AUX
iajs-3928	34	3	been	be	AUX
iajs-3928	34	4	shown	show	VERB
iajs-3928	34	5	that	that	SCONJ
iajs-3928	34	6	low	low	ADJ
iajs-3928	34	7	buckling	buckle	VERB
iajs-3928	34	8	axial	axial	ADJ
iajs-3928	34	9	loads	load	NOUN
iajs-3928	34	10	cause	cause	VERB
iajs-3928	34	11	the	the	DET
iajs-3928	34	12	columns	column	NOUN
iajs-3928	34	13	to	to	PART
iajs-3928	34	14	fail	fail	VERB
iajs-3928	34	15	.	.	PUNCT
iajs-3928	35	1	according	accord	VERB
iajs-3928	35	2	to	to	ADP
iajs-3928	35	3	euler	euler	PROPN
iajs-3928	35	4	's	's	PART
iajs-3928	35	5	theory	theory	NOUN
iajs-3928	35	6	of	of	ADP
iajs-3928	35	7	columns	column	NOUN
iajs-3928	35	8	,	,	PUNCT
iajs-3928	35	9	a	a	DET
iajs-3928	35	10	column	column	NOUN
iajs-3928	35	11	behaves	behave	VERB
iajs-3928	35	12	to	to	PART
iajs-3928	35	13	resist	resist	VERB
iajs-3928	35	14	buckling	buckling	NOUN
iajs-3928	35	15	.	.	PUNCT
iajs-3928	36	1	buckling	buckling	NOUN
iajs-3928	36	2	is	be	AUX
iajs-3928	36	3	influenced	influence	VERB
iajs-3928	36	4	by	by	ADP
iajs-3928	36	5	the	the	DET
iajs-3928	36	6	end	end	NOUN
iajs-3928	36	7	condition	condition	NOUN
iajs-3928	36	8	of	of	ADP
iajs-3928	36	9	the	the	DET
iajs-3928	36	10	columns	column	NOUN
iajs-3928	36	11	and	and	CCONJ
iajs-3928	36	12	flexural	flexural	ADJ
iajs-3928	36	13	rigidity	rigidity	NOUN
iajs-3928	36	14	.	.	PUNCT
iajs-3928	37	1	commonly	commonly	ADV
iajs-3928	37	2	,	,	PUNCT
iajs-3928	37	3	standard	standard	ADJ
iajs-3928	37	4	methods	method	NOUN
iajs-3928	37	5	like	like	ADP
iajs-3928	37	6	the	the	DET
iajs-3928	37	7	calculus	calculus	NOUN
iajs-3928	37	8	technique	technique	NOUN
iajs-3928	37	9	are	be	AUX
iajs-3928	37	10	used	use	VERB
iajs-3928	37	11	to	to	PART
iajs-3928	37	12	analyze	analyze	VERB
iajs-3928	37	13	loaded	load	VERB
iajs-3928	37	14	beams	beam	NOUN
iajs-3928	37	15	supported	support	VERB
iajs-3928	37	16	at	at	ADP
iajs-3928	37	17	their	their	PRON
iajs-3928	37	18	ends	end	NOUN
iajs-3928	37	19	,	,	PUNCT
iajs-3928	37	20	cantilevers	cantilever	NOUN
iajs-3928	37	21	,	,	PUNCT
iajs-3928	37	22	and	and	CCONJ
iajs-3928	37	23	elongated	elongate	VERB
iajs-3928	37	24	columns	column	NOUN
iajs-3928	37	25	with	with	ADP
iajs-3928	37	26	low	low	ADJ
iajs-3928	37	27	buckling	buckle	VERB
iajs-3928	37	28	axial	axial	ADJ
iajs-3928	37	29	loads	load	NOUN
iajs-3928	38	1	[	[	X
iajs-3928	38	2	5–8	5–8	NOUN
iajs-3928	38	3	]	]	PUNCT
iajs-3928	38	4	.	.	PUNCT
iajs-3928	39	1	moreover	moreover	ADV
iajs-3928	39	2	,	,	PUNCT
iajs-3928	39	3	euler	euler	PROPN
iajs-3928	39	4	's	's	PART
iajs-3928	39	5	theory	theory	NOUN
iajs-3928	39	6	of	of	ADP
iajs-3928	39	7	columns	column	NOUN
iajs-3928	39	8	is	be	AUX
iajs-3928	39	9	used	use	VERB
iajs-3928	39	10	to	to	PART
iajs-3928	39	11	find	find	VERB
iajs-3928	39	12	out	out	ADP
iajs-3928	39	13	the	the	DET
iajs-3928	39	14	buckling	buckle	VERB
iajs-3928	39	15	load	load	NOUN
iajs-3928	39	16	of	of	ADP
iajs-3928	39	17	the	the	DET
iajs-3928	39	18	column	column	NOUN
iajs-3928	39	19	.	.	PUNCT
iajs-3928	40	1	this	this	DET
iajs-3928	40	2	study	study	NOUN
iajs-3928	40	3	presents	present	VERB
iajs-3928	40	4	the	the	DET
iajs-3928	40	5	analysis	analysis	NOUN
iajs-3928	40	6	of	of	ADP
iajs-3928	40	7	the	the	DET
iajs-3928	40	8	loaded	load	VERB
iajs-3928	40	9	beam	beam	NOUN
iajs-3928	40	10	supported	support	VERB
iajs-3928	40	11	at	at	ADP
iajs-3928	40	12	its	its	PRON
iajs-3928	40	13	ends	end	NOUN
iajs-3928	40	14	,	,	PUNCT
iajs-3928	40	15	the	the	DET
iajs-3928	40	16	cantilever	cantilever	NOUN
iajs-3928	40	17	,	,	PUNCT
iajs-3928	40	18	and	and	CCONJ
iajs-3928	40	19	the	the	DET
iajs-3928	40	20	elongated	elongate	VERB
iajs-3928	40	21	columns	column	NOUN
iajs-3928	40	22	with	with	ADP
iajs-3928	40	23	modest	modest	ADJ
iajs-3928	40	24	buckling	buckle	VERB
iajs-3928	40	25	axial	axial	ADJ
iajs-3928	40	26	loads	load	NOUN
iajs-3928	40	27	via	via	ADP
iajs-3928	40	28	the	the	DET
iajs-3928	40	29	integral	integral	ADJ
iajs-3928	40	30	rohit	rohit	NOUN
iajs-3928	40	31	transform	transform	NOUN
iajs-3928	40	32	.	.	PUNCT
iajs-3928	41	1	this	this	DET
iajs-3928	41	2	integral	integral	ADJ
iajs-3928	41	3	transform	transform	NOUN
iajs-3928	41	4	[	[	X
iajs-3928	41	5	9	9	NUM
iajs-3928	41	6	]	]	PUNCT
iajs-3928	41	7	has	have	AUX
iajs-3928	41	8	been	be	AUX
iajs-3928	41	9	proposed	propose	VERB
iajs-3928	41	10	by	by	ADP
iajs-3928	41	11	the	the	DET
iajs-3928	41	12	author	author	NOUN
iajs-3928	41	13	rohit	rohit	PROPN
iajs-3928	41	14	gupta	gupta	PROPN
iajs-3928	41	15	in	in	ADP
iajs-3928	41	16	the	the	DET
iajs-3928	41	17	year	year	NOUN
iajs-3928	41	18	2020	2020	NUM
iajs-3928	41	19	.	.	PUNCT
iajs-3928	42	1	it	it	PRON
iajs-3928	42	2	has	have	AUX
iajs-3928	42	3	been	be	AUX
iajs-3928	42	4	applied	apply	VERB
iajs-3928	42	5	to	to	PART
iajs-3928	42	6	solve	solve	VERB
iajs-3928	42	7	initial	initial	ADJ
iajs-3928	42	8	value	value	NOUN
iajs-3928	42	9	problems	problem	NOUN
iajs-3928	42	10	in	in	ADP
iajs-3928	42	11	science	science	NOUN
iajs-3928	42	12	and	and	CCONJ
iajs-3928	42	13	engineering	engineering	NOUN
iajs-3928	42	14	[	[	X
iajs-3928	42	15	10	10	NUM
iajs-3928	42	16	-	-	SYM
iajs-3928	42	17	12	12	NUM
iajs-3928	42	18	]	]	PUNCT
iajs-3928	42	19	.	.	PUNCT
iajs-3928	43	1	in	in	ADP
iajs-3928	43	2	contrast	contrast	NOUN
iajs-3928	43	3	to	to	ADP
iajs-3928	43	4	the	the	DET
iajs-3928	43	5	calculus	calculus	NOUN
iajs-3928	43	6	method	method	NOUN
iajs-3928	43	7	,	,	PUNCT
iajs-3928	43	8	the	the	DET
iajs-3928	43	9	suggested	suggest	VERB
iajs-3928	43	10	method	method	NOUN
iajs-3928	43	11	presents	present	VERB
iajs-3928	43	12	an	an	DET
iajs-3928	43	13	alternate	alternate	ADJ
iajs-3928	43	14	approach	approach	NOUN
iajs-3928	43	15	for	for	ADP
iajs-3928	43	16	the	the	DET
iajs-3928	43	17	analysis	analysis	NOUN
iajs-3928	43	18	of	of	ADP
iajs-3928	43	19	loaded	load	VERB
iajs-3928	43	20	beams	beam	NOUN
iajs-3928	43	21	supported	support	VERB
iajs-3928	43	22	at	at	ADP
iajs-3928	43	23	their	their	PRON
iajs-3928	43	24	ends	end	NOUN
iajs-3928	43	25	,	,	PUNCT
iajs-3928	43	26	cantilevers	cantilever	NOUN
iajs-3928	43	27	,	,	PUNCT
iajs-3928	43	28	and	and	CCONJ
iajs-3928	43	29	elongated	elongate	VERB
iajs-3928	43	30	columns	column	NOUN
iajs-3928	43	31	with	with	ADP
iajs-3928	43	32	low	low	ADJ
iajs-3928	43	33	buckling	buckle	VERB
iajs-3928	43	34	axial	axial	ADJ
iajs-3928	43	35	loads	load	NOUN
iajs-3928	43	36	.	.	PUNCT
iajs-3928	44	1	2	2	X
iajs-3928	44	2	.	.	X
iajs-3928	44	3	rohit	rohit	PROPN
iajs-3928	44	4	transform	transform	NOUN
iajs-3928	44	5	and	and	CCONJ
iajs-3928	44	6	its	its	PRON
iajs-3928	44	7	properties	property	NOUN
iajs-3928	44	8	the	the	DET
iajs-3928	44	9	integral	integral	ADJ
iajs-3928	44	10	rohit	rohit	NOUN
iajs-3928	44	11	transform	transform	NOUN
iajs-3928	44	12	,	,	PUNCT
iajs-3928	44	13	also	also	ADV
iajs-3928	44	14	written	write	VERB
iajs-3928	44	15	as	as	ADP
iajs-3928	44	16	integral	integral	ADJ
iajs-3928	44	17	rt	rt	PROPN
iajs-3928	44	18	,	,	PUNCT
iajs-3928	44	19	[	[	X
iajs-3928	44	20	9	9	NUM
iajs-3928	44	21	]	]	PUNCT
iajs-3928	44	22	is	be	AUX
iajs-3928	44	23	defined	define	VERB
iajs-3928	44	24	for	for	ADP
iajs-3928	44	25	a	a	DET
iajs-3928	44	26	function	function	NOUN
iajs-3928	44	27	of	of	ADP
iajs-3928	44	28	exponential	exponential	ADJ
iajs-3928	44	29	order	order	NOUN
iajs-3928	44	30	by	by	ADP
iajs-3928	44	31	the	the	DET
iajs-3928	44	32	integral	integral	ADJ
iajs-3928	44	33	equations	equation	NOUN
iajs-3928	44	34	as	as	ADP
iajs-3928	44	35	r{h(t	r{h(t	NOUN
iajs-3928	44	36	)	)	PUNCT
iajs-3928	44	37	}	}	PUNCT
iajs-3928	45	1	=	=	PUNCT
iajs-3928	46	1	𝑞3	𝑞3	PROPN
iajs-3928	46	2	∫	∫	PROPN
iajs-3928	46	3	𝑒−𝑞𝑡∞	𝑒−𝑞𝑡∞	PROPN
iajs-3928	46	4	0	0	NUM
iajs-3928	46	5	ℎ(𝑡)𝑑𝑡	ℎ(𝑡)𝑑𝑡	PROPN
iajs-3928	46	6	,	,	PUNCT
iajs-3928	46	7	𝑡	𝑡	X
iajs-3928	46	8	≥	≥	NOUN
iajs-3928	46	9	0	0	NUM
iajs-3928	46	10	,	,	PUNCT
iajs-3928	46	11	𝑞1	𝑞1	PROPN
iajs-3928	46	12	≤	≤	PUNCT
iajs-3928	46	13	𝑞	𝑞	PROPN
iajs-3928	46	14	≤	≤	ADJ
iajs-3928	46	15	𝑞2	𝑞2	NOUN
iajs-3928	46	16	.	.	PUNCT
iajs-3928	47	1	the	the	DET
iajs-3928	47	2	variable	variable	ADJ
iajs-3928	47	3	q	q	NOUN
iajs-3928	47	4	is	be	AUX
iajs-3928	47	5	used	use	VERB
iajs-3928	47	6	to	to	PART
iajs-3928	47	7	factor	factor	VERB
iajs-3928	47	8	the	the	DET
iajs-3928	47	9	variable	variable	ADJ
iajs-3928	47	10	t	t	NOUN
iajs-3928	47	11	in	in	ADP
iajs-3928	47	12	the	the	DET
iajs-3928	47	13	argument	argument	NOUN
iajs-3928	47	14	of	of	ADP
iajs-3928	47	15	the	the	DET
iajs-3928	47	16	function	function	NOUN
iajs-3928	47	17	h.	h.	PROPN
iajs-3928	48	1	the	the	DET
iajs-3928	48	2	rohit	rohit	NOUN
iajs-3928	48	3	transforms	transform	VERB
iajs-3928	48	4	of	of	ADP
iajs-3928	48	5	unidentified	unidentified	ADJ
iajs-3928	48	6	functions	function	NOUN
iajs-3928	48	7	[	[	X
iajs-3928	48	8	10	10	NUM
iajs-3928	48	9	]	]	PUNCT
iajs-3928	48	10	are	be	AUX
iajs-3928	48	11	given	give	VERB
iajs-3928	48	12	by	by	ADP
iajs-3928	48	13			ADJ
iajs-3928	48	14	𝑅	𝑅	PROPN
iajs-3928	48	15	{	{	PUNCT
iajs-3928	48	16	𝑡𝑛	𝑡𝑛	PROPN
iajs-3928	48	17	}	}	PUNCT
iajs-3928	48	18	=	=	SYM
iajs-3928	48	19	𝑛	𝑛	PROPN
iajs-3928	48	20	!	!	PUNCT
iajs-3928	48	21	𝑞𝑛−2	𝑞𝑛−2	NOUN
iajs-3928	48	22			PROPN
iajs-3928	48	23	𝑅	𝑅	PROPN
iajs-3928	48	24	{	{	PUNCT
iajs-3928	48	25	𝑠𝑖𝑛𝑏𝑡	𝑠𝑖𝑛𝑏𝑡	NOUN
iajs-3928	48	26	}	}	PUNCT
iajs-3928	48	27	=	=	SYM
iajs-3928	48	28	𝑏	𝑏	PROPN
iajs-3928	48	29	𝑞3	𝑞3	PROPN
iajs-3928	48	30	𝑞2+𝑏2	𝑞2+𝑏2	PROPN
iajs-3928	48	31			PROPN
iajs-3928	48	32	𝑅	𝑅	PROPN
iajs-3928	48	33	{	{	PUNCT
iajs-3928	48	34	𝑐𝑜𝑠𝑏𝑡	𝑐𝑜𝑠𝑏𝑡	NOUN
iajs-3928	48	35	}	}	PUNCT
iajs-3928	48	36	=	=	SYM
iajs-3928	48	37	𝑞4	𝑞4	PROPN
iajs-3928	48	38	𝑞2+𝑏2	𝑞2+𝑏2	PROPN
iajs-3928	48	39			PROPN
iajs-3928	48	40	𝑅	𝑅	PROPN
iajs-3928	48	41	{	{	PUNCT
iajs-3928	48	42	𝑒𝑏𝑡	𝑒𝑏𝑡	PROPN
iajs-3928	48	43	}	}	PUNCT
iajs-3928	48	44	=	=	PUNCT
iajs-3928	49	1	𝑞3	𝑞3	NOUN
iajs-3928	49	2	𝑞−𝑏	𝑞−𝑏	NOUN
iajs-3928	49	3	ihjpas	ihjpa	VERB
iajs-3928	49	4	.	.	PUNCT
iajs-3928	50	1	2024	2024	NUM
iajs-3928	50	2	,	,	PUNCT
iajs-3928	50	3	37(4	37(4	PRON
iajs-3928	50	4	)	)	PUNCT
iajs-3928	50	5	383	383	NUM
iajs-3928	50	6	the	the	DET
iajs-3928	50	7	rohit	rohit	NOUN
iajs-3928	50	8	transforms	transform	VERB
iajs-3928	50	9	(	(	PUNCT
iajs-3928	50	10	rt	rt	INTJ
iajs-3928	50	11	)	)	PUNCT
iajs-3928	50	12	of	of	ADP
iajs-3928	50	13	some	some	DET
iajs-3928	50	14	derivatives	derivative	NOUN
iajs-3928	50	15	are	be	AUX
iajs-3928	50	16	[	[	X
iajs-3928	50	17	11	11	NUM
iajs-3928	50	18	]	]	PUNCT
iajs-3928	50	19	given	give	VERB
iajs-3928	50	20	by	by	ADP
iajs-3928	50	21	𝑅	𝑅	PROPN
iajs-3928	50	22	{	{	PUNCT
iajs-3928	50	23	𝑔′(𝑡	𝑔′(𝑡	NOUN
iajs-3928	50	24	)	)	PUNCT
iajs-3928	50	25	}	}	PUNCT
iajs-3928	50	26	=	=	PUNCT
iajs-3928	50	27	𝑞𝐺(𝑞	𝑞𝐺(𝑞	NUM
iajs-3928	50	28	)	)	PUNCT
iajs-3928	50	29	−	−	PROPN
iajs-3928	50	30	𝑞3𝑔(0	𝑞3𝑔(0	NOUN
iajs-3928	50	31	)	)	PUNCT
iajs-3928	50	32	,	,	PUNCT
iajs-3928	50	33	𝑅{𝑔′′(𝑡	𝑅{𝑔′′(𝑡	PROPN
iajs-3928	50	34	)	)	PUNCT
iajs-3928	50	35	}	}	PUNCT
iajs-3928	50	36	=	=	SYM
iajs-3928	50	37	𝑞2𝐺(𝑞	𝑞2𝐺(𝑞	NOUN
iajs-3928	50	38	)	)	PUNCT
iajs-3928	50	39	−	−	PROPN
iajs-3928	51	1	𝑞4𝑔(0	𝑞4𝑔(0	PROPN
iajs-3928	51	2	)	)	PUNCT
iajs-3928	51	3	−	−	PROPN
iajs-3928	52	1	𝑞3𝑔′(0	𝑞3𝑔′(0	NOUN
iajs-3928	52	2	)	)	PUNCT
iajs-3928	52	3	,	,	PUNCT
iajs-3928	52	4	𝑅{𝑔′′′(𝑡	𝑅{𝑔′′′(𝑡	PROPN
iajs-3928	52	5	)	)	PUNCT
iajs-3928	52	6	}	}	PUNCT
iajs-3928	52	7	=	=	PUNCT
iajs-3928	52	8	𝑞3𝐺(𝑞	𝑞3𝐺(𝑞	X
iajs-3928	52	9	)	)	PUNCT
iajs-3928	52	10	−	−	PROPN
iajs-3928	52	11	𝑞5𝑔(0	𝑞5𝑔(0	NUM
iajs-3928	52	12	)	)	PUNCT
iajs-3928	52	13	−	−	PROPN
iajs-3928	53	1	𝑞4𝑔′(0	𝑞4𝑔′(0	NOUN
iajs-3928	53	2	)	)	PUNCT
iajs-3928	53	3	−	−	PROPN
iajs-3928	53	4	𝑞3𝑔′′(0	𝑞3𝑔′′(0	NOUN
iajs-3928	53	5	)	)	PUNCT
iajs-3928	53	6	.	.	PUNCT
iajs-3928	54	1	in	in	ADP
iajs-3928	54	2	general	general	ADJ
iajs-3928	54	3	,	,	PUNCT
iajs-3928	54	4	𝑅{𝑔n(𝑡	𝑅{𝑔n(𝑡	NOUN
iajs-3928	54	5	)	)	PUNCT
iajs-3928	54	6	}	}	PUNCT
iajs-3928	54	7	=	=	SYM
iajs-3928	54	8	𝑞n𝑅{𝑔(𝑡	𝑞n𝑅{𝑔(𝑡	NUM
iajs-3928	54	9	)	)	PUNCT
iajs-3928	54	10	}	}	PUNCT
iajs-3928	54	11	−	−	ADP
iajs-3928	54	12	∑	∑	PUNCT
iajs-3928	54	13	𝑞𝑛−𝑘+3𝑛	𝑞𝑛−𝑘+3𝑛	PROPN
iajs-3928	54	14	𝑘=1	𝑘=1	X
iajs-3928	54	15	𝑔k−1(0	𝑔k−1(0	PROPN
iajs-3928	54	16	)	)	PUNCT
iajs-3928	54	17	.	.	PUNCT
iajs-3928	55	1	a	a	DET
iajs-3928	55	2	unit	unit	NOUN
iajs-3928	55	3	step	step	NOUN
iajs-3928	55	4	function	function	NOUN
iajs-3928	55	5	is	be	AUX
iajs-3928	55	6	written	write	VERB
iajs-3928	55	7	as	as	ADP
iajs-3928	55	8	𝑈(𝑡	𝑈(𝑡	ADP
iajs-3928	55	9	−	−	NUM
iajs-3928	55	10	𝑎	𝑎	NOUN
iajs-3928	55	11	)	)	PUNCT
iajs-3928	55	12	=	=	SYM
iajs-3928	55	13	0	0	NUM
iajs-3928	55	14	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3928	55	15	𝑡	𝑡	X
iajs-3928	55	16	<	<	X
iajs-3928	55	17	𝑎	𝑎	NOUN
iajs-3928	55	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	55	19	1	1	NUM
iajs-3928	55	20	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3928	55	21	𝑡	𝑡	PROPN
iajs-3928	55	22	≥	≥	PROPN
iajs-3928	55	23	a.	a.	NOUN
iajs-3928	55	24	the	the	DET
iajs-3928	55	25	rohit	rohit	NOUN
iajs-3928	55	26	transform	transform	NOUN
iajs-3928	55	27	of	of	ADP
iajs-3928	55	28	a	a	DET
iajs-3928	55	29	unit	unit	NOUN
iajs-3928	55	30	step	step	NOUN
iajs-3928	55	31	function	function	NOUN
iajs-3928	55	32	is	be	AUX
iajs-3928	55	33	given	give	VERB
iajs-3928	55	34	by	by	ADP
iajs-3928	55	35	r{𝑈(𝑡	r{𝑈(𝑡	PROPN
iajs-3928	55	36	−	−	NUM
iajs-3928	55	37	𝑎	𝑎	NOUN
iajs-3928	55	38	)	)	PUNCT
iajs-3928	55	39	}	}	PUNCT
iajs-3928	55	40	=	=	PUNCT
iajs-3928	56	1	𝑞3	𝑞3	NOUN
iajs-3928	56	2	∫	∫	PROPN
iajs-3928	56	3	𝑒−𝑞𝑡	𝑒−𝑞𝑡	PROPN
iajs-3928	56	4	∞	∞	PROPN
iajs-3928	56	5	0	0	NUM
iajs-3928	56	6	𝑈(𝑡	𝑈(𝑡	PRON
iajs-3928	56	7	−	−	NOUN
iajs-3928	56	8	𝑎)𝑑𝑡	𝑎)𝑑𝑡	PROPN
iajs-3928	56	9	,	,	PUNCT
iajs-3928	56	10	r{𝑈(𝑡	r{𝑈(𝑡	PROPN
iajs-3928	56	11	−	−	ADP
iajs-3928	56	12	𝑎	𝑎	NOUN
iajs-3928	56	13	)	)	PUNCT
iajs-3928	56	14	}	}	PUNCT
iajs-3928	56	15	=	=	PUNCT
iajs-3928	57	1	𝑞3	𝑞3	NOUN
iajs-3928	57	2	∫	∫	PROPN
iajs-3928	57	3	𝑒−𝑞𝑡	𝑒−𝑞𝑡	NOUN
iajs-3928	57	4	∞	∞	PROPN
iajs-3928	57	5	𝑎	𝑎	NOUN
iajs-3928	57	6	𝑑𝑡	𝑑𝑡	NOUN
iajs-3928	57	7	,	,	PUNCT
iajs-3928	57	8	r{𝑈(𝑡	r{𝑈(𝑡	PROPN
iajs-3928	57	9	−	−	ADP
iajs-3928	57	10	𝑎	𝑎	NOUN
iajs-3928	57	11	)	)	PUNCT
iajs-3928	57	12	}	}	PUNCT
iajs-3928	57	13	=	=	SYM
iajs-3928	57	14	𝑞2𝑒−𝑞𝑎	𝑞2𝑒−𝑞𝑎	NOUN
iajs-3928	57	15	.	.	PUNCT
iajs-3928	58	1	shifting	shift	VERB
iajs-3928	58	2	property	property	NOUN
iajs-3928	58	3	of	of	ADP
iajs-3928	58	4	rohit	rohit	PROPN
iajs-3928	58	5	transform	transform	NOUN
iajs-3928	58	6	let	let	VERB
iajs-3928	58	7	r{g(t	r{g(t	NOUN
iajs-3928	58	8	)	)	PUNCT
iajs-3928	58	9	}	}	PUNCT
iajs-3928	58	10	=	=	PUNCT
iajs-3928	59	1	𝐺(𝑞	𝐺(𝑞	NUM
iajs-3928	59	2	)	)	PUNCT
iajs-3928	60	1	,	,	PUNCT
iajs-3928	60	2	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
iajs-3928	60	3	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	60	4	−	−	NOUN
iajs-3928	60	5	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	60	6	−	−	ADP
iajs-3928	60	7	𝑎	𝑎	NOUN
iajs-3928	60	8	)	)	PUNCT
iajs-3928	60	9	]	]	PUNCT
iajs-3928	61	1	=	=	PUNCT
iajs-3928	61	2	𝑒−𝑞𝑎𝐺(𝑞	𝑒−𝑞𝑎𝐺(𝑞	ADV
iajs-3928	61	3	)	)	PUNCT
iajs-3928	61	4	.	.	PUNCT
iajs-3928	62	1	proof	proof	NOUN
iajs-3928	62	2	:	:	PUNCT
iajs-3928	62	3	the	the	DET
iajs-3928	62	4	rohit	rohit	PROPN
iajs-3928	62	5	transform	transform	NOUN
iajs-3928	62	6	of	of	ADP
iajs-3928	62	7	[	[	X
iajs-3928	62	8	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-3928	62	9	−	−	NOUN
iajs-3928	62	10	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	62	11	−	−	ADP
iajs-3928	62	12	𝑎	𝑎	NOUN
iajs-3928	62	13	)	)	PUNCT
iajs-3928	62	14	]	]	PUNCT
iajs-3928	62	15	is	be	AUX
iajs-3928	62	16	given	give	VERB
iajs-3928	62	17	by	by	ADP
iajs-3928	62	18	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	62	19	−	−	NOUN
iajs-3928	62	20	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	62	21	−	−	ADP
iajs-3928	62	22	𝑎	𝑎	NOUN
iajs-3928	62	23	)	)	PUNCT
iajs-3928	62	24	]	]	PUNCT
iajs-3928	63	1	=	=	PUNCT
iajs-3928	63	2	𝑞3	𝑞3	PROPN
iajs-3928	63	3	∫	∫	PROPN
iajs-3928	63	4	𝑒−𝑞𝑡	𝑒−𝑞𝑡	PROPN
iajs-3928	63	5	∞	∞	PROPN
iajs-3928	63	6	0	0	NUM
iajs-3928	64	1	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-3928	64	2	−	−	PROPN
iajs-3928	64	3	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	64	4	−	−	ADP
iajs-3928	64	5	𝑎)𝑑𝑡	𝑎)𝑑𝑡	NOUN
iajs-3928	64	6	,	,	PUNCT
iajs-3928	64	7	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	64	8	−	−	NOUN
iajs-3928	64	9	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	64	10	−	−	ADP
iajs-3928	64	11	𝑎	𝑎	NOUN
iajs-3928	64	12	]	]	X
iajs-3928	64	13	)	)	PUNCT
iajs-3928	65	1	=	=	PUNCT
iajs-3928	66	1	𝑞3	𝑞3	PROPN
iajs-3928	66	2	∫	∫	PROPN
iajs-3928	66	3	𝑒−𝑞𝑡	𝑒−𝑞𝑡	NOUN
iajs-3928	66	4	∞	∞	PROPN
iajs-3928	66	5	𝑎	𝑎	PROPN
iajs-3928	66	6	𝑔(𝑡	𝑔(𝑡	NOUN
iajs-3928	66	7	−	−	NOUN
iajs-3928	66	8	𝑎)𝑑𝑡	𝑎)𝑑𝑡	NOUN
iajs-3928	66	9	,	,	PUNCT
iajs-3928	66	10	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	66	11	−	−	NOUN
iajs-3928	66	12	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	66	13	−	−	ADP
iajs-3928	66	14	𝑎	𝑎	NOUN
iajs-3928	66	15	)	)	PUNCT
iajs-3928	66	16	]	]	PUNCT
iajs-3928	67	1	=	=	PUNCT
iajs-3928	67	2	𝑞3	𝑞3	PROPN
iajs-3928	67	3	∫	∫	PROPN
iajs-3928	67	4	𝑒−𝑞(𝑣+𝑎	𝑒−𝑞(𝑣+𝑎	PUNCT
iajs-3928	67	5	)	)	PUNCT
iajs-3928	67	6	∞	∞	NOUN
iajs-3928	67	7	0	0	NUM
iajs-3928	67	8	𝑔(𝑣)𝑑𝑣	𝑔(𝑣)𝑑𝑣	PROPN
iajs-3928	67	9	,	,	PUNCT
iajs-3928	67	10	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3928	67	11	𝑣	𝑣	X
iajs-3928	67	12	=	=	SYM
iajs-3928	67	13	𝑡	𝑡	PROPN
iajs-3928	67	14	−	−	NOUN
iajs-3928	67	15	𝑎	𝑎	NOUN
iajs-3928	67	16	,	,	PUNCT
iajs-3928	67	17	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	67	18	−	−	NOUN
iajs-3928	67	19	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	67	20	−	−	ADP
iajs-3928	67	21	𝑎	𝑎	NOUN
iajs-3928	67	22	)	)	PUNCT
iajs-3928	67	23	]	]	PUNCT
iajs-3928	68	1	=	=	SYM
iajs-3928	68	2	𝑒−𝑞(𝑎	𝑒−𝑞(𝑎	NOUN
iajs-3928	68	3	)	)	PUNCT
iajs-3928	68	4	𝑞3	𝑞3	PROPN
iajs-3928	68	5	∫	∫	PROPN
iajs-3928	68	6	𝑒−𝑞(𝑣	𝑒−𝑞(𝑣	PROPN
iajs-3928	68	7	)	)	PUNCT
iajs-3928	68	8	∞	∞	PROPN
iajs-3928	68	9	0	0	NUM
iajs-3928	68	10	𝑔(𝑣)𝑑𝑣	𝑔(𝑣)𝑑𝑣	NOUN
iajs-3928	68	11	,	,	PUNCT
iajs-3928	68	12	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	68	13	−	−	NOUN
iajs-3928	68	14	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	68	15	−	−	ADP
iajs-3928	68	16	𝑎	𝑎	NOUN
iajs-3928	68	17	)	)	PUNCT
iajs-3928	68	18	]	]	PUNCT
iajs-3928	68	19	=	=	SYM
iajs-3928	68	20	𝑒−𝑞(𝑎	𝑒−𝑞(𝑎	NOUN
iajs-3928	68	21	)	)	PUNCT
iajs-3928	68	22	𝑞3	𝑞3	PROPN
iajs-3928	68	23	∫	∫	PROPN
iajs-3928	68	24	𝑒−𝑞(𝑡	𝑒−𝑞(𝑡	PROPN
iajs-3928	68	25	)	)	PUNCT
iajs-3928	68	26	∞	∞	NOUN
iajs-3928	68	27	0	0	NUM
iajs-3928	69	1	𝑔(𝑡)𝑑𝑡	𝑔(𝑡)𝑑𝑡	NUM
iajs-3928	69	2	,	,	PUNCT
iajs-3928	69	3	𝑅[𝑔(𝑡	𝑅[𝑔(𝑡	NOUN
iajs-3928	69	4	−	−	NOUN
iajs-3928	69	5	𝑎)𝑈(𝑡	𝑎)𝑈(𝑡	PROPN
iajs-3928	69	6	−	−	ADP
iajs-3928	69	7	𝑎	𝑎	NOUN
iajs-3928	69	8	)	)	PUNCT
iajs-3928	69	9	]	]	PUNCT
iajs-3928	70	1	=	=	PUNCT
iajs-3928	70	2	𝑒−𝑞(𝑎)𝐺(𝑞	𝑒−𝑞(𝑎)𝐺(𝑞	NUM
iajs-3928	70	3	)	)	PUNCT
iajs-3928	70	4	.	.	PUNCT
iajs-3928	71	1	3	3	X
iajs-3928	71	2	.	.	X
iajs-3928	71	3	algorithm	algorithm	NOUN
iajs-3928	71	4	for	for	ADP
iajs-3928	71	5	proposed	propose	VERB
iajs-3928	71	6	method	method	NOUN
iajs-3928	71	7	the	the	DET
iajs-3928	71	8	algorithm	algorithm	NOUN
iajs-3928	71	9	for	for	ADP
iajs-3928	71	10	the	the	DET
iajs-3928	71	11	proposed	propose	VERB
iajs-3928	71	12	method	method	NOUN
iajs-3928	71	13	is	be	AUX
iajs-3928	71	14	as	as	SCONJ
iajs-3928	71	15	follows	follow	VERB
iajs-3928	71	16	:	:	PUNCT
iajs-3928	71	17	firstly	firstly	ADV
iajs-3928	71	18	,	,	PUNCT
iajs-3928	71	19	brief	brief	ADJ
iajs-3928	71	20	information	information	NOUN
iajs-3928	71	21	of	of	ADP
iajs-3928	71	22	the	the	DET
iajs-3928	71	23	integral	integral	ADJ
iajs-3928	71	24	rohit	rohit	NOUN
iajs-3928	71	25	transform	transform	NOUN
iajs-3928	71	26	and	and	CCONJ
iajs-3928	71	27	its	its	PRON
iajs-3928	71	28	attributes	attribute	NOUN
iajs-3928	71	29	is	be	AUX
iajs-3928	71	30	provided	provide	VERB
iajs-3928	71	31	.	.	PUNCT
iajs-3928	72	1	secondly	secondly	ADV
iajs-3928	72	2	,	,	PUNCT
iajs-3928	72	3	the	the	DET
iajs-3928	72	4	analysis	analysis	NOUN
iajs-3928	72	5	of	of	ADP
iajs-3928	72	6	loaded	load	VERB
iajs-3928	72	7	beam	beam	NOUN
iajs-3928	72	8	supported	support	VERB
iajs-3928	72	9	at	at	ADP
iajs-3928	72	10	ends	end	NOUN
iajs-3928	72	11	,	,	PUNCT
iajs-3928	72	12	cantilever	cantilever	NOUN
iajs-3928	72	13	,	,	PUNCT
iajs-3928	72	14	and	and	CCONJ
iajs-3928	72	15	elongated	elongate	VERB
iajs-3928	72	16	columns	column	NOUN
iajs-3928	72	17	with	with	ADP
iajs-3928	72	18	low	low	ADJ
iajs-3928	72	19	buckling	buckle	VERB
iajs-3928	72	20	axial	axial	ADJ
iajs-3928	72	21	loads	load	NOUN
iajs-3928	72	22	is	be	AUX
iajs-3928	72	23	done	do	VERB
iajs-3928	72	24	via	via	ADP
iajs-3928	72	25	the	the	DET
iajs-3928	72	26	integral	integral	ADJ
iajs-3928	72	27	rohit	rohit	NOUN
iajs-3928	72	28	transform	transform	NOUN
iajs-3928	72	29	.	.	PUNCT
iajs-3928	73	1	thirdly	thirdly	ADV
iajs-3928	73	2	,	,	PUNCT
iajs-3928	73	3	the	the	DET
iajs-3928	73	4	obtained	obtain	VERB
iajs-3928	73	5	solutions	solution	NOUN
iajs-3928	73	6	are	be	AUX
iajs-3928	73	7	graphically	graphically	ADV
iajs-3928	73	8	represented	represent	VERB
iajs-3928	73	9	,	,	PUNCT
iajs-3928	73	10	and	and	CCONJ
iajs-3928	73	11	the	the	DET
iajs-3928	73	12	results	result	NOUN
iajs-3928	73	13	obtained	obtain	VERB
iajs-3928	73	14	are	be	AUX
iajs-3928	73	15	compared	compare	VERB
iajs-3928	73	16	to	to	ADP
iajs-3928	73	17	existing	exist	VERB
iajs-3928	73	18	methods	method	NOUN
iajs-3928	73	19	in	in	ADP
iajs-3928	73	20	the	the	DET
iajs-3928	73	21	literature	literature	NOUN
iajs-3928	73	22	.	.	PUNCT
iajs-3928	74	1	finally	finally	ADV
iajs-3928	74	2	,	,	PUNCT
iajs-3928	74	3	the	the	DET
iajs-3928	74	4	conclusions	conclusion	NOUN
iajs-3928	74	5	of	of	ADP
iajs-3928	74	6	the	the	DET
iajs-3928	74	7	study	study	NOUN
iajs-3928	74	8	are	be	AUX
iajs-3928	74	9	presented	present	VERB
iajs-3928	74	10	.	.	PUNCT
iajs-3928	75	1	ihjpas	ihjpas	PROPN
iajs-3928	75	2	.	.	PUNCT
iajs-3928	76	1	2024	2024	NUM
iajs-3928	76	2	,	,	PUNCT
iajs-3928	76	3	37(4	37(4	PRON
iajs-3928	76	4	)	)	PUNCT
iajs-3928	76	5	384	384	NUM
iajs-3928	76	6	4	4	NUM
iajs-3928	76	7	.	.	PUNCT
iajs-3928	76	8	material	material	NOUN
iajs-3928	76	9	and	and	CCONJ
iajs-3928	76	10	method	method	NOUN
iajs-3928	76	11	in	in	ADP
iajs-3928	76	12	this	this	DET
iajs-3928	76	13	section	section	NOUN
iajs-3928	76	14	,	,	PUNCT
iajs-3928	76	15	the	the	DET
iajs-3928	76	16	analysis	analysis	NOUN
iajs-3928	76	17	of	of	ADP
iajs-3928	76	18	loaded	load	VERB
iajs-3928	76	19	beam	beam	NOUN
iajs-3928	76	20	supported	support	VERB
iajs-3928	76	21	at	at	ADP
iajs-3928	76	22	its	its	PRON
iajs-3928	76	23	ends	end	NOUN
iajs-3928	76	24	,	,	PUNCT
iajs-3928	76	25	cantilevers	cantilever	NOUN
iajs-3928	76	26	,	,	PUNCT
iajs-3928	76	27	and	and	CCONJ
iajs-3928	76	28	elongated	elongate	VERB
iajs-3928	76	29	columns	column	NOUN
iajs-3928	76	30	with	with	ADP
iajs-3928	76	31	low	low	ADJ
iajs-3928	76	32	buckling	buckle	VERB
iajs-3928	76	33	axial	axial	ADJ
iajs-3928	76	34	loads	load	NOUN
iajs-3928	76	35	is	be	AUX
iajs-3928	76	36	carried	carry	VERB
iajs-3928	76	37	out	out	ADP
iajs-3928	76	38	via	via	ADP
iajs-3928	76	39	the	the	DET
iajs-3928	76	40	integral	integral	ADJ
iajs-3928	76	41	rohit	rohit	NOUN
iajs-3928	76	42	transform	transform	NOUN
iajs-3928	76	43	.	.	PUNCT
iajs-3928	77	1	4.1	4.1	NUM
iajs-3928	77	2	analysis	analysis	NOUN
iajs-3928	77	3	of	of	ADP
iajs-3928	77	4	loaded	load	VERB
iajs-3928	77	5	beam	beam	NOUN
iajs-3928	77	6	supported	support	VERB
iajs-3928	77	7	at	at	ADP
iajs-3928	77	8	its	its	PRON
iajs-3928	77	9	ends	end	NOUN
iajs-3928	77	10	in	in	ADP
iajs-3928	77	11	this	this	DET
iajs-3928	77	12	study	study	NOUN
iajs-3928	77	13	,	,	PUNCT
iajs-3928	77	14	consider	consider	VERB
iajs-3928	77	15	a	a	DET
iajs-3928	77	16	beam	beam	NOUN
iajs-3928	77	17	supported	support	VERB
iajs-3928	77	18	on	on	ADP
iajs-3928	77	19	the	the	DET
iajs-3928	77	20	two	two	NUM
iajs-3928	77	21	knife	knife	NOUN
iajs-3928	77	22	edges	edge	VERB
iajs-3928	77	23	a	a	PRON
iajs-3928	77	24	and	and	CCONJ
iajs-3928	77	25	b	b	NOUN
iajs-3928	77	26	and	and	CCONJ
iajs-3928	77	27	loaded	load	VERB
iajs-3928	77	28	in	in	ADP
iajs-3928	77	29	the	the	DET
iajs-3928	77	30	middle	middle	NOUN
iajs-3928	77	31	with	with	ADP
iajs-3928	77	32	a	a	DET
iajs-3928	77	33	load	load	NOUN
iajs-3928	77	34	w	w	ADP
iajs-3928	77	35	vertically	vertically	ADV
iajs-3928	77	36	downwards	downward	NOUN
iajs-3928	77	37	.	.	PUNCT
iajs-3928	78	1	let	let	VERB
iajs-3928	78	2	l	l	NOUN
iajs-3928	78	3	be	be	AUX
iajs-3928	78	4	the	the	DET
iajs-3928	78	5	length	length	NOUN
iajs-3928	78	6	of	of	ADP
iajs-3928	78	7	the	the	DET
iajs-3928	78	8	beam	beam	NOUN
iajs-3928	78	9	between	between	ADP
iajs-3928	78	10	the	the	DET
iajs-3928	78	11	points	point	NOUN
iajs-3928	78	12	a	a	DET
iajs-3928	78	13	(	(	PUNCT
iajs-3928	78	14	at	at	ADP
iajs-3928	78	15	x	x	X
iajs-3928	78	16	=	=	NOUN
iajs-3928	78	17	0	0	NUM
iajs-3928	78	18	)	)	PUNCT
iajs-3928	78	19	and	and	CCONJ
iajs-3928	78	20	b	b	X
iajs-3928	78	21	(	(	PUNCT
iajs-3928	78	22	at	at	ADP
iajs-3928	78	23	x	x	X
iajs-3928	78	24	=	=	SYM
iajs-3928	78	25	l	l	NOUN
iajs-3928	78	26	)	)	PUNCT
iajs-3928	78	27	.	.	PUNCT
iajs-3928	79	1	the	the	DET
iajs-3928	79	2	bending	bend	VERB
iajs-3928	79	3	moment	moment	NOUN
iajs-3928	79	4	[	[	X
iajs-3928	79	5	1	1	NUM
iajs-3928	79	6	]	]	PUNCT
iajs-3928	79	7	,	,	PUNCT
iajs-3928	79	8	[	[	X
iajs-3928	79	9	12	12	NUM
iajs-3928	79	10	]	]	PUNCT
iajs-3928	79	11	at	at	ADP
iajs-3928	79	12	the	the	DET
iajs-3928	79	13	section	section	NOUN
iajs-3928	79	14	x	x	PUNCT
iajs-3928	79	15	is	be	AUX
iajs-3928	79	16	given	give	VERB
iajs-3928	79	17	by	by	ADP
iajs-3928	79	18	the	the	DET
iajs-3928	79	19	differential	differential	ADJ
iajs-3928	79	20	equation	equation	NOUN
iajs-3928	79	21	:	:	PUNCT
iajs-3928	79	22	�	�	PROPN
iajs-3928	79	23	̈	̈	X
iajs-3928	79	24	�	�	NOUN
iajs-3928	79	25	(x	(x	NUM
iajs-3928	79	26	)	)	PUNCT
iajs-3928	80	1	+	+	CCONJ
iajs-3928	80	2	w	w	NOUN
iajs-3928	80	3	2yi	2yi	ADJ
iajs-3928	80	4	𝑥	𝑥	X
iajs-3928	81	1	=	=	SYM
iajs-3928	81	2	0	0	NUM
iajs-3928	81	3	(	(	PUNCT
iajs-3928	81	4	1	1	NUM
iajs-3928	81	5	)	)	PUNCT
iajs-3928	81	6	where	where	SCONJ
iajs-3928	81	7	‘	'	PUNCT
iajs-3928	81	8	i	i	PRON
iajs-3928	81	9	’	'	PUNCT
iajs-3928	81	10	is	be	AUX
iajs-3928	81	11	the	the	DET
iajs-3928	81	12	geometrical	geometrical	ADJ
iajs-3928	81	13	moment	moment	NOUN
iajs-3928	81	14	of	of	ADP
iajs-3928	81	15	inertia	inertia	NOUN
iajs-3928	81	16	and	and	CCONJ
iajs-3928	81	17	y	y	PROPN
iajs-3928	81	18	is	be	AUX
iajs-3928	81	19	the	the	DET
iajs-3928	81	20	young	young	ADJ
iajs-3928	81	21	’s	’s	PART
iajs-3928	81	22	modulus	modulus	NOUN
iajs-3928	81	23	.	.	PUNCT
iajs-3928	82	1	here	here	ADV
iajs-3928	82	2	y	y	PROPN
iajs-3928	82	3	is	be	AUX
iajs-3928	82	4	the	the	DET
iajs-3928	82	5	depression	depression	NOUN
iajs-3928	82	6	of	of	ADP
iajs-3928	82	7	the	the	DET
iajs-3928	82	8	beam	beam	NOUN
iajs-3928	82	9	at	at	ADP
iajs-3928	82	10	the	the	DET
iajs-3928	82	11	section	section	NOUN
iajs-3928	82	12	x	x	PUNCT
iajs-3928	82	13	at	at	ADP
iajs-3928	82	14	the	the	DET
iajs-3928	82	15	distance	distance	NOUN
iajs-3928	82	16	x	x	PUNCT
iajs-3928	82	17	from	from	ADP
iajs-3928	82	18	the	the	DET
iajs-3928	82	19	end	end	NOUN
iajs-3928	82	20	a.	a.	NOUN
iajs-3928	82	21	on	on	ADP
iajs-3928	82	22	taking	take	VERB
iajs-3928	82	23	the	the	DET
iajs-3928	82	24	rohit	rohit	NOUN
iajs-3928	82	25	transform	transform	NOUN
iajs-3928	82	26	of	of	ADP
iajs-3928	82	27	equation	equation	NOUN
iajs-3928	82	28	(	(	PUNCT
iajs-3928	82	29	1	1	NUM
iajs-3928	82	30	)	)	PUNCT
iajs-3928	82	31	,	,	PUNCT
iajs-3928	82	32	we	we	PRON
iajs-3928	82	33	have	have	VERB
iajs-3928	82	34	𝑅{	𝑅{	VERB
iajs-3928	82	35	�	�	NOUN
iajs-3928	82	36	̈	̈	X
iajs-3928	82	37	�	�	NOUN
iajs-3928	82	38	(x	(x	NUM
iajs-3928	82	39	)	)	PUNCT
iajs-3928	82	40	}	}	PUNCT
iajs-3928	83	1	+	+	CCONJ
iajs-3928	83	2	w	w	X
iajs-3928	83	3	2yi	2yi	ADJ
iajs-3928	83	4	𝑅{𝑥	𝑅{𝑥	NOUN
iajs-3928	83	5	}	}	PUNCT
iajs-3928	83	6	=	=	SYM
iajs-3928	83	7	0	0	NUM
iajs-3928	83	8	,	,	PUNCT
iajs-3928	83	9	𝑞3	𝑞3	PROPN
iajs-3928	83	10	∫	∫	PROPN
iajs-3928	83	11	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	83	12	∞	∞	PROPN
iajs-3928	83	13	0	0	SYM
iajs-3928	83	14	�	�	PROPN
iajs-3928	83	15	̈	̈	X
iajs-3928	83	16	�	�	NOUN
iajs-3928	83	17	(x	(x	NUM
iajs-3928	83	18	)	)	PUNCT
iajs-3928	83	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	84	1	+	+	NOUN
iajs-3928	84	2	w	w	NOUN
iajs-3928	84	3	2yi	2yi	ADJ
iajs-3928	84	4	𝑞	𝑞	X
iajs-3928	84	5	=	=	SYM
iajs-3928	84	6	0	0	PROPN
iajs-3928	85	1	,	,	PUNCT
iajs-3928	85	2	𝑞3	𝑞3	PROPN
iajs-3928	85	3	[	[	X
iajs-3928	85	4	∫	∫	X
iajs-3928	85	5	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	85	6	𝐿	𝐿	PROPN
iajs-3928	85	7	0	0	NUM
iajs-3928	85	8	�	�	PROPN
iajs-3928	85	9	̈	̈	X
iajs-3928	85	10	�	�	NOUN
iajs-3928	85	11	(x	(x	NUM
iajs-3928	85	12	)	)	PUNCT
iajs-3928	85	13	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	85	14	+	+	NUM
iajs-3928	85	15	∫	∫	NOUN
iajs-3928	85	16	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	85	17	∞	∞	PROPN
iajs-3928	85	18	𝐿	𝐿	PROPN
iajs-3928	85	19	�	�	PROPN
iajs-3928	85	20	̈	̈	X
iajs-3928	85	21	�	�	PROPN
iajs-3928	85	22	(x	(x	NUM
iajs-3928	85	23	)	)	PUNCT
iajs-3928	85	24	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	85	25	]	]	X
iajs-3928	86	1	+	+	CCONJ
iajs-3928	86	2	w	w	NOUN
iajs-3928	86	3	2yi	2yi	ADJ
iajs-3928	86	4	𝑞	𝑞	X
iajs-3928	86	5	=	=	NOUN
iajs-3928	86	6	0	0	PROPN
iajs-3928	86	7	.	.	PUNCT
iajs-3928	87	1	as	as	ADP
iajs-3928	87	2	0	0	NUM
iajs-3928	87	3	<	<	X
iajs-3928	87	4	x	x	X
iajs-3928	87	5	<	<	X
iajs-3928	87	6	l	l	NOUN
iajs-3928	87	7	,	,	PUNCT
iajs-3928	87	8	therefore	therefore	ADV
iajs-3928	87	9	,	,	PUNCT
iajs-3928	87	10	∫	∫	PROPN
iajs-3928	87	11	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	87	12	𝐿	𝐿	PROPN
iajs-3928	87	13	�	�	PROPN
iajs-3928	87	14	̈	̈	X
iajs-3928	87	15	�	�	NOUN
iajs-3928	87	16	(x	(x	NUM
iajs-3928	87	17	)	)	PUNCT
iajs-3928	87	18	𝑑𝑥	𝑑𝑥	ADP
iajs-3928	87	19	=	=	SYM
iajs-3928	87	20	0	0	NUM
iajs-3928	87	21	.	.	PUNCT
iajs-3928	88	1	thus	thus	ADV
iajs-3928	88	2	,	,	PUNCT
iajs-3928	88	3	𝑞3	𝑞3	PROPN
iajs-3928	88	4	∫	∫	PROPN
iajs-3928	88	5	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	88	6	𝐿	𝐿	PROPN
iajs-3928	88	7	0	0	NUM
iajs-3928	88	8	�	�	PROPN
iajs-3928	88	9	̈	̈	X
iajs-3928	88	10	�	�	NOUN
iajs-3928	88	11	(x	(x	NUM
iajs-3928	88	12	)	)	PUNCT
iajs-3928	88	13	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	88	14	+	+	NOUN
iajs-3928	88	15	w	w	NOUN
iajs-3928	88	16	2yi	2yi	ADJ
iajs-3928	88	17	𝑞	𝑞	X
iajs-3928	88	18	=	=	SYM
iajs-3928	88	19	0	0	PROPN
iajs-3928	88	20	,	,	PUNCT
iajs-3928	88	21	𝑞3	𝑞3	PROPN
iajs-3928	88	22	[	[	X
iajs-3928	88	23	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	88	24	)	)	PUNCT
iajs-3928	88	25	−	−	PROPN
iajs-3928	89	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	89	2	)	)	PUNCT
iajs-3928	89	3	+	+	NUM
iajs-3928	89	4	𝑞	𝑞	PROPN
iajs-3928	89	5	∫	∫	PROPN
iajs-3928	89	6	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	89	7	𝐿	𝐿	PROPN
iajs-3928	89	8	0	0	NUM
iajs-3928	89	9	y′(𝑥)𝑑𝑥	y′(𝑥)𝑑𝑥	PROPN
iajs-3928	89	10	]	]	X
iajs-3928	90	1	+	+	CCONJ
iajs-3928	90	2	w	w	NOUN
iajs-3928	90	3	2yi	2yi	ADJ
iajs-3928	90	4	𝑞	𝑞	X
iajs-3928	90	5	=	=	SYM
iajs-3928	90	6	0	0	PROPN
iajs-3928	90	7	,	,	PUNCT
iajs-3928	90	8	𝑞3	𝑞3	PROPN
iajs-3928	90	9	[	[	X
iajs-3928	90	10	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	90	11	)	)	PUNCT
iajs-3928	90	12	−	−	PROPN
iajs-3928	91	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	91	2	)	)	PUNCT
iajs-3928	91	3	+	+	NUM
iajs-3928	91	4	𝑞	𝑞	X
iajs-3928	91	5	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	ADJ
iajs-3928	91	6	)	)	PUNCT
iajs-3928	91	7	−	−	PROPN
iajs-3928	91	8	𝑞	𝑞	X
iajs-3928	91	9	𝑦(0	𝑦(0	PROPN
iajs-3928	91	10	)	)	PUNCT
iajs-3928	91	11	+	+	NUM
iajs-3928	91	12	𝑞2	𝑞2	PROPN
iajs-3928	91	13	∫	∫	PROPN
iajs-3928	91	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	91	15	𝐿	𝐿	PROPN
iajs-3928	91	16	0	0	NUM
iajs-3928	91	17	y(x	y(x	NOUN
iajs-3928	91	18	)	)	PUNCT
iajs-3928	91	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	91	20	]	]	X
iajs-3928	91	21	+	+	CCONJ
iajs-3928	91	22	w	w	NOUN
iajs-3928	91	23	2yi	2yi	ADJ
iajs-3928	91	24	𝑞	𝑞	X
iajs-3928	91	25	=	=	SYM
iajs-3928	91	26	0	0	NUM
iajs-3928	91	27	,	,	PUNCT
iajs-3928	91	28	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	91	29	)	)	PUNCT
iajs-3928	91	30	−	−	PROPN
iajs-3928	92	1	𝑞3𝑦′(0	𝑞3𝑦′(0	NOUN
iajs-3928	92	2	)	)	PUNCT
iajs-3928	93	1	+	+	CCONJ
iajs-3928	93	2	𝑞4	𝑞4	PROPN
iajs-3928	93	3	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	NOUN
iajs-3928	93	4	)	)	PUNCT
iajs-3928	93	5	−	−	ADP
iajs-3928	93	6	𝑞4	𝑞4	PROPN
iajs-3928	93	7	𝑦(0	𝑦(0	PROPN
iajs-3928	93	8	)	)	PUNCT
iajs-3928	93	9	+	+	NUM
iajs-3928	93	10	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	93	11	)	)	PUNCT
iajs-3928	93	12	}	}	PUNCT
iajs-3928	94	1	+	+	CCONJ
iajs-3928	94	2	w	w	NUM
iajs-3928	94	3	2yi	2yi	ADJ
iajs-3928	94	4	𝑞	𝑞	AUX
iajs-3928	94	5	=	=	SYM
iajs-3928	94	6	0	0	NUM
iajs-3928	94	7	(	(	PUNCT
iajs-3928	94	8	2	2	X
iajs-3928	94	9	)	)	PUNCT
iajs-3928	94	10	applying	apply	VERB
iajs-3928	94	11	initial	initial	ADJ
iajs-3928	94	12	conditions	condition	NOUN
iajs-3928	94	13	:	:	PUNCT
iajs-3928	94	14	𝑦	𝑦	X
iajs-3928	94	15	(	(	PUNCT
iajs-3928	94	16	0	0	NUM
iajs-3928	94	17	)	)	PUNCT
iajs-3928	94	18	=	=	SYM
iajs-3928	95	1	y(l	y(l	NOUN
iajs-3928	95	2	)	)	PUNCT
iajs-3928	95	3	=	=	SYM
iajs-3928	95	4	0	0	NUM
iajs-3928	95	5	,	,	PUNCT
iajs-3928	95	6	ẏ(0	ẏ(0	NOUN
iajs-3928	95	7	)	)	PUNCT
iajs-3928	95	8	=	=	SYM
iajs-3928	95	9	𝐶	𝐶	PROPN
iajs-3928	95	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	95	11	ẏ(l	ẏ(l	PROPN
iajs-3928	95	12	)	)	PUNCT
iajs-3928	95	13	=	=	SYM
iajs-3928	95	14	𝐷.	𝐷.	NOUN
iajs-3928	95	15	equation	equation	NOUN
iajs-3928	95	16	(	(	PUNCT
iajs-3928	95	17	2	2	X
iajs-3928	95	18	)	)	PUNCT
iajs-3928	95	19	becomes	become	VERB
iajs-3928	95	20	𝑞3𝑒−𝑞𝐿𝐷	𝑞3𝑒−𝑞𝐿𝐷	NOUN
iajs-3928	95	21	−	−	NOUN
iajs-3928	95	22	𝑞3𝐶	𝑞3𝐶	ADV
iajs-3928	95	23	+	+	CCONJ
iajs-3928	95	24	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	X
iajs-3928	95	25	)	)	PUNCT
iajs-3928	96	1	+	+	CCONJ
iajs-3928	96	2	w	w	NUM
iajs-3928	96	3	2yi	2yi	ADJ
iajs-3928	96	4	𝑞	𝑞	X
iajs-3928	96	5	=	=	SYM
iajs-3928	96	6	0	0	NUM
iajs-3928	96	7	,	,	PUNCT
iajs-3928	96	8	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	PUNCT
iajs-3928	96	9	)	)	PUNCT
iajs-3928	96	10	}	}	PUNCT
iajs-3928	97	1	=	=	PUNCT
iajs-3928	97	2	𝑞𝐶	𝑞𝐶	NOUN
iajs-3928	97	3	−	−	NOUN
iajs-3928	97	4	𝑞𝑒−𝑞𝐿𝐷	𝑞𝑒−𝑞𝐿𝐷	NOUN
iajs-3928	97	5	+	+	NOUN
iajs-3928	97	6	w	w	NOUN
iajs-3928	97	7	2yi	2yi	ADJ
iajs-3928	97	8	1	1	NUM
iajs-3928	97	9	𝑞	𝑞	NOUN
iajs-3928	97	10	.	.	PUNCT
iajs-3928	98	1	taking	take	VERB
iajs-3928	98	2	inverse	inverse	NOUN
iajs-3928	98	3	rohit	rohit	NOUN
iajs-3928	98	4	transform	transform	NOUN
iajs-3928	98	5	,	,	PUNCT
iajs-3928	98	6	we	we	PRON
iajs-3928	98	7	have	have	VERB
iajs-3928	98	8	y	y	PROPN
iajs-3928	98	9	(	(	PUNCT
iajs-3928	98	10	x	x	NOUN
iajs-3928	98	11	)	)	PUNCT
iajs-3928	98	12	=	=	PUNCT
iajs-3928	99	1	𝐶𝑥	𝐶𝑥	ADV
iajs-3928	99	2	−	−	PROPN
iajs-3928	99	3	𝐷(𝑥	𝐷(𝑥	PUNCT
iajs-3928	99	4	−	−	PROPN
iajs-3928	99	5	𝐿	𝐿	PROPN
iajs-3928	99	6	)	)	PUNCT
iajs-3928	99	7	𝑈(𝑡	𝑈(𝑡	ADP
iajs-3928	99	8	−	−	PROPN
iajs-3928	99	9	𝐿	𝐿	PROPN
iajs-3928	99	10	)	)	PUNCT
iajs-3928	99	11	−	−	PROPN
iajs-3928	100	1	w	w	PROPN
iajs-3928	100	2	2yi	2yi	ADJ
iajs-3928	100	3	𝑥3	𝑥3	NOUN
iajs-3928	100	4	3	3	NUM
iajs-3928	100	5	!	!	PUNCT
iajs-3928	100	6	.	.	PUNCT
iajs-3928	101	1	(	(	PUNCT
iajs-3928	101	2	3	3	X
iajs-3928	101	3	)	)	PUNCT
iajs-3928	101	4	now	now	ADV
iajs-3928	101	5	,	,	PUNCT
iajs-3928	101	6	for	for	ADP
iajs-3928	101	7	x	x	X
iajs-3928	101	8	<	<	X
iajs-3928	101	9	l	l	NOUN
iajs-3928	101	10	,	,	PUNCT
iajs-3928	101	11	𝑈(𝑥	𝑈(𝑥	PROPN
iajs-3928	101	12	−	−	PROPN
iajs-3928	101	13	𝐿	𝐿	PROPN
iajs-3928	101	14	)	)	PUNCT
iajs-3928	101	15	=	=	SYM
iajs-3928	101	16	0	0	X
iajs-3928	101	17	.	.	PUNCT
iajs-3928	102	1	thus	thus	ADV
iajs-3928	102	2	,	,	PUNCT
iajs-3928	102	3	y	y	PROPN
iajs-3928	102	4	(	(	PUNCT
iajs-3928	102	5	x	x	NOUN
iajs-3928	102	6	)	)	PUNCT
iajs-3928	102	7	=	=	PUNCT
iajs-3928	102	8	𝐶𝑥	𝐶𝑥	ADV
iajs-3928	102	9	−	−	PROPN
iajs-3928	102	10	w	w	NOUN
iajs-3928	102	11	2yi	2yi	ADJ
iajs-3928	102	12	𝑥3	𝑥3	NOUN
iajs-3928	102	13	3	3	X
iajs-3928	102	14	!	!	PUNCT
iajs-3928	102	15	(	(	PUNCT
iajs-3928	102	16	4	4	X
iajs-3928	102	17	)	)	PUNCT
iajs-3928	102	18	at	at	ADP
iajs-3928	102	19	x	x	X
iajs-3928	102	20	=	=	PUNCT
iajs-3928	102	21	l	l	NOUN
iajs-3928	102	22	2	2	NUM
iajs-3928	102	23	and	and	CCONJ
iajs-3928	102	24	ẏ	ẏ	PRON
iajs-3928	102	25	(	(	PUNCT
iajs-3928	102	26	l	l	NOUN
iajs-3928	102	27	2	2	X
iajs-3928	102	28	)	)	PUNCT
iajs-3928	102	29	=	=	SYM
iajs-3928	102	30	0	0	X
iajs-3928	102	31	.	.	PUNCT
iajs-3928	102	32	therefore	therefore	ADV
iajs-3928	102	33	,	,	PUNCT
iajs-3928	102	34	using	use	VERB
iajs-3928	102	35	equation	equation	NOUN
iajs-3928	102	36	(	(	PUNCT
iajs-3928	102	37	4	4	NUM
iajs-3928	102	38	)	)	PUNCT
iajs-3928	102	39	and	and	CCONJ
iajs-3928	102	40	solving	solve	VERB
iajs-3928	102	41	for	for	ADP
iajs-3928	102	42	c	c	NOUN
iajs-3928	102	43	,	,	PUNCT
iajs-3928	102	44	we	we	PRON
iajs-3928	102	45	get	get	VERB
iajs-3928	102	46	𝐶	𝐶	PROPN
iajs-3928	102	47	=	=	SYM
iajs-3928	102	48	3w𝐿2	3w𝐿2	NUM
iajs-3928	102	49	32yi	32yi	NOUN
iajs-3928	102	50	(	(	PUNCT
iajs-3928	102	51	5	5	NUM
iajs-3928	102	52	)	)	PUNCT
iajs-3928	102	53	ihjpas	ihjpa	NOUN
iajs-3928	102	54	.	.	PUNCT
iajs-3928	103	1	2024	2024	NUM
iajs-3928	103	2	,	,	PUNCT
iajs-3928	103	3	37(4	37(4	PRON
iajs-3928	103	4	)	)	PUNCT
iajs-3928	103	5	385	385	NUM
iajs-3928	103	6	using	use	VERB
iajs-3928	103	7	equation	equation	NOUN
iajs-3928	103	8	(	(	PUNCT
iajs-3928	103	9	5	5	NUM
iajs-3928	103	10	)	)	PUNCT
iajs-3928	103	11	in	in	ADP
iajs-3928	103	12	equation	equation	NOUN
iajs-3928	103	13	(	(	PUNCT
iajs-3928	103	14	4	4	NUM
iajs-3928	103	15	)	)	PUNCT
iajs-3928	103	16	,	,	PUNCT
iajs-3928	103	17	we	we	PRON
iajs-3928	103	18	have	have	VERB
iajs-3928	103	19	y	y	PROPN
iajs-3928	103	20	(	(	PUNCT
iajs-3928	103	21	x	x	NOUN
iajs-3928	103	22	)	)	PUNCT
iajs-3928	103	23	=	=	SYM
iajs-3928	104	1	(	(	PUNCT
iajs-3928	104	2	3w𝐿2	3w𝐿2	NUM
iajs-3928	104	3	32yi	32yi	NOUN
iajs-3928	104	4	𝑥	𝑥	NOUN
iajs-3928	105	1	−	−	NOUN
iajs-3928	105	2	w	w	NOUN
iajs-3928	105	3	2yi	2yi	ADJ
iajs-3928	105	4	𝑥3	𝑥3	NOUN
iajs-3928	105	5	3	3	NUM
iajs-3928	105	6	!	!	PUNCT
iajs-3928	105	7	)	)	PUNCT
iajs-3928	106	1	,	,	PUNCT
iajs-3928	106	2	where	where	SCONJ
iajs-3928	106	3	0	0	PUNCT
iajs-3928	106	4	<	<	X
iajs-3928	106	5	x	x	X
iajs-3928	106	6	<	<	X
iajs-3928	106	7	l	l	X
iajs-3928	106	8	(	(	PUNCT
iajs-3928	106	9	6	6	NUM
iajs-3928	106	10	)	)	PUNCT
iajs-3928	106	11	taking	taking	NOUN
iajs-3928	106	12	,	,	PUNCT
iajs-3928	106	13	for	for	ADP
iajs-3928	106	14	example	example	NOUN
iajs-3928	106	15	,	,	PUNCT
iajs-3928	106	16	w	w	PROPN
iajs-3928	106	17	yi	yi	NOUN
iajs-3928	106	18	=	=	SYM
iajs-3928	106	19	32	32	NUM
iajs-3928	106	20	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3928	106	21	𝐿	𝐿	PROPN
iajs-3928	106	22	=	=	PROPN
iajs-3928	106	23	10	10	NUM
iajs-3928	106	24	,	,	PUNCT
iajs-3928	106	25	the	the	DET
iajs-3928	106	26	graph	graph	NOUN
iajs-3928	106	27	of	of	ADP
iajs-3928	106	28	y(x	y(x	NOUN
iajs-3928	106	29	)	)	PUNCT
iajs-3928	106	30	is	be	AUX
iajs-3928	106	31	shown	show	VERB
iajs-3928	106	32	in	in	ADP
iajs-3928	106	33	the	the	DET
iajs-3928	106	34	figure	figure	NOUN
iajs-3928	106	35	1	1	NUM
iajs-3928	106	36	.	.	PUNCT
iajs-3928	106	37	figure	figure	NOUN
iajs-3928	106	38	1	1	NUM
iajs-3928	106	39	.	.	PUNCT
iajs-3928	106	40	numerical	numerical	ADJ
iajs-3928	106	41	solution	solution	NOUN
iajs-3928	106	42	of	of	ADP
iajs-3928	106	43	equation	equation	NOUN
iajs-3928	106	44	(	(	PUNCT
iajs-3928	106	45	1	1	NUM
iajs-3928	106	46	)	)	PUNCT
iajs-3928	106	47	.	.	PUNCT
iajs-3928	107	1	at	at	ADP
iajs-3928	107	2	the	the	DET
iajs-3928	107	3	middle	middle	NOUN
iajs-3928	107	4	,	,	PUNCT
iajs-3928	107	5	the	the	DET
iajs-3928	107	6	total	total	ADJ
iajs-3928	107	7	depression	depression	NOUN
iajs-3928	107	8	is	be	AUX
iajs-3928	107	9	given	give	VERB
iajs-3928	107	10	by	by	ADP
iajs-3928	107	11	y	y	PROPN
iajs-3928	107	12	(	(	PUNCT
iajs-3928	107	13	l/2	l/2	NUM
iajs-3928	107	14	)	)	PUNCT
iajs-3928	107	15	=	=	SYM
iajs-3928	107	16	1	1	NUM
iajs-3928	107	17	3	3	NUM
iajs-3928	107	18	!	!	PUNCT
iajs-3928	108	1	[	[	PUNCT
iajs-3928	108	2	3w𝐿2	3w𝐿2	NUM
iajs-3928	108	3	8yi	8yi	NOUN
iajs-3928	108	4	𝐿/2	𝐿/2	PUNCT
iajs-3928	108	5	−	−	PROPN
iajs-3928	108	6	w	w	PROPN
iajs-3928	108	7	2yi	2yi	ADJ
iajs-3928	108	8	(	(	PUNCT
iajs-3928	108	9	𝐿/2)3	𝐿/2)3	PROPN
iajs-3928	108	10	]	]	X
iajs-3928	108	11	,	,	PUNCT
iajs-3928	108	12	⇒	⇒	PROPN
iajs-3928	108	13	y	y	PROPN
iajs-3928	108	14	(	(	PUNCT
iajs-3928	108	15	l/2	l/2	NUM
iajs-3928	108	16	)	)	PUNCT
iajs-3928	108	17	=	=	SYM
iajs-3928	109	1	w𝐿3	w𝐿3	PROPN
iajs-3928	109	2	48yi	48yi	NOUN
iajs-3928	109	3	(	(	PUNCT
iajs-3928	109	4	7	7	NUM
iajs-3928	109	5	)	)	PUNCT
iajs-3928	109	6	for	for	ADP
iajs-3928	109	7	a	a	DET
iajs-3928	109	8	beam	beam	NOUN
iajs-3928	109	9	of	of	ADP
iajs-3928	109	10	circular	circular	ADJ
iajs-3928	109	11	cross	cross	NOUN
iajs-3928	109	12	-	-	NOUN
iajs-3928	109	13	section	section	NOUN
iajs-3928	109	14	[	[	X
iajs-3928	109	15	4	4	NUM
iajs-3928	109	16	]	]	PUNCT
iajs-3928	109	17	,	,	PUNCT
iajs-3928	109	18	[	[	X
iajs-3928	109	19	13	13	NUM
iajs-3928	109	20	]	]	PUNCT
iajs-3928	109	21	,	,	PUNCT
iajs-3928	109	22	we	we	PRON
iajs-3928	109	23	have	have	VERB
iajs-3928	109	24	i	i	PRON
iajs-3928	109	25	=	=	NOUN
iajs-3928	109	26	𝜋𝑟4/4	𝜋𝑟4/4	PROPN
iajs-3928	109	27	hence	hence	ADV
iajs-3928	109	28	,	,	PUNCT
iajs-3928	109	29	from	from	ADP
iajs-3928	109	30	equation	equation	NOUN
iajs-3928	109	31	(	(	PUNCT
iajs-3928	109	32	7	7	NUM
iajs-3928	109	33	)	)	PUNCT
iajs-3928	109	34	,	,	PUNCT
iajs-3928	109	35	we	we	PRON
iajs-3928	109	36	have	have	VERB
iajs-3928	109	37	y(l/2	y(l/2	PROPN
iajs-3928	109	38	)	)	PUNCT
iajs-3928	110	1	=	=	SYM
iajs-3928	110	2	w𝐿3	w𝐿3	PROPN
iajs-3928	110	3	12y𝜋𝑟4	12y𝜋𝑟4	NUM
iajs-3928	111	1	4.2	4.2	NUM
iajs-3928	111	2	analysis	analysis	NOUN
iajs-3928	111	3	of	of	ADP
iajs-3928	111	4	cantilever	cantilever	NOUN
iajs-3928	111	5	beam	beam	NOUN
iajs-3928	111	6	in	in	ADP
iajs-3928	111	7	this	this	DET
iajs-3928	111	8	study	study	NOUN
iajs-3928	111	9	,	,	PUNCT
iajs-3928	111	10	consider	consider	VERB
iajs-3928	111	11	a	a	DET
iajs-3928	111	12	horizontal	horizontal	ADJ
iajs-3928	111	13	beam	beam	NOUN
iajs-3928	111	14	ab	ab	PROPN
iajs-3928	111	15	of	of	ADP
iajs-3928	111	16	length	length	PROPN
iajs-3928	111	17	l	l	PROPN
iajs-3928	111	18	attached	attach	VERB
iajs-3928	111	19	at	at	ADP
iajs-3928	111	20	end	end	NOUN
iajs-3928	111	21	a	a	DET
iajs-3928	111	22	(	(	PUNCT
iajs-3928	111	23	at	at	ADP
iajs-3928	111	24	x	x	X
iajs-3928	111	25	=	=	NOUN
iajs-3928	111	26	0	0	NUM
iajs-3928	111	27	)	)	PUNCT
iajs-3928	111	28	and	and	CCONJ
iajs-3928	111	29	loaded	load	VERB
iajs-3928	111	30	with	with	ADP
iajs-3928	111	31	a	a	DET
iajs-3928	111	32	load	load	NOUN
iajs-3928	111	33	w	w	ADP
iajs-3928	111	34	vertically	vertically	ADV
iajs-3928	111	35	downward	downward	ADV
iajs-3928	111	36	from	from	ADP
iajs-3928	111	37	the	the	DET
iajs-3928	111	38	free	free	ADJ
iajs-3928	111	39	end	end	NOUN
iajs-3928	111	40	b	b	PROPN
iajs-3928	111	41	(	(	PUNCT
iajs-3928	111	42	at	at	ADP
iajs-3928	111	43	x	x	X
iajs-3928	111	44	=	=	SYM
iajs-3928	111	45	l	l	NOUN
iajs-3928	111	46	)	)	PUNCT
iajs-3928	111	47	.	.	PUNCT
iajs-3928	112	1	the	the	DET
iajs-3928	112	2	bending	bend	VERB
iajs-3928	112	3	moment	moment	NOUN
iajs-3928	112	4	[	[	X
iajs-3928	112	5	3	3	NUM
iajs-3928	112	6	]	]	PUNCT
iajs-3928	112	7	,	,	PUNCT
iajs-3928	112	8	[	[	X
iajs-3928	112	9	4	4	X
iajs-3928	112	10	]	]	X
iajs-3928	112	11	at	at	ADP
iajs-3928	112	12	point	point	NOUN
iajs-3928	112	13	x	x	VERB
iajs-3928	112	14	is	be	AUX
iajs-3928	112	15	obtained	obtain	VERB
iajs-3928	112	16	from	from	ADP
iajs-3928	112	17	the	the	DET
iajs-3928	112	18	differential	differential	ADJ
iajs-3928	112	19	equation	equation	NOUN
iajs-3928	112	20	:	:	PUNCT
iajs-3928	112	21	�	�	PROPN
iajs-3928	112	22	̈	̈	X
iajs-3928	112	23	�	�	NOUN
iajs-3928	112	24	(x	(x	NUM
iajs-3928	112	25	)	)	PUNCT
iajs-3928	113	1	+	+	NUM
iajs-3928	113	2	w	w	PROPN
iajs-3928	113	3	yi	yi	NOUN
iajs-3928	113	4	(	(	PUNCT
iajs-3928	113	5	l	l	NOUN
iajs-3928	113	6	−	−	PROPN
iajs-3928	113	7	x	x	NOUN
iajs-3928	113	8	)	)	PUNCT
iajs-3928	113	9	=	=	SYM
iajs-3928	113	10	0	0	PUNCT
iajs-3928	113	11	(	(	PUNCT
iajs-3928	113	12	8)	8)	NUM
iajs-3928	113	13	where	where	SCONJ
iajs-3928	113	14	i	i	PRON
iajs-3928	113	15	is	be	AUX
iajs-3928	113	16	the	the	DET
iajs-3928	113	17	geometrical	geometrical	ADJ
iajs-3928	113	18	moment	moment	NOUN
iajs-3928	113	19	of	of	ADP
iajs-3928	113	20	inertia	inertia	NOUN
iajs-3928	113	21	and	and	CCONJ
iajs-3928	113	22	y	y	PROPN
iajs-3928	113	23	is	be	AUX
iajs-3928	113	24	the	the	DET
iajs-3928	113	25	young	young	ADJ
iajs-3928	113	26	’s	’s	PART
iajs-3928	113	27	modulus	modulus	NOUN
iajs-3928	113	28	.	.	PUNCT
iajs-3928	114	1	here	here	ADV
iajs-3928	114	2	,	,	PUNCT
iajs-3928	114	3	y	y	PROPN
iajs-3928	114	4	is	be	AUX
iajs-3928	114	5	the	the	DET
iajs-3928	114	6	depression	depression	NOUN
iajs-3928	114	7	of	of	ADP
iajs-3928	114	8	the	the	DET
iajs-3928	114	9	beam	beam	NOUN
iajs-3928	114	10	at	at	ADP
iajs-3928	114	11	the	the	DET
iajs-3928	114	12	section	section	NOUN
iajs-3928	114	13	x	x	PUNCT
iajs-3928	114	14	at	at	ADP
iajs-3928	114	15	the	the	DET
iajs-3928	114	16	distance	distance	NOUN
iajs-3928	114	17	x	x	PUNCT
iajs-3928	114	18	from	from	ADP
iajs-3928	114	19	fixed	fix	VERB
iajs-3928	114	20	end	end	NOUN
iajs-3928	114	21	a.	a.	NOUN
iajs-3928	114	22	on	on	ADP
iajs-3928	114	23	taking	take	VERB
iajs-3928	114	24	the	the	DET
iajs-3928	114	25	rohit	rohit	NOUN
iajs-3928	114	26	transform	transform	NOUN
iajs-3928	114	27	[	[	X
iajs-3928	114	28	10	10	NUM
iajs-3928	114	29	]	]	PUNCT
iajs-3928	114	30	,	,	PUNCT
iajs-3928	114	31	[	[	X
iajs-3928	114	32	11	11	NUM
iajs-3928	114	33	]	]	PUNCT
iajs-3928	114	34	of	of	ADP
iajs-3928	114	35	equation	equation	NOUN
iajs-3928	114	36	(	(	PUNCT
iajs-3928	114	37	8)	8)	NUM
iajs-3928	114	38	,	,	PUNCT
iajs-3928	114	39	we	we	PRON
iajs-3928	114	40	get	get	AUX
iajs-3928	114	41	𝑞3	𝑞3	PROPN
iajs-3928	114	42	∫	∫	NOUN
iajs-3928	114	43	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	114	44	∞	∞	PROPN
iajs-3928	114	45	0	0	SYM
iajs-3928	114	46	�	�	PROPN
iajs-3928	114	47	̈	̈	X
iajs-3928	114	48	�	�	NOUN
iajs-3928	114	49	(x	(x	NUM
iajs-3928	114	50	)	)	PUNCT
iajs-3928	114	51	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	114	52	+	+	NOUN
iajs-3928	114	53	w	w	PROPN
iajs-3928	114	54	yi	yi	NOUN
iajs-3928	114	55	(	(	PUNCT
iajs-3928	114	56	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	114	57	−	−	PROPN
iajs-3928	114	58	𝑞	𝑞	PROPN
iajs-3928	114	59	)	)	PUNCT
iajs-3928	114	60	=	=	SYM
iajs-3928	114	61	0	0	NUM
iajs-3928	114	62	,	,	PUNCT
iajs-3928	114	63	𝑞3	𝑞3	PROPN
iajs-3928	115	1	[	[	X
iajs-3928	115	2	∫	∫	X
iajs-3928	115	3	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	115	4	𝐿	𝐿	PROPN
iajs-3928	115	5	0	0	NUM
iajs-3928	115	6	�	�	PROPN
iajs-3928	115	7	̈	̈	X
iajs-3928	115	8	�	�	NOUN
iajs-3928	115	9	(x	(x	NUM
iajs-3928	115	10	)	)	PUNCT
iajs-3928	115	11	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	115	12	+	+	NUM
iajs-3928	115	13	∫	∫	NOUN
iajs-3928	115	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	115	15	∞	∞	PROPN
iajs-3928	115	16	𝐿	𝐿	PROPN
iajs-3928	115	17	�	�	PROPN
iajs-3928	115	18	̈	̈	X
iajs-3928	115	19	�	�	PROPN
iajs-3928	115	20	(x	(x	NUM
iajs-3928	115	21	)	)	PUNCT
iajs-3928	115	22	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	115	23	]	]	X
iajs-3928	115	24	+	+	CCONJ
iajs-3928	115	25	w	w	PROPN
iajs-3928	115	26	yi	yi	PROPN
iajs-3928	115	27	(	(	PUNCT
iajs-3928	115	28	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	115	29	−	−	PROPN
iajs-3928	115	30	𝑞	𝑞	PROPN
iajs-3928	115	31	)	)	PUNCT
iajs-3928	115	32	=	=	SYM
iajs-3928	115	33	0	0	X
iajs-3928	115	34	.	.	PUNCT
iajs-3928	116	1	as	as	ADP
iajs-3928	116	2	0	0	NUM
iajs-3928	116	3	<	<	X
iajs-3928	116	4	x	x	X
iajs-3928	116	5	<	<	X
iajs-3928	116	6	l	l	NOUN
iajs-3928	116	7	,	,	PUNCT
iajs-3928	116	8	therefore	therefore	ADV
iajs-3928	116	9	,	,	PUNCT
iajs-3928	116	10	∫	∫	PROPN
iajs-3928	116	11	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	116	12	𝐿	𝐿	PROPN
iajs-3928	116	13	�	�	PROPN
iajs-3928	116	14	̈	̈	X
iajs-3928	116	15	�	�	NOUN
iajs-3928	116	16	(x	(x	NUM
iajs-3928	116	17	)	)	PUNCT
iajs-3928	116	18	𝑑𝑥	𝑑𝑥	ADP
iajs-3928	116	19	=	=	SYM
iajs-3928	116	20	0	0	NUM
iajs-3928	116	21	.	.	PUNCT
iajs-3928	117	1	thus	thus	ADV
iajs-3928	117	2	,	,	PUNCT
iajs-3928	117	3	𝑞3	𝑞3	PROPN
iajs-3928	117	4	∫	∫	PROPN
iajs-3928	117	5	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	117	6	𝐿	𝐿	PROPN
iajs-3928	117	7	0	0	NUM
iajs-3928	117	8	�	�	PROPN
iajs-3928	117	9	̈	̈	X
iajs-3928	117	10	�	�	NOUN
iajs-3928	117	11	(x	(x	NUM
iajs-3928	117	12	)	)	PUNCT
iajs-3928	117	13	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	117	14	+	+	NOUN
iajs-3928	117	15	w	w	PROPN
iajs-3928	117	16	yi	yi	NOUN
iajs-3928	117	17	(	(	PUNCT
iajs-3928	117	18	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	117	19	−	−	PROPN
iajs-3928	117	20	𝑞	𝑞	PROPN
iajs-3928	117	21	)	)	PUNCT
iajs-3928	117	22	=	=	SYM
iajs-3928	117	23	0	0	NUM
iajs-3928	117	24	,	,	PUNCT
iajs-3928	117	25	𝑞3	𝑞3	PROPN
iajs-3928	117	26	[	[	X
iajs-3928	117	27	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	117	28	)	)	PUNCT
iajs-3928	117	29	−	−	PROPN
iajs-3928	118	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	118	2	)	)	PUNCT
iajs-3928	118	3	+	+	NUM
iajs-3928	118	4	𝑞	𝑞	PROPN
iajs-3928	118	5	∫	∫	PROPN
iajs-3928	118	6	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	118	7	𝐿	𝐿	PROPN
iajs-3928	118	8	0	0	NUM
iajs-3928	118	9	y′(𝑥)𝑑𝑥	y′(𝑥)𝑑𝑥	PROPN
iajs-3928	118	10	]	]	X
iajs-3928	119	1	+	+	CCONJ
iajs-3928	119	2	w	w	PROPN
iajs-3928	119	3	yi	yi	PROPN
iajs-3928	119	4	(	(	PUNCT
iajs-3928	119	5	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	119	6	−	−	PROPN
iajs-3928	119	7	𝑞	𝑞	PROPN
iajs-3928	119	8	)	)	PUNCT
iajs-3928	119	9	=	=	SYM
iajs-3928	119	10	0	0	NUM
iajs-3928	119	11	,	,	PUNCT
iajs-3928	119	12	ihjpas	ihjpa	VERB
iajs-3928	119	13	.	.	PUNCT
iajs-3928	120	1	2024	2024	NUM
iajs-3928	120	2	,	,	PUNCT
iajs-3928	120	3	37(4	37(4	PROPN
iajs-3928	120	4	)	)	PUNCT
iajs-3928	120	5	386	386	NUM
iajs-3928	120	6	𝑞3	𝑞3	NOUN
iajs-3928	120	7	[	[	X
iajs-3928	120	8	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	120	9	)	)	PUNCT
iajs-3928	120	10	−	−	PROPN
iajs-3928	121	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	121	2	)	)	PUNCT
iajs-3928	121	3	+	+	NUM
iajs-3928	121	4	𝑞	𝑞	X
iajs-3928	121	5	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	ADJ
iajs-3928	121	6	)	)	PUNCT
iajs-3928	121	7	−	−	PROPN
iajs-3928	121	8	𝑞	𝑞	X
iajs-3928	121	9	𝑦(0	𝑦(0	PROPN
iajs-3928	121	10	)	)	PUNCT
iajs-3928	121	11	+	+	NUM
iajs-3928	121	12	𝑞2	𝑞2	PROPN
iajs-3928	121	13	∫	∫	PROPN
iajs-3928	121	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	121	15	𝐿	𝐿	PROPN
iajs-3928	121	16	0	0	NUM
iajs-3928	121	17	y(x	y(x	NOUN
iajs-3928	121	18	)	)	PUNCT
iajs-3928	121	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	121	20	]	]	X
iajs-3928	121	21	+	+	CCONJ
iajs-3928	121	22	w	w	PROPN
iajs-3928	121	23	yi	yi	PROPN
iajs-3928	121	24	(	(	PUNCT
iajs-3928	121	25	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	121	26	−	−	PROPN
iajs-3928	121	27	𝑞	𝑞	PROPN
iajs-3928	121	28	)	)	PUNCT
iajs-3928	121	29	=	=	SYM
iajs-3928	121	30	0	0	NUM
iajs-3928	121	31	,	,	PUNCT
iajs-3928	121	32	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	121	33	)	)	PUNCT
iajs-3928	121	34	−	−	PROPN
iajs-3928	122	1	𝑞3𝑦′(0	𝑞3𝑦′(0	NOUN
iajs-3928	122	2	)	)	PUNCT
iajs-3928	123	1	+	+	CCONJ
iajs-3928	123	2	𝑞4	𝑞4	PROPN
iajs-3928	123	3	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	NOUN
iajs-3928	123	4	)	)	PUNCT
iajs-3928	123	5	−	−	ADP
iajs-3928	123	6	𝑞4	𝑞4	PROPN
iajs-3928	123	7	𝑦(0	𝑦(0	PROPN
iajs-3928	123	8	)	)	PUNCT
iajs-3928	123	9	+	+	NUM
iajs-3928	123	10	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	123	11	)	)	PUNCT
iajs-3928	123	12	}	}	PUNCT
iajs-3928	124	1	+	+	CCONJ
iajs-3928	124	2	w	w	PROPN
iajs-3928	124	3	yi	yi	NOUN
iajs-3928	124	4	(	(	PUNCT
iajs-3928	124	5	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	124	6	−	−	PROPN
iajs-3928	124	7	𝑞	𝑞	PROPN
iajs-3928	124	8	)	)	PUNCT
iajs-3928	124	9	=	=	SYM
iajs-3928	124	10	0	0	NUM
iajs-3928	124	11	(	(	PUNCT
iajs-3928	124	12	9	9	X
iajs-3928	124	13	)	)	PUNCT
iajs-3928	124	14	applying	apply	VERB
iajs-3928	124	15	initial	initial	ADJ
iajs-3928	124	16	conditions	condition	NOUN
iajs-3928	124	17	:	:	PUNCT
iajs-3928	124	18	𝑦	𝑦	X
iajs-3928	124	19	(	(	PUNCT
iajs-3928	124	20	0	0	NUM
iajs-3928	124	21	)	)	PUNCT
iajs-3928	124	22	=	=	SYM
iajs-3928	124	23	0	0	NUM
iajs-3928	124	24	,	,	PUNCT
iajs-3928	124	25	ẏ(0	ẏ(0	NOUN
iajs-3928	124	26	)	)	PUNCT
iajs-3928	124	27	=	=	SYM
iajs-3928	124	28	0	0	NUM
iajs-3928	124	29	,	,	PUNCT
iajs-3928	124	30	𝑦′(𝐿	𝑦′(𝐿	NOUN
iajs-3928	124	31	)	)	PUNCT
iajs-3928	124	32	=	=	SYM
iajs-3928	124	33	𝐷	𝐷	PROPN
iajs-3928	124	34	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	124	35	𝑦(𝐿	𝑦(𝐿	PROPN
iajs-3928	124	36	)	)	PUNCT
iajs-3928	124	37	=	=	SYM
iajs-3928	124	38	𝐶.	𝐶.	NOUN
iajs-3928	124	39	equation	equation	NOUN
iajs-3928	124	40	(	(	PUNCT
iajs-3928	124	41	9	9	X
iajs-3928	124	42	)	)	PUNCT
iajs-3928	124	43	becomes	become	VERB
iajs-3928	124	44	,	,	PUNCT
iajs-3928	124	45	𝑞3𝑒−𝑞𝐿𝐷	𝑞3𝑒−𝑞𝐿𝐷	NOUN
iajs-3928	124	46	+	+	CCONJ
iajs-3928	124	47	𝑞4	𝑞4	NOUN
iajs-3928	124	48	𝑒−𝑞𝐿𝐶	𝑒−𝑞𝐿𝐶	NOUN
iajs-3928	124	49	+	+	CCONJ
iajs-3928	124	50	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	124	51	)	)	PUNCT
iajs-3928	124	52	}	}	PUNCT
iajs-3928	125	1	+	+	CCONJ
iajs-3928	125	2	w	w	PROPN
iajs-3928	125	3	yi	yi	NOUN
iajs-3928	125	4	(	(	PUNCT
iajs-3928	125	5	𝐿𝑞2	𝐿𝑞2	NOUN
iajs-3928	125	6	−	−	PROPN
iajs-3928	125	7	𝑞	𝑞	PROPN
iajs-3928	125	8	)	)	PUNCT
iajs-3928	125	9	=	=	SYM
iajs-3928	125	10	0	0	NUM
iajs-3928	125	11	,	,	PUNCT
iajs-3928	125	12	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	NUM
iajs-3928	125	13	)	)	PUNCT
iajs-3928	125	14	}	}	PUNCT
iajs-3928	125	15	=	=	PUNCT
iajs-3928	125	16	−𝑞𝑒−𝑞𝐿𝐷	−𝑞𝑒−𝑞𝐿𝐷	NOUN
iajs-3928	125	17	−	−	NOUN
iajs-3928	125	18	𝑞2	𝑞2	NOUN
iajs-3928	125	19	𝑒−𝑞𝐿𝐶	𝑒−𝑞𝐿𝐶	NOUN
iajs-3928	125	20	−	−	PROPN
iajs-3928	125	21	w	w	PROPN
iajs-3928	125	22	yi	yi	PROPN
iajs-3928	125	23	(	(	PUNCT
iajs-3928	125	24	𝐿	𝐿	PROPN
iajs-3928	125	25	−	−	PROPN
iajs-3928	125	26	1	1	NUM
iajs-3928	125	27	𝑞	𝑞	PROPN
iajs-3928	125	28	)	)	PUNCT
iajs-3928	125	29	(	(	PUNCT
iajs-3928	125	30	10	10	X
iajs-3928	125	31	)	)	PUNCT
iajs-3928	125	32	taking	take	VERB
iajs-3928	125	33	inverse	inverse	NOUN
iajs-3928	125	34	rohit	rohit	NOUN
iajs-3928	125	35	transform	transform	NOUN
iajs-3928	125	36	,	,	PUNCT
iajs-3928	125	37	we	we	PRON
iajs-3928	125	38	have	have	VERB
iajs-3928	125	39	y(x	y(x	NOUN
iajs-3928	125	40	)	)	PUNCT
iajs-3928	126	1	=	=	VERB
iajs-3928	126	2	−d	−d	ADJ
iajs-3928	126	3	(	(	PUNCT
iajs-3928	126	4	𝑥	𝑥	PROPN
iajs-3928	126	5	−	−	PROPN
iajs-3928	126	6	𝐿)𝑈(𝑥	𝐿)𝑈(𝑥	PROPN
iajs-3928	126	7	−	−	PROPN
iajs-3928	126	8	𝐿	𝐿	PROPN
iajs-3928	126	9	)	)	PUNCT
iajs-3928	126	10	−	−	PROPN
iajs-3928	126	11	c𝑈(𝑥	c𝑈(𝑥	PROPN
iajs-3928	126	12	−	−	PROPN
iajs-3928	126	13	𝐿	𝐿	PROPN
iajs-3928	126	14	)	)	PUNCT
iajs-3928	126	15	+	+	PROPN
iajs-3928	126	16	w	w	PROPN
iajs-3928	126	17	yi	yi	PROPN
iajs-3928	126	18	(	(	PUNCT
iajs-3928	126	19	𝐿𝑥2	𝐿𝑥2	VERB
iajs-3928	126	20	−	−	PROPN
iajs-3928	126	21	𝑥3	𝑥3	NOUN
iajs-3928	126	22	3	3	NUM
iajs-3928	126	23	!	!	PUNCT
iajs-3928	126	24	)	)	PUNCT
iajs-3928	127	1	now	now	ADV
iajs-3928	127	2	,	,	PUNCT
iajs-3928	127	3	for	for	ADP
iajs-3928	127	4	x	x	X
iajs-3928	127	5	<	<	X
iajs-3928	127	6	l	l	NOUN
iajs-3928	127	7	,	,	PUNCT
iajs-3928	127	8	𝑈(𝑥	𝑈(𝑥	PROPN
iajs-3928	127	9	−	−	PROPN
iajs-3928	127	10	𝐿	𝐿	PROPN
iajs-3928	127	11	)	)	PUNCT
iajs-3928	127	12	=	=	SYM
iajs-3928	127	13	0	0	X
iajs-3928	127	14	.	.	PUNCT
iajs-3928	128	1	therefore	therefore	ADV
iajs-3928	128	2	,	,	PUNCT
iajs-3928	128	3	y(x	y(x	PROPN
iajs-3928	128	4	)	)	PUNCT
iajs-3928	129	1	=	=	SYM
iajs-3928	129	2	w	w	PROPN
iajs-3928	129	3	yi	yi	PROPN
iajs-3928	129	4	(	(	PUNCT
iajs-3928	129	5	𝐿𝑥2	𝐿𝑥2	VERB
iajs-3928	129	6	−	−	PROPN
iajs-3928	129	7	𝑥3	𝑥3	NOUN
iajs-3928	129	8	3	3	NUM
iajs-3928	129	9	!	!	PUNCT
iajs-3928	129	10	)	)	PUNCT
iajs-3928	130	1	(	(	PUNCT
iajs-3928	130	2	11	11	X
iajs-3928	130	3	)	)	PUNCT
iajs-3928	130	4	taking	taking	NOUN
iajs-3928	130	5	,	,	PUNCT
iajs-3928	130	6	for	for	ADP
iajs-3928	130	7	example	example	NOUN
iajs-3928	130	8	,	,	PUNCT
iajs-3928	130	9	w	w	PROPN
iajs-3928	130	10	yi	yi	NOUN
iajs-3928	130	11	=	=	SYM
iajs-3928	130	12	32	32	NUM
iajs-3928	130	13	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3928	130	14	𝐿	𝐿	PROPN
iajs-3928	130	15	=	=	PROPN
iajs-3928	130	16	10	10	NUM
iajs-3928	130	17	,	,	PUNCT
iajs-3928	130	18	the	the	DET
iajs-3928	130	19	graph	graph	NOUN
iajs-3928	130	20	of	of	ADP
iajs-3928	130	21	y(x	y(x	NOUN
iajs-3928	130	22	)	)	PUNCT
iajs-3928	130	23	is	be	AUX
iajs-3928	130	24	shown	show	VERB
iajs-3928	130	25	in	in	ADP
iajs-3928	130	26	the	the	DET
iajs-3928	130	27	figure	figure	NOUN
iajs-3928	130	28	2	2	NUM
iajs-3928	130	29	.	.	PUNCT
iajs-3928	130	30	figure	figure	NOUN
iajs-3928	130	31	2	2	NUM
iajs-3928	130	32	.	.	PUNCT
iajs-3928	130	33	numerical	numerical	ADJ
iajs-3928	130	34	solution	solution	NOUN
iajs-3928	130	35	of	of	ADP
iajs-3928	130	36	equation	equation	NOUN
iajs-3928	130	37	(	(	PUNCT
iajs-3928	130	38	8)	8)	NUM
iajs-3928	130	39	.	.	PUNCT
iajs-3928	131	1	4.3	4.3	NUM
iajs-3928	131	2	analysis	analysis	NOUN
iajs-3928	131	3	of	of	ADP
iajs-3928	131	4	elongated	elongate	VERB
iajs-3928	131	5	vertical	vertical	ADJ
iajs-3928	131	6	column	column	NOUN
iajs-3928	131	7	in	in	ADP
iajs-3928	131	8	this	this	DET
iajs-3928	131	9	study	study	NOUN
iajs-3928	131	10	,	,	PUNCT
iajs-3928	131	11	consider	consider	VERB
iajs-3928	131	12	an	an	DET
iajs-3928	131	13	elongated	elongate	VERB
iajs-3928	131	14	vertical	vertical	ADJ
iajs-3928	131	15	column	column	NOUN
iajs-3928	131	16	ab	ab	PROPN
iajs-3928	131	17	(	(	PUNCT
iajs-3928	131	18	a	a	PRON
iajs-3928	131	19	is	be	AUX
iajs-3928	131	20	at	at	ADP
iajs-3928	131	21	top	top	NOUN
iajs-3928	131	22	and	and	CCONJ
iajs-3928	131	23	b	b	NOUN
iajs-3928	131	24	is	be	AUX
iajs-3928	131	25	at	at	ADP
iajs-3928	131	26	bottom	bottom	NOUN
iajs-3928	131	27	)	)	PUNCT
iajs-3928	131	28	of	of	ADP
iajs-3928	131	29	length	length	NOUN
iajs-3928	131	30	'	'	PUNCT
iajs-3928	131	31	l	l	NOUN
iajs-3928	131	32	'	'	PUNCT
iajs-3928	131	33	and	and	CCONJ
iajs-3928	131	34	of	of	ADP
iajs-3928	131	35	uniform	uniform	ADJ
iajs-3928	131	36	cross	cross	NOUN
iajs-3928	131	37	-	-	NOUN
iajs-3928	131	38	section	section	NOUN
iajs-3928	131	39	.	.	PUNCT
iajs-3928	132	1	let	let	VERB
iajs-3928	132	2	"	"	PUNCT
iajs-3928	132	3	y	y	PROPN
iajs-3928	132	4	"	"	PUNCT
iajs-3928	132	5	be	be	AUX
iajs-3928	132	6	the	the	DET
iajs-3928	132	7	lateral	lateral	ADJ
iajs-3928	132	8	deflection	deflection	NOUN
iajs-3928	132	9	of	of	ADP
iajs-3928	132	10	the	the	DET
iajs-3928	132	11	column	column	NOUN
iajs-3928	132	12	section	section	NOUN
iajs-3928	132	13	at	at	ADP
iajs-3928	132	14	height	height	NOUN
iajs-3928	132	15	"	"	PUNCT
iajs-3928	132	16	x	x	NOUN
iajs-3928	132	17	"	"	PUNCT
iajs-3928	132	18	.	.	PUNCT
iajs-3928	133	1	we	we	PRON
iajs-3928	133	2	now	now	ADV
iajs-3928	133	3	consider	consider	VERB
iajs-3928	133	4	three	three	NUM
iajs-3928	133	5	different	different	ADJ
iajs-3928	133	6	cases	case	NOUN
iajs-3928	133	7	:	:	PUNCT
iajs-3928	133	8	case	case	NOUN
iajs-3928	133	9	-	-	PUNCT
iajs-3928	133	10	i	i	NOUN
iajs-3928	133	11	:	:	PUNCT
iajs-3928	133	12	when	when	SCONJ
iajs-3928	133	13	both	both	PRON
iajs-3928	133	14	ends	end	VERB
iajs-3928	133	15	a	a	PRON
iajs-3928	133	16	and	and	CCONJ
iajs-3928	133	17	b	b	NOUN
iajs-3928	133	18	of	of	ADP
iajs-3928	133	19	the	the	DET
iajs-3928	133	20	column	column	NOUN
iajs-3928	133	21	are	be	AUX
iajs-3928	133	22	pinned	pin	VERB
iajs-3928	133	23	or	or	CCONJ
iajs-3928	133	24	hinged	hinge	VERB
iajs-3928	133	25	in	in	ADP
iajs-3928	133	26	this	this	DET
iajs-3928	133	27	case	case	NOUN
iajs-3928	133	28	,	,	PUNCT
iajs-3928	133	29	the	the	DET
iajs-3928	133	30	bending	bend	VERB
iajs-3928	133	31	moment	moment	NOUN
iajs-3928	133	32	[	[	X
iajs-3928	133	33	1	1	NUM
iajs-3928	133	34	]	]	PUNCT
iajs-3928	133	35	,	,	PUNCT
iajs-3928	133	36	[	[	X
iajs-3928	133	37	13	13	NUM
iajs-3928	133	38	]	]	PUNCT
iajs-3928	133	39	at	at	ADP
iajs-3928	133	40	the	the	DET
iajs-3928	133	41	section	section	NOUN
iajs-3928	133	42	is	be	AUX
iajs-3928	133	43	given	give	VERB
iajs-3928	133	44	by	by	ADP
iajs-3928	133	45	�	�	PROPN
iajs-3928	133	46	̈	̈	X
iajs-3928	133	47	�	�	NOUN
iajs-3928	133	48	(𝑥	(𝑥	NOUN
iajs-3928	133	49	)	)	PUNCT
iajs-3928	134	1	+	+	NUM
iajs-3928	134	2	𝑘2𝑦(𝑥	𝑘2𝑦(𝑥	PROPN
iajs-3928	134	3	)	)	PUNCT
iajs-3928	135	1	=	=	SYM
iajs-3928	135	2	0	0	NUM
iajs-3928	135	3	,	,	PUNCT
iajs-3928	135	4	(	(	PUNCT
iajs-3928	135	5	12	12	NUM
iajs-3928	135	6	)	)	PUNCT
iajs-3928	135	7	where	where	SCONJ
iajs-3928	135	8	k	k	NOUN
iajs-3928	135	9	=	=	PUNCT
iajs-3928	135	10	√	√	ADP
iajs-3928	135	11	𝑃	𝑃	NOUN
iajs-3928	135	12	𝑌i	𝑌i	PROPN
iajs-3928	135	13	.	.	PUNCT
iajs-3928	136	1	taking	take	VERB
iajs-3928	136	2	rohit	rohit	NOUN
iajs-3928	136	3	transform	transform	NOUN
iajs-3928	136	4	of	of	ADP
iajs-3928	136	5	equation	equation	NOUN
iajs-3928	136	6	(	(	PUNCT
iajs-3928	136	7	12	12	NUM
iajs-3928	136	8	)	)	PUNCT
iajs-3928	136	9	,	,	PUNCT
iajs-3928	136	10	we	we	PRON
iajs-3928	136	11	get	get	VERB
iajs-3928	136	12	𝑞3	𝑞3	PROPN
iajs-3928	137	1	∫	∫	NOUN
iajs-3928	138	1	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	138	2	∞	∞	PROPN
iajs-3928	138	3	0	0	SYM
iajs-3928	138	4	�	�	PROPN
iajs-3928	138	5	̈	̈	X
iajs-3928	138	6	�	�	NOUN
iajs-3928	138	7	(x	(x	NUM
iajs-3928	138	8	)	)	PUNCT
iajs-3928	138	9	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	138	10	+	+	NOUN
iajs-3928	138	11	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	138	12	)	)	PUNCT
iajs-3928	138	13	}	}	PUNCT
iajs-3928	138	14	=	=	SYM
iajs-3928	138	15	0	0	NUM
iajs-3928	138	16	,	,	PUNCT
iajs-3928	138	17	𝑞3	𝑞3	PROPN
iajs-3928	138	18	[	[	X
iajs-3928	138	19	∫	∫	PROPN
iajs-3928	138	20	𝑒−𝑞𝑥𝐿	𝑒−𝑞𝑥𝐿	PROPN
iajs-3928	138	21	0	0	SYM
iajs-3928	138	22	�	�	PROPN
iajs-3928	138	23	̈	̈	X
iajs-3928	138	24	�	�	NOUN
iajs-3928	138	25	(x	(x	NUM
iajs-3928	138	26	)	)	PUNCT
iajs-3928	138	27	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	138	28	+	+	NUM
iajs-3928	138	29	∫	∫	PROPN
iajs-3928	138	30	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	138	31	𝐿	𝐿	PROPN
iajs-3928	138	32	�	�	PROPN
iajs-3928	138	33	̈	̈	X
iajs-3928	138	34	�	�	PROPN
iajs-3928	138	35	(x	(x	NUM
iajs-3928	138	36	)	)	PUNCT
iajs-3928	138	37	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	138	38	]	]	X
iajs-3928	138	39	+	+	CCONJ
iajs-3928	138	40	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	138	41	)	)	PUNCT
iajs-3928	138	42	}	}	PUNCT
iajs-3928	138	43	=	=	SYM
iajs-3928	138	44	0	0	PUNCT
iajs-3928	138	45	(	(	PUNCT
iajs-3928	138	46	13	13	NUM
iajs-3928	138	47	)	)	PUNCT
iajs-3928	138	48	as	as	ADP
iajs-3928	138	49	0	0	NUM
iajs-3928	138	50	<	<	X
iajs-3928	138	51	x	x	X
iajs-3928	138	52	<	<	X
iajs-3928	138	53	l	l	NOUN
iajs-3928	138	54	,	,	PUNCT
iajs-3928	138	55	therefore	therefore	ADV
iajs-3928	138	56	,	,	PUNCT
iajs-3928	138	57	∫	∫	PROPN
iajs-3928	138	58	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	138	59	𝐿	𝐿	PROPN
iajs-3928	138	60	�	�	PROPN
iajs-3928	138	61	̈	̈	X
iajs-3928	138	62	�	�	NOUN
iajs-3928	138	63	(x	(x	NUM
iajs-3928	138	64	)	)	PUNCT
iajs-3928	138	65	𝑑𝑥	𝑑𝑥	ADP
iajs-3928	138	66	=	=	SYM
iajs-3928	138	67	0	0	X
iajs-3928	138	68	.	.	PUNCT
iajs-3928	138	69	ihjpas	ihjpas	PROPN
iajs-3928	138	70	.	.	PUNCT
iajs-3928	139	1	2024	2024	NUM
iajs-3928	139	2	,	,	PUNCT
iajs-3928	139	3	37(4	37(4	NUM
iajs-3928	139	4	)	)	PUNCT
iajs-3928	139	5	387	387	NUM
iajs-3928	139	6	thus	thus	ADV
iajs-3928	139	7	,	,	PUNCT
iajs-3928	139	8	𝑞3	𝑞3	PROPN
iajs-3928	139	9	∫	∫	PROPN
iajs-3928	139	10	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	139	11	𝐿	𝐿	PROPN
iajs-3928	139	12	0	0	NUM
iajs-3928	139	13	�	�	PROPN
iajs-3928	139	14	̈	̈	X
iajs-3928	139	15	�	�	NOUN
iajs-3928	139	16	(x	(x	NUM
iajs-3928	139	17	)	)	PUNCT
iajs-3928	139	18	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	139	19	+	+	NOUN
iajs-3928	139	20	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	139	21	)	)	PUNCT
iajs-3928	139	22	}	}	PUNCT
iajs-3928	139	23	=	=	SYM
iajs-3928	139	24	0	0	NUM
iajs-3928	139	25	,	,	PUNCT
iajs-3928	139	26	𝑞3	𝑞3	PROPN
iajs-3928	139	27	[	[	X
iajs-3928	139	28	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	139	29	)	)	PUNCT
iajs-3928	139	30	−	−	PROPN
iajs-3928	140	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	140	2	)	)	PUNCT
iajs-3928	140	3	+	+	NUM
iajs-3928	140	4	𝑞	𝑞	PROPN
iajs-3928	140	5	∫	∫	PROPN
iajs-3928	140	6	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	140	7	𝐿	𝐿	PROPN
iajs-3928	140	8	0	0	NUM
iajs-3928	140	9	y′(𝑥)𝑑𝑥	y′(𝑥)𝑑𝑥	PROPN
iajs-3928	140	10	]	]	PUNCT
iajs-3928	140	11	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	NOUN
iajs-3928	140	12	)	)	PUNCT
iajs-3928	140	13	=	=	SYM
iajs-3928	140	14	0	0	NUM
iajs-3928	140	15	,	,	PUNCT
iajs-3928	140	16	𝑞3	𝑞3	PROPN
iajs-3928	140	17	[	[	X
iajs-3928	140	18	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	140	19	)	)	PUNCT
iajs-3928	140	20	−	−	PROPN
iajs-3928	141	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	141	2	)	)	PUNCT
iajs-3928	141	3	+	+	NUM
iajs-3928	141	4	𝑞	𝑞	X
iajs-3928	141	5	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	ADJ
iajs-3928	141	6	)	)	PUNCT
iajs-3928	141	7	−	−	PROPN
iajs-3928	141	8	𝑞	𝑞	X
iajs-3928	141	9	𝑦(0	𝑦(0	PROPN
iajs-3928	141	10	)	)	PUNCT
iajs-3928	141	11	+	+	NUM
iajs-3928	141	12	𝑞2	𝑞2	PROPN
iajs-3928	141	13	∫	∫	PROPN
iajs-3928	141	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	141	15	𝐿	𝐿	PROPN
iajs-3928	141	16	0	0	NUM
iajs-3928	141	17	y(x	y(x	NOUN
iajs-3928	141	18	)	)	PUNCT
iajs-3928	141	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	141	20	]	]	X
iajs-3928	141	21	+	+	CCONJ
iajs-3928	141	22	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	141	23	)	)	PUNCT
iajs-3928	141	24	=	=	SYM
iajs-3928	141	25	0	0	NUM
iajs-3928	141	26	,	,	PUNCT
iajs-3928	141	27	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	141	28	)	)	PUNCT
iajs-3928	141	29	−	−	PROPN
iajs-3928	142	1	𝑞3𝑦′(0	𝑞3𝑦′(0	NOUN
iajs-3928	142	2	)	)	PUNCT
iajs-3928	143	1	+	+	CCONJ
iajs-3928	143	2	𝑞4	𝑞4	PROPN
iajs-3928	143	3	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	NOUN
iajs-3928	143	4	)	)	PUNCT
iajs-3928	143	5	−	−	ADP
iajs-3928	143	6	𝑞4	𝑞4	PROPN
iajs-3928	143	7	𝑦(0	𝑦(0	PROPN
iajs-3928	143	8	)	)	PUNCT
iajs-3928	143	9	+	+	NUM
iajs-3928	143	10	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	143	11	)	)	PUNCT
iajs-3928	143	12	}	}	PUNCT
iajs-3928	143	13	+	+	CCONJ
iajs-3928	144	1	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	144	2	)	)	PUNCT
iajs-3928	144	3	}	}	PUNCT
iajs-3928	145	1	=	=	SYM
iajs-3928	145	2	0	0	NUM
iajs-3928	145	3	(	(	PUNCT
iajs-3928	145	4	14	14	NUM
iajs-3928	145	5	)	)	PUNCT
iajs-3928	145	6	applying	apply	VERB
iajs-3928	145	7	initial	initial	ADJ
iajs-3928	145	8	conditions	condition	NOUN
iajs-3928	145	9	:	:	PUNCT
iajs-3928	145	10	𝑦(0	𝑦(0	PROPN
iajs-3928	145	11	)	)	PUNCT
iajs-3928	145	12	=	=	SYM
iajs-3928	145	13	0	0	NUM
iajs-3928	145	14	,	,	PUNCT
iajs-3928	145	15	y(l	y(l	NOUN
iajs-3928	145	16	)	)	PUNCT
iajs-3928	145	17	=	=	SYM
iajs-3928	145	18	0	0	NUM
iajs-3928	145	19	,	,	PUNCT
iajs-3928	145	20	𝑦′(0	𝑦′(0	NOUN
iajs-3928	145	21	)	)	PUNCT
iajs-3928	145	22	=	=	SYM
iajs-3928	145	23	𝐴	𝐴	PROPN
iajs-3928	145	24	,	,	PUNCT
iajs-3928	145	25	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	145	26	𝑦′(𝐿	𝑦′(𝐿	NOUN
iajs-3928	145	27	)	)	PUNCT
iajs-3928	145	28	=	=	SYM
iajs-3928	145	29	𝐵.	𝐵.	NOUN
iajs-3928	145	30	equation	equation	NOUN
iajs-3928	145	31	(	(	PUNCT
iajs-3928	145	32	14	14	NUM
iajs-3928	145	33	)	)	PUNCT
iajs-3928	145	34	becomes	become	VERB
iajs-3928	145	35	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADV
iajs-3928	145	36	−	−	NOUN
iajs-3928	145	37	𝑞3𝐴	𝑞3𝐴	NOUN
iajs-3928	145	38	+	+	CCONJ
iajs-3928	145	39	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	145	40	)	)	PUNCT
iajs-3928	145	41	}	}	PUNCT
iajs-3928	146	1	+	+	CCONJ
iajs-3928	147	1	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	147	2	)	)	PUNCT
iajs-3928	147	3	}	}	PUNCT
iajs-3928	148	1	=	=	SYM
iajs-3928	148	2	0	0	NUM
iajs-3928	148	3	,	,	PUNCT
iajs-3928	148	4	𝑅{𝑦(𝑥)}(𝑞2	𝑅{𝑦(𝑥)}(𝑞2	PUNCT
iajs-3928	149	1	+	+	CCONJ
iajs-3928	149	2	𝑘2	𝑘2	NOUN
iajs-3928	149	3	)	)	PUNCT
iajs-3928	149	4	=	=	PUNCT
iajs-3928	150	1	−	−	PROPN
iajs-3928	150	2	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	NOUN
iajs-3928	150	3	+	+	CCONJ
iajs-3928	150	4	𝑞3𝐴	𝑞3𝐴	NUM
iajs-3928	150	5	,	,	PUNCT
iajs-3928	150	6	{	{	PUNCT
iajs-3928	150	7	𝑦(𝑥	𝑦(𝑥	X
iajs-3928	150	8	)	)	PUNCT
iajs-3928	150	9	}	}	PUNCT
iajs-3928	150	10	=	=	SYM
iajs-3928	151	1	−	−	PROPN
iajs-3928	151	2	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	NOUN
iajs-3928	151	3	𝑞2+𝑘2	𝑞2+𝑘2	PROPN
iajs-3928	151	4	+	+	PUNCT
iajs-3928	151	5	𝑞3𝐴	𝑞3𝐴	ADP
iajs-3928	151	6	𝑞2+𝑘2	𝑞2+𝑘2	PROPN
iajs-3928	151	7	(	(	PUNCT
iajs-3928	151	8	15	15	NUM
iajs-3928	151	9	)	)	PUNCT
iajs-3928	151	10	r	r	NOUN
iajs-3928	151	11	taking	take	VERB
iajs-3928	151	12	inverse	inverse	NOUN
iajs-3928	151	13	rohit	rohit	NOUN
iajs-3928	151	14	transform	transform	NOUN
iajs-3928	151	15	of	of	ADP
iajs-3928	151	16	equation	equation	NOUN
iajs-3928	151	17	(	(	PUNCT
iajs-3928	151	18	15	15	NUM
iajs-3928	151	19	)	)	PUNCT
iajs-3928	151	20	,	,	PUNCT
iajs-3928	151	21	we	we	PRON
iajs-3928	151	22	get	get	VERB
iajs-3928	151	23	𝑦(x	𝑦(x	NUM
iajs-3928	151	24	)	)	PUNCT
iajs-3928	152	1	=	=	PUNCT
iajs-3928	152	2	−	−	PROPN
iajs-3928	152	3	𝐵	𝐵	NOUN
iajs-3928	152	4	𝑘	𝑘	PRON
iajs-3928	152	5	sin	sin	NOUN
iajs-3928	152	6	k	k	NOUN
iajs-3928	152	7	(	(	PUNCT
iajs-3928	152	8	x	x	X
iajs-3928	152	9	−	−	NOUN
iajs-3928	152	10	l)u(x	l)u(x	NOUN
iajs-3928	152	11	−	−	PROPN
iajs-3928	152	12	l	l	NOUN
iajs-3928	152	13	)	)	PUNCT
iajs-3928	153	1	+	+	CCONJ
iajs-3928	153	2	𝐴	𝐴	PROPN
iajs-3928	153	3	𝑘	𝑘	PRON
iajs-3928	153	4	sin	sin	NOUN
iajs-3928	153	5	(	(	PUNCT
iajs-3928	153	6	k	k	NOUN
iajs-3928	153	7	x	x	PROPN
iajs-3928	153	8	)	)	PUNCT
iajs-3928	153	9	.	.	PUNCT
iajs-3928	154	1	now	now	ADV
iajs-3928	154	2	,	,	PUNCT
iajs-3928	154	3	for	for	ADP
iajs-3928	154	4	x	x	X
iajs-3928	154	5	<	<	X
iajs-3928	154	6	l	l	NOUN
iajs-3928	154	7	,	,	PUNCT
iajs-3928	154	8	𝑈(𝑥	𝑈(𝑥	PROPN
iajs-3928	154	9	−	−	PROPN
iajs-3928	154	10	𝐿	𝐿	PROPN
iajs-3928	154	11	)	)	PUNCT
iajs-3928	154	12	=	=	SYM
iajs-3928	154	13	0	0	X
iajs-3928	154	14	.	.	PUNCT
iajs-3928	155	1	thus	thus	ADV
iajs-3928	155	2	,	,	PUNCT
iajs-3928	155	3	𝑦(𝑥	𝑦(𝑥	X
iajs-3928	155	4	)	)	PUNCT
iajs-3928	155	5	=	=	SYM
iajs-3928	155	6	𝐴	𝐴	PROPN
iajs-3928	155	7	𝑘	𝑘	PRON
iajs-3928	155	8	𝑠𝑖𝑛(𝑘𝑥	𝑠𝑖𝑛(𝑘𝑥	NOUN
iajs-3928	155	9	)	)	PUNCT
iajs-3928	155	10	(	(	PUNCT
iajs-3928	155	11	16	16	NUM
iajs-3928	155	12	)	)	PUNCT
iajs-3928	155	13	as	as	ADP
iajs-3928	155	14	𝑦(l	𝑦(l	NOUN
iajs-3928	155	15	)	)	PUNCT
iajs-3928	155	16	=	=	SYM
iajs-3928	156	1	0	0	NUM
iajs-3928	156	2	,	,	PUNCT
iajs-3928	156	3	therefore	therefore	ADV
iajs-3928	156	4	,	,	PUNCT
iajs-3928	156	5	equation	equation	NOUN
iajs-3928	156	6	(	(	PUNCT
iajs-3928	156	7	16	16	NUM
iajs-3928	156	8	)	)	PUNCT
iajs-3928	156	9	gives	give	VERB
iajs-3928	156	10	sin	sin	NOUN
iajs-3928	156	11	(	(	PUNCT
iajs-3928	156	12	k	k	NOUN
iajs-3928	156	13	l	l	NOUN
iajs-3928	156	14	)	)	PUNCT
iajs-3928	157	1	=	=	SYM
iajs-3928	157	2	0	0	NUM
iajs-3928	157	3	,	,	PUNCT
iajs-3928	157	4	where	where	SCONJ
iajs-3928	157	5	n	n	PRON
iajs-3928	157	6	is	be	AUX
iajs-3928	157	7	an	an	DET
iajs-3928	157	8	integer	integer	NOUN
iajs-3928	157	9	greater	great	ADJ
iajs-3928	157	10	than	than	ADP
iajs-3928	157	11	equal	equal	ADJ
iajs-3928	157	12	to	to	ADP
iajs-3928	157	13	zero	zero	NUM
iajs-3928	157	14	.	.	PUNCT
iajs-3928	158	1	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	158	2	=	=	SYM
iajs-3928	158	3	𝑛	𝑛	DET
iajs-3928	158	4	𝜋	𝜋	NOUN
iajs-3928	158	5	,	,	PUNCT
iajs-3928	158	6	k	k	X
iajs-3928	158	7	=	=	SYM
iajs-3928	158	8	n𝜋	n𝜋	PROPN
iajs-3928	158	9	𝐿	𝐿	PROPN
iajs-3928	158	10	(	(	PUNCT
iajs-3928	158	11	17	17	NUM
iajs-3928	158	12	)	)	PUNCT
iajs-3928	158	13	the	the	DET
iajs-3928	158	14	least	least	ADV
iajs-3928	158	15	practical	practical	ADJ
iajs-3928	158	16	value	value	NOUN
iajs-3928	158	17	of	of	ADP
iajs-3928	158	18	n	n	NUM
iajs-3928	158	19	is	be	AUX
iajs-3928	158	20	1	1	NUM
iajs-3928	158	21	,	,	PUNCT
iajs-3928	158	22	therefore	therefore	ADV
iajs-3928	158	23	,	,	PUNCT
iajs-3928	158	24	considering	consider	VERB
iajs-3928	158	25	n	n	X
iajs-3928	158	26	=	=	SYM
iajs-3928	158	27	1	1	NUM
iajs-3928	158	28	,	,	PUNCT
iajs-3928	158	29	we	we	PRON
iajs-3928	158	30	have	have	VERB
iajs-3928	158	31	𝑘	𝑘	PRON
iajs-3928	158	32	=	=	PUNCT
iajs-3928	158	33	𝜋	𝜋	NOUN
iajs-3928	158	34	𝐿	𝐿	PROPN
iajs-3928	158	35	,	,	PUNCT
iajs-3928	158	36	√	√	PROPN
iajs-3928	158	37	p	p	NOUN
iajs-3928	158	38	yi	yi	NOUN
iajs-3928	159	1	=	=	PUNCT
iajs-3928	159	2	π	π	PROPN
iajs-3928	159	3	l	l	NOUN
iajs-3928	159	4	,	,	PUNCT
iajs-3928	159	5	p	p	NOUN
iajs-3928	159	6	=	=	NOUN
iajs-3928	159	7	π2yi	π2yi	PRON
iajs-3928	159	8	l2	l2	NOUN
iajs-3928	159	9	(	(	PUNCT
iajs-3928	159	10	18	18	NUM
iajs-3928	159	11	)	)	PUNCT
iajs-3928	159	12	the	the	DET
iajs-3928	159	13	euler	euler	NOUN
iajs-3928	159	14	's	's	PART
iajs-3928	159	15	formula	formula	NOUN
iajs-3928	159	16	for	for	ADP
iajs-3928	159	17	the	the	DET
iajs-3928	159	18	critical	critical	ADJ
iajs-3928	159	19	buckling	buckling	NOUN
iajs-3928	159	20	load	load	NOUN
iajs-3928	159	21	of	of	ADP
iajs-3928	159	22	the	the	DET
iajs-3928	159	23	elongated	elongate	VERB
iajs-3928	159	24	column	column	NOUN
iajs-3928	159	25	with	with	ADP
iajs-3928	159	26	pins	pin	NOUN
iajs-3928	159	27	at	at	ADP
iajs-3928	159	28	both	both	DET
iajs-3928	159	29	ends	end	NOUN
iajs-3928	159	30	is	be	AUX
iajs-3928	159	31	found	find	VERB
iajs-3928	159	32	in	in	ADP
iajs-3928	159	33	equation	equation	NOUN
iajs-3928	159	34	(	(	PUNCT
iajs-3928	159	35	18	18	NUM
iajs-3928	159	36	)	)	PUNCT
iajs-3928	159	37	.	.	PUNCT
iajs-3928	160	1	case	case	NOUN
iajs-3928	160	2	-	-	PUNCT
iajs-3928	160	3	ii	ii	NOUN
iajs-3928	160	4	:	:	PUNCT
iajs-3928	160	5	when	when	SCONJ
iajs-3928	160	6	the	the	DET
iajs-3928	160	7	bottom	bottom	NOUN
iajs-3928	160	8	end	end	NOUN
iajs-3928	160	9	b	b	PROPN
iajs-3928	160	10	of	of	ADP
iajs-3928	160	11	the	the	DET
iajs-3928	160	12	column	column	NOUN
iajs-3928	160	13	is	be	AUX
iajs-3928	160	14	fixed	fix	VERB
iajs-3928	160	15	and	and	CCONJ
iajs-3928	160	16	the	the	DET
iajs-3928	160	17	upper	upper	ADJ
iajs-3928	160	18	end	end	NOUN
iajs-3928	160	19	a	a	PRON
iajs-3928	160	20	is	be	AUX
iajs-3928	160	21	hinged	hinge	VERB
iajs-3928	160	22	in	in	ADP
iajs-3928	160	23	this	this	DET
iajs-3928	160	24	case	case	NOUN
iajs-3928	160	25	,	,	PUNCT
iajs-3928	160	26	the	the	DET
iajs-3928	160	27	bending	bend	VERB
iajs-3928	160	28	moment	moment	NOUN
iajs-3928	160	29	[	[	X
iajs-3928	160	30	4	4	X
iajs-3928	160	31	]	]	PUNCT
iajs-3928	160	32	at	at	ADP
iajs-3928	160	33	the	the	DET
iajs-3928	160	34	section	section	NOUN
iajs-3928	160	35	is	be	AUX
iajs-3928	160	36	given	give	VERB
iajs-3928	160	37	by	by	ADP
iajs-3928	160	38	�	�	PROPN
iajs-3928	160	39	̈	̈	X
iajs-3928	160	40	�	�	NOUN
iajs-3928	160	41	(𝑥	(𝑥	NOUN
iajs-3928	160	42	)	)	PUNCT
iajs-3928	160	43	+	+	NUM
iajs-3928	160	44	𝑘2𝑦(𝑥	𝑘2𝑦(𝑥	PROPN
iajs-3928	160	45	)	)	PUNCT
iajs-3928	161	1	=	=	PUNCT
iajs-3928	161	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	161	3	−	−	DET
iajs-3928	161	4	𝑥	𝑥	NOUN
iajs-3928	161	5	)	)	PUNCT
iajs-3928	161	6	(	(	PUNCT
iajs-3928	161	7	19	19	NUM
iajs-3928	161	8	)	)	PUNCT
iajs-3928	161	9	where	where	SCONJ
iajs-3928	161	10	h	h	NOUN
iajs-3928	161	11	=	=	SYM
iajs-3928	161	12	h0	h0	PROPN
iajs-3928	161	13	ei	ei	NOUN
iajs-3928	161	14	.	.	PUNCT
iajs-3928	162	1	here	here	ADV
iajs-3928	162	2	,	,	PUNCT
iajs-3928	162	3	h0	h0	PROPN
iajs-3928	162	4	is	be	AUX
iajs-3928	162	5	horizontal	horizontal	ADJ
iajs-3928	162	6	force	force	NOUN
iajs-3928	162	7	at	at	ADP
iajs-3928	162	8	the	the	DET
iajs-3928	162	9	fixed	fixed	ADJ
iajs-3928	162	10	end	end	NOUN
iajs-3928	162	11	𝐵.	𝐵.	PROPN
iajs-3928	162	12	taking	take	VERB
iajs-3928	162	13	rohit	rohit	NOUN
iajs-3928	162	14	transform	transform	NOUN
iajs-3928	162	15	of	of	ADP
iajs-3928	162	16	equation	equation	NOUN
iajs-3928	162	17	(	(	PUNCT
iajs-3928	162	18	19	19	NUM
iajs-3928	162	19	)	)	PUNCT
iajs-3928	162	20	,	,	PUNCT
iajs-3928	162	21	we	we	PRON
iajs-3928	162	22	get	get	VERB
iajs-3928	162	23	𝑞3	𝑞3	PROPN
iajs-3928	162	24	∫	∫	NOUN
iajs-3928	163	1	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	163	2	∞	∞	PROPN
iajs-3928	163	3	0	0	SYM
iajs-3928	163	4	�	�	PROPN
iajs-3928	163	5	̈	̈	X
iajs-3928	163	6	�	�	NOUN
iajs-3928	163	7	(x	(x	NUM
iajs-3928	163	8	)	)	PUNCT
iajs-3928	163	9	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	163	10	+	+	NOUN
iajs-3928	163	11	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	163	12	)	)	PUNCT
iajs-3928	163	13	}	}	PUNCT
iajs-3928	164	1	=	=	PUNCT
iajs-3928	164	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	164	3	𝑞2	𝑞2	NOUN
iajs-3928	164	4	−	−	PROPN
iajs-3928	164	5	𝑞	𝑞	PROPN
iajs-3928	164	6	)	)	PUNCT
iajs-3928	164	7	,	,	PUNCT
iajs-3928	164	8	𝑞3	𝑞3	PROPN
iajs-3928	164	9	[	[	X
iajs-3928	164	10	∫	∫	X
iajs-3928	164	11	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	164	12	𝐿	𝐿	PROPN
iajs-3928	164	13	0	0	NUM
iajs-3928	164	14	�	�	PROPN
iajs-3928	164	15	̈	̈	X
iajs-3928	164	16	�	�	NOUN
iajs-3928	164	17	(x	(x	NUM
iajs-3928	164	18	)	)	PUNCT
iajs-3928	164	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	164	20	+	+	NUM
iajs-3928	164	21	∫	∫	NOUN
iajs-3928	164	22	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	164	23	∞	∞	PROPN
iajs-3928	164	24	𝐿	𝐿	PROPN
iajs-3928	164	25	�	�	PROPN
iajs-3928	164	26	̈	̈	X
iajs-3928	164	27	�	�	PROPN
iajs-3928	164	28	(x	(x	NUM
iajs-3928	164	29	)	)	PUNCT
iajs-3928	164	30	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	164	31	]	]	X
iajs-3928	164	32	+	+	CCONJ
iajs-3928	164	33	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	164	34	)	)	PUNCT
iajs-3928	164	35	}	}	PUNCT
iajs-3928	165	1	=	=	PUNCT
iajs-3928	165	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	165	3	𝑞2	𝑞2	NOUN
iajs-3928	165	4	−	−	PROPN
iajs-3928	165	5	𝑞	𝑞	PROPN
iajs-3928	165	6	)	)	PUNCT
iajs-3928	165	7	.	.	PUNCT
iajs-3928	166	1	as	as	ADP
iajs-3928	166	2	0	0	NUM
iajs-3928	166	3	<	<	X
iajs-3928	166	4	x	x	X
iajs-3928	166	5	<	<	X
iajs-3928	166	6	l	l	NOUN
iajs-3928	166	7	,	,	PUNCT
iajs-3928	166	8	therefore	therefore	ADV
iajs-3928	166	9	,	,	PUNCT
iajs-3928	166	10	∫	∫	PROPN
iajs-3928	166	11	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	166	12	𝐿	𝐿	PROPN
iajs-3928	166	13	�	�	PROPN
iajs-3928	166	14	̈	̈	X
iajs-3928	166	15	�	�	NOUN
iajs-3928	166	16	(x	(x	NUM
iajs-3928	166	17	)	)	PUNCT
iajs-3928	166	18	𝑑𝑥	𝑑𝑥	ADP
iajs-3928	166	19	=	=	SYM
iajs-3928	166	20	0	0	X
iajs-3928	166	21	.	.	PUNCT
iajs-3928	166	22	ihjpas	ihjpas	PROPN
iajs-3928	166	23	.	.	PUNCT
iajs-3928	167	1	2024	2024	NUM
iajs-3928	167	2	,	,	PUNCT
iajs-3928	167	3	37(4	37(4	PRON
iajs-3928	167	4	)	)	PUNCT
iajs-3928	167	5	388	388	NUM
iajs-3928	167	6	thus	thus	ADV
iajs-3928	167	7	,	,	PUNCT
iajs-3928	167	8	𝑞3	𝑞3	PROPN
iajs-3928	167	9	∫	∫	PROPN
iajs-3928	167	10	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	167	11	𝐿	𝐿	PROPN
iajs-3928	167	12	0	0	NUM
iajs-3928	167	13	�	�	PROPN
iajs-3928	167	14	̈	̈	X
iajs-3928	167	15	�	�	NOUN
iajs-3928	167	16	(x	(x	NUM
iajs-3928	167	17	)	)	PUNCT
iajs-3928	167	18	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	167	19	+	+	NOUN
iajs-3928	167	20	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	167	21	)	)	PUNCT
iajs-3928	167	22	}	}	PUNCT
iajs-3928	168	1	=	=	PUNCT
iajs-3928	168	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	168	3	𝑞2	𝑞2	NOUN
iajs-3928	168	4	−	−	PROPN
iajs-3928	168	5	𝑞	𝑞	PROPN
iajs-3928	168	6	)	)	PUNCT
iajs-3928	168	7	,	,	PUNCT
iajs-3928	168	8	𝑞3	𝑞3	PROPN
iajs-3928	168	9	[	[	X
iajs-3928	168	10	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	168	11	)	)	PUNCT
iajs-3928	168	12	−	−	PROPN
iajs-3928	169	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	169	2	)	)	PUNCT
iajs-3928	169	3	+	+	NUM
iajs-3928	169	4	𝑞	𝑞	PROPN
iajs-3928	169	5	∫	∫	PROPN
iajs-3928	169	6	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	169	7	𝐿	𝐿	PROPN
iajs-3928	169	8	0	0	NUM
iajs-3928	169	9	y′(𝑥)𝑑𝑥	y′(𝑥)𝑑𝑥	PROPN
iajs-3928	169	10	]	]	X
iajs-3928	169	11	+	+	PUNCT
iajs-3928	169	12	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	169	13	)	)	PUNCT
iajs-3928	169	14	=	=	PUNCT
iajs-3928	169	15	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	169	16	𝑞2	𝑞2	NOUN
iajs-3928	169	17	−	−	PROPN
iajs-3928	169	18	𝑞	𝑞	PROPN
iajs-3928	169	19	)	)	PUNCT
iajs-3928	169	20	,	,	PUNCT
iajs-3928	169	21	𝑞3	𝑞3	PROPN
iajs-3928	169	22	[	[	X
iajs-3928	169	23	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	169	24	)	)	PUNCT
iajs-3928	169	25	−	−	PROPN
iajs-3928	170	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	170	2	)	)	PUNCT
iajs-3928	170	3	+	+	NUM
iajs-3928	170	4	𝑞	𝑞	X
iajs-3928	170	5	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	ADJ
iajs-3928	170	6	)	)	PUNCT
iajs-3928	170	7	−	−	PROPN
iajs-3928	170	8	𝑞	𝑞	X
iajs-3928	170	9	𝑦(0	𝑦(0	PROPN
iajs-3928	170	10	)	)	PUNCT
iajs-3928	170	11	+	+	NUM
iajs-3928	170	12	𝑞2	𝑞2	PROPN
iajs-3928	170	13	∫	∫	PROPN
iajs-3928	170	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	170	15	𝐿	𝐿	PROPN
iajs-3928	170	16	0	0	NUM
iajs-3928	170	17	y(x	y(x	NOUN
iajs-3928	170	18	)	)	PUNCT
iajs-3928	170	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	170	20	]	]	X
iajs-3928	170	21	+	+	CCONJ
iajs-3928	170	22	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	170	23	)	)	PUNCT
iajs-3928	170	24	=	=	PUNCT
iajs-3928	170	25	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	170	26	𝑞2	𝑞2	NOUN
iajs-3928	170	27	−	−	PROPN
iajs-3928	170	28	𝑞	𝑞	PROPN
iajs-3928	170	29	)	)	PUNCT
iajs-3928	170	30	,	,	PUNCT
iajs-3928	170	31	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	170	32	)	)	PUNCT
iajs-3928	170	33	−	−	PROPN
iajs-3928	171	1	𝑞3𝑦′(0	𝑞3𝑦′(0	NOUN
iajs-3928	171	2	)	)	PUNCT
iajs-3928	171	3	+	+	CCONJ
iajs-3928	171	4	𝑞4𝑒−𝑞𝐿𝑦(𝐿	𝑞4𝑒−𝑞𝐿𝑦(𝐿	X
iajs-3928	171	5	)	)	PUNCT
iajs-3928	171	6	−	−	PROPN
iajs-3928	171	7	𝑞4	𝑞4	PROPN
iajs-3928	171	8	𝑦(0	𝑦(0	PROPN
iajs-3928	171	9	)	)	PUNCT
iajs-3928	171	10	+	+	NUM
iajs-3928	171	11	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	171	12	)	)	PUNCT
iajs-3928	171	13	}	}	PUNCT
iajs-3928	172	1	+	+	CCONJ
iajs-3928	173	1	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	173	2	)	)	PUNCT
iajs-3928	173	3	}	}	PUNCT
iajs-3928	174	1	=	=	PUNCT
iajs-3928	174	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	174	3	𝑞2	𝑞2	NOUN
iajs-3928	174	4	−	−	PROPN
iajs-3928	174	5	𝑞	𝑞	SYM
iajs-3928	174	6	)	)	PUNCT
iajs-3928	174	7	(	(	PUNCT
iajs-3928	174	8	20	20	NUM
iajs-3928	174	9	)	)	PUNCT
iajs-3928	174	10	applying	apply	VERB
iajs-3928	174	11	initial	initial	ADJ
iajs-3928	174	12	conditions	condition	NOUN
iajs-3928	174	13	:	:	PUNCT
iajs-3928	174	14	𝑦(0	𝑦(0	PROPN
iajs-3928	174	15	)	)	PUNCT
iajs-3928	174	16	=	=	SYM
iajs-3928	174	17	0	0	NUM
iajs-3928	174	18	,	,	PUNCT
iajs-3928	174	19	y(l	y(l	NOUN
iajs-3928	174	20	)	)	PUNCT
iajs-3928	174	21	=	=	SYM
iajs-3928	174	22	0	0	NUM
iajs-3928	174	23	,	,	PUNCT
iajs-3928	174	24	𝑦′(0	𝑦′(0	NOUN
iajs-3928	174	25	)	)	PUNCT
iajs-3928	174	26	=	=	SYM
iajs-3928	174	27	0	0	NUM
iajs-3928	174	28	,	,	PUNCT
iajs-3928	174	29	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	174	30	𝑦′(𝐿	𝑦′(𝐿	NOUN
iajs-3928	174	31	)	)	PUNCT
iajs-3928	174	32	=	=	SYM
iajs-3928	174	33	𝐵.	𝐵.	NOUN
iajs-3928	174	34	equation	equation	NOUN
iajs-3928	174	35	(	(	PUNCT
iajs-3928	174	36	20	20	NUM
iajs-3928	174	37	)	)	PUNCT
iajs-3928	174	38	becomes	become	VERB
iajs-3928	174	39	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	174	40	+	+	CCONJ
iajs-3928	174	41	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	X
iajs-3928	174	42	)	)	PUNCT
iajs-3928	174	43	}	}	PUNCT
iajs-3928	175	1	+	+	CCONJ
iajs-3928	176	1	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	176	2	)	)	PUNCT
iajs-3928	176	3	}	}	PUNCT
iajs-3928	177	1	=	=	PUNCT
iajs-3928	177	2	𝐻(𝐿	𝐻(𝐿	ADP
iajs-3928	177	3	𝑞2	𝑞2	NOUN
iajs-3928	177	4	−	−	PROPN
iajs-3928	177	5	𝑞	𝑞	PROPN
iajs-3928	177	6	)	)	PUNCT
iajs-3928	177	7	,	,	PUNCT
iajs-3928	177	8	𝑅{𝑦(𝑥)}(𝑞2	𝑅{𝑦(𝑥)}(𝑞2	PUNCT
iajs-3928	177	9	+	+	CCONJ
iajs-3928	177	10	𝑘2	𝑘2	NOUN
iajs-3928	177	11	)	)	PUNCT
iajs-3928	177	12	=	=	PUNCT
iajs-3928	178	1	−	−	PROPN
iajs-3928	178	2	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	178	3	+	+	CCONJ
iajs-3928	178	4	𝑘2𝑑	𝑘2𝑑	ADJ
iajs-3928	178	5	𝑞2	𝑞2	NOUN
iajs-3928	178	6	,	,	PUNCT
iajs-3928	178	7	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	NUM
iajs-3928	178	8	)	)	PUNCT
iajs-3928	178	9	}	}	PUNCT
iajs-3928	178	10	=	=	PUNCT
iajs-3928	178	11	−	−	ADP
iajs-3928	178	12	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	178	13	𝑞2	𝑞2	NOUN
iajs-3928	178	14	+	+	CCONJ
iajs-3928	178	15	𝑘2	𝑘2	PROPN
iajs-3928	178	16	+	+	CCONJ
iajs-3928	178	17	𝐻𝐿	𝐻𝐿	PROPN
iajs-3928	178	18	𝑞2	𝑞2	NOUN
iajs-3928	178	19	𝑞2	𝑞2	NOUN
iajs-3928	178	20	+	+	CCONJ
iajs-3928	178	21	𝑘2	𝑘2	PROPN
iajs-3928	178	22	−	−	PROPN
iajs-3928	178	23	𝐻𝑞	𝐻𝑞	PROPN
iajs-3928	178	24	𝑞2	𝑞2	NOUN
iajs-3928	178	25	+	+	CCONJ
iajs-3928	178	26	𝑘2	𝑘2	PROPN
iajs-3928	178	27	,	,	PUNCT
iajs-3928	178	28	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	NUM
iajs-3928	178	29	)	)	PUNCT
iajs-3928	178	30	}	}	PUNCT
iajs-3928	178	31	=	=	PUNCT
iajs-3928	178	32	−	−	ADP
iajs-3928	178	33	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	178	34	𝑞2	𝑞2	NOUN
iajs-3928	178	35	+	+	CCONJ
iajs-3928	178	36	𝑘2	𝑘2	PROPN
iajs-3928	178	37	+	+	CCONJ
iajs-3928	178	38	𝐻𝐿	𝐻𝐿	PROPN
iajs-3928	178	39	𝑘2	𝑘2	PROPN
iajs-3928	178	40	[	[	X
iajs-3928	178	41	𝑞2	𝑞2	NOUN
iajs-3928	178	42	−	−	PROPN
iajs-3928	178	43	𝑞4	𝑞4	ADJ
iajs-3928	178	44	𝑞2	𝑞2	NOUN
iajs-3928	178	45	+	+	CCONJ
iajs-3928	178	46	𝑘2	𝑘2	PROPN
iajs-3928	178	47	]	]	PUNCT
iajs-3928	178	48	−	−	PROPN
iajs-3928	179	1	𝐻	𝐻	PROPN
iajs-3928	179	2	𝑘2	𝑘2	PROPN
iajs-3928	180	1	[	[	X
iajs-3928	180	2	𝑞	𝑞	X
iajs-3928	180	3	−	−	PROPN
iajs-3928	180	4	𝑞3	𝑞3	PROPN
iajs-3928	180	5	𝑞2	𝑞2	NOUN
iajs-3928	180	6	+	+	CCONJ
iajs-3928	180	7	𝑘2	𝑘2	PROPN
iajs-3928	180	8	]	]	PUNCT
iajs-3928	180	9	(	(	PUNCT
iajs-3928	180	10	21	21	NUM
iajs-3928	180	11	)	)	PUNCT
iajs-3928	180	12	taking	take	VERB
iajs-3928	180	13	inverse	inverse	NOUN
iajs-3928	180	14	rohit	rohit	NOUN
iajs-3928	180	15	transform	transform	NOUN
iajs-3928	180	16	of	of	ADP
iajs-3928	180	17	equation	equation	NOUN
iajs-3928	180	18	(	(	PUNCT
iajs-3928	180	19	21	21	NUM
iajs-3928	180	20	)	)	PUNCT
iajs-3928	180	21	,	,	PUNCT
iajs-3928	180	22	we	we	PRON
iajs-3928	180	23	get	get	VERB
iajs-3928	180	24	𝑦(x	𝑦(x	NUM
iajs-3928	180	25	)	)	PUNCT
iajs-3928	180	26	=	=	PUNCT
iajs-3928	181	1	−	−	PROPN
iajs-3928	181	2	𝐵	𝐵	NOUN
iajs-3928	181	3	𝑘	𝑘	PRON
iajs-3928	181	4	sin	sin	NOUN
iajs-3928	181	5	k	k	NOUN
iajs-3928	181	6	(	(	PUNCT
iajs-3928	181	7	x	x	X
iajs-3928	181	8	−	−	NOUN
iajs-3928	181	9	l)u(x	l)u(x	NOUN
iajs-3928	181	10	−	−	PROPN
iajs-3928	181	11	l	l	NOUN
iajs-3928	181	12	)	)	PUNCT
iajs-3928	182	1	+	+	NUM
iajs-3928	182	2	h	h	NOUN
iajs-3928	182	3	[	[	PUNCT
iajs-3928	182	4	𝐿	𝐿	PROPN
iajs-3928	182	5	𝑘2	𝑘2	PROPN
iajs-3928	182	6	−	−	PROPN
iajs-3928	182	7	𝐿	𝐿	PROPN
iajs-3928	182	8	𝑘2	𝑘2	PROPN
iajs-3928	182	9	cos	cos	PROPN
iajs-3928	182	10	(	(	PUNCT
iajs-3928	182	11	k	k	PROPN
iajs-3928	182	12	x	x	PROPN
iajs-3928	182	13	)	)	PUNCT
iajs-3928	182	14	]	]	PUNCT
iajs-3928	182	15	−	−	PROPN
iajs-3928	182	16	h	h	NOUN
iajs-3928	182	17	[	[	PUNCT
iajs-3928	182	18	𝑥	𝑥	X
iajs-3928	182	19	𝑘2	𝑘2	PROPN
iajs-3928	182	20	−	−	PROPN
iajs-3928	182	21	sin	sin	NOUN
iajs-3928	182	22	𝑘𝑥	𝑘𝑥	PROPN
iajs-3928	182	23	𝑘3	𝑘3	PROPN
iajs-3928	182	24	]	]	PUNCT
iajs-3928	182	25	(	(	PUNCT
iajs-3928	182	26	22	22	NUM
iajs-3928	182	27	)	)	PUNCT
iajs-3928	182	28	now	now	ADV
iajs-3928	182	29	for	for	ADP
iajs-3928	182	30	x	x	SYM
iajs-3928	182	31	<	<	X
iajs-3928	182	32	l	l	NOUN
iajs-3928	182	33	,	,	PUNCT
iajs-3928	182	34	𝑈(𝑥	𝑈(𝑥	PROPN
iajs-3928	182	35	−	−	PROPN
iajs-3928	182	36	𝐿	𝐿	PROPN
iajs-3928	182	37	)	)	PUNCT
iajs-3928	182	38	=	=	SYM
iajs-3928	182	39	0	0	X
iajs-3928	182	40	.	.	PUNCT
iajs-3928	183	1	thus	thus	ADV
iajs-3928	183	2	,	,	PUNCT
iajs-3928	183	3	from	from	ADP
iajs-3928	183	4	equation	equation	NOUN
iajs-3928	183	5	(	(	PUNCT
iajs-3928	183	6	22	22	NUM
iajs-3928	183	7	)	)	PUNCT
iajs-3928	183	8	,	,	PUNCT
iajs-3928	183	9	we	we	PRON
iajs-3928	183	10	have	have	VERB
iajs-3928	183	11	𝑦(x	𝑦(x	NUM
iajs-3928	183	12	)	)	PUNCT
iajs-3928	184	1	=	=	SYM
iajs-3928	184	2	h	h	NOUN
iajs-3928	184	3	[	[	PUNCT
iajs-3928	184	4	𝐿	𝐿	PROPN
iajs-3928	184	5	𝑘2	𝑘2	PROPN
iajs-3928	184	6	−	−	PROPN
iajs-3928	184	7	𝐿	𝐿	PROPN
iajs-3928	184	8	𝑘2	𝑘2	PROPN
iajs-3928	184	9	cos	cos	PROPN
iajs-3928	184	10	(	(	PUNCT
iajs-3928	184	11	k	k	X
iajs-3928	184	12	x	x	PROPN
iajs-3928	184	13	)	)	PUNCT
iajs-3928	184	14	−	−	PROPN
iajs-3928	185	1	𝑥	𝑥	PRON
iajs-3928	185	2	𝑘2	𝑘2	PROPN
iajs-3928	185	3	+	+	CCONJ
iajs-3928	185	4	sin	sin	NOUN
iajs-3928	185	5	𝑘𝑥	𝑘𝑥	PROPN
iajs-3928	185	6	𝑘3	𝑘3	PROPN
iajs-3928	185	7	]	]	PUNCT
iajs-3928	185	8	(	(	PUNCT
iajs-3928	185	9	23	23	NUM
iajs-3928	185	10	)	)	PUNCT
iajs-3928	185	11	applying	apply	VERB
iajs-3928	185	12	the	the	DET
iajs-3928	185	13	condition	condition	NOUN
iajs-3928	185	14	:	:	PUNCT
iajs-3928	185	15	𝑦(l	𝑦(l	NOUN
iajs-3928	185	16	)	)	PUNCT
iajs-3928	185	17	=	=	SYM
iajs-3928	185	18	0	0	X
iajs-3928	185	19	.	.	PUNCT
iajs-3928	186	1	equation	equation	NOUN
iajs-3928	186	2	(	(	PUNCT
iajs-3928	186	3	23	23	NUM
iajs-3928	186	4	)	)	PUNCT
iajs-3928	186	5	gives	give	VERB
iajs-3928	186	6	h	h	NOUN
iajs-3928	186	7	[	[	PUNCT
iajs-3928	186	8	𝐿	𝐿	PROPN
iajs-3928	186	9	𝑘2	𝑘2	PROPN
iajs-3928	186	10	−	−	PROPN
iajs-3928	186	11	𝐿	𝐿	PROPN
iajs-3928	186	12	𝑘2	𝑘2	PROPN
iajs-3928	186	13	cos	cos	PROPN
iajs-3928	186	14	(	(	PUNCT
iajs-3928	186	15	k	k	PROPN
iajs-3928	186	16	l	l	NOUN
iajs-3928	186	17	)	)	PUNCT
iajs-3928	186	18	−	−	PROPN
iajs-3928	187	1	𝐿	𝐿	PROPN
iajs-3928	187	2	𝑘2	𝑘2	PROPN
iajs-3928	187	3	+	+	CCONJ
iajs-3928	187	4	sin	sin	NOUN
iajs-3928	187	5	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	6	𝑘3	𝑘3	PROPN
iajs-3928	187	7	]	]	X
iajs-3928	187	8	=	=	PUNCT
iajs-3928	187	9	0	0	NUM
iajs-3928	187	10	,	,	PUNCT
iajs-3928	187	11	[	[	X
iajs-3928	187	12	−	−	X
iajs-3928	187	13	𝐿	𝐿	PROPN
iajs-3928	187	14	𝑘2	𝑘2	PROPN
iajs-3928	187	15	cos	cos	PROPN
iajs-3928	187	16	(	(	PUNCT
iajs-3928	187	17	k	k	PROPN
iajs-3928	187	18	l	l	NOUN
iajs-3928	187	19	)	)	PUNCT
iajs-3928	187	20	+	+	CCONJ
iajs-3928	187	21	sin	sin	NOUN
iajs-3928	187	22	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	23	𝑘3	𝑘3	PROPN
iajs-3928	187	24	]	]	X
iajs-3928	187	25	=	=	SYM
iajs-3928	187	26	0	0	NUM
iajs-3928	187	27	,	,	PUNCT
iajs-3928	187	28	𝐿	𝐿	PROPN
iajs-3928	187	29	𝑘2	𝑘2	PROPN
iajs-3928	187	30	cos	cos	PROPN
iajs-3928	187	31	(	(	PUNCT
iajs-3928	187	32	k	k	PROPN
iajs-3928	187	33	l	l	NOUN
iajs-3928	187	34	)	)	PUNCT
iajs-3928	187	35	=	=	SYM
iajs-3928	187	36	sin	sin	NOUN
iajs-3928	187	37	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	38	𝑘3	𝑘3	PROPN
iajs-3928	187	39	tan	tan	PROPN
iajs-3928	187	40	(	(	PUNCT
iajs-3928	187	41	k	k	PROPN
iajs-3928	187	42	l	l	NOUN
iajs-3928	187	43	)	)	PUNCT
iajs-3928	187	44	=	=	SYM
iajs-3928	187	45	kl	kl	X
iajs-3928	187	46	(	(	PUNCT
iajs-3928	187	47	24	24	NUM
iajs-3928	187	48	)	)	PUNCT
iajs-3928	187	49	and	and	CCONJ
iajs-3928	187	50	solving	solving	NOUN
iajs-3928	187	51	,	,	PUNCT
iajs-3928	187	52	we	we	PRON
iajs-3928	187	53	get	get	VERB
iajs-3928	187	54	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	55	power	power	NOUN
iajs-3928	187	56	of	of	ADP
iajs-3928	187	57	thupto	thupto	NOUN
iajs-3928	187	58	5	5	NUM
iajs-3928	187	59	tan	tan	PROPN
iajs-3928	187	60	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	61	on	on	ADP
iajs-3928	187	62	expanding	expand	VERB
iajs-3928	187	63	𝑘𝐿	𝑘𝐿	NOUN
iajs-3928	187	64	=	=	SYM
iajs-3928	187	65	4.5	4.5	NUM
iajs-3928	187	66	radians	radian	NOUN
iajs-3928	187	67	,	,	PUNCT
iajs-3928	187	68	√	√	PROPN
iajs-3928	187	69	p	p	NOUN
iajs-3928	187	70	yi	yi	NOUN
iajs-3928	187	71	𝐿	𝐿	PROPN
iajs-3928	187	72	=	=	SYM
iajs-3928	187	73	4.5	4.5	NUM
iajs-3928	187	74	radians	radian	VERB
iajs-3928	187	75	p	p	NOUN
iajs-3928	187	76	=	=	PUNCT
iajs-3928	187	77	20.25yi	20.25yi	NUM
iajs-3928	187	78	𝐿2	𝐿2	NOUN
iajs-3928	187	79	,	,	PUNCT
iajs-3928	187	80	p	p	X
iajs-3928	187	81	=	=	SYM
iajs-3928	187	82	2π2yi	2π2yi	NUM
iajs-3928	187	83	𝐿2	𝐿2	NOUN
iajs-3928	187	84	(	(	PUNCT
iajs-3928	187	85	25	25	NUM
iajs-3928	187	86	)	)	PUNCT
iajs-3928	187	87	the	the	DET
iajs-3928	187	88	equation	equation	NOUN
iajs-3928	187	89	(	(	PUNCT
iajs-3928	187	90	25	25	NUM
iajs-3928	187	91	)	)	PUNCT
iajs-3928	187	92	is	be	AUX
iajs-3928	187	93	euler	euler	NOUN
iajs-3928	187	94	's	's	PART
iajs-3928	187	95	formula	formula	NOUN
iajs-3928	187	96	for	for	ADP
iajs-3928	187	97	the	the	DET
iajs-3928	187	98	critical	critical	ADJ
iajs-3928	187	99	buckling	buckling	NOUN
iajs-3928	187	100	load	load	NOUN
iajs-3928	187	101	of	of	ADP
iajs-3928	187	102	the	the	DET
iajs-3928	187	103	elongated	elongate	VERB
iajs-3928	187	104	column	column	NOUN
iajs-3928	187	105	with	with	ADP
iajs-3928	187	106	a	a	DET
iajs-3928	187	107	fixed	fix	VERB
iajs-3928	187	108	lower	low	ADJ
iajs-3928	187	109	end	end	NOUN
iajs-3928	187	110	and	and	CCONJ
iajs-3928	187	111	a	a	DET
iajs-3928	187	112	fixed	fix	VERB
iajs-3928	187	113	upper	upper	ADJ
iajs-3928	187	114	end	end	NOUN
iajs-3928	187	115	.	.	PUNCT
iajs-3928	188	1	case	case	NOUN
iajs-3928	188	2	-	-	PUNCT
iajs-3928	188	3	iii	iii	NOUN
iajs-3928	188	4	:	:	PUNCT
iajs-3928	188	5	when	when	SCONJ
iajs-3928	188	6	both	both	PRON
iajs-3928	188	7	the	the	PRON
iajs-3928	188	8	ends	end	VERB
iajs-3928	188	9	a	a	PRON
iajs-3928	188	10	and	and	CCONJ
iajs-3928	188	11	b	b	NOUN
iajs-3928	188	12	of	of	ADP
iajs-3928	188	13	the	the	DET
iajs-3928	188	14	column	column	NOUN
iajs-3928	188	15	are	be	AUX
iajs-3928	188	16	fixed	fix	VERB
iajs-3928	188	17	in	in	ADP
iajs-3928	188	18	this	this	DET
iajs-3928	188	19	case	case	NOUN
iajs-3928	188	20	,	,	PUNCT
iajs-3928	188	21	the	the	DET
iajs-3928	188	22	bending	bend	VERB
iajs-3928	188	23	moment	moment	NOUN
iajs-3928	188	24	at	at	ADP
iajs-3928	188	25	the	the	DET
iajs-3928	188	26	section	section	NOUN
iajs-3928	188	27	is	be	AUX
iajs-3928	188	28	given	give	VERB
iajs-3928	188	29	by	by	ADP
iajs-3928	188	30	�	�	PROPN
iajs-3928	188	31	̈	̈	X
iajs-3928	188	32	�	�	NOUN
iajs-3928	188	33	(𝑥	(𝑥	NOUN
iajs-3928	188	34	)	)	PUNCT
iajs-3928	189	1	+	+	NUM
iajs-3928	189	2	𝑘2𝑦(𝑥	𝑘2𝑦(𝑥	PROPN
iajs-3928	189	3	)	)	PUNCT
iajs-3928	190	1	=	=	SYM
iajs-3928	190	2	m	m	PROPN
iajs-3928	190	3	(	(	PUNCT
iajs-3928	190	4	26	26	NUM
iajs-3928	190	5	)	)	PUNCT
iajs-3928	190	6	where	where	SCONJ
iajs-3928	190	7	m	m	NOUN
iajs-3928	190	8	=	=	VERB
iajs-3928	190	9	m0	m0	PROPN
iajs-3928	190	10	ei	ei	X
iajs-3928	190	11	.	.	PUNCT
iajs-3928	191	1	here	here	ADV
iajs-3928	191	2	,	,	PUNCT
iajs-3928	191	3	m0is	m0is	VERB
iajs-3928	191	4	the	the	DET
iajs-3928	191	5	restraint	restraint	NOUN
iajs-3928	191	6	moment	moment	NOUN
iajs-3928	191	7	at	at	ADP
iajs-3928	191	8	each	each	DET
iajs-3928	191	9	end	end	NOUN
iajs-3928	191	10	.	.	PUNCT
iajs-3928	192	1	ihjpas	ihjpas	PROPN
iajs-3928	192	2	.	.	PUNCT
iajs-3928	193	1	2024	2024	NUM
iajs-3928	193	2	,	,	PUNCT
iajs-3928	193	3	37(4	37(4	PRON
iajs-3928	193	4	)	)	PUNCT
iajs-3928	193	5	389	389	NUM
iajs-3928	193	6	taking	take	VERB
iajs-3928	193	7	rohit	rohit	NOUN
iajs-3928	193	8	transform	transform	NOUN
iajs-3928	193	9	of	of	ADP
iajs-3928	193	10	equation	equation	NOUN
iajs-3928	193	11	(	(	PUNCT
iajs-3928	193	12	26	26	NUM
iajs-3928	193	13	)	)	PUNCT
iajs-3928	193	14	,	,	PUNCT
iajs-3928	193	15	we	we	PRON
iajs-3928	193	16	get	get	VERB
iajs-3928	193	17	𝑞3	𝑞3	PROPN
iajs-3928	194	1	∫	∫	NOUN
iajs-3928	195	1	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	195	2	∞	∞	PROPN
iajs-3928	195	3	0	0	SYM
iajs-3928	195	4	�	�	PROPN
iajs-3928	195	5	̈	̈	X
iajs-3928	195	6	�	�	NOUN
iajs-3928	195	7	(x	(x	NUM
iajs-3928	195	8	)	)	PUNCT
iajs-3928	195	9	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	195	10	+	+	NOUN
iajs-3928	195	11	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	195	12	)	)	PUNCT
iajs-3928	195	13	}	}	PUNCT
iajs-3928	195	14	=	=	SYM
iajs-3928	195	15	𝑀	𝑀	PROPN
iajs-3928	195	16	𝑞2	𝑞2	NOUN
iajs-3928	195	17	,	,	PUNCT
iajs-3928	195	18	𝑞3	𝑞3	PROPN
iajs-3928	195	19	[	[	X
iajs-3928	195	20	∫	∫	X
iajs-3928	195	21	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	195	22	𝐿	𝐿	PROPN
iajs-3928	195	23	0	0	NUM
iajs-3928	195	24	�	�	PROPN
iajs-3928	195	25	̈	̈	X
iajs-3928	195	26	�	�	NOUN
iajs-3928	195	27	(x	(x	NUM
iajs-3928	195	28	)	)	PUNCT
iajs-3928	195	29	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	195	30	+	+	NUM
iajs-3928	195	31	∫	∫	NOUN
iajs-3928	195	32	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	195	33	∞	∞	PROPN
iajs-3928	195	34	𝐿	𝐿	PROPN
iajs-3928	195	35	�	�	PROPN
iajs-3928	195	36	̈	̈	X
iajs-3928	195	37	�	�	PROPN
iajs-3928	195	38	(x	(x	NUM
iajs-3928	195	39	)	)	PUNCT
iajs-3928	195	40	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	195	41	]	]	X
iajs-3928	195	42	+	+	CCONJ
iajs-3928	195	43	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	195	44	)	)	PUNCT
iajs-3928	195	45	}	}	PUNCT
iajs-3928	195	46	=	=	SYM
iajs-3928	195	47	𝑀	𝑀	PROPN
iajs-3928	195	48	𝑞2	𝑞2	NOUN
iajs-3928	195	49	.	.	PUNCT
iajs-3928	196	1	as	as	ADP
iajs-3928	196	2	0	0	NUM
iajs-3928	196	3	<	<	X
iajs-3928	196	4	x	x	X
iajs-3928	196	5	<	<	X
iajs-3928	196	6	l	l	NOUN
iajs-3928	196	7	,	,	PUNCT
iajs-3928	196	8	therefore	therefore	ADV
iajs-3928	196	9	,	,	PUNCT
iajs-3928	196	10	∫	∫	PROPN
iajs-3928	196	11	𝑒−𝑞𝑥∞	𝑒−𝑞𝑥∞	PROPN
iajs-3928	196	12	𝐿	𝐿	PROPN
iajs-3928	196	13	�	�	PROPN
iajs-3928	196	14	̈	̈	X
iajs-3928	196	15	�	�	NOUN
iajs-3928	196	16	(x	(x	NUM
iajs-3928	196	17	)	)	PUNCT
iajs-3928	196	18	𝑑𝑥	𝑑𝑥	ADP
iajs-3928	196	19	=	=	SYM
iajs-3928	196	20	0	0	NUM
iajs-3928	196	21	.	.	PUNCT
iajs-3928	197	1	thus	thus	ADV
iajs-3928	197	2	,	,	PUNCT
iajs-3928	197	3	𝑞3	𝑞3	PROPN
iajs-3928	197	4	∫	∫	PROPN
iajs-3928	197	5	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	197	6	𝐿	𝐿	PROPN
iajs-3928	197	7	0	0	NUM
iajs-3928	197	8	�	�	PROPN
iajs-3928	197	9	̈	̈	X
iajs-3928	197	10	�	�	NOUN
iajs-3928	197	11	(x	(x	NUM
iajs-3928	197	12	)	)	PUNCT
iajs-3928	197	13	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	197	14	+	+	NOUN
iajs-3928	197	15	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	197	16	)	)	PUNCT
iajs-3928	197	17	}	}	PUNCT
iajs-3928	197	18	=	=	SYM
iajs-3928	197	19	𝑀	𝑀	PROPN
iajs-3928	197	20	𝑞2	𝑞2	NOUN
iajs-3928	197	21	,	,	PUNCT
iajs-3928	197	22	𝑞3	𝑞3	PROPN
iajs-3928	197	23	[	[	X
iajs-3928	197	24	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	197	25	)	)	PUNCT
iajs-3928	197	26	−	−	PROPN
iajs-3928	198	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	198	2	)	)	PUNCT
iajs-3928	198	3	+	+	NUM
iajs-3928	198	4	𝑞	𝑞	PROPN
iajs-3928	198	5	∫	∫	PROPN
iajs-3928	198	6	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	198	7	𝐿	𝐿	PROPN
iajs-3928	198	8	0	0	NUM
iajs-3928	198	9	y′(𝑥)𝑑𝑥	y′(𝑥)𝑑𝑥	PROPN
iajs-3928	198	10	]	]	X
iajs-3928	198	11	+	+	PUNCT
iajs-3928	198	12	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	198	13	)	)	PUNCT
iajs-3928	198	14	=	=	SYM
iajs-3928	198	15	𝑀	𝑀	PROPN
iajs-3928	198	16	𝑞2	𝑞2	NOUN
iajs-3928	198	17	,	,	PUNCT
iajs-3928	198	18	𝑞3	𝑞3	PROPN
iajs-3928	198	19	[	[	X
iajs-3928	198	20	𝑒−𝑞𝐿𝑦′(𝐿	𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	198	21	)	)	PUNCT
iajs-3928	198	22	−	−	PROPN
iajs-3928	199	1	𝑦′(0	𝑦′(0	NOUN
iajs-3928	199	2	)	)	PUNCT
iajs-3928	199	3	+	+	NUM
iajs-3928	199	4	𝑞	𝑞	X
iajs-3928	199	5	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	ADJ
iajs-3928	199	6	)	)	PUNCT
iajs-3928	199	7	−	−	PROPN
iajs-3928	199	8	𝑞	𝑞	X
iajs-3928	199	9	𝑦(0	𝑦(0	PROPN
iajs-3928	199	10	)	)	PUNCT
iajs-3928	199	11	+	+	NUM
iajs-3928	199	12	𝑞2	𝑞2	PROPN
iajs-3928	199	13	∫	∫	PROPN
iajs-3928	199	14	𝑒−𝑞𝑥	𝑒−𝑞𝑥	PROPN
iajs-3928	199	15	𝐿	𝐿	PROPN
iajs-3928	199	16	0	0	NUM
iajs-3928	199	17	y(x	y(x	NOUN
iajs-3928	199	18	)	)	PUNCT
iajs-3928	199	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3928	199	20	]	]	X
iajs-3928	199	21	+	+	CCONJ
iajs-3928	199	22	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	199	23	)	)	PUNCT
iajs-3928	199	24	=	=	SYM
iajs-3928	199	25	𝑀	𝑀	PROPN
iajs-3928	199	26	𝑞2	𝑞2	NOUN
iajs-3928	199	27	,	,	PUNCT
iajs-3928	199	28	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	𝑞3𝑒−𝑞𝐿𝑦′(𝐿	NOUN
iajs-3928	199	29	)	)	PUNCT
iajs-3928	199	30	−	−	PROPN
iajs-3928	200	1	𝑞3𝑦′(0	𝑞3𝑦′(0	NOUN
iajs-3928	200	2	)	)	PUNCT
iajs-3928	201	1	+	+	CCONJ
iajs-3928	201	2	𝑞4	𝑞4	PROPN
iajs-3928	201	3	𝑒−𝑞𝐿𝑦(𝐿	𝑒−𝑞𝐿𝑦(𝐿	NOUN
iajs-3928	201	4	)	)	PUNCT
iajs-3928	201	5	−	−	ADP
iajs-3928	201	6	𝑞4	𝑞4	PROPN
iajs-3928	201	7	𝑦(0	𝑦(0	PROPN
iajs-3928	201	8	)	)	PUNCT
iajs-3928	201	9	+	+	NUM
iajs-3928	201	10	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	NOUN
iajs-3928	201	11	)	)	PUNCT
iajs-3928	201	12	}	}	PUNCT
iajs-3928	201	13	+	+	CCONJ
iajs-3928	202	1	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	202	2	)	)	PUNCT
iajs-3928	202	3	}	}	PUNCT
iajs-3928	202	4	=	=	SYM
iajs-3928	202	5	𝑀	𝑀	PROPN
iajs-3928	202	6	𝑞2	𝑞2	NOUN
iajs-3928	202	7	(	(	PUNCT
iajs-3928	202	8	27	27	NUM
iajs-3928	202	9	)	)	PUNCT
iajs-3928	202	10	applying	apply	VERB
iajs-3928	202	11	initial	initial	ADJ
iajs-3928	202	12	conditions	condition	NOUN
iajs-3928	202	13	:	:	PUNCT
iajs-3928	202	14	𝑦(0	𝑦(0	PROPN
iajs-3928	202	15	)	)	PUNCT
iajs-3928	202	16	=	=	SYM
iajs-3928	202	17	0	0	NUM
iajs-3928	202	18	,	,	PUNCT
iajs-3928	202	19	y(l	y(l	NOUN
iajs-3928	202	20	)	)	PUNCT
iajs-3928	202	21	=	=	SYM
iajs-3928	202	22	0	0	NUM
iajs-3928	202	23	,	,	PUNCT
iajs-3928	202	24	𝑦′(0	𝑦′(0	NOUN
iajs-3928	202	25	)	)	PUNCT
iajs-3928	202	26	=	=	SYM
iajs-3928	202	27	0	0	NUM
iajs-3928	202	28	,	,	PUNCT
iajs-3928	202	29	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3928	202	30	𝑦′(𝐿	𝑦′(𝐿	NOUN
iajs-3928	202	31	)	)	PUNCT
iajs-3928	202	32	=	=	SYM
iajs-3928	202	33	𝐵.	𝐵.	NOUN
iajs-3928	202	34	equation	equation	NOUN
iajs-3928	202	35	(	(	PUNCT
iajs-3928	202	36	27	27	NUM
iajs-3928	202	37	)	)	PUNCT
iajs-3928	202	38	becomes	become	VERB
iajs-3928	202	39	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	202	40	+	+	CCONJ
iajs-3928	202	41	𝑞2𝑅{𝑦(𝑥	𝑞2𝑅{𝑦(𝑥	X
iajs-3928	202	42	)	)	PUNCT
iajs-3928	202	43	}	}	PUNCT
iajs-3928	203	1	+	+	CCONJ
iajs-3928	203	2	𝑘2𝑅{𝑦(𝑥	𝑘2𝑅{𝑦(𝑥	ADJ
iajs-3928	203	3	)	)	PUNCT
iajs-3928	203	4	}	}	PUNCT
iajs-3928	203	5	=	=	SYM
iajs-3928	203	6	𝑀	𝑀	PROPN
iajs-3928	203	7	𝑞2	𝑞2	NOUN
iajs-3928	203	8	,	,	PUNCT
iajs-3928	203	9	𝑅{𝑦(𝑥)}(𝑞2	𝑅{𝑦(𝑥)}(𝑞2	PUNCT
iajs-3928	203	10	+	+	CCONJ
iajs-3928	203	11	𝑘2	𝑘2	NOUN
iajs-3928	203	12	)	)	PUNCT
iajs-3928	203	13	=	=	PUNCT
iajs-3928	204	1	−	−	PROPN
iajs-3928	204	2	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	204	3	+	+	CCONJ
iajs-3928	204	4	𝑘2𝑑	𝑘2𝑑	ADJ
iajs-3928	204	5	𝑞2	𝑞2	NOUN
iajs-3928	204	6	,	,	PUNCT
iajs-3928	204	7	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	NUM
iajs-3928	204	8	)	)	PUNCT
iajs-3928	204	9	}	}	PUNCT
iajs-3928	204	10	=	=	PUNCT
iajs-3928	204	11	−	−	ADP
iajs-3928	204	12	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	204	13	𝑞2	𝑞2	NOUN
iajs-3928	204	14	+	+	CCONJ
iajs-3928	204	15	𝑘2	𝑘2	PROPN
iajs-3928	204	16	+	+	CCONJ
iajs-3928	204	17	𝑀	𝑀	PROPN
iajs-3928	204	18	𝑞2	𝑞2	VERB
iajs-3928	204	19	𝑞2	𝑞2	NOUN
iajs-3928	204	20	+	+	CCONJ
iajs-3928	204	21	𝑘2	𝑘2	PROPN
iajs-3928	204	22	,	,	PUNCT
iajs-3928	204	23	𝑅{𝑦(𝑥	𝑅{𝑦(𝑥	NUM
iajs-3928	204	24	)	)	PUNCT
iajs-3928	204	25	}	}	PUNCT
iajs-3928	204	26	=	=	PUNCT
iajs-3928	204	27	−	−	ADP
iajs-3928	204	28	𝑞3𝑒−𝑞𝐿𝐵	𝑞3𝑒−𝑞𝐿𝐵	ADJ
iajs-3928	204	29	𝑞2	𝑞2	NOUN
iajs-3928	204	30	+	+	CCONJ
iajs-3928	204	31	𝑘2	𝑘2	PROPN
iajs-3928	205	1	+	+	CCONJ
iajs-3928	205	2	𝑀	𝑀	PROPN
iajs-3928	205	3	𝑘2	𝑘2	PROPN
iajs-3928	205	4	[	[	X
iajs-3928	205	5	𝑞2	𝑞2	NOUN
iajs-3928	205	6	−	−	PROPN
iajs-3928	205	7	𝑞4	𝑞4	ADJ
iajs-3928	205	8	𝑞2	𝑞2	NOUN
iajs-3928	205	9	+	+	CCONJ
iajs-3928	205	10	𝑘2	𝑘2	PROPN
iajs-3928	205	11	]	]	PUNCT
iajs-3928	205	12	(	(	PUNCT
iajs-3928	205	13	28	28	X
iajs-3928	205	14	)	)	PUNCT
iajs-3928	205	15	taking	take	VERB
iajs-3928	205	16	inverse	inverse	NOUN
iajs-3928	205	17	rohit	rohit	NOUN
iajs-3928	205	18	transform	transform	NOUN
iajs-3928	205	19	of	of	ADP
iajs-3928	205	20	equation	equation	NOUN
iajs-3928	205	21	(	(	PUNCT
iajs-3928	205	22	28	28	NUM
iajs-3928	205	23	)	)	PUNCT
iajs-3928	205	24	,	,	PUNCT
iajs-3928	205	25	we	we	PRON
iajs-3928	205	26	get	get	VERB
iajs-3928	205	27	y(x	y(x	NOUN
iajs-3928	205	28	)	)	PUNCT
iajs-3928	205	29	=	=	PUNCT
iajs-3928	206	1	−	−	PROPN
iajs-3928	206	2	𝐵	𝐵	NOUN
iajs-3928	206	3	𝑘	𝑘	PRON
iajs-3928	206	4	sin	sin	NOUN
iajs-3928	206	5	k	k	NOUN
iajs-3928	206	6	(	(	PUNCT
iajs-3928	206	7	x	x	X
iajs-3928	206	8	−	−	NOUN
iajs-3928	206	9	l)u(x	l)u(x	NOUN
iajs-3928	206	10	−	−	PROPN
iajs-3928	206	11	l	l	NOUN
iajs-3928	206	12	)	)	PUNCT
iajs-3928	207	1	+	+	CCONJ
iajs-3928	207	2	𝑀	𝑀	PROPN
iajs-3928	207	3	𝑘2	𝑘2	PROPN
iajs-3928	208	1	[	[	X
iajs-3928	208	2	1cos	1cos	PROPN
iajs-3928	208	3	(	(	PUNCT
iajs-3928	208	4	k	k	NOUN
iajs-3928	208	5	x	x	PROPN
iajs-3928	208	6	)	)	PUNCT
iajs-3928	208	7	]	]	PUNCT
iajs-3928	208	8	(	(	PUNCT
iajs-3928	208	9	29	29	NUM
iajs-3928	208	10	)	)	PUNCT
iajs-3928	208	11	now	now	ADV
iajs-3928	208	12	,	,	PUNCT
iajs-3928	208	13	for	for	ADP
iajs-3928	208	14	x	x	X
iajs-3928	208	15	<	<	X
iajs-3928	208	16	l	l	NOUN
iajs-3928	208	17	,	,	PUNCT
iajs-3928	208	18	𝑈(𝑥	𝑈(𝑥	PROPN
iajs-3928	208	19	−	−	PROPN
iajs-3928	208	20	𝐿	𝐿	PROPN
iajs-3928	208	21	)	)	PUNCT
iajs-3928	208	22	=	=	SYM
iajs-3928	208	23	0	0	X
iajs-3928	208	24	.	.	PUNCT
iajs-3928	209	1	thus	thus	ADV
iajs-3928	209	2	,	,	PUNCT
iajs-3928	209	3	from	from	ADP
iajs-3928	209	4	equation	equation	NOUN
iajs-3928	209	5	(	(	PUNCT
iajs-3928	209	6	29	29	NUM
iajs-3928	209	7	)	)	PUNCT
iajs-3928	209	8	,	,	PUNCT
iajs-3928	209	9	we	we	PRON
iajs-3928	209	10	have	have	VERB
iajs-3928	209	11	y(x	y(x	NOUN
iajs-3928	209	12	)	)	PUNCT
iajs-3928	210	1	=	=	SYM
iajs-3928	210	2	𝑀	𝑀	PROPN
iajs-3928	210	3	𝑘2	𝑘2	PROPN
iajs-3928	211	1	[	[	X
iajs-3928	211	2	1cos	1cos	PROPN
iajs-3928	211	3	(	(	PUNCT
iajs-3928	211	4	k	k	NOUN
iajs-3928	211	5	x	x	PROPN
iajs-3928	211	6	)	)	PUNCT
iajs-3928	211	7	]	]	PUNCT
iajs-3928	211	8	(	(	PUNCT
iajs-3928	211	9	30	30	X
iajs-3928	211	10	)	)	PUNCT
iajs-3928	211	11	applying	apply	VERB
iajs-3928	211	12	the	the	DET
iajs-3928	211	13	condition	condition	NOUN
iajs-3928	211	14	:	:	PUNCT
iajs-3928	211	15	𝑦(l	𝑦(l	NOUN
iajs-3928	211	16	)	)	PUNCT
iajs-3928	211	17	=	=	SYM
iajs-3928	212	1	0	0	X
iajs-3928	212	2	.	.	PUNCT
iajs-3928	212	3	equation	equation	NOUN
iajs-3928	212	4	(	(	PUNCT
iajs-3928	212	5	30	30	NUM
iajs-3928	212	6	)	)	PUNCT
iajs-3928	212	7	gives	give	VERB
iajs-3928	212	8	𝑀	𝑀	PROPN
iajs-3928	212	9	𝑘2	𝑘2	PROPN
iajs-3928	212	10	−	−	PROPN
iajs-3928	212	11	𝑀	𝑀	PROPN
iajs-3928	212	12	𝑘2	𝑘2	PROPN
iajs-3928	213	1	cos	cos	PROPN
iajs-3928	213	2	(	(	PUNCT
iajs-3928	213	3	k	k	PROPN
iajs-3928	213	4	l	l	NOUN
iajs-3928	213	5	)	)	PUNCT
iajs-3928	213	6	=	=	SYM
iajs-3928	213	7	0	0	NUM
iajs-3928	213	8	,	,	PUNCT
iajs-3928	213	9	cos	cos	X
iajs-3928	213	10	(	(	PUNCT
iajs-3928	213	11	k	k	PROPN
iajs-3928	213	12	l	l	NOUN
iajs-3928	213	13	)	)	PUNCT
iajs-3928	213	14	=	=	SYM
iajs-3928	213	15	1	1	NUM
iajs-3928	213	16	,	,	PUNCT
iajs-3928	213	17	𝑘	𝑘	PROPN
iajs-3928	213	18	=	=	SYM
iajs-3928	213	19	2n𝜋	2n𝜋	PROPN
iajs-3928	213	20	𝐿	𝐿	PROPN
iajs-3928	213	21	(	(	PUNCT
iajs-3928	213	22	31	31	NUM
iajs-3928	213	23	)	)	PUNCT
iajs-3928	213	24	the	the	DET
iajs-3928	213	25	least	least	ADV
iajs-3928	213	26	practical	practical	ADJ
iajs-3928	213	27	value	value	NOUN
iajs-3928	213	28	of	of	ADP
iajs-3928	213	29	n	n	NUM
iajs-3928	213	30	is	be	AUX
iajs-3928	213	31	1	1	NUM
iajs-3928	213	32	,	,	PUNCT
iajs-3928	213	33	therefore	therefore	ADV
iajs-3928	213	34	,	,	PUNCT
iajs-3928	213	35	considering	consider	VERB
iajs-3928	213	36	n	n	X
iajs-3928	213	37	=	=	SYM
iajs-3928	213	38	1	1	NUM
iajs-3928	213	39	,	,	PUNCT
iajs-3928	213	40	we	we	PRON
iajs-3928	213	41	have	have	VERB
iajs-3928	213	42	𝑘	𝑘	PRON
iajs-3928	213	43	=	=	SYM
iajs-3928	213	44	2𝜋	2𝜋	NUM
iajs-3928	213	45	𝐿	𝐿	PROPN
iajs-3928	213	46	,	,	PUNCT
iajs-3928	213	47	√	√	PROPN
iajs-3928	213	48	p	p	NOUN
iajs-3928	213	49	yi	yi	NOUN
iajs-3928	213	50	=	=	PUNCT
iajs-3928	213	51	2π	2π	PROPN
iajs-3928	213	52	l	l	NOUN
iajs-3928	213	53	,	,	PUNCT
iajs-3928	213	54	p	p	NOUN
iajs-3928	213	55	=	=	SYM
iajs-3928	213	56	4π2yi	4π2yi	NUM
iajs-3928	213	57	l2	l2	NOUN
iajs-3928	213	58	(	(	PUNCT
iajs-3928	213	59	32	32	NUM
iajs-3928	213	60	)	)	PUNCT
iajs-3928	213	61	the	the	DET
iajs-3928	213	62	equation	equation	NOUN
iajs-3928	213	63	(	(	PUNCT
iajs-3928	213	64	32	32	NUM
iajs-3928	213	65	)	)	PUNCT
iajs-3928	213	66	is	be	AUX
iajs-3928	213	67	the	the	DET
iajs-3928	213	68	euler	euler	NOUN
iajs-3928	213	69	’s	’s	PART
iajs-3928	213	70	formula	formula	NOUN
iajs-3928	213	71	for	for	ADP
iajs-3928	213	72	critical	critical	ADJ
iajs-3928	213	73	buckling	buckling	NOUN
iajs-3928	213	74	load	load	NOUN
iajs-3928	213	75	for	for	ADP
iajs-3928	213	76	the	the	DET
iajs-3928	213	77	elongated	elongate	VERB
iajs-3928	213	78	column	column	NOUN
iajs-3928	213	79	whose	whose	DET
iajs-3928	213	80	both	both	DET
iajs-3928	213	81	ends	end	VERB
iajs-3928	213	82	are	be	AUX
iajs-3928	213	83	fixed	fix	VERB
iajs-3928	213	84	.	.	PUNCT
iajs-3928	214	1	5	5	X
iajs-3928	214	2	.	.	X
iajs-3928	214	3	discussion	discussion	NOUN
iajs-3928	214	4	the	the	DET
iajs-3928	214	5	integral	integral	ADJ
iajs-3928	214	6	rohit	rohit	NOUN
iajs-3928	214	7	transform	transform	NOUN
iajs-3928	214	8	has	have	AUX
iajs-3928	214	9	effectively	effectively	ADV
iajs-3928	214	10	handled	handle	VERB
iajs-3928	214	11	the	the	DET
iajs-3928	214	12	analysis	analysis	NOUN
iajs-3928	214	13	of	of	ADP
iajs-3928	214	14	a	a	DET
iajs-3928	214	15	beam	beam	NOUN
iajs-3928	214	16	supported	support	VERB
iajs-3928	214	17	at	at	ADP
iajs-3928	214	18	both	both	DET
iajs-3928	214	19	ends	end	NOUN
iajs-3928	214	20	ihjpas	ihjpas	PROPN
iajs-3928	214	21	.	.	PUNCT
iajs-3928	215	1	2024	2024	NUM
iajs-3928	215	2	,	,	PUNCT
iajs-3928	215	3	37(4	37(4	PRON
iajs-3928	215	4	)	)	PUNCT
iajs-3928	215	5	390	390	NUM
iajs-3928	215	6	and	and	CCONJ
iajs-3928	215	7	loaded	load	VERB
iajs-3928	215	8	in	in	ADP
iajs-3928	215	9	the	the	DET
iajs-3928	215	10	middle	middle	NOUN
iajs-3928	215	11	,	,	PUNCT
iajs-3928	215	12	as	as	ADV
iajs-3928	215	13	well	well	ADV
iajs-3928	215	14	as	as	ADP
iajs-3928	215	15	cantilevers	cantilever	NOUN
iajs-3928	215	16	and	and	CCONJ
iajs-3928	215	17	elongated	elongate	VERB
iajs-3928	215	18	columns	column	NOUN
iajs-3928	215	19	with	with	ADP
iajs-3928	215	20	modest	modest	ADJ
iajs-3928	215	21	buckling	buckle	VERB
iajs-3928	215	22	axial	axial	ADJ
iajs-3928	215	23	stress	stress	NOUN
iajs-3928	215	24	.	.	PUNCT
iajs-3928	216	1	figures	figure	NOUN
iajs-3928	216	2	1	1	NUM
iajs-3928	216	3	and	and	CCONJ
iajs-3928	216	4	2	2	NUM
iajs-3928	216	5	make	make	VERB
iajs-3928	216	6	it	it	PRON
iajs-3928	216	7	abundantly	abundantly	ADV
iajs-3928	216	8	evident	evident	ADJ
iajs-3928	216	9	that	that	SCONJ
iajs-3928	216	10	the	the	DET
iajs-3928	216	11	depression	depression	NOUN
iajs-3928	216	12	grows	grow	VERB
iajs-3928	216	13	as	as	ADP
iajs-3928	216	14	the	the	DET
iajs-3928	216	15	cantilever	cantilever	NOUN
iajs-3928	216	16	and	and	CCONJ
iajs-3928	216	17	beam	beam	NOUN
iajs-3928	216	18	lengths	length	NOUN
iajs-3928	216	19	that	that	PRON
iajs-3928	216	20	are	be	AUX
iajs-3928	216	21	loaded	load	VERB
iajs-3928	216	22	in	in	ADP
iajs-3928	216	23	the	the	DET
iajs-3928	216	24	middle	middle	NOUN
iajs-3928	216	25	and	and	CCONJ
iajs-3928	216	26	supported	support	VERB
iajs-3928	216	27	at	at	ADP
iajs-3928	216	28	both	both	DET
iajs-3928	216	29	ends	end	NOUN
iajs-3928	216	30	rise	rise	NOUN
iajs-3928	216	31	.	.	PUNCT
iajs-3928	217	1	an	an	DET
iajs-3928	217	2	attempt	attempt	NOUN
iajs-3928	217	3	has	have	AUX
iajs-3928	217	4	been	be	AUX
iajs-3928	217	5	made	make	VERB
iajs-3928	217	6	to	to	PART
iajs-3928	217	7	provide	provide	VERB
iajs-3928	217	8	an	an	DET
iajs-3928	217	9	example	example	NOUN
iajs-3928	217	10	of	of	ADP
iajs-3928	217	11	the	the	DET
iajs-3928	217	12	rohit	rohit	NOUN
iajs-3928	217	13	transform	transform	NOUN
iajs-3928	217	14	in	in	ADP
iajs-3928	217	15	order	order	NOUN
iajs-3928	217	16	to	to	PART
iajs-3928	217	17	analyze	analyze	VERB
iajs-3928	217	18	the	the	DET
iajs-3928	217	19	elongated	elongate	VERB
iajs-3928	217	20	column	column	NOUN
iajs-3928	217	21	with	with	ADP
iajs-3928	217	22	low	low	ADJ
iajs-3928	217	23	axial	axial	ADJ
iajs-3928	217	24	buckling	buckling	NOUN
iajs-3928	217	25	loads	load	NOUN
iajs-3928	217	26	and	and	CCONJ
iajs-3928	217	27	derive	derive	VERB
iajs-3928	217	28	the	the	DET
iajs-3928	217	29	buckling	buckle	VERB
iajs-3928	217	30	load	load	NOUN
iajs-3928	217	31	euler	euler	NOUN
iajs-3928	217	32	's	's	PART
iajs-3928	217	33	formula	formula	NOUN
iajs-3928	217	34	.	.	PUNCT
iajs-3928	218	1	it	it	PRON
iajs-3928	218	2	is	be	AUX
iajs-3928	218	3	found	find	VERB
iajs-3928	218	4	that	that	SCONJ
iajs-3928	218	5	the	the	DET
iajs-3928	218	6	critical	critical	ADJ
iajs-3928	218	7	buckling	buckling	NOUN
iajs-3928	218	8	load	load	NOUN
iajs-3928	218	9	for	for	ADP
iajs-3928	218	10	elongated	elongate	VERB
iajs-3928	218	11	columns	column	NOUN
iajs-3928	218	12	subjected	subject	VERB
iajs-3928	218	13	to	to	ADP
iajs-3928	218	14	axial	axial	ADJ
iajs-3928	218	15	loads	load	NOUN
iajs-3928	218	16	is	be	AUX
iajs-3928	218	17	inversely	inversely	ADV
iajs-3928	218	18	related	relate	VERB
iajs-3928	218	19	to	to	ADP
iajs-3928	218	20	the	the	DET
iajs-3928	218	21	square	square	NOUN
iajs-3928	218	22	of	of	ADP
iajs-3928	218	23	length	length	NOUN
iajs-3928	218	24	of	of	ADP
iajs-3928	218	25	the	the	DET
iajs-3928	218	26	column	column	NOUN
iajs-3928	218	27	in	in	ADP
iajs-3928	218	28	all	all	PRON
iajs-3928	218	29	of	of	ADP
iajs-3928	218	30	the	the	DET
iajs-3928	218	31	cases	case	NOUN
iajs-3928	218	32	that	that	PRON
iajs-3928	218	33	were	be	AUX
iajs-3928	218	34	studied	study	VERB
iajs-3928	218	35	.	.	PUNCT
iajs-3928	219	1	6	6	X
iajs-3928	219	2	.	.	X
iajs-3928	219	3	conclusion	conclusion	NOUN
iajs-3928	219	4	according	accord	VERB
iajs-3928	219	5	to	to	ADP
iajs-3928	219	6	the	the	DET
iajs-3928	219	7	calculus	calculus	NOUN
iajs-3928	219	8	approach	approach	NOUN
iajs-3928	219	9	described	describe	VERB
iajs-3928	219	10	in	in	ADP
iajs-3928	219	11	the	the	DET
iajs-3928	219	12	literature	literature	NOUN
iajs-3928	220	1	[	[	X
iajs-3928	220	2	14	14	NUM
iajs-3928	220	3	-	-	SYM
iajs-3928	220	4	21	21	NUM
iajs-3928	220	5	]	]	PUNCT
iajs-3928	220	6	,	,	PUNCT
iajs-3928	220	7	the	the	DET
iajs-3928	220	8	results	result	NOUN
iajs-3928	220	9	obtained	obtain	VERB
iajs-3928	220	10	by	by	ADP
iajs-3928	220	11	the	the	DET
iajs-3928	220	12	integral	integral	ADJ
iajs-3928	220	13	rohit	rohit	NOUN
iajs-3928	220	14	transform	transform	NOUN
iajs-3928	220	15	are	be	AUX
iajs-3928	220	16	accurate	accurate	ADJ
iajs-3928	220	17	.	.	PUNCT
iajs-3928	221	1	this	this	PRON
iajs-3928	221	2	demonstrates	demonstrate	VERB
iajs-3928	221	3	the	the	DET
iajs-3928	221	4	efficacy	efficacy	NOUN
iajs-3928	221	5	and	and	CCONJ
iajs-3928	221	6	ability	ability	NOUN
iajs-3928	221	7	of	of	ADP
iajs-3928	221	8	the	the	DET
iajs-3928	221	9	method	method	NOUN
iajs-3928	221	10	to	to	PART
iajs-3928	221	11	analyze	analyze	VERB
iajs-3928	221	12	beams	beam	NOUN
iajs-3928	221	13	supported	support	VERB
iajs-3928	221	14	at	at	ADP
iajs-3928	221	15	both	both	DET
iajs-3928	221	16	ends	end	NOUN
iajs-3928	221	17	and	and	CCONJ
iajs-3928	221	18	loaded	load	VERB
iajs-3928	221	19	in	in	ADP
iajs-3928	221	20	the	the	DET
iajs-3928	221	21	middle	middle	NOUN
iajs-3928	221	22	,	,	PUNCT
iajs-3928	221	23	as	as	ADV
iajs-3928	221	24	well	well	ADV
iajs-3928	221	25	as	as	ADP
iajs-3928	221	26	cantilevers	cantilever	NOUN
iajs-3928	221	27	and	and	CCONJ
iajs-3928	221	28	elongated	elongate	VERB
iajs-3928	221	29	columns	column	NOUN
iajs-3928	221	30	with	with	ADP
iajs-3928	221	31	minimal	minimal	ADJ
iajs-3928	221	32	axial	axial	ADJ
iajs-3928	221	33	buckling	buckling	NOUN
iajs-3928	221	34	loads	load	NOUN
iajs-3928	221	35	.	.	PUNCT
iajs-3928	222	1	in	in	ADP
iajs-3928	222	2	contrast	contrast	NOUN
iajs-3928	222	3	to	to	ADP
iajs-3928	222	4	the	the	DET
iajs-3928	222	5	calculus	calculus	NOUN
iajs-3928	222	6	method	method	NOUN
iajs-3928	222	7	,	,	PUNCT
iajs-3928	222	8	the	the	DET
iajs-3928	222	9	suggested	suggest	VERB
iajs-3928	222	10	method	method	NOUN
iajs-3928	222	11	presents	present	VERB
iajs-3928	222	12	an	an	DET
iajs-3928	222	13	alternate	alternate	ADJ
iajs-3928	222	14	approach	approach	NOUN
iajs-3928	222	15	for	for	ADP
iajs-3928	222	16	the	the	DET
iajs-3928	222	17	analysis	analysis	NOUN
iajs-3928	222	18	of	of	ADP
iajs-3928	222	19	loaded	load	VERB
iajs-3928	222	20	beams	beam	NOUN
iajs-3928	222	21	supported	support	VERB
iajs-3928	222	22	at	at	ADP
iajs-3928	222	23	their	their	PRON
iajs-3928	222	24	ends	end	NOUN
iajs-3928	222	25	,	,	PUNCT
iajs-3928	222	26	cantilevers	cantilever	NOUN
iajs-3928	222	27	,	,	PUNCT
iajs-3928	222	28	and	and	CCONJ
iajs-3928	222	29	elongated	elongate	VERB
iajs-3928	222	30	columns	column	NOUN
iajs-3928	222	31	with	with	ADP
iajs-3928	222	32	low	low	ADJ
iajs-3928	222	33	buckling	buckle	VERB
iajs-3928	222	34	axial	axial	ADJ
iajs-3928	222	35	loads	load	NOUN
iajs-3928	222	36	.	.	PUNCT
iajs-3928	223	1	the	the	DET
iajs-3928	223	2	dominance	dominance	NOUN
iajs-3928	223	3	of	of	ADP
iajs-3928	223	4	integral	integral	ADJ
iajs-3928	223	5	rohit	rohit	NOUN
iajs-3928	223	6	transform	transform	NOUN
iajs-3928	223	7	over	over	ADP
iajs-3928	223	8	other	other	ADJ
iajs-3928	223	9	methods	method	NOUN
iajs-3928	223	10	available	available	ADJ
iajs-3928	223	11	in	in	ADP
iajs-3928	223	12	the	the	DET
iajs-3928	223	13	literature	literature	NOUN
iajs-3928	223	14	is	be	AUX
iajs-3928	223	15	in	in	ADP
iajs-3928	223	16	terms	term	NOUN
iajs-3928	223	17	of	of	ADP
iajs-3928	223	18	simplicity	simplicity	NOUN
iajs-3928	223	19	,	,	PUNCT
iajs-3928	223	20	speed	speed	NOUN
iajs-3928	223	21	,	,	PUNCT
iajs-3928	223	22	and	and	CCONJ
iajs-3928	223	23	accuracy	accuracy	NOUN
iajs-3928	223	24	.	.	PUNCT
iajs-3928	224	1	it	it	PRON
iajs-3928	224	2	involves	involve	VERB
iajs-3928	224	3	simple	simple	ADJ
iajs-3928	224	4	formulation	formulation	NOUN
iajs-3928	224	5	and	and	CCONJ
iajs-3928	224	6	less	less	ADV
iajs-3928	224	7	computational	computational	ADJ
iajs-3928	224	8	work	work	NOUN
iajs-3928	224	9	compared	compare	VERB
iajs-3928	224	10	to	to	ADP
iajs-3928	224	11	other	other	ADJ
iajs-3928	224	12	methods	method	NOUN
iajs-3928	224	13	available	available	ADJ
iajs-3928	224	14	in	in	ADP
iajs-3928	224	15	the	the	DET
iajs-3928	224	16	literature	literature	NOUN
iajs-3928	224	17	.	.	PUNCT
iajs-3928	225	1	acknowledgment	acknowledgment	NOUN
iajs-3928	225	2	the	the	DET
iajs-3928	225	3	authors	author	NOUN
iajs-3928	225	4	would	would	AUX
iajs-3928	225	5	like	like	VERB
iajs-3928	225	6	to	to	PART
iajs-3928	225	7	thank	thank	VERB
iajs-3928	225	8	prof	prof	PROPN
iajs-3928	225	9	.	.	PUNCT
iajs-3928	226	1	dinesh	dinesh	PROPN
iajs-3928	226	2	verma	verma	PROPN
iajs-3928	226	3	for	for	ADP
iajs-3928	226	4	his	his	PRON
iajs-3928	226	5	guidance	guidance	NOUN
iajs-3928	226	6	.	.	PUNCT
iajs-3928	227	1	conflict	conflict	NOUN
iajs-3928	227	2	of	of	ADP
iajs-3928	227	3	interest	interest	NOUN
iajs-3928	227	4	the	the	DET
iajs-3928	227	5	authors	author	NOUN
iajs-3928	227	6	declare	declare	VERB
iajs-3928	227	7	that	that	SCONJ
iajs-3928	227	8	they	they	PRON
iajs-3928	227	9	have	have	VERB
iajs-3928	227	10	no	no	DET
iajs-3928	227	11	conflicts	conflict	NOUN
iajs-3928	227	12	of	of	ADP
iajs-3928	227	13	interest	interest	NOUN
iajs-3928	227	14	.	.	PUNCT
iajs-3928	228	1	funding	funding	NOUN
iajs-3928	228	2	there	there	PRON
iajs-3928	228	3	is	be	VERB
iajs-3928	228	4	no	no	DET
iajs-3928	228	5	financial	financial	ADJ
iajs-3928	228	6	support	support	NOUN
iajs-3928	228	7	in	in	ADP
iajs-3928	228	8	preparation	preparation	NOUN
iajs-3928	228	9	for	for	ADP
iajs-3928	228	10	the	the	DET
iajs-3928	228	11	publication	publication	NOUN
iajs-3928	228	12	.	.	PUNCT
iajs-3928	229	1	references	reference	NOUN
iajs-3928	229	2	1	1	NUM
iajs-3928	229	3	.	.	PUNCT
iajs-3928	230	1	ramamrutham	ramamrutham	NOUN
iajs-3928	230	2	,	,	PUNCT
iajs-3928	230	3	s.	s.	PROPN
iajs-3928	230	4	;	;	PUNCT
iajs-3928	230	5	narayan	narayan	PROPN
iajs-3928	230	6	,	,	PUNCT
iajs-3928	230	7	r.	r.	PROPN
iajs-3928	230	8	theory	theory	NOUN
iajs-3928	230	9	of	of	ADP
iajs-3928	230	10	structures	structure	NOUN
iajs-3928	230	11	.	.	PUNCT
iajs-3928	231	1	danpat	danpat	PROPN
iajs-3928	231	2	rai	rai	PROPN
iajs-3928	231	3	publishing	publishing	PROPN
iajs-3928	231	4	company	company	NOUN
iajs-3928	231	5	,	,	PUNCT
iajs-3928	231	6	9th	9th	ADJ
iajs-3928	231	7	ed	ed	NOUN
iajs-3928	231	8	.	.	PROPN
iajs-3928	231	9	,	,	PUNCT
iajs-3928	231	10	2014	2014	NUM
iajs-3928	231	11	.	.	PUNCT
iajs-3928	232	1	2	2	X
iajs-3928	232	2	.	.	X
iajs-3928	232	3	khurmi	khurmi	PROPN
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iajs-3928	235	2	.	.	PUNCT
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iajs-3928	239	18	.	.	PUNCT
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iajs-3928	245	33	.	.	PUNCT
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iajs-3928	247	5	.	.	PUNCT
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iajs-3928	248	17	.	.	PUNCT
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iajs-3928	251	43	.	.	PUNCT
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iajs-3928	253	4	)	)	PUNCT
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iajs-3928	253	7	.	.	PUNCT
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iajs-3928	254	31	,	,	PUNCT
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iajs-3928	254	36	-	-	SYM
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iajs-3928	254	38	.	.	PUNCT
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iajs-3928	256	26	.	.	PUNCT
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iajs-3928	256	29	.	.	PUNCT
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iajs-3928	257	35	.	.	PUNCT
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iajs-3928	258	6	,	,	PUNCT
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iajs-3928	261	2	.	.	PROPN
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iajs-3928	261	4	.	.	PUNCT
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iajs-3928	263	19	.	.	PUNCT
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iajs-3928	264	3	.	.	PUNCT
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iajs-3928	264	43	.	.	PUNCT
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iajs-3928	265	3	.	.	PUNCT
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iajs-3928	275	20	;	;	PUNCT
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