id	sid	tid	token	lemma	pos
ejpam-5339	1	1	european	european	PROPN
ejpam-5339	1	2	journal	journal	PROPN
ejpam-5339	1	3	of	of	ADP
ejpam-5339	1	4	pure	pure	ADJ
ejpam-5339	1	5	and	and	CCONJ
ejpam-5339	1	6	applied	apply	VERB
ejpam-5339	1	7	mathematics	mathematic	NOUN
ejpam-5339	1	8	vol	vol	NOUN
ejpam-5339	1	9	.	.	PROPN
ejpam-5339	2	1	17	17	NUM
ejpam-5339	2	2	,	,	PUNCT
ejpam-5339	2	3	no	no	INTJ
ejpam-5339	2	4	.	.	NOUN
ejpam-5339	2	5	3	3	NUM
ejpam-5339	2	6	,	,	PUNCT
ejpam-5339	2	7	2024	2024	NUM
ejpam-5339	2	8	,	,	PUNCT
ejpam-5339	2	9	2155	2155	NUM
ejpam-5339	2	10	-	-	SYM
ejpam-5339	2	11	2172	2172	NUM
ejpam-5339	2	12	issn	issn	VERB
ejpam-5339	2	13	1307	1307	NUM
ejpam-5339	2	14	-	-	SYM
ejpam-5339	2	15	5543	5543	NUM
ejpam-5339	2	16	–	–	PUNCT
ejpam-5339	3	1	ejpam.com	ejpam.com	X
ejpam-5339	3	2	published	publish	VERB
ejpam-5339	3	3	by	by	ADP
ejpam-5339	3	4	new	new	PROPN
ejpam-5339	3	5	york	york	PROPN
ejpam-5339	3	6	business	business	PROPN
ejpam-5339	3	7	global	global	ADJ
ejpam-5339	3	8	periodic	periodic	ADJ
ejpam-5339	3	9	solutions	solution	NOUN
ejpam-5339	3	10	of	of	ADP
ejpam-5339	3	11	strongly	strongly	ADV
ejpam-5339	3	12	nonlinear	nonlinear	ADJ
ejpam-5339	3	13	oscillators	oscillator	NOUN
ejpam-5339	3	14	using	use	VERB
ejpam-5339	3	15	he	he	PRON
ejpam-5339	3	16	’s	’s	PART
ejpam-5339	3	17	frequency	frequency	NOUN
ejpam-5339	3	18	formulation	formulation	NOUN
ejpam-5339	3	19	gamal	gamal	PROPN
ejpam-5339	3	20	m.	m.	PROPN
ejpam-5339	3	21	ismail1,∗	ismail1,∗	PROPN
ejpam-5339	3	22	,	,	PUNCT
ejpam-5339	3	23	galal	galal	PROPN
ejpam-5339	3	24	m.	m.	PROPN
ejpam-5339	3	25	moatimid2	moatimid2	PROPN
ejpam-5339	3	26	,	,	PUNCT
ejpam-5339	3	27	mohammed	mohammed	PROPN
ejpam-5339	3	28	i.	i.	PROPN
ejpam-5339	3	29	yamani1	yamani1	PROPN
ejpam-5339	3	30	1	1	NUM
ejpam-5339	3	31	department	department	NOUN
ejpam-5339	3	32	of	of	ADP
ejpam-5339	3	33	mathematics	mathematic	NOUN
ejpam-5339	3	34	,	,	PUNCT
ejpam-5339	3	35	faculty	faculty	NOUN
ejpam-5339	3	36	of	of	ADP
ejpam-5339	3	37	science	science	NOUN
ejpam-5339	3	38	,	,	PUNCT
ejpam-5339	3	39	islamic	islamic	PROPN
ejpam-5339	3	40	university	university	PROPN
ejpam-5339	3	41	of	of	ADP
ejpam-5339	3	42	madinah	madinah	PROPN
ejpam-5339	3	43	,	,	PUNCT
ejpam-5339	3	44	madinah	madinah	PROPN
ejpam-5339	3	45	,	,	PUNCT
ejpam-5339	3	46	42351	42351	NUM
ejpam-5339	3	47	,	,	PUNCT
ejpam-5339	3	48	saudi	saudi	PROPN
ejpam-5339	3	49	arabia	arabia	PROPN
ejpam-5339	3	50	2	2	NUM
ejpam-5339	3	51	department	department	NOUN
ejpam-5339	3	52	of	of	ADP
ejpam-5339	3	53	mathematics	mathematic	NOUN
ejpam-5339	3	54	,	,	PUNCT
ejpam-5339	3	55	faculty	faculty	NOUN
ejpam-5339	3	56	of	of	ADP
ejpam-5339	3	57	education	education	NOUN
ejpam-5339	3	58	,	,	PUNCT
ejpam-5339	3	59	ain	ain	PROPN
ejpam-5339	3	60	shams	shams	PROPN
ejpam-5339	3	61	university	university	PROPN
ejpam-5339	3	62	,	,	PUNCT
ejpam-5339	3	63	roxy	roxy	PROPN
ejpam-5339	3	64	,	,	PUNCT
ejpam-5339	3	65	cairo	cairo	PROPN
ejpam-5339	3	66	,	,	PUNCT
ejpam-5339	3	67	egypt	egypt	PROPN
ejpam-5339	3	68	abstract	abstract	PROPN
ejpam-5339	3	69	.	.	PUNCT
ejpam-5339	4	1	in	in	ADP
ejpam-5339	4	2	this	this	DET
ejpam-5339	4	3	paper	paper	NOUN
ejpam-5339	4	4	,	,	PUNCT
ejpam-5339	4	5	we	we	PRON
ejpam-5339	4	6	address	address	VERB
ejpam-5339	4	7	several	several	ADJ
ejpam-5339	4	8	scientific	scientific	ADJ
ejpam-5339	4	9	and	and	CCONJ
ejpam-5339	4	10	technological	technological	ADJ
ejpam-5339	4	11	challenges	challenge	NOUN
ejpam-5339	4	12	with	with	ADP
ejpam-5339	4	13	a	a	DET
ejpam-5339	4	14	novel	novel	NOUN
ejpam-5339	4	15	he	he	PRON
ejpam-5339	4	16	’s	’	VERB
ejpam-5339	4	17	non	non	ADJ
ejpam-5339	4	18	-	-	ADJ
ejpam-5339	4	19	perturbative	perturbative	ADJ
ejpam-5339	4	20	approach	approach	NOUN
ejpam-5339	4	21	(	(	PUNCT
ejpam-5339	4	22	npa	npa	NOUN
ejpam-5339	4	23	)	)	PUNCT
ejpam-5339	4	24	,	,	PUNCT
ejpam-5339	4	25	it	it	PRON
ejpam-5339	4	26	simplifying	simplify	VERB
ejpam-5339	4	27	processing	processing	NOUN
ejpam-5339	4	28	time	time	NOUN
ejpam-5339	4	29	compared	compare	VERB
ejpam-5339	4	30	to	to	ADP
ejpam-5339	4	31	traditional	traditional	ADJ
ejpam-5339	4	32	methods	method	NOUN
ejpam-5339	4	33	.	.	PUNCT
ejpam-5339	5	1	the	the	DET
ejpam-5339	5	2	proposed	propose	VERB
ejpam-5339	5	3	approach	approach	NOUN
ejpam-5339	5	4	transforms	transform	VERB
ejpam-5339	5	5	nonlinear	nonlinear	ADJ
ejpam-5339	5	6	ordinary	ordinary	ADJ
ejpam-5339	5	7	differential	differential	ADJ
ejpam-5339	5	8	equations	equation	NOUN
ejpam-5339	5	9	(	(	PUNCT
ejpam-5339	5	10	odes	ode	NOUN
ejpam-5339	5	11	)	)	PUNCT
ejpam-5339	5	12	into	into	ADP
ejpam-5339	5	13	linear	linear	ADJ
ejpam-5339	5	14	ones	one	NOUN
ejpam-5339	5	15	,	,	PUNCT
ejpam-5339	5	16	analogous	analogous	ADJ
ejpam-5339	5	17	to	to	ADP
ejpam-5339	5	18	simple	simple	ADJ
ejpam-5339	5	19	harmonic	harmonic	ADJ
ejpam-5339	5	20	motion	motion	NOUN
ejpam-5339	5	21	,	,	PUNCT
ejpam-5339	5	22	and	and	CCONJ
ejpam-5339	5	23	producing	produce	VERB
ejpam-5339	5	24	a	a	DET
ejpam-5339	5	25	new	new	ADJ
ejpam-5339	5	26	frequency	frequency	NOUN
ejpam-5339	5	27	.	.	PUNCT
ejpam-5339	6	1	studying	study	VERB
ejpam-5339	6	2	the	the	DET
ejpam-5339	6	3	periodic	periodic	ADJ
ejpam-5339	6	4	solutions	solution	NOUN
ejpam-5339	6	5	leads	lead	VERB
ejpam-5339	6	6	to	to	ADP
ejpam-5339	6	7	enhanced	enhanced	ADJ
ejpam-5339	6	8	design	design	NOUN
ejpam-5339	6	9	,	,	PUNCT
ejpam-5339	6	10	performance	performance	NOUN
ejpam-5339	6	11	,	,	PUNCT
ejpam-5339	6	12	reliability	reliability	NOUN
ejpam-5339	6	13	,	,	PUNCT
ejpam-5339	6	14	and	and	CCONJ
ejpam-5339	6	15	efficiency	efficiency	NOUN
ejpam-5339	6	16	across	across	ADP
ejpam-5339	6	17	these	these	DET
ejpam-5339	6	18	fields	field	NOUN
ejpam-5339	6	19	.	.	PUNCT
ejpam-5339	7	1	this	this	DET
ejpam-5339	7	2	new	new	ADJ
ejpam-5339	7	3	approach	approach	NOUN
ejpam-5339	7	4	is	be	AUX
ejpam-5339	7	5	based	base	VERB
ejpam-5339	7	6	mainly	mainly	ADV
ejpam-5339	7	7	on	on	ADP
ejpam-5339	7	8	the	the	DET
ejpam-5339	7	9	he	he	PRON
ejpam-5339	7	10	’s	’s	PART
ejpam-5339	7	11	frequency	frequency	NOUN
ejpam-5339	7	12	formulation	formulation	NOUN
ejpam-5339	7	13	(	(	PUNCT
ejpam-5339	7	14	hff	hff	NOUN
ejpam-5339	7	15	)	)	PUNCT
ejpam-5339	7	16	.	.	PUNCT
ejpam-5339	8	1	this	this	DET
ejpam-5339	8	2	method	method	NOUN
ejpam-5339	8	3	yields	yield	VERB
ejpam-5339	8	4	highly	highly	ADV
ejpam-5339	8	5	accurate	accurate	ADJ
ejpam-5339	8	6	outcomes	outcome	NOUN
ejpam-5339	8	7	,	,	PUNCT
ejpam-5339	8	8	surpassing	surpass	VERB
ejpam-5339	8	9	well	well	ADV
ejpam-5339	8	10	-	-	PUNCT
ejpam-5339	8	11	known	know	VERB
ejpam-5339	8	12	approximate	approximate	ADJ
ejpam-5339	8	13	methodologies	methodology	NOUN
ejpam-5339	8	14	,	,	PUNCT
ejpam-5339	8	15	as	as	SCONJ
ejpam-5339	8	16	validated	validate	VERB
ejpam-5339	8	17	through	through	ADP
ejpam-5339	8	18	numerical	numerical	ADJ
ejpam-5339	8	19	comparisons	comparison	NOUN
ejpam-5339	8	20	in	in	ADP
ejpam-5339	8	21	the	the	DET
ejpam-5339	8	22	mathematical	mathematical	ADJ
ejpam-5339	8	23	software	software	NOUN
ejpam-5339	8	24	(	(	PUNCT
ejpam-5339	8	25	ms	ms	NOUN
ejpam-5339	8	26	)	)	PUNCT
ejpam-5339	8	27	.	.	PUNCT
ejpam-5339	9	1	the	the	DET
ejpam-5339	9	2	congruence	congruence	NOUN
ejpam-5339	9	3	between	between	ADP
ejpam-5339	9	4	numerical	numerical	ADJ
ejpam-5339	9	5	solution	solution	NOUN
ejpam-5339	9	6	tests	test	NOUN
ejpam-5339	9	7	and	and	CCONJ
ejpam-5339	9	8	theoretical	theoretical	ADJ
ejpam-5339	9	9	predictions	prediction	NOUN
ejpam-5339	9	10	further	far	ADV
ejpam-5339	9	11	supports	support	VERB
ejpam-5339	9	12	our	our	PRON
ejpam-5339	9	13	findings	finding	NOUN
ejpam-5339	9	14	.	.	PUNCT
ejpam-5339	10	1	while	while	SCONJ
ejpam-5339	10	2	classical	classical	ADJ
ejpam-5339	10	3	perturbation	perturbation	NOUN
ejpam-5339	10	4	methods	method	NOUN
ejpam-5339	10	5	rely	rely	VERB
ejpam-5339	10	6	on	on	ADP
ejpam-5339	10	7	taylor	taylor	PROPN
ejpam-5339	10	8	expansions	expansion	NOUN
ejpam-5339	10	9	to	to	PART
ejpam-5339	10	10	simplify	simplify	VERB
ejpam-5339	10	11	restoring	restore	VERB
ejpam-5339	10	12	forces	force	NOUN
ejpam-5339	10	13	,	,	PUNCT
ejpam-5339	10	14	the	the	DET
ejpam-5339	10	15	npa	npa	NOUN
ejpam-5339	10	16	also	also	ADV
ejpam-5339	10	17	enables	enable	VERB
ejpam-5339	10	18	stability	stability	NOUN
ejpam-5339	10	19	analysis	analysis	NOUN
ejpam-5339	10	20	.	.	PUNCT
ejpam-5339	11	1	consequently	consequently	ADV
ejpam-5339	11	2	,	,	PUNCT
ejpam-5339	11	3	for	for	ADP
ejpam-5339	11	4	analyzing	analyze	VERB
ejpam-5339	11	5	approximations	approximation	NOUN
ejpam-5339	11	6	of	of	ADP
ejpam-5339	11	7	highly	highly	ADV
ejpam-5339	11	8	non	non	ADJ
ejpam-5339	11	9	-	-	ADJ
ejpam-5339	11	10	linear	linear	ADJ
ejpam-5339	11	11	oscillators	oscillator	NOUN
ejpam-5339	11	12	in	in	ADP
ejpam-5339	11	13	ms	ms	PROPN
ejpam-5339	11	14	,	,	PUNCT
ejpam-5339	11	15	the	the	DET
ejpam-5339	11	16	npa	npa	NOUN
ejpam-5339	11	17	serves	serve	VERB
ejpam-5339	11	18	as	as	ADP
ejpam-5339	11	19	a	a	DET
ejpam-5339	11	20	more	more	ADV
ejpam-5339	11	21	reliable	reliable	ADJ
ejpam-5339	11	22	tool	tool	NOUN
ejpam-5339	11	23	.	.	PUNCT
ejpam-5339	12	1	2020	2020	NUM
ejpam-5339	12	2	mathematics	mathematic	NOUN
ejpam-5339	12	3	subject	subject	NOUN
ejpam-5339	12	4	classifications	classification	NOUN
ejpam-5339	12	5	:	:	PUNCT
ejpam-5339	12	6	34a34	34a34	NUM
ejpam-5339	12	7	,	,	PUNCT
ejpam-5339	12	8	34c15	34c15	NUM
ejpam-5339	12	9	,	,	PUNCT
ejpam-5339	12	10	34c25	34c25	NUM
ejpam-5339	12	11	,	,	PUNCT
ejpam-5339	12	12	35l65	35l65	NUM
ejpam-5339	12	13	,	,	PUNCT
ejpam-5339	12	14	37n30	37n30	NUM
ejpam-5339	12	15	.	.	PUNCT
ejpam-5339	13	1	key	key	ADJ
ejpam-5339	13	2	words	word	NOUN
ejpam-5339	13	3	and	and	CCONJ
ejpam-5339	13	4	phrases	phrase	NOUN
ejpam-5339	13	5	:	:	PUNCT
ejpam-5339	13	6	nonlinear	nonlinear	ADJ
ejpam-5339	13	7	oscillators	oscillator	NOUN
ejpam-5339	13	8	,	,	PUNCT
ejpam-5339	13	9	non	non	ADJ
ejpam-5339	13	10	-	-	ADJ
ejpam-5339	13	11	perturbative	perturbative	ADJ
ejpam-5339	13	12	approach	approach	NOUN
ejpam-5339	13	13	,	,	PUNCT
ejpam-5339	13	14	stability	stability	NOUN
ejpam-5339	13	15	analysis	analysis	NOUN
ejpam-5339	13	16	,	,	PUNCT
ejpam-5339	13	17	numerical	numerical	ADJ
ejpam-5339	13	18	techniques	technique	NOUN
ejpam-5339	13	19	1	1	NUM
ejpam-5339	13	20	.	.	PUNCT
ejpam-5339	13	21	introduction	introduction	NOUN
ejpam-5339	13	22	differential	differential	NOUN
ejpam-5339	13	23	equations	equation	NOUN
ejpam-5339	13	24	,	,	PUNCT
ejpam-5339	13	25	both	both	CCONJ
ejpam-5339	13	26	linear	linear	ADJ
ejpam-5339	13	27	and	and	CCONJ
ejpam-5339	13	28	nonlinear	nonlinear	ADJ
ejpam-5339	13	29	,	,	PUNCT
ejpam-5339	13	30	are	be	AUX
ejpam-5339	13	31	used	use	VERB
ejpam-5339	13	32	in	in	ADP
ejpam-5339	13	33	many	many	ADJ
ejpam-5339	13	34	domains	domain	NOUN
ejpam-5339	13	35	to	to	PART
ejpam-5339	13	36	characterize	characterize	VERB
ejpam-5339	13	37	concerns	concern	NOUN
ejpam-5339	13	38	appropriate	appropriate	ADJ
ejpam-5339	13	39	to	to	ADP
ejpam-5339	13	40	mathematics	mathematic	NOUN
ejpam-5339	13	41	,	,	PUNCT
ejpam-5339	13	42	physics	physics	NOUN
ejpam-5339	13	43	,	,	PUNCT
ejpam-5339	13	44	biology	biology	NOUN
ejpam-5339	13	45	,	,	PUNCT
ejpam-5339	13	46	chemistry	chemistry	NOUN
ejpam-5339	13	47	,	,	PUNCT
ejpam-5339	13	48	and	and	CCONJ
ejpam-5339	13	49	engineering	engineering	NOUN
ejpam-5339	13	50	.	.	PUNCT
ejpam-5339	14	1	the	the	DET
ejpam-5339	14	2	solutions	solution	NOUN
ejpam-5339	14	3	of	of	ADP
ejpam-5339	14	4	a	a	DET
ejpam-5339	14	5	linear	linear	ADJ
ejpam-5339	14	6	ode	ode	NOUN
ejpam-5339	14	7	can	can	AUX
ejpam-5339	14	8	be	be	AUX
ejpam-5339	14	9	readily	readily	ADV
ejpam-5339	14	10	found	find	VERB
ejpam-5339	14	11	using	use	VERB
ejpam-5339	14	12	some	some	PRON
ejpam-5339	14	13	of	of	ADP
ejpam-5339	14	14	the	the	DET
ejpam-5339	14	15	well	well	ADV
ejpam-5339	14	16	-	-	PUNCT
ejpam-5339	14	17	established	establish	VERB
ejpam-5339	14	18	techniques	technique	NOUN
ejpam-5339	14	19	,	,	PUNCT
ejpam-5339	14	20	in	in	ADP
ejpam-5339	14	21	comparison	comparison	NOUN
ejpam-5339	14	22	with	with	ADP
ejpam-5339	14	23	nonlinear	nonlinear	ADJ
ejpam-5339	14	24	ode	ode	PROPN
ejpam-5339	14	25	,	,	PUNCT
ejpam-5339	14	26	which	which	PRON
ejpam-5339	14	27	are	be	AUX
ejpam-5339	14	28	typically	typically	ADV
ejpam-5339	14	29	considered	consider	VERB
ejpam-5339	14	30	to	to	PART
ejpam-5339	14	31	have	have	VERB
ejpam-5339	14	32	approximate	approximate	ADJ
ejpam-5339	14	33	solutions	solution	NOUN
ejpam-5339	14	34	via	via	ADP
ejpam-5339	14	35	several	several	ADJ
ejpam-5339	14	36	perturbation	perturbation	NOUN
ejpam-5339	14	37	techniques	technique	NOUN
ejpam-5339	14	38	.	.	PUNCT
ejpam-5339	15	1	moreover	moreover	ADV
ejpam-5339	15	2	,	,	PUNCT
ejpam-5339	15	3	nonlinear	nonlinear	ADJ
ejpam-5339	15	4	oscillations	oscillation	NOUN
ejpam-5339	15	5	have	have	AUX
ejpam-5339	15	6	drawn	draw	VERB
ejpam-5339	15	7	an	an	DET
ejpam-5339	15	8	interest	interest	NOUN
ejpam-5339	15	9	of	of	ADP
ejpam-5339	15	10	the	the	DET
ejpam-5339	15	11	increasing	increase	VERB
ejpam-5339	15	12	number	number	NOUN
ejpam-5339	15	13	of	of	ADP
ejpam-5339	15	14	scientists	scientist	NOUN
ejpam-5339	15	15	since	since	SCONJ
ejpam-5339	15	16	most	most	ADJ
ejpam-5339	15	17	vibration	vibration	NOUN
ejpam-5339	15	18	-	-	PUNCT
ejpam-5339	15	19	related	relate	VERB
ejpam-5339	15	20	∗corresponding	∗corresponding	NOUN
ejpam-5339	15	21	author	author	NOUN
ejpam-5339	15	22	.	.	PUNCT
ejpam-5339	16	1	doi	doi	NOUN
ejpam-5339	16	2	:	:	PUNCT
ejpam-5339	16	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5339	https://doi.org/10.29020/nybg.ejpam.v17i3.5339	PROPN
ejpam-5339	16	4	email	email	NOUN
ejpam-5339	16	5	addresses	address	NOUN
ejpam-5339	16	6	:	:	PUNCT
ejpam-5339	16	7	gismail@iu.edu.sa	gismail@iu.edu.sa	PROPN
ejpam-5339	16	8	(	(	PUNCT
ejpam-5339	16	9	g.	g.	PROPN
ejpam-5339	16	10	m.	m.	PROPN
ejpam-5339	16	11	ismail	ismail	PROPN
ejpam-5339	16	12	)	)	PUNCT
ejpam-5339	16	13	,	,	PUNCT
ejpam-5339	16	14	gal−moa@edu.asu.edu.eg	gal−moa@edu.asu.edu.eg	PROPN
ejpam-5339	16	15	(	(	PUNCT
ejpam-5339	16	16	g.	g.	PROPN
ejpam-5339	16	17	m.	m.	PROPN
ejpam-5339	16	18	moatimid	moatimid	PROPN
ejpam-5339	16	19	)	)	PUNCT
ejpam-5339	16	20	,	,	PUNCT
ejpam-5339	16	21	shingl6600@gmail.com	shingl6600@gmail.com	X
ejpam-5339	17	1	(	(	PUNCT
ejpam-5339	17	2	m.	m.	NOUN
ejpam-5339	17	3	i.	i.	PROPN
ejpam-5339	17	4	yamani	yamani	PROPN
ejpam-5339	17	5	)	)	PUNCT
ejpam-5339	17	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5339	17	7	2155	2155	NUM
ejpam-5339	18	1	©	©	PROPN
ejpam-5339	18	2	2024	2024	NUM
ejpam-5339	18	3	ejpam	ejpam	NOUN
ejpam-5339	18	4	all	all	DET
ejpam-5339	18	5	rights	right	NOUN
ejpam-5339	18	6	reserved	reserve	VERB
ejpam-5339	18	7	.	.	PUNCT
ejpam-5339	19	1	g.	g.	PROPN
ejpam-5339	19	2	m.	m.	PROPN
ejpam-5339	19	3	ismail	ismail	PROPN
ejpam-5339	19	4	,	,	PUNCT
ejpam-5339	19	5	g.	g.	PROPN
ejpam-5339	19	6	m.	m.	PROPN
ejpam-5339	19	7	moatimid	moatimid	PROPN
ejpam-5339	19	8	,	,	PUNCT
ejpam-5339	19	9	m.	m.	NOUN
ejpam-5339	19	10	i.	i.	PROPN
ejpam-5339	19	11	yamani	yamani	PROPN
ejpam-5339	19	12	/	/	SYM
ejpam-5339	19	13	eur	eur	PROPN
ejpam-5339	19	14	.	.	PUNCT
ejpam-5339	20	1	j.	j.	PROPN
ejpam-5339	20	2	pure	pure	PROPN
ejpam-5339	20	3	appl	appl	PROPN
ejpam-5339	20	4	.	.	PROPN
ejpam-5339	20	5	math	math	PROPN
ejpam-5339	20	6	,	,	PUNCT
ejpam-5339	20	7	17	17	NUM
ejpam-5339	20	8	(	(	PUNCT
ejpam-5339	20	9	3	3	NUM
ejpam-5339	20	10	)	)	PUNCT
ejpam-5339	20	11	(	(	PUNCT
ejpam-5339	20	12	2024	2024	NUM
ejpam-5339	20	13	)	)	PUNCT
ejpam-5339	20	14	,	,	PUNCT
ejpam-5339	20	15	2155	2155	NUM
ejpam-5339	20	16	-	-	SYM
ejpam-5339	20	17	2172	2172	NUM
ejpam-5339	20	18	2156	2156	NUM
ejpam-5339	20	19	issues	issue	NOUN
ejpam-5339	20	20	are	be	AUX
ejpam-5339	20	21	of	of	ADP
ejpam-5339	20	22	nonlinear	nonlinear	ADJ
ejpam-5339	20	23	features	feature	NOUN
ejpam-5339	20	24	.	.	PUNCT
ejpam-5339	21	1	therefore	therefore	ADV
ejpam-5339	21	2	,	,	PUNCT
ejpam-5339	21	3	the	the	DET
ejpam-5339	21	4	nonlinear	nonlinear	ADJ
ejpam-5339	21	5	ode	ode	NOUN
ejpam-5339	21	6	is	be	AUX
ejpam-5339	21	7	very	very	ADV
ejpam-5339	21	8	useful	useful	ADJ
ejpam-5339	21	9	in	in	ADP
ejpam-5339	21	10	describing	describe	VERB
ejpam-5339	21	11	scientific	scientific	ADJ
ejpam-5339	21	12	and	and	CCONJ
ejpam-5339	21	13	engineering	engineering	NOUN
ejpam-5339	21	14	phenomena	phenomenon	NOUN
ejpam-5339	21	15	,	,	PUNCT
ejpam-5339	21	16	which	which	PRON
ejpam-5339	21	17	often	often	ADV
ejpam-5339	21	18	took	take	VERB
ejpam-5339	21	19	the	the	DET
ejpam-5339	21	20	form	form	NOUN
ejpam-5339	21	21	of	of	ADP
ejpam-5339	21	22	nonlinear	nonlinear	ADJ
ejpam-5339	21	23	types	type	NOUN
ejpam-5339	21	24	.	.	PUNCT
ejpam-5339	22	1	for	for	ADP
ejpam-5339	22	2	this	this	DET
ejpam-5339	22	3	reason	reason	NOUN
ejpam-5339	22	4	,	,	PUNCT
ejpam-5339	22	5	nonlinear	nonlinear	ADJ
ejpam-5339	22	6	odes	ode	NOUN
ejpam-5339	22	7	are	be	AUX
ejpam-5339	22	8	fundamental	fundamental	ADJ
ejpam-5339	22	9	in	in	ADP
ejpam-5339	22	10	engineering	engineering	NOUN
ejpam-5339	22	11	,	,	PUNCT
ejpam-5339	22	12	physics	physics	NOUN
ejpam-5339	22	13	,	,	PUNCT
ejpam-5339	22	14	and	and	CCONJ
ejpam-5339	22	15	applied	apply	VERB
ejpam-5339	22	16	mathematics	mathematic	NOUN
ejpam-5339	22	17	[	[	X
ejpam-5339	22	18	17	17	NUM
ejpam-5339	22	19	]	]	PUNCT
ejpam-5339	22	20	.	.	PUNCT
ejpam-5339	23	1	it	it	PRON
ejpam-5339	23	2	is	be	AUX
ejpam-5339	23	3	important	important	ADJ
ejpam-5339	23	4	to	to	PART
ejpam-5339	23	5	highlight	highlight	VERB
ejpam-5339	23	6	the	the	DET
ejpam-5339	23	7	role	role	NOUN
ejpam-5339	23	8	of	of	ADP
ejpam-5339	23	9	mathematical	mathematical	ADJ
ejpam-5339	23	10	computations	computation	NOUN
ejpam-5339	23	11	in	in	ADP
ejpam-5339	23	12	numerous	numerous	ADJ
ejpam-5339	23	13	research	research	NOUN
ejpam-5339	23	14	works	work	NOUN
ejpam-5339	23	15	of	of	ADP
ejpam-5339	23	16	literature	literature	NOUN
ejpam-5339	23	17	that	that	PRON
ejpam-5339	23	18	deal	deal	VERB
ejpam-5339	23	19	with	with	ADP
ejpam-5339	23	20	nonlinear	nonlinear	ADJ
ejpam-5339	23	21	odes	ode	NOUN
ejpam-5339	23	22	that	that	PRON
ejpam-5339	23	23	arise	arise	VERB
ejpam-5339	23	24	in	in	ADP
ejpam-5339	23	25	diverse	diverse	ADJ
ejpam-5339	23	26	scientific	scientific	ADJ
ejpam-5339	23	27	and	and	CCONJ
ejpam-5339	23	28	engineering	engineering	NOUN
ejpam-5339	23	29	areas	area	NOUN
ejpam-5339	23	30	[	[	X
ejpam-5339	23	31	13	13	NUM
ejpam-5339	23	32	]	]	PUNCT
ejpam-5339	23	33	.	.	PUNCT
ejpam-5339	24	1	while	while	SCONJ
ejpam-5339	24	2	many	many	ADJ
ejpam-5339	24	3	nonlinear	nonlinear	ADJ
ejpam-5339	24	4	odes	ode	NOUN
ejpam-5339	24	5	have	have	VERB
ejpam-5339	24	6	numerical	numerical	ADJ
ejpam-5339	24	7	approximations	approximation	NOUN
ejpam-5339	24	8	,	,	PUNCT
ejpam-5339	24	9	only	only	ADV
ejpam-5339	24	10	insufficient	insufficient	ADJ
ejpam-5339	24	11	of	of	ADP
ejpam-5339	24	12	them	they	PRON
ejpam-5339	24	13	have	have	VERB
ejpam-5339	24	14	direct	direct	ADJ
ejpam-5339	24	15	solutions	solution	NOUN
ejpam-5339	24	16	.	.	PUNCT
ejpam-5339	25	1	many	many	ADJ
ejpam-5339	25	2	approximation	approximation	NOUN
ejpam-5339	25	3	analytical	analytical	ADJ
ejpam-5339	25	4	methods	method	NOUN
ejpam-5339	25	5	are	be	AUX
ejpam-5339	25	6	applied	apply	VERB
ejpam-5339	25	7	in	in	ADP
ejpam-5339	25	8	the	the	DET
ejpam-5339	25	9	literature	literature	NOUN
ejpam-5339	25	10	to	to	PART
ejpam-5339	25	11	determine	determine	VERB
ejpam-5339	25	12	the	the	DET
ejpam-5339	25	13	connection	connection	NOUN
ejpam-5339	25	14	between	between	ADP
ejpam-5339	25	15	the	the	DET
ejpam-5339	25	16	amplitude	amplitude	NOUN
ejpam-5339	25	17	and	and	CCONJ
ejpam-5339	25	18	frequency	frequency	NOUN
ejpam-5339	25	19	of	of	ADP
ejpam-5339	25	20	the	the	DET
ejpam-5339	25	21	non	non	ADJ
ejpam-5339	25	22	-	-	ADJ
ejpam-5339	25	23	linear	linear	ADJ
ejpam-5339	25	24	oscillators	oscillator	NOUN
ejpam-5339	25	25	.	.	PUNCT
ejpam-5339	26	1	the	the	DET
ejpam-5339	26	2	perturbation	perturbation	NOUN
ejpam-5339	26	3	approach	approach	NOUN
ejpam-5339	26	4	,	,	PUNCT
ejpam-5339	26	5	which	which	PRON
ejpam-5339	26	6	is	be	AUX
ejpam-5339	26	7	widely	widely	ADV
ejpam-5339	26	8	used	use	VERB
ejpam-5339	26	9	to	to	PART
ejpam-5339	26	10	obtain	obtain	VERB
ejpam-5339	26	11	approximate	approximate	ADJ
ejpam-5339	26	12	analytical	analytical	ADJ
ejpam-5339	26	13	solutions	solution	NOUN
ejpam-5339	26	14	to	to	ADP
ejpam-5339	26	15	nonlinear	nonlinear	ADJ
ejpam-5339	26	16	odes	ode	NOUN
ejpam-5339	26	17	,	,	PUNCT
ejpam-5339	26	18	is	be	AUX
ejpam-5339	26	19	the	the	DET
ejpam-5339	26	20	most	most	ADV
ejpam-5339	26	21	multipurpose	multipurpose	ADJ
ejpam-5339	26	22	tool	tool	NOUN
ejpam-5339	26	23	for	for	ADP
ejpam-5339	26	24	analyzing	analyze	VERB
ejpam-5339	26	25	nonlinear	nonlinear	ADJ
ejpam-5339	26	26	engineering	engineering	NOUN
ejpam-5339	26	27	problems	problem	NOUN
ejpam-5339	26	28	[	[	X
ejpam-5339	26	29	37	37	NUM
ejpam-5339	26	30	]	]	PUNCT
ejpam-5339	26	31	.	.	PUNCT
ejpam-5339	27	1	the	the	DET
ejpam-5339	27	2	explosive	explosive	ADJ
ejpam-5339	27	3	growth	growth	NOUN
ejpam-5339	27	4	of	of	ADP
ejpam-5339	27	5	nonlinear	nonlinear	ADJ
ejpam-5339	27	6	sciences	science	NOUN
ejpam-5339	27	7	over	over	ADP
ejpam-5339	27	8	the	the	DET
ejpam-5339	27	9	past	past	ADJ
ejpam-5339	27	10	two	two	NUM
ejpam-5339	27	11	decades	decade	NOUN
ejpam-5339	27	12	led	lead	VERB
ejpam-5339	27	13	to	to	ADP
ejpam-5339	27	14	a	a	DET
ejpam-5339	27	15	growing	grow	VERB
ejpam-5339	27	16	interest	interest	NOUN
ejpam-5339	27	17	among	among	ADP
ejpam-5339	27	18	scientists	scientist	NOUN
ejpam-5339	27	19	and	and	CCONJ
ejpam-5339	27	20	engineers	engineer	NOUN
ejpam-5339	27	21	in	in	ADP
ejpam-5339	27	22	analytical	analytical	ADJ
ejpam-5339	27	23	techniques	technique	NOUN
ejpam-5339	27	24	for	for	ADP
ejpam-5339	27	25	nonlinear	nonlinear	ADJ
ejpam-5339	27	26	challenges	challenge	NOUN
ejpam-5339	27	27	.	.	PUNCT
ejpam-5339	28	1	it	it	PRON
ejpam-5339	28	2	is	be	AUX
ejpam-5339	28	3	created	create	VERB
ejpam-5339	28	4	to	to	PART
ejpam-5339	28	5	investigate	investigate	VERB
ejpam-5339	28	6	how	how	SCONJ
ejpam-5339	28	7	these	these	DET
ejpam-5339	28	8	nonlinear	nonlinear	ADJ
ejpam-5339	28	9	odes	ode	NOUN
ejpam-5339	28	10	behaved	behave	VERB
ejpam-5339	28	11	through	through	ADP
ejpam-5339	28	12	the	the	DET
ejpam-5339	28	13	use	use	NOUN
ejpam-5339	28	14	of	of	ADP
ejpam-5339	28	15	approximation	approximation	NOUN
ejpam-5339	28	16	techniques	technique	NOUN
ejpam-5339	28	17	,	,	PUNCT
ejpam-5339	28	18	both	both	PRON
ejpam-5339	28	19	numerical	numerical	ADJ
ejpam-5339	28	20	and	and	CCONJ
ejpam-5339	28	21	otherwise	otherwise	ADV
ejpam-5339	28	22	[	[	X
ejpam-5339	28	23	18	18	NUM
ejpam-5339	28	24	,	,	PUNCT
ejpam-5339	28	25	19	19	NUM
ejpam-5339	28	26	,	,	PUNCT
ejpam-5339	28	27	21	21	NUM
ejpam-5339	28	28	,	,	PUNCT
ejpam-5339	28	29	23	23	NUM
ejpam-5339	28	30	,	,	PUNCT
ejpam-5339	28	31	24	24	NUM
ejpam-5339	28	32	,	,	PUNCT
ejpam-5339	28	33	28	28	NUM
ejpam-5339	28	34	,	,	PUNCT
ejpam-5339	28	35	39	39	NUM
ejpam-5339	28	36	]	]	PUNCT
ejpam-5339	28	37	.	.	PUNCT
ejpam-5339	29	1	recently	recently	ADV
ejpam-5339	29	2	,	,	PUNCT
ejpam-5339	29	3	several	several	ADJ
ejpam-5339	29	4	new	new	ADJ
ejpam-5339	29	5	methods	method	NOUN
ejpam-5339	29	6	have	have	AUX
ejpam-5339	29	7	been	be	AUX
ejpam-5339	29	8	developed	develop	VERB
ejpam-5339	29	9	for	for	ADP
ejpam-5339	29	10	solving	solve	VERB
ejpam-5339	29	11	the	the	DET
ejpam-5339	29	12	nonlinear	nonlinear	ADJ
ejpam-5339	29	13	odes	ode	VERB
ejpam-5339	29	14	analytically	analytically	ADV
ejpam-5339	29	15	[	[	X
ejpam-5339	29	16	9–11	9–11	NOUN
ejpam-5339	29	17	,	,	PUNCT
ejpam-5339	29	18	36	36	NUM
ejpam-5339	29	19	]	]	PUNCT
ejpam-5339	29	20	.	.	PUNCT
ejpam-5339	30	1	consequently	consequently	ADV
ejpam-5339	30	2	,	,	PUNCT
ejpam-5339	30	3	numerous	numerous	ADJ
ejpam-5339	30	4	researchers	researcher	NOUN
ejpam-5339	30	5	created	create	VERB
ejpam-5339	30	6	a	a	DET
ejpam-5339	30	7	few	few	ADJ
ejpam-5339	30	8	unique	unique	ADJ
ejpam-5339	30	9	techniques	technique	NOUN
ejpam-5339	30	10	.	.	PUNCT
ejpam-5339	31	1	to	to	PART
ejpam-5339	31	2	achieve	achieve	VERB
ejpam-5339	31	3	analytical	analytical	ADJ
ejpam-5339	31	4	responses	response	NOUN
ejpam-5339	31	5	that	that	PRON
ejpam-5339	31	6	are	be	AUX
ejpam-5339	31	7	approximately	approximately	ADV
ejpam-5339	31	8	near	near	ADP
ejpam-5339	31	9	the	the	DET
ejpam-5339	31	10	exact	exact	ADJ
ejpam-5339	31	11	solutions	solution	NOUN
ejpam-5339	31	12	,	,	PUNCT
ejpam-5339	31	13	a	a	DET
ejpam-5339	31	14	number	number	NOUN
ejpam-5339	31	15	of	of	ADP
ejpam-5339	31	16	scientists	scientist	NOUN
ejpam-5339	31	17	were	be	AUX
ejpam-5339	31	18	explored	explore	VERB
ejpam-5339	31	19	a	a	DET
ejpam-5339	31	20	range	range	NOUN
ejpam-5339	31	21	of	of	ADP
ejpam-5339	31	22	innovative	innovative	ADJ
ejpam-5339	31	23	and	and	CCONJ
ejpam-5339	31	24	unique	unique	ADJ
ejpam-5339	31	25	approaches	approach	NOUN
ejpam-5339	31	26	.	.	PUNCT
ejpam-5339	32	1	the	the	DET
ejpam-5339	32	2	lindstedt	lindstedt	VERB
ejpam-5339	32	3	-	-	PUNCT
ejpam-5339	32	4	poincaré	poincaré	ADJ
ejpam-5339	32	5	methodology	methodology	NOUN
ejpam-5339	32	6	was	be	AUX
ejpam-5339	32	7	conducted	conduct	VERB
ejpam-5339	32	8	[	[	X
ejpam-5339	32	9	14	14	NUM
ejpam-5339	32	10	]	]	PUNCT
ejpam-5339	32	11	.	.	PUNCT
ejpam-5339	33	1	among	among	ADP
ejpam-5339	33	2	these	these	DET
ejpam-5339	33	3	methods	method	NOUN
ejpam-5339	33	4	is	be	AUX
ejpam-5339	33	5	the	the	DET
ejpam-5339	33	6	homotopy	homotopy	NOUN
ejpam-5339	33	7	perturbation	perturbation	NOUN
ejpam-5339	33	8	method	method	NOUN
ejpam-5339	33	9	(	(	PUNCT
ejpam-5339	33	10	hpm	hpm	NOUN
ejpam-5339	33	11	)	)	PUNCT
ejpam-5339	34	1	[	[	X
ejpam-5339	34	2	6	6	NUM
ejpam-5339	34	3	]	]	PUNCT
ejpam-5339	34	4	.	.	PUNCT
ejpam-5339	35	1	because	because	SCONJ
ejpam-5339	35	2	nonlinearity	nonlinearity	NOUN
ejpam-5339	35	3	exists	exist	VERB
ejpam-5339	35	4	in	in	ADP
ejpam-5339	35	5	many	many	ADJ
ejpam-5339	35	6	practical	practical	ADJ
ejpam-5339	35	7	aspects	aspect	NOUN
ejpam-5339	35	8	,	,	PUNCT
ejpam-5339	35	9	it	it	PRON
ejpam-5339	35	10	has	have	AUX
ejpam-5339	35	11	been	be	AUX
ejpam-5339	35	12	difficult	difficult	ADJ
ejpam-5339	35	13	for	for	SCONJ
ejpam-5339	35	14	investigators	investigator	NOUN
ejpam-5339	35	15	and	and	CCONJ
ejpam-5339	35	16	physicists	physicist	NOUN
ejpam-5339	35	17	to	to	PART
ejpam-5339	35	18	arrive	arrive	VERB
ejpam-5339	35	19	at	at	ADP
ejpam-5339	35	20	a	a	DET
ejpam-5339	35	21	precise	precise	ADJ
ejpam-5339	35	22	solution	solution	NOUN
ejpam-5339	35	23	,	,	PUNCT
ejpam-5339	35	24	or	or	CCONJ
ejpam-5339	35	25	even	even	ADV
ejpam-5339	35	26	one	one	NUM
ejpam-5339	35	27	that	that	PRON
ejpam-5339	35	28	was	be	AUX
ejpam-5339	35	29	very	very	ADV
ejpam-5339	35	30	close	close	ADJ
ejpam-5339	35	31	to	to	ADP
ejpam-5339	35	32	the	the	DET
ejpam-5339	35	33	exact	exact	ADJ
ejpam-5339	35	34	one	one	NUM
ejpam-5339	35	35	.	.	PUNCT
ejpam-5339	36	1	weak	weak	ADJ
ejpam-5339	36	2	non	non	ADJ
ejpam-5339	36	3	-	-	ADJ
ejpam-5339	36	4	linear	linear	ADJ
ejpam-5339	36	5	odes	ode	NOUN
ejpam-5339	36	6	were	be	AUX
ejpam-5339	36	7	demonstrated	demonstrate	VERB
ejpam-5339	36	8	using	use	VERB
ejpam-5339	36	9	the	the	DET
ejpam-5339	36	10	averaging	averaging	NOUN
ejpam-5339	36	11	method	method	NOUN
ejpam-5339	36	12	and	and	CCONJ
ejpam-5339	36	13	the	the	DET
ejpam-5339	36	14	least	least	ADJ
ejpam-5339	36	15	factor	factor	NOUN
ejpam-5339	36	16	methodology	methodology	NOUN
ejpam-5339	36	17	,	,	PUNCT
ejpam-5339	36	18	respectively	respectively	ADV
ejpam-5339	36	19	[	[	X
ejpam-5339	36	20	12	12	NUM
ejpam-5339	36	21	]	]	PUNCT
ejpam-5339	36	22	.	.	PUNCT
ejpam-5339	37	1	in	in	ADP
ejpam-5339	37	2	the	the	DET
ejpam-5339	37	3	situation	situation	NOUN
ejpam-5339	37	4	of	of	ADP
ejpam-5339	37	5	low	low	ADJ
ejpam-5339	37	6	-	-	PUNCT
ejpam-5339	37	7	intensity	intensity	NOUN
ejpam-5339	37	8	noises	noise	NOUN
ejpam-5339	37	9	,	,	PUNCT
ejpam-5339	37	10	the	the	DET
ejpam-5339	37	11	exact	exact	ADJ
ejpam-5339	37	12	asymptotic	asymptotic	ADJ
ejpam-5339	37	13	equations	equation	NOUN
ejpam-5339	37	14	were	be	AUX
ejpam-5339	37	15	calculated	calculate	VERB
ejpam-5339	37	16	using	use	VERB
ejpam-5339	37	17	the	the	DET
ejpam-5339	37	18	hpm	hpm	NOUN
ejpam-5339	37	19	.	.	PUNCT
ejpam-5339	38	1	the	the	DET
ejpam-5339	38	2	method	method	NOUN
ejpam-5339	38	3	of	of	ADP
ejpam-5339	38	4	multiple	multiple	ADJ
ejpam-5339	38	5	time	time	NOUN
ejpam-5339	38	6	scales	scale	NOUN
ejpam-5339	38	7	was	be	AUX
ejpam-5339	38	8	applied	apply	VERB
ejpam-5339	38	9	to	to	PART
ejpam-5339	38	10	determine	determine	VERB
ejpam-5339	38	11	the	the	DET
ejpam-5339	38	12	solutions	solution	NOUN
ejpam-5339	38	13	of	of	ADP
ejpam-5339	38	14	the	the	DET
ejpam-5339	38	15	oscillation	oscillation	NOUN
ejpam-5339	38	16	systems	system	NOUN
ejpam-5339	38	17	.	.	PUNCT
ejpam-5339	39	1	finding	find	VERB
ejpam-5339	39	2	the	the	DET
ejpam-5339	39	3	minor	minor	ADJ
ejpam-5339	39	4	parameter	parameter	NOUN
ejpam-5339	39	5	necessary	necessary	ADJ
ejpam-5339	39	6	to	to	PART
ejpam-5339	39	7	describe	describe	VERB
ejpam-5339	39	8	the	the	DET
ejpam-5339	39	9	fundamental	fundamental	ADJ
ejpam-5339	39	10	equations	equation	NOUN
ejpam-5339	39	11	in	in	ADP
ejpam-5339	39	12	a	a	DET
ejpam-5339	39	13	more	more	ADV
ejpam-5339	39	14	realistic	realistic	ADJ
ejpam-5339	39	15	and	and	CCONJ
ejpam-5339	39	16	useful	useful	ADJ
ejpam-5339	39	17	manner	manner	NOUN
ejpam-5339	39	18	was	be	AUX
ejpam-5339	39	19	a	a	DET
ejpam-5339	39	20	crucial	crucial	ADJ
ejpam-5339	39	21	first	first	ADJ
ejpam-5339	39	22	step	step	NOUN
ejpam-5339	39	23	in	in	ADP
ejpam-5339	39	24	any	any	DET
ejpam-5339	39	25	perturbation	perturbation	NOUN
ejpam-5339	39	26	or	or	CCONJ
ejpam-5339	39	27	asymptotic	asymptotic	ADJ
ejpam-5339	39	28	method	method	NOUN
ejpam-5339	39	29	.	.	PUNCT
ejpam-5339	40	1	many	many	ADJ
ejpam-5339	40	2	hpm	hpm	NOUN
ejpam-5339	40	3	-	-	PUNCT
ejpam-5339	40	4	based	base	VERB
ejpam-5339	40	5	methods	method	NOUN
ejpam-5339	40	6	were	be	AUX
ejpam-5339	40	7	become	become	VERB
ejpam-5339	40	8	more	more	ADV
ejpam-5339	40	9	popular	popular	ADJ
ejpam-5339	40	10	recently	recently	ADV
ejpam-5339	40	11	for	for	ADP
ejpam-5339	40	12	estimating	estimate	VERB
ejpam-5339	40	13	a	a	DET
ejpam-5339	40	14	wide	wide	ADJ
ejpam-5339	40	15	range	range	NOUN
ejpam-5339	40	16	of	of	ADP
ejpam-5339	40	17	nonlinear	nonlinear	ADJ
ejpam-5339	40	18	odes	ode	NOUN
ejpam-5339	40	19	with	with	ADP
ejpam-5339	40	20	the	the	DET
ejpam-5339	40	21	initial	initial	ADJ
ejpam-5339	40	22	and	and	CCONJ
ejpam-5339	40	23	arbitrary	arbitrary	ADJ
ejpam-5339	40	24	constants	constant	NOUN
ejpam-5339	40	25	and	and	CCONJ
ejpam-5339	40	26	getting	get	VERB
ejpam-5339	40	27	them	they	PRON
ejpam-5339	40	28	somewhat	somewhat	ADV
ejpam-5339	40	29	closer	close	ADV
ejpam-5339	40	30	to	to	ADP
ejpam-5339	40	31	their	their	PRON
ejpam-5339	40	32	closed	close	VERB
ejpam-5339	40	33	-	-	PUNCT
ejpam-5339	40	34	form	form	NOUN
ejpam-5339	40	35	solutions	solution	NOUN
ejpam-5339	40	36	[	[	X
ejpam-5339	40	37	3	3	NUM
ejpam-5339	40	38	,	,	PUNCT
ejpam-5339	40	39	7	7	NUM
ejpam-5339	40	40	]	]	PUNCT
ejpam-5339	40	41	.	.	PUNCT
ejpam-5339	41	1	consequently	consequently	ADV
ejpam-5339	41	2	,	,	PUNCT
ejpam-5339	41	3	the	the	DET
ejpam-5339	41	4	procedure	procedure	NOUN
ejpam-5339	41	5	would	would	AUX
ejpam-5339	41	6	diverge	diverge	VERB
ejpam-5339	41	7	and	and	CCONJ
ejpam-5339	41	8	fail	fail	VERB
ejpam-5339	41	9	to	to	PART
ejpam-5339	41	10	produce	produce	VERB
ejpam-5339	41	11	the	the	DET
ejpam-5339	41	12	intended	intend	VERB
ejpam-5339	41	13	results	result	NOUN
ejpam-5339	41	14	if	if	SCONJ
ejpam-5339	41	15	the	the	DET
ejpam-5339	41	16	original	original	ADJ
ejpam-5339	41	17	guess	guess	NOUN
ejpam-5339	41	18	did	do	AUX
ejpam-5339	41	19	not	not	PART
ejpam-5339	41	20	match	match	VERB
ejpam-5339	41	21	the	the	DET
ejpam-5339	41	22	approach	approach	NOUN
ejpam-5339	41	23	employed	employ	VERB
ejpam-5339	41	24	to	to	PART
ejpam-5339	41	25	solve	solve	VERB
ejpam-5339	41	26	the	the	DET
ejpam-5339	41	27	problem	problem	NOUN
ejpam-5339	41	28	.	.	PUNCT
ejpam-5339	42	1	these	these	DET
ejpam-5339	42	2	techniques	technique	NOUN
ejpam-5339	42	3	are	be	AUX
ejpam-5339	42	4	dependent	dependent	ADJ
ejpam-5339	42	5	on	on	ADP
ejpam-5339	42	6	the	the	DET
ejpam-5339	42	7	initial	initial	ADJ
ejpam-5339	42	8	approximation	approximation	NOUN
ejpam-5339	42	9	solution	solution	NOUN
ejpam-5339	42	10	.	.	PUNCT
ejpam-5339	43	1	analytical	analytical	ADJ
ejpam-5339	43	2	approximations	approximation	NOUN
ejpam-5339	43	3	for	for	ADP
ejpam-5339	43	4	magnetic	magnetic	ADJ
ejpam-5339	43	5	spherical	spherical	ADJ
ejpam-5339	43	6	pendulums	pendulum	NOUN
ejpam-5339	43	7	were	be	AUX
ejpam-5339	43	8	analyzed	analyze	VERB
ejpam-5339	43	9	using	use	VERB
ejpam-5339	43	10	the	the	DET
ejpam-5339	43	11	hpm	hpm	NOUN
ejpam-5339	43	12	[	[	X
ejpam-5339	43	13	20	20	NUM
ejpam-5339	43	14	]	]	PUNCT
ejpam-5339	43	15	.	.	PUNCT
ejpam-5339	44	1	in	in	ADP
ejpam-5339	44	2	the	the	DET
ejpam-5339	44	3	case	case	NOUN
ejpam-5339	44	4	of	of	ADP
ejpam-5339	44	5	non	non	ADJ
ejpam-5339	44	6	-	-	ADJ
ejpam-5339	44	7	conservative	conservative	ADJ
ejpam-5339	44	8	oscillators	oscillator	NOUN
ejpam-5339	44	9	,	,	PUNCT
ejpam-5339	44	10	the	the	DET
ejpam-5339	44	11	hpm	hpm	NOUN
ejpam-5339	44	12	proved	prove	VERB
ejpam-5339	44	13	to	to	PART
ejpam-5339	44	14	be	be	AUX
ejpam-5339	44	15	difficult	difficult	ADJ
ejpam-5339	44	16	to	to	PART
ejpam-5339	44	17	operate	operate	VERB
ejpam-5339	44	18	even	even	ADV
ejpam-5339	44	19	with	with	ADP
ejpam-5339	44	20	the	the	DET
ejpam-5339	44	21	seeming	seem	VERB
ejpam-5339	44	22	many	many	ADJ
ejpam-5339	44	23	advancements	advancement	NOUN
ejpam-5339	44	24	.	.	PUNCT
ejpam-5339	45	1	to	to	PART
ejpam-5339	45	2	solve	solve	VERB
ejpam-5339	45	3	the	the	DET
ejpam-5339	45	4	non	non	ADJ
ejpam-5339	45	5	-	-	ADJ
ejpam-5339	45	6	linear	linear	ADJ
ejpam-5339	45	7	oscillators	oscillator	NOUN
ejpam-5339	45	8	,	,	PUNCT
ejpam-5339	45	9	prof	prof	NOUN
ejpam-5339	45	10	.	.	PUNCT
ejpam-5339	46	1	he	he	PRON
ejpam-5339	46	2	proposed	propose	VERB
ejpam-5339	46	3	a	a	DET
ejpam-5339	46	4	simple	simple	ADJ
ejpam-5339	46	5	but	but	CCONJ
ejpam-5339	46	6	effective	effective	ADJ
ejpam-5339	46	7	approach	approach	NOUN
ejpam-5339	46	8	named	name	VERB
ejpam-5339	46	9	hff	hff	NOUN
ejpam-5339	46	10	[	[	X
ejpam-5339	46	11	4	4	NUM
ejpam-5339	46	12	]	]	PUNCT
ejpam-5339	46	13	.	.	PUNCT
ejpam-5339	47	1	the	the	DET
ejpam-5339	47	2	hff	hff	NOUN
ejpam-5339	47	3	was	be	AUX
ejpam-5339	47	4	used	use	VERB
ejpam-5339	47	5	by	by	ADP
ejpam-5339	47	6	many	many	ADJ
ejpam-5339	47	7	authors	author	NOUN
ejpam-5339	47	8	with	with	ADP
ejpam-5339	47	9	great	great	ADJ
ejpam-5339	47	10	success	success	NOUN
ejpam-5339	47	11	.	.	PUNCT
ejpam-5339	48	1	when	when	SCONJ
ejpam-5339	48	2	dealing	deal	VERB
ejpam-5339	48	3	with	with	ADP
ejpam-5339	48	4	nonlinear	nonlinear	ADJ
ejpam-5339	48	5	oscillator	oscillator	NOUN
ejpam-5339	48	6	problems	problem	NOUN
ejpam-5339	48	7	,	,	PUNCT
ejpam-5339	48	8	the	the	DET
ejpam-5339	48	9	hff	hff	NOUN
ejpam-5339	48	10	method	method	NOUN
ejpam-5339	48	11	was	be	AUX
ejpam-5339	48	12	a	a	DET
ejpam-5339	48	13	simple	simple	ADJ
ejpam-5339	48	14	and	and	CCONJ
ejpam-5339	48	15	efficient	efficient	ADJ
ejpam-5339	48	16	way	way	NOUN
ejpam-5339	48	17	to	to	PART
ejpam-5339	48	18	create	create	VERB
ejpam-5339	48	19	a	a	DET
ejpam-5339	48	20	conservation	conservation	NOUN
ejpam-5339	48	21	nonlinear	nonlinear	ADJ
ejpam-5339	48	22	oscillator	oscillator	NOUN
ejpam-5339	48	23	[	[	X
ejpam-5339	48	24	40	40	NUM
ejpam-5339	48	25	]	]	PUNCT
ejpam-5339	48	26	.	.	PUNCT
ejpam-5339	49	1	under	under	ADP
ejpam-5339	49	2	generalized	generalized	ADJ
ejpam-5339	49	3	beginning	beginning	NOUN
ejpam-5339	49	4	conditions	condition	NOUN
ejpam-5339	49	5	,	,	PUNCT
ejpam-5339	49	6	an	an	DET
ejpam-5339	49	7	analysis	analysis	NOUN
ejpam-5339	49	8	of	of	ADP
ejpam-5339	49	9	the	the	DET
ejpam-5339	49	10	duffing	duffing	NOUN
ejpam-5339	49	11	oscillator	oscillator	NOUN
ejpam-5339	49	12	(	(	PUNCT
ejpam-5339	49	13	do	do	AUX
ejpam-5339	49	14	)	)	PUNCT
ejpam-5339	49	15	in	in	ADP
ejpam-5339	49	16	vibration	vibration	NOUN
ejpam-5339	49	17	periodic	periodic	ADJ
ejpam-5339	49	18	behavior	behavior	NOUN
ejpam-5339	49	19	was	be	AUX
ejpam-5339	49	20	conducted	conduct	VERB
ejpam-5339	49	21	[	[	X
ejpam-5339	49	22	15	15	NUM
ejpam-5339	49	23	]	]	PUNCT
ejpam-5339	49	24	.	.	PUNCT
ejpam-5339	50	1	numerical	numerical	PROPN
ejpam-5339	50	2	testing	testing	PROPN
ejpam-5339	50	3	showed	show	VERB
ejpam-5339	50	4	that	that	SCONJ
ejpam-5339	50	5	the	the	DET
ejpam-5339	50	6	hff	hff	NOUN
ejpam-5339	50	7	was	be	AUX
ejpam-5339	50	8	practically	practically	ADV
ejpam-5339	50	9	beneficial	beneficial	ADJ
ejpam-5339	50	10	,	,	PUNCT
ejpam-5339	50	11	physically	physically	ADV
ejpam-5339	50	12	perceptive	perceptive	ADJ
ejpam-5339	50	13	,	,	PUNCT
ejpam-5339	50	14	and	and	CCONJ
ejpam-5339	50	15	mathematically	mathematically	ADV
ejpam-5339	50	16	simple	simple	ADJ
ejpam-5339	50	17	.	.	PUNCT
ejpam-5339	51	1	engineers	engineer	NOUN
ejpam-5339	51	2	can	can	AUX
ejpam-5339	51	3	use	use	VERB
ejpam-5339	51	4	the	the	DET
ejpam-5339	51	5	novel	novel	ADJ
ejpam-5339	51	6	method	method	NOUN
ejpam-5339	51	7	in	in	ADP
ejpam-5339	51	8	quickly	quickly	ADV
ejpam-5339	51	9	and	and	CCONJ
ejpam-5339	51	10	accurately	accurately	ADV
ejpam-5339	51	11	analyze	analyze	VERB
ejpam-5339	51	12	nonlinear	nonlinear	ADJ
ejpam-5339	51	13	vibration	vibration	NOUN
ejpam-5339	51	14	g.	g.	PROPN
ejpam-5339	51	15	m.	m.	PROPN
ejpam-5339	51	16	ismail	ismail	PROPN
ejpam-5339	51	17	,	,	PUNCT
ejpam-5339	51	18	g.	g.	PROPN
ejpam-5339	51	19	m.	m.	PROPN
ejpam-5339	51	20	moatimid	moatimid	PROPN
ejpam-5339	51	21	,	,	PUNCT
ejpam-5339	51	22	m.	m.	NOUN
ejpam-5339	51	23	i.	i.	PROPN
ejpam-5339	51	24	yamani	yamani	PROPN
ejpam-5339	51	25	/	/	SYM
ejpam-5339	51	26	eur	eur	PROPN
ejpam-5339	51	27	.	.	PUNCT
ejpam-5339	52	1	j.	j.	PROPN
ejpam-5339	52	2	pure	pure	PROPN
ejpam-5339	52	3	appl	appl	PROPN
ejpam-5339	52	4	.	.	PROPN
ejpam-5339	52	5	math	math	PROPN
ejpam-5339	52	6	,	,	PUNCT
ejpam-5339	52	7	17	17	NUM
ejpam-5339	52	8	(	(	PUNCT
ejpam-5339	52	9	3	3	NUM
ejpam-5339	52	10	)	)	PUNCT
ejpam-5339	52	11	(	(	PUNCT
ejpam-5339	52	12	2024	2024	NUM
ejpam-5339	52	13	)	)	PUNCT
ejpam-5339	52	14	,	,	PUNCT
ejpam-5339	52	15	2155	2155	NUM
ejpam-5339	52	16	-	-	SYM
ejpam-5339	52	17	2172	2172	NUM
ejpam-5339	52	18	2157	2157	NUM
ejpam-5339	52	19	systems	system	NOUN
ejpam-5339	52	20	utilizing	utilize	VERB
ejpam-5339	52	21	the	the	DET
ejpam-5339	52	22	hff	hff	NOUN
ejpam-5339	52	23	.	.	PUNCT
ejpam-5339	53	1	it	it	PRON
ejpam-5339	53	2	was	be	AUX
ejpam-5339	53	3	proposed	propose	VERB
ejpam-5339	53	4	to	to	PART
ejpam-5339	53	5	separate	separate	VERB
ejpam-5339	53	6	the	the	DET
ejpam-5339	53	7	oscillators	oscillator	NOUN
ejpam-5339	53	8	into	into	ADP
ejpam-5339	53	9	two	two	NUM
ejpam-5339	53	10	extreme	extreme	ADJ
ejpam-5339	53	11	situations	situation	NOUN
ejpam-5339	53	12	in	in	ADP
ejpam-5339	53	13	order	order	NOUN
ejpam-5339	53	14	to	to	PART
ejpam-5339	53	15	change	change	VERB
ejpam-5339	53	16	the	the	DET
ejpam-5339	53	17	hff	hff	NOUN
ejpam-5339	53	18	as	as	ADP
ejpam-5339	53	19	a	a	DET
ejpam-5339	53	20	new	new	ADJ
ejpam-5339	53	21	method	method	NOUN
ejpam-5339	53	22	[	[	X
ejpam-5339	53	23	16	16	NUM
ejpam-5339	53	24	]	]	PUNCT
ejpam-5339	53	25	.	.	PUNCT
ejpam-5339	54	1	when	when	SCONJ
ejpam-5339	54	2	the	the	DET
ejpam-5339	54	3	approximate	approximate	ADJ
ejpam-5339	54	4	and	and	CCONJ
ejpam-5339	54	5	exact	exact	ADJ
ejpam-5339	54	6	frequencies	frequency	NOUN
ejpam-5339	54	7	for	for	ADP
ejpam-5339	54	8	various	various	ADJ
ejpam-5339	54	9	amplitudes	amplitude	NOUN
ejpam-5339	54	10	were	be	AUX
ejpam-5339	54	11	compared	compare	VERB
ejpam-5339	54	12	,	,	PUNCT
ejpam-5339	54	13	there	there	PRON
ejpam-5339	54	14	was	be	VERB
ejpam-5339	54	15	good	good	ADJ
ejpam-5339	54	16	agreement	agreement	NOUN
ejpam-5339	54	17	.	.	PUNCT
ejpam-5339	55	1	the	the	DET
ejpam-5339	55	2	hamiltonian	hamiltonian	NOUN
ejpam-5339	55	3	-	-	PUNCT
ejpam-5339	55	4	based	base	VERB
ejpam-5339	55	5	on	on	ADP
ejpam-5339	55	6	the	the	DET
ejpam-5339	55	7	hff	hff	NOUN
ejpam-5339	55	8	was	be	AUX
ejpam-5339	55	9	addressed	address	VERB
ejpam-5339	55	10	as	as	ADP
ejpam-5339	55	11	a	a	DET
ejpam-5339	55	12	remarkable	remarkable	ADJ
ejpam-5339	55	13	accomplishment	accomplishment	NOUN
ejpam-5339	55	14	since	since	SCONJ
ejpam-5339	55	15	it	it	PRON
ejpam-5339	55	16	made	make	VERB
ejpam-5339	55	17	a	a	DET
ejpam-5339	55	18	complex	complex	ADJ
ejpam-5339	55	19	nonlinear	nonlinear	ADJ
ejpam-5339	55	20	vibration	vibration	NOUN
ejpam-5339	55	21	system	system	NOUN
ejpam-5339	55	22	easily	easily	ADV
ejpam-5339	55	23	comprehensible	comprehensible	ADJ
ejpam-5339	55	24	through	through	ADP
ejpam-5339	55	25	computing	computing	NOUN
ejpam-5339	55	26	.	.	PUNCT
ejpam-5339	56	1	the	the	DET
ejpam-5339	56	2	cubic	cubic	ADJ
ejpam-5339	56	3	-	-	PUNCT
ejpam-5339	56	4	quintic	quintic	ADJ
ejpam-5339	56	5	do	do	NOUN
ejpam-5339	56	6	was	be	AUX
ejpam-5339	56	7	given	give	VERB
ejpam-5339	56	8	as	as	ADP
ejpam-5339	56	9	an	an	DET
ejpam-5339	56	10	example	example	NOUN
ejpam-5339	56	11	to	to	PART
ejpam-5339	56	12	show	show	VERB
ejpam-5339	56	13	how	how	SCONJ
ejpam-5339	56	14	remarkably	remarkably	ADV
ejpam-5339	56	15	accurate	accurate	ADJ
ejpam-5339	56	16	and	and	CCONJ
ejpam-5339	56	17	straightforward	straightforward	ADJ
ejpam-5339	56	18	calculation	calculation	NOUN
ejpam-5339	56	19	.	.	PUNCT
ejpam-5339	57	1	a	a	DET
ejpam-5339	57	2	simple	simple	ADJ
ejpam-5339	57	3	approach	approach	NOUN
ejpam-5339	57	4	to	to	ADP
ejpam-5339	57	5	the	the	DET
ejpam-5339	57	6	cubic	cubic	ADJ
ejpam-5339	57	7	-	-	PUNCT
ejpam-5339	57	8	quintic	quintic	ADJ
ejpam-5339	57	9	do	do	NOUN
ejpam-5339	57	10	was	be	AUX
ejpam-5339	57	11	described	describe	VERB
ejpam-5339	57	12	[	[	X
ejpam-5339	57	13	5	5	NUM
ejpam-5339	57	14	]	]	PUNCT
ejpam-5339	57	15	.	.	PUNCT
ejpam-5339	58	1	the	the	DET
ejpam-5339	58	2	method	method	NOUN
ejpam-5339	58	3	provided	provide	VERB
ejpam-5339	58	4	a	a	DET
ejpam-5339	58	5	very	very	ADV
ejpam-5339	58	6	efficient	efficient	ADJ
ejpam-5339	58	7	and	and	CCONJ
ejpam-5339	58	8	reasonably	reasonably	ADV
ejpam-5339	58	9	accurate	accurate	ADJ
ejpam-5339	58	10	means	mean	NOUN
ejpam-5339	58	11	of	of	ADP
ejpam-5339	58	12	estimating	estimate	VERB
ejpam-5339	58	13	the	the	DET
ejpam-5339	58	14	frequency	frequency	NOUN
ejpam-5339	58	15	of	of	ADP
ejpam-5339	58	16	a	a	DET
ejpam-5339	58	17	nonlinear	nonlinear	ADJ
ejpam-5339	58	18	conservative	conservative	ADJ
ejpam-5339	58	19	oscillator	oscillator	NOUN
ejpam-5339	58	20	.	.	PUNCT
ejpam-5339	59	1	the	the	DET
ejpam-5339	59	2	simplified	simplified	ADJ
ejpam-5339	59	3	hff	hff	NOUN
ejpam-5339	59	4	of	of	ADP
ejpam-5339	59	5	nonlinear	nonlinear	ADJ
ejpam-5339	59	6	oscillators	oscillator	NOUN
ejpam-5339	59	7	was	be	AUX
ejpam-5339	59	8	presented	present	VERB
ejpam-5339	59	9	and	and	CCONJ
ejpam-5339	59	10	demonstrated	demonstrate	VERB
ejpam-5339	59	11	[	[	PUNCT
ejpam-5339	59	12	2	2	NUM
ejpam-5339	59	13	]	]	PUNCT
ejpam-5339	59	14	.	.	PUNCT
ejpam-5339	60	1	a	a	DET
ejpam-5339	60	2	fractal	fractal	ADJ
ejpam-5339	60	3	vibration	vibration	NOUN
ejpam-5339	60	4	was	be	AUX
ejpam-5339	60	5	shown	show	VERB
ejpam-5339	60	6	in	in	ADP
ejpam-5339	60	7	a	a	DET
ejpam-5339	60	8	porous	porous	ADJ
ejpam-5339	60	9	medium	medium	NOUN
ejpam-5339	60	10	,	,	PUNCT
ejpam-5339	60	11	and	and	CCONJ
ejpam-5339	60	12	its	its	PRON
ejpam-5339	60	13	low	low	ADJ
ejpam-5339	60	14	-	-	PUNCT
ejpam-5339	60	15	frequency	frequency	NOUN
ejpam-5339	60	16	characteristic	characteristic	NOUN
ejpam-5339	60	17	was	be	AUX
ejpam-5339	60	18	explained	explain	VERB
ejpam-5339	60	19	by	by	ADP
ejpam-5339	60	20	the	the	DET
ejpam-5339	60	21	hff	hff	NOUN
ejpam-5339	60	22	.	.	PUNCT
ejpam-5339	61	1	in	in	ADP
ejpam-5339	61	2	a	a	DET
ejpam-5339	61	3	fractal	fractal	ADJ
ejpam-5339	61	4	space	space	NOUN
ejpam-5339	61	5	,	,	PUNCT
ejpam-5339	61	6	it	it	PRON
ejpam-5339	61	7	was	be	AUX
ejpam-5339	61	8	discovered	discover	VERB
ejpam-5339	61	9	that	that	SCONJ
ejpam-5339	61	10	the	the	DET
ejpam-5339	61	11	inertia	inertia	NOUN
ejpam-5339	61	12	force	force	NOUN
ejpam-5339	61	13	was	be	AUX
ejpam-5339	61	14	equivalent	equivalent	ADJ
ejpam-5339	61	15	to	to	ADP
ejpam-5339	61	16	a	a	DET
ejpam-5339	61	17	few	few	ADJ
ejpam-5339	61	18	damping	damp	VERB
ejpam-5339	61	19	and	and	CCONJ
ejpam-5339	61	20	inertia	inertia	NOUN
ejpam-5339	61	21	forces	force	NOUN
ejpam-5339	61	22	.	.	PUNCT
ejpam-5339	62	1	a	a	DET
ejpam-5339	62	2	modification	modification	NOUN
ejpam-5339	62	3	was	be	AUX
ejpam-5339	62	4	suggested	suggest	VERB
ejpam-5339	62	5	,	,	PUNCT
ejpam-5339	62	6	and	and	CCONJ
ejpam-5339	62	7	the	the	DET
ejpam-5339	62	8	most	most	ADV
ejpam-5339	62	9	straightforward	straightforward	ADJ
ejpam-5339	62	10	frequency	frequency	NOUN
ejpam-5339	62	11	formulation	formulation	NOUN
ejpam-5339	62	12	for	for	ADP
ejpam-5339	62	13	nonlinear	nonlinear	ADJ
ejpam-5339	62	14	oscillators	oscillator	NOUN
ejpam-5339	62	15	was	be	AUX
ejpam-5339	62	16	presented	present	VERB
ejpam-5339	62	17	and	and	CCONJ
ejpam-5339	62	18	validated	validate	VERB
ejpam-5339	63	1	[	[	X
ejpam-5339	63	2	1	1	NUM
ejpam-5339	63	3	]	]	PUNCT
ejpam-5339	63	4	.	.	PUNCT
ejpam-5339	64	1	it	it	PRON
ejpam-5339	64	2	was	be	AUX
ejpam-5339	64	3	demonstrated	demonstrate	VERB
ejpam-5339	64	4	that	that	SCONJ
ejpam-5339	64	5	the	the	DET
ejpam-5339	64	6	inertia	inertia	NOUN
ejpam-5339	64	7	force	force	NOUN
ejpam-5339	64	8	for	for	ADP
ejpam-5339	64	9	the	the	DET
ejpam-5339	64	10	standard	standard	ADJ
ejpam-5339	64	11	differential	differential	ADJ
ejpam-5339	64	12	model	model	NOUN
ejpam-5339	64	13	is	be	AUX
ejpam-5339	64	14	equal	equal	ADJ
ejpam-5339	64	15	to	to	ADP
ejpam-5339	64	16	the	the	DET
ejpam-5339	64	17	total	total	NOUN
ejpam-5339	64	18	of	of	ADP
ejpam-5339	64	19	the	the	DET
ejpam-5339	64	20	damping	damp	VERB
ejpam-5339	64	21	force	force	NOUN
ejpam-5339	64	22	and	and	CCONJ
ejpam-5339	64	23	the	the	DET
ejpam-5339	64	24	inertia	inertia	NOUN
ejpam-5339	64	25	force	force	NOUN
ejpam-5339	64	26	in	in	ADP
ejpam-5339	64	27	a	a	DET
ejpam-5339	64	28	fractal	fractal	ADJ
ejpam-5339	64	29	space	space	NOUN
ejpam-5339	64	30	.	.	PUNCT
ejpam-5339	65	1	in	in	ADP
ejpam-5339	65	2	the	the	DET
ejpam-5339	65	3	event	event	NOUN
ejpam-5339	65	4	of	of	ADP
ejpam-5339	65	5	any	any	DET
ejpam-5339	65	6	non	non	ADJ
ejpam-5339	65	7	-	-	NOUN
ejpam-5339	65	8	linearity	linearity	NOUN
ejpam-5339	65	9	,	,	PUNCT
ejpam-5339	65	10	a	a	DET
ejpam-5339	65	11	modification	modification	NOUN
ejpam-5339	65	12	to	to	ADP
ejpam-5339	65	13	the	the	DET
ejpam-5339	65	14	hff	hff	NOUN
ejpam-5339	65	15	was	be	AUX
ejpam-5339	65	16	recommended	recommend	VERB
ejpam-5339	65	17	[	[	PUNCT
ejpam-5339	65	18	38	38	NUM
ejpam-5339	65	19	]	]	PUNCT
ejpam-5339	65	20	.	.	PUNCT
ejpam-5339	66	1	a	a	DET
ejpam-5339	66	2	simple	simple	ADJ
ejpam-5339	66	3	frequency	frequency	NOUN
ejpam-5339	66	4	formula	formula	NOUN
ejpam-5339	66	5	for	for	ADP
ejpam-5339	66	6	fractal	fractal	ADJ
ejpam-5339	66	7	systems	system	NOUN
ejpam-5339	66	8	,	,	PUNCT
ejpam-5339	66	9	obtained	obtain	VERB
ejpam-5339	66	10	from	from	ADP
ejpam-5339	66	11	the	the	DET
ejpam-5339	66	12	hff	hff	NOUN
ejpam-5339	66	13	,	,	PUNCT
ejpam-5339	66	14	was	be	AUX
ejpam-5339	66	15	examined	examine	VERB
ejpam-5339	66	16	[	[	PUNCT
ejpam-5339	66	17	22	22	NUM
ejpam-5339	66	18	]	]	PUNCT
ejpam-5339	66	19	.	.	PUNCT
ejpam-5339	67	1	the	the	DET
ejpam-5339	67	2	coupled	couple	VERB
ejpam-5339	67	3	simple	simple	ADJ
ejpam-5339	67	4	calculation	calculation	NOUN
ejpam-5339	67	5	with	with	ADP
ejpam-5339	67	6	reliable	reliable	ADJ
ejpam-5339	67	7	results	result	NOUN
ejpam-5339	67	8	produced	produce	VERB
ejpam-5339	67	9	a	a	DET
ejpam-5339	67	10	valuable	valuable	ADJ
ejpam-5339	67	11	instrument	instrument	NOUN
ejpam-5339	67	12	of	of	ADP
ejpam-5339	67	13	detailed	detailed	ADJ
ejpam-5339	67	14	study	study	NOUN
ejpam-5339	67	15	of	of	ADP
ejpam-5339	67	16	fractal	fractal	ADJ
ejpam-5339	67	17	vibration	vibration	NOUN
ejpam-5339	67	18	phenomena	phenomenon	NOUN
ejpam-5339	67	19	.	.	PUNCT
ejpam-5339	68	1	the	the	DET
ejpam-5339	68	2	non	non	ADJ
ejpam-5339	68	3	-	-	ADJ
ejpam-5339	68	4	newtonian	newtonian	ADJ
ejpam-5339	68	5	fluids	fluid	NOUN
ejpam-5339	68	6	were	be	AUX
ejpam-5339	68	7	essential	essential	ADJ
ejpam-5339	68	8	in	in	ADP
ejpam-5339	68	9	numerous	numerous	ADJ
ejpam-5339	68	10	fields	field	NOUN
ejpam-5339	68	11	,	,	PUNCT
ejpam-5339	68	12	including	include	VERB
ejpam-5339	68	13	manufacture	manufacture	NOUN
ejpam-5339	68	14	and	and	CCONJ
ejpam-5339	68	15	technology	technology	NOUN
ejpam-5339	68	16	.	.	PUNCT
ejpam-5339	69	1	investigation	investigation	NOUN
ejpam-5339	69	2	into	into	ADP
ejpam-5339	69	3	these	these	DET
ejpam-5339	69	4	fluids	fluid	NOUN
ejpam-5339	69	5	was	be	AUX
ejpam-5339	69	6	therefore	therefore	ADV
ejpam-5339	69	7	quite	quite	ADV
ejpam-5339	69	8	appealing	appealing	ADJ
ejpam-5339	69	9	.	.	PUNCT
ejpam-5339	70	1	the	the	DET
ejpam-5339	70	2	work	work	NOUN
ejpam-5339	70	3	of	of	ADP
ejpam-5339	70	4	nonlinear	nonlinear	ADJ
ejpam-5339	70	5	stability	stability	NOUN
ejpam-5339	70	6	assessment	assessment	NOUN
ejpam-5339	70	7	was	be	AUX
ejpam-5339	70	8	directed	direct	VERB
ejpam-5339	70	9	towards	towards	ADP
ejpam-5339	70	10	some	some	PRON
ejpam-5339	70	11	of	of	ADP
ejpam-5339	70	12	the	the	DET
ejpam-5339	70	13	non	non	ADJ
ejpam-5339	70	14	-	-	ADJ
ejpam-5339	70	15	newtonian	newtonian	ADJ
ejpam-5339	70	16	fluids	fluid	NOUN
ejpam-5339	70	17	.	.	PUNCT
ejpam-5339	71	1	a	a	DET
ejpam-5339	71	2	representation	representation	NOUN
ejpam-5339	71	3	was	be	AUX
ejpam-5339	71	4	constructed	construct	VERB
ejpam-5339	71	5	for	for	ADP
ejpam-5339	71	6	the	the	DET
ejpam-5339	71	7	composition	composition	NOUN
ejpam-5339	71	8	of	of	ADP
ejpam-5339	71	9	a	a	DET
ejpam-5339	71	10	flat	flat	ADJ
ejpam-5339	71	11	disturbed	disturbed	ADJ
ejpam-5339	71	12	interface	interface	NOUN
ejpam-5339	71	13	as	as	ADV
ejpam-5339	71	14	well	well	ADV
ejpam-5339	71	15	as	as	ADP
ejpam-5339	71	16	some	some	DET
ejpam-5339	71	17	dynamical	dynamical	ADJ
ejpam-5339	71	18	systems	system	NOUN
ejpam-5339	71	19	.	.	PUNCT
ejpam-5339	72	1	using	use	VERB
ejpam-5339	72	2	the	the	DET
ejpam-5339	72	3	npa	npa	NOUN
ejpam-5339	72	4	,	,	PUNCT
ejpam-5339	72	5	as	as	ADP
ejpam-5339	72	6	an	an	DET
ejpam-5339	72	7	addition	addition	NOUN
ejpam-5339	72	8	performance	performance	NOUN
ejpam-5339	72	9	,	,	PUNCT
ejpam-5339	72	10	was	be	AUX
ejpam-5339	72	11	the	the	DET
ejpam-5339	72	12	main	main	ADJ
ejpam-5339	72	13	goal	goal	NOUN
ejpam-5339	72	14	of	of	ADP
ejpam-5339	72	15	the	the	DET
ejpam-5339	72	16	theoretical	theoretical	ADJ
ejpam-5339	72	17	inquiry	inquiry	NOUN
ejpam-5339	72	18	[	[	X
ejpam-5339	72	19	25–27	25–27	NUM
ejpam-5339	72	20	,	,	PUNCT
ejpam-5339	72	21	29–35	29–35	NUM
ejpam-5339	72	22	]	]	PUNCT
ejpam-5339	72	23	.	.	PUNCT
ejpam-5339	73	1	in	in	ADP
ejpam-5339	73	2	the	the	DET
ejpam-5339	73	3	current	current	ADJ
ejpam-5339	73	4	study	study	NOUN
ejpam-5339	73	5	,	,	PUNCT
ejpam-5339	73	6	we	we	PRON
ejpam-5339	73	7	will	will	AUX
ejpam-5339	73	8	suggest	suggest	VERB
ejpam-5339	73	9	an	an	DET
ejpam-5339	73	10	alternative	alternative	ADJ
ejpam-5339	73	11	form	form	NOUN
ejpam-5339	73	12	of	of	ADP
ejpam-5339	73	13	the	the	DET
ejpam-5339	73	14	hff	hff	NOUN
ejpam-5339	73	15	to	to	PART
ejpam-5339	73	16	analyze	analyze	VERB
ejpam-5339	73	17	some	some	DET
ejpam-5339	73	18	highly	highly	ADV
ejpam-5339	73	19	non	non	ADJ
ejpam-5339	73	20	-	-	ADJ
ejpam-5339	73	21	linear	linear	ADJ
ejpam-5339	73	22	oscillators	oscillator	NOUN
ejpam-5339	73	23	.	.	PUNCT
ejpam-5339	74	1	the	the	DET
ejpam-5339	74	2	npa	npa	NOUN
ejpam-5339	74	3	is	be	AUX
ejpam-5339	74	4	a	a	DET
ejpam-5339	74	5	key	key	ADJ
ejpam-5339	74	6	technique	technique	NOUN
ejpam-5339	74	7	in	in	ADP
ejpam-5339	74	8	the	the	DET
ejpam-5339	74	9	current	current	ADJ
ejpam-5339	74	10	study	study	NOUN
ejpam-5339	74	11	,	,	PUNCT
ejpam-5339	74	12	for	for	ADP
ejpam-5339	74	13	locating	locate	VERB
ejpam-5339	74	14	the	the	DET
ejpam-5339	74	15	analytical	analytical	ADJ
ejpam-5339	74	16	approximation	approximation	NOUN
ejpam-5339	74	17	solutions	solution	NOUN
ejpam-5339	74	18	of	of	ADP
ejpam-5339	74	19	some	some	DET
ejpam-5339	74	20	nonlinear	nonlinear	ADJ
ejpam-5339	74	21	odes	ode	NOUN
ejpam-5339	74	22	.	.	PUNCT
ejpam-5339	75	1	comparing	compare	VERB
ejpam-5339	75	2	the	the	DET
ejpam-5339	75	3	numerical	numerical	ADJ
ejpam-5339	75	4	solution	solution	NOUN
ejpam-5339	75	5	(	(	PUNCT
ejpam-5339	75	6	ns	ns	NUM
ejpam-5339	75	7	)	)	PUNCT
ejpam-5339	75	8	and	and	CCONJ
ejpam-5339	75	9	the	the	DET
ejpam-5339	75	10	present	present	ADJ
ejpam-5339	75	11	results	result	NOUN
ejpam-5339	75	12	to	to	PART
ejpam-5339	75	13	show	show	VERB
ejpam-5339	75	14	the	the	DET
ejpam-5339	75	15	effectiveness	effectiveness	NOUN
ejpam-5339	75	16	and	and	CCONJ
ejpam-5339	75	17	precision	precision	NOUN
ejpam-5339	75	18	of	of	ADP
ejpam-5339	75	19	the	the	DET
ejpam-5339	75	20	npa	npa	NOUN
ejpam-5339	75	21	.	.	PUNCT
ejpam-5339	76	1	it	it	PRON
ejpam-5339	76	2	is	be	AUX
ejpam-5339	76	3	evident	evident	ADJ
ejpam-5339	76	4	that	that	SCONJ
ejpam-5339	76	5	the	the	DET
ejpam-5339	76	6	present	present	ADJ
ejpam-5339	76	7	method	method	NOUN
ejpam-5339	76	8	yields	yield	VERB
ejpam-5339	76	9	more	more	ADV
ejpam-5339	76	10	precise	precise	ADJ
ejpam-5339	76	11	results	result	NOUN
ejpam-5339	76	12	than	than	ADP
ejpam-5339	76	13	similar	similar	ADJ
ejpam-5339	76	14	the	the	DET
ejpam-5339	76	15	approximations	approximation	NOUN
ejpam-5339	76	16	for	for	ADP
ejpam-5339	76	17	the	the	DET
ejpam-5339	76	18	previously	previously	ADV
ejpam-5339	76	19	discussed	discuss	VERB
ejpam-5339	76	20	problems	problem	NOUN
ejpam-5339	76	21	.	.	PUNCT
ejpam-5339	77	1	the	the	DET
ejpam-5339	77	2	npa	npa	PROPN
ejpam-5339	77	3	has	have	VERB
ejpam-5339	77	4	wonderful	wonderful	ADJ
ejpam-5339	77	5	potential	potential	NOUN
ejpam-5339	77	6	and	and	CCONJ
ejpam-5339	77	7	may	may	AUX
ejpam-5339	77	8	be	be	AUX
ejpam-5339	77	9	applied	apply	VERB
ejpam-5339	77	10	to	to	PART
ejpam-5339	77	11	address	address	VERB
ejpam-5339	77	12	additional	additional	ADJ
ejpam-5339	77	13	substantially	substantially	ADV
ejpam-5339	77	14	nonlinear	nonlinear	ADJ
ejpam-5339	77	15	situations	situation	NOUN
ejpam-5339	77	16	,	,	PUNCT
ejpam-5339	77	17	as	as	SCONJ
ejpam-5339	77	18	is	be	AUX
ejpam-5339	77	19	proven	prove	VERB
ejpam-5339	77	20	at	at	ADP
ejpam-5339	77	21	the	the	DET
ejpam-5339	77	22	conclusion	conclusion	NOUN
ejpam-5339	77	23	.	.	PUNCT
ejpam-5339	78	1	when	when	SCONJ
ejpam-5339	78	2	combined	combine	VERB
ejpam-5339	78	3	,	,	PUNCT
ejpam-5339	78	4	the	the	DET
ejpam-5339	78	5	npa	npa	NOUN
ejpam-5339	78	6	resolves	resolve	VERB
ejpam-5339	78	7	several	several	ADJ
ejpam-5339	78	8	real	real	ADJ
ejpam-5339	78	9	-	-	PUNCT
ejpam-5339	78	10	world	world	NOUN
ejpam-5339	78	11	situations	situation	NOUN
ejpam-5339	78	12	.	.	PUNCT
ejpam-5339	79	1	previously	previously	ADV
ejpam-5339	79	2	,	,	PUNCT
ejpam-5339	79	3	these	these	DET
ejpam-5339	79	4	realworld	realworld	PROPN
ejpam-5339	79	5	cases	case	NOUN
ejpam-5339	79	6	were	be	AUX
ejpam-5339	79	7	resolved	resolve	VERB
ejpam-5339	79	8	with	with	ADP
ejpam-5339	79	9	other	other	ADJ
ejpam-5339	79	10	well	well	ADV
ejpam-5339	79	11	-	-	PUNCT
ejpam-5339	79	12	known	know	VERB
ejpam-5339	79	13	analytical	analytical	ADJ
ejpam-5339	79	14	methods	method	NOUN
ejpam-5339	79	15	that	that	PRON
ejpam-5339	79	16	were	be	AUX
ejpam-5339	79	17	previously	previously	ADV
ejpam-5339	79	18	documented	document	VERB
ejpam-5339	79	19	in	in	ADP
ejpam-5339	79	20	the	the	DET
ejpam-5339	79	21	literature	literature	NOUN
ejpam-5339	79	22	.	.	PUNCT
ejpam-5339	80	1	however	however	ADV
ejpam-5339	80	2	,	,	PUNCT
ejpam-5339	80	3	the	the	DET
ejpam-5339	80	4	best	good	ADJ
ejpam-5339	80	5	results	result	NOUN
ejpam-5339	80	6	are	be	AUX
ejpam-5339	80	7	obtained	obtain	VERB
ejpam-5339	80	8	faster	fast	ADV
ejpam-5339	80	9	using	use	VERB
ejpam-5339	80	10	our	our	PRON
ejpam-5339	80	11	existing	exist	VERB
ejpam-5339	80	12	methods	method	NOUN
ejpam-5339	80	13	.	.	PUNCT
ejpam-5339	81	1	on	on	ADP
ejpam-5339	81	2	the	the	DET
ejpam-5339	81	3	other	other	ADJ
ejpam-5339	81	4	hand	hand	NOUN
ejpam-5339	81	5	,	,	PUNCT
ejpam-5339	81	6	the	the	DET
ejpam-5339	81	7	calculations	calculation	NOUN
ejpam-5339	81	8	using	use	VERB
ejpam-5339	81	9	ms	ms	ADJ
ejpam-5339	81	10	assistance	assistance	NOUN
ejpam-5339	81	11	are	be	AUX
ejpam-5339	81	12	even	even	ADV
ejpam-5339	81	13	more	more	ADV
ejpam-5339	81	14	straightforward	straightforward	ADJ
ejpam-5339	81	15	with	with	ADP
ejpam-5339	81	16	the	the	DET
ejpam-5339	81	17	npa	npa	NOUN
ejpam-5339	81	18	than	than	SCONJ
ejpam-5339	81	19	they	they	PRON
ejpam-5339	81	20	are	be	AUX
ejpam-5339	81	21	with	with	ADP
ejpam-5339	81	22	other	other	ADJ
ejpam-5339	81	23	analytical	analytical	ADJ
ejpam-5339	81	24	techniques	technique	NOUN
ejpam-5339	81	25	,	,	PUNCT
ejpam-5339	81	26	and	and	CCONJ
ejpam-5339	81	27	the	the	DET
ejpam-5339	81	28	procedures	procedure	NOUN
ejpam-5339	81	29	for	for	ADP
ejpam-5339	81	30	determining	determine	VERB
ejpam-5339	81	31	the	the	DET
ejpam-5339	81	32	analytical	analytical	ADJ
ejpam-5339	81	33	solutions	solution	NOUN
ejpam-5339	81	34	are	be	AUX
ejpam-5339	81	35	fully	fully	ADV
ejpam-5339	81	36	illustrated	illustrate	VERB
ejpam-5339	81	37	.	.	PUNCT
ejpam-5339	82	1	other	other	ADJ
ejpam-5339	82	2	calculation	calculation	NOUN
ejpam-5339	82	3	methods	method	NOUN
ejpam-5339	82	4	were	be	AUX
ejpam-5339	82	5	extensive	extensive	ADJ
ejpam-5339	82	6	to	to	PART
ejpam-5339	82	7	use	use	VERB
ejpam-5339	82	8	or	or	CCONJ
ejpam-5339	82	9	required	require	VERB
ejpam-5339	82	10	a	a	DET
ejpam-5339	82	11	lengthy	lengthy	ADJ
ejpam-5339	82	12	time	time	NOUN
ejpam-5339	82	13	to	to	PART
ejpam-5339	82	14	analyze	analyze	VERB
ejpam-5339	82	15	the	the	DET
ejpam-5339	82	16	solution	solution	NOUN
ejpam-5339	82	17	.	.	PUNCT
ejpam-5339	83	1	regarding	regard	VERB
ejpam-5339	83	2	the	the	DET
ejpam-5339	83	3	unique	unique	ADJ
ejpam-5339	83	4	approach	approach	NOUN
ejpam-5339	83	5	used	use	VERB
ejpam-5339	83	6	or	or	CCONJ
ejpam-5339	83	7	notable	notable	ADJ
ejpam-5339	83	8	results	result	NOUN
ejpam-5339	83	9	,	,	PUNCT
ejpam-5339	83	10	the	the	DET
ejpam-5339	83	11	following	follow	VERB
ejpam-5339	83	12	details	detail	NOUN
ejpam-5339	83	13	have	have	AUX
ejpam-5339	83	14	been	be	AUX
ejpam-5339	83	15	emphasized	emphasize	VERB
ejpam-5339	83	16	:	:	PUNCT
ejpam-5339	83	17	(	(	PUNCT
ejpam-5339	83	18	i	i	NOUN
ejpam-5339	83	19	)	)	PUNCT
ejpam-5339	83	20	the	the	DET
ejpam-5339	83	21	current	current	ADJ
ejpam-5339	83	22	non	non	ADJ
ejpam-5339	83	23	-	-	ADJ
ejpam-5339	83	24	linear	linear	ADJ
ejpam-5339	83	25	ode	ode	NOUN
ejpam-5339	83	26	is	be	AUX
ejpam-5339	83	27	equivalent	equivalent	ADJ
ejpam-5339	83	28	to	to	ADP
ejpam-5339	83	29	the	the	DET
ejpam-5339	83	30	alternate	alternate	ADJ
ejpam-5339	83	31	comparable	comparable	ADJ
ejpam-5339	83	32	linear	linear	PROPN
ejpam-5339	83	33	one	one	NUM
ejpam-5339	83	34	.	.	PUNCT
ejpam-5339	84	1	g.	g.	PROPN
ejpam-5339	84	2	m.	m.	PROPN
ejpam-5339	84	3	ismail	ismail	PROPN
ejpam-5339	84	4	,	,	PUNCT
ejpam-5339	84	5	g.	g.	PROPN
ejpam-5339	84	6	m.	m.	PROPN
ejpam-5339	84	7	moatimid	moatimid	PROPN
ejpam-5339	84	8	,	,	PUNCT
ejpam-5339	84	9	m.	m.	NOUN
ejpam-5339	84	10	i.	i.	PROPN
ejpam-5339	84	11	yamani	yamani	PROPN
ejpam-5339	84	12	/	/	SYM
ejpam-5339	84	13	eur	eur	PROPN
ejpam-5339	84	14	.	.	PUNCT
ejpam-5339	85	1	j.	j.	PROPN
ejpam-5339	85	2	pure	pure	PROPN
ejpam-5339	85	3	appl	appl	PROPN
ejpam-5339	85	4	.	.	PROPN
ejpam-5339	85	5	math	math	PROPN
ejpam-5339	85	6	,	,	PUNCT
ejpam-5339	85	7	17	17	NUM
ejpam-5339	85	8	(	(	PUNCT
ejpam-5339	85	9	3	3	NUM
ejpam-5339	85	10	)	)	PUNCT
ejpam-5339	85	11	(	(	PUNCT
ejpam-5339	85	12	2024	2024	NUM
ejpam-5339	85	13	)	)	PUNCT
ejpam-5339	85	14	,	,	PUNCT
ejpam-5339	85	15	2155	2155	NUM
ejpam-5339	85	16	-	-	SYM
ejpam-5339	85	17	2172	2172	NUM
ejpam-5339	85	18	2158	2158	NUM
ejpam-5339	85	19	(	(	PUNCT
ejpam-5339	85	20	ii	ii	NOUN
ejpam-5339	85	21	)	)	PUNCT
ejpam-5339	85	22	these	these	DET
ejpam-5339	85	23	two	two	NUM
ejpam-5339	85	24	equations	equation	NOUN
ejpam-5339	85	25	match	match	VERB
ejpam-5339	85	26	each	each	DET
ejpam-5339	85	27	other	other	ADJ
ejpam-5339	85	28	exactly	exactly	ADV
ejpam-5339	85	29	when	when	SCONJ
ejpam-5339	85	30	using	use	VERB
ejpam-5339	85	31	the	the	DET
ejpam-5339	85	32	ns	ns	NOUN
ejpam-5339	85	33	.	.	PUNCT
ejpam-5339	85	34	(	(	PUNCT
ejpam-5339	85	35	iii	iii	NOUN
ejpam-5339	85	36	)	)	PUNCT
ejpam-5339	85	37	every	every	DET
ejpam-5339	85	38	traditional	traditional	ADJ
ejpam-5339	85	39	method	method	NOUN
ejpam-5339	85	40	employs	employ	VERB
ejpam-5339	85	41	expansion	expansion	NOUN
ejpam-5339	85	42	of	of	ADP
ejpam-5339	85	43	taylor	taylor	PROPN
ejpam-5339	85	44	to	to	PART
ejpam-5339	85	45	simplify	simplify	VERB
ejpam-5339	85	46	the	the	DET
ejpam-5339	85	47	challenge	challenge	NOUN
ejpam-5339	85	48	of	of	ADP
ejpam-5339	85	49	restoring	restore	VERB
ejpam-5339	85	50	forces	force	NOUN
ejpam-5339	85	51	.	.	PUNCT
ejpam-5339	86	1	the	the	DET
ejpam-5339	86	2	current	current	ADJ
ejpam-5339	86	3	npa	npa	NOUN
ejpam-5339	86	4	eliminates	eliminate	VERB
ejpam-5339	86	5	this	this	DET
ejpam-5339	86	6	issue	issue	NOUN
ejpam-5339	86	7	(	(	PUNCT
ejpam-5339	86	8	iv	iv	X
ejpam-5339	86	9	)	)	PUNCT
ejpam-5339	86	10	in	in	ADP
ejpam-5339	86	11	contrast	contrast	NOUN
ejpam-5339	86	12	to	to	ADP
ejpam-5339	86	13	other	other	ADJ
ejpam-5339	86	14	traditional	traditional	ADJ
ejpam-5339	86	15	methods	method	NOUN
ejpam-5339	86	16	,	,	PUNCT
ejpam-5339	86	17	the	the	DET
ejpam-5339	86	18	npa	npa	NOUN
ejpam-5339	86	19	enables	enable	VERB
ejpam-5339	86	20	us	we	PRON
ejpam-5339	86	21	to	to	PART
ejpam-5339	86	22	investigate	investigate	VERB
ejpam-5339	86	23	the	the	DET
ejpam-5339	86	24	stability	stability	NOUN
ejpam-5339	86	25	analysis	analysis	NOUN
ejpam-5339	86	26	of	of	ADP
ejpam-5339	86	27	the	the	DET
ejpam-5339	86	28	problem	problem	NOUN
ejpam-5339	86	29	.	.	PUNCT
ejpam-5339	87	1	(	(	PUNCT
ejpam-5339	87	2	v	v	X
ejpam-5339	87	3	)	)	PUNCT
ejpam-5339	87	4	the	the	DET
ejpam-5339	87	5	new	new	ADJ
ejpam-5339	87	6	technique	technique	NOUN
ejpam-5339	87	7	seems	seem	VERB
ejpam-5339	87	8	to	to	PART
ejpam-5339	87	9	be	be	AUX
ejpam-5339	87	10	a	a	DET
ejpam-5339	87	11	simple	simple	ADJ
ejpam-5339	87	12	,	,	PUNCT
ejpam-5339	87	13	convenient	convenient	ADJ
ejpam-5339	87	14	,	,	PUNCT
ejpam-5339	87	15	and	and	CCONJ
ejpam-5339	87	16	intriguing	intriguing	ADJ
ejpam-5339	87	17	instrument	instrument	NOUN
ejpam-5339	87	18	.	.	PUNCT
ejpam-5339	88	1	it	it	PRON
ejpam-5339	88	2	can	can	AUX
ejpam-5339	88	3	be	be	AUX
ejpam-5339	88	4	utilized	utilize	VERB
ejpam-5339	88	5	for	for	ADP
ejpam-5339	88	6	studying	study	VERB
ejpam-5339	88	7	various	various	ADJ
ejpam-5339	88	8	categories	category	NOUN
ejpam-5339	88	9	of	of	ADP
ejpam-5339	88	10	nonlinear	nonlinear	ADJ
ejpam-5339	88	11	oscillators	oscillator	NOUN
ejpam-5339	88	12	.	.	PUNCT
ejpam-5339	89	1	finally	finally	ADV
ejpam-5339	89	2	,	,	PUNCT
ejpam-5339	89	3	the	the	DET
ejpam-5339	89	4	npa	npa	NOUN
ejpam-5339	89	5	is	be	AUX
ejpam-5339	89	6	beneficial	beneficial	ADJ
ejpam-5339	89	7	in	in	ADP
ejpam-5339	89	8	the	the	DET
ejpam-5339	89	9	fields	field	NOUN
ejpam-5339	89	10	of	of	ADP
ejpam-5339	89	11	science	science	NOUN
ejpam-5339	89	12	,	,	PUNCT
ejpam-5339	89	13	technology	technology	NOUN
ejpam-5339	89	14	,	,	PUNCT
ejpam-5339	89	15	and	and	CCONJ
ejpam-5339	89	16	applied	apply	VERB
ejpam-5339	89	17	research	research	NOUN
ejpam-5339	89	18	as	as	SCONJ
ejpam-5339	89	19	it	it	PRON
ejpam-5339	89	20	can	can	AUX
ejpam-5339	89	21	easily	easily	ADV
ejpam-5339	89	22	be	be	AUX
ejpam-5339	89	23	adjusted	adjust	VERB
ejpam-5339	89	24	to	to	PART
ejpam-5339	89	25	address	address	VERB
ejpam-5339	89	26	various	various	ADJ
ejpam-5339	89	27	nonlinear	nonlinear	ADJ
ejpam-5339	89	28	issues	issue	NOUN
ejpam-5339	89	29	.	.	PUNCT
ejpam-5339	90	1	there	there	PRON
ejpam-5339	90	2	are	be	VERB
ejpam-5339	90	3	five	five	NUM
ejpam-5339	90	4	sections	section	NOUN
ejpam-5339	90	5	in	in	ADP
ejpam-5339	90	6	the	the	DET
ejpam-5339	90	7	current	current	ADJ
ejpam-5339	90	8	paper	paper	NOUN
ejpam-5339	90	9	,	,	PUNCT
ejpam-5339	90	10	which	which	PRON
ejpam-5339	90	11	help	help	VERB
ejpam-5339	90	12	readers	reader	NOUN
ejpam-5339	90	13	to	to	PART
ejpam-5339	90	14	clarify	clarify	VERB
ejpam-5339	90	15	how	how	SCONJ
ejpam-5339	90	16	it	it	PRON
ejpam-5339	90	17	is	be	AUX
ejpam-5339	90	18	accessible	accessible	ADJ
ejpam-5339	90	19	.	.	PUNCT
ejpam-5339	91	1	we	we	PRON
ejpam-5339	91	2	demonstrate	demonstrate	VERB
ejpam-5339	91	3	and	and	CCONJ
ejpam-5339	91	4	briefly	briefly	ADV
ejpam-5339	91	5	review	review	VERB
ejpam-5339	91	6	the	the	DET
ejpam-5339	91	7	npa	npa	NOUN
ejpam-5339	91	8	description	description	NOUN
ejpam-5339	91	9	in	in	ADP
ejpam-5339	91	10	§	§	PROPN
ejpam-5339	91	11	2	2	NUM
ejpam-5339	91	12	.	.	PUNCT
ejpam-5339	91	13	using	use	VERB
ejpam-5339	91	14	the	the	DET
ejpam-5339	91	15	npa	npa	NOUN
ejpam-5339	91	16	,	,	PUNCT
ejpam-5339	91	17	few	few	ADJ
ejpam-5339	91	18	nonlinear	nonlinear	ADJ
ejpam-5339	91	19	odes	ode	NOUN
ejpam-5339	91	20	from	from	ADP
ejpam-5339	91	21	the	the	DET
ejpam-5339	91	22	actual	actual	ADJ
ejpam-5339	91	23	world	world	NOUN
ejpam-5339	91	24	are	be	AUX
ejpam-5339	91	25	examined	examine	VERB
ejpam-5339	91	26	in	in	ADP
ejpam-5339	91	27	§	§	PROPN
ejpam-5339	91	28	3	3	NUM
ejpam-5339	91	29	.	.	PUNCT
ejpam-5339	91	30	in	in	ADP
ejpam-5339	91	31	§	§	PROPN
ejpam-5339	91	32	4	4	NUM
ejpam-5339	91	33	,	,	PUNCT
ejpam-5339	91	34	a	a	DET
ejpam-5339	91	35	summary	summary	NOUN
ejpam-5339	91	36	is	be	AUX
ejpam-5339	91	37	given	give	VERB
ejpam-5339	91	38	of	of	ADP
ejpam-5339	91	39	the	the	DET
ejpam-5339	91	40	dissections	dissection	NOUN
ejpam-5339	91	41	of	of	ADP
ejpam-5339	91	42	the	the	DET
ejpam-5339	91	43	current	current	ADJ
ejpam-5339	91	44	study	study	NOUN
ejpam-5339	91	45	.	.	PUNCT
ejpam-5339	92	1	finally	finally	ADV
ejpam-5339	92	2	,	,	PUNCT
ejpam-5339	92	3	§	§	PROPN
ejpam-5339	92	4	5	5	NUM
ejpam-5339	92	5	provides	provide	VERB
ejpam-5339	92	6	a	a	DET
ejpam-5339	92	7	summary	summary	NOUN
ejpam-5339	92	8	of	of	ADP
ejpam-5339	92	9	the	the	DET
ejpam-5339	92	10	final	final	ADJ
ejpam-5339	92	11	explanations	explanation	NOUN
ejpam-5339	92	12	.	.	PUNCT
ejpam-5339	93	1	2	2	X
ejpam-5339	93	2	.	.	X
ejpam-5339	93	3	explanation	explanation	NOUN
ejpam-5339	93	4	of	of	ADP
ejpam-5339	93	5	the	the	DET
ejpam-5339	93	6	npa	npa	NOUN
ejpam-5339	93	7	consider	consider	VERB
ejpam-5339	93	8	a	a	DET
ejpam-5339	93	9	highly	highly	ADV
ejpam-5339	93	10	non	non	ADJ
ejpam-5339	93	11	-	-	ADJ
ejpam-5339	93	12	linear	linear	ADJ
ejpam-5339	93	13	ode	ode	PROPN
ejpam-5339	93	14	,	,	PUNCT
ejpam-5339	93	15	up	up	ADP
ejpam-5339	93	16	to	to	ADP
ejpam-5339	93	17	the	the	DET
ejpam-5339	93	18	third	third	ADJ
ejpam-5339	93	19	order	order	NOUN
ejpam-5339	93	20	,	,	PUNCT
ejpam-5339	93	21	of	of	ADP
ejpam-5339	93	22	the	the	DET
ejpam-5339	93	23	form	form	NOUN
ejpam-5339	93	24	:	:	PUNCT
ejpam-5339	93	25	η′′	η′′	PROPN
ejpam-5339	93	26	+	+	CCONJ
ejpam-5339	93	27	f	f	PROPN
ejpam-5339	93	28	(	(	PUNCT
ejpam-5339	93	29	η	η	PROPN
ejpam-5339	93	30	,	,	PUNCT
ejpam-5339	93	31	η′	η′	NOUN
ejpam-5339	93	32	,	,	PUNCT
ejpam-5339	93	33	η′′	η′′	PROPN
ejpam-5339	93	34	)	)	PUNCT
ejpam-5339	94	1	+	+	ADV
ejpam-5339	94	2	g(η	g(η	PROPN
ejpam-5339	94	3	,	,	PUNCT
ejpam-5339	94	4	η′	η′	NOUN
ejpam-5339	94	5	,	,	PUNCT
ejpam-5339	94	6	η′′	η′′	NOUN
ejpam-5339	94	7	)	)	PUNCT
ejpam-5339	94	8	=	=	SYM
ejpam-5339	94	9	h(η	h(η	PROPN
ejpam-5339	94	10	,	,	PUNCT
ejpam-5339	94	11	η′	η′	NOUN
ejpam-5339	94	12	,	,	PUNCT
ejpam-5339	94	13	η′′	η′′	PROPN
ejpam-5339	94	14	)	)	PUNCT
ejpam-5339	94	15	,	,	PUNCT
ejpam-5339	94	16	(	(	PUNCT
ejpam-5339	94	17	1	1	X
ejpam-5339	94	18	)	)	PUNCT
ejpam-5339	94	19	where	where	SCONJ
ejpam-5339	94	20	both	both	DET
ejpam-5339	94	21	f	f	PROPN
ejpam-5339	94	22	(	(	PUNCT
ejpam-5339	94	23	η	η	PROPN
ejpam-5339	94	24	,	,	PUNCT
ejpam-5339	94	25	η′	η′	NOUN
ejpam-5339	94	26	,	,	PUNCT
ejpam-5339	94	27	η′′	η′′	NOUN
ejpam-5339	94	28	)	)	PUNCT
ejpam-5339	94	29	and	and	CCONJ
ejpam-5339	94	30	g(η	g(η	PROPN
ejpam-5339	94	31	,	,	PUNCT
ejpam-5339	94	32	η′	η′	PROPN
ejpam-5339	94	33	,	,	PUNCT
ejpam-5339	94	34	η′′	η′′	NOUN
ejpam-5339	94	35	)	)	PUNCT
ejpam-5339	94	36	are	be	AUX
ejpam-5339	94	37	functions	function	NOUN
ejpam-5339	94	38	of	of	ADP
ejpam-5339	94	39	the	the	DET
ejpam-5339	94	40	third	third	ADJ
ejpam-5339	94	41	order	order	NOUN
ejpam-5339	94	42	.	.	PUNCT
ejpam-5339	95	1	simultaneously	simultaneously	ADV
ejpam-5339	95	2	,	,	PUNCT
ejpam-5339	95	3	h(η	h(η	ADV
ejpam-5339	95	4	,	,	PUNCT
ejpam-5339	95	5	η′	η′	NOUN
ejpam-5339	95	6	,	,	PUNCT
ejpam-5339	95	7	η′′	η′′	PROPN
ejpam-5339	95	8	)	)	PUNCT
ejpam-5339	95	9	is	be	AUX
ejpam-5339	95	10	a	a	DET
ejpam-5339	95	11	quadratic	quadratic	ADJ
ejpam-5339	95	12	function	function	NOUN
ejpam-5339	95	13	.	.	PUNCT
ejpam-5339	96	1	generally	generally	ADV
ejpam-5339	96	2	,	,	PUNCT
ejpam-5339	96	3	these	these	DET
ejpam-5339	96	4	functions	function	NOUN
ejpam-5339	96	5	may	may	AUX
ejpam-5339	96	6	be	be	AUX
ejpam-5339	96	7	represented	represent	VERB
ejpam-5339	96	8	as	as	ADP
ejpam-5339	96	9	:	:	PUNCT
ejpam-5339	96	10	f	f	PROPN
ejpam-5339	96	11	(	(	PUNCT
ejpam-5339	96	12	η	η	PROPN
ejpam-5339	96	13	,	,	PUNCT
ejpam-5339	96	14	η′	η′	NOUN
ejpam-5339	96	15	,	,	PUNCT
ejpam-5339	96	16	η′′	η′′	NOUN
ejpam-5339	96	17	)	)	PUNCT
ejpam-5339	96	18	=	=	PUNCT
ejpam-5339	97	1	a1η	a1η	PROPN
ejpam-5339	97	2	′	′	NUM
ejpam-5339	98	1	+	+	NUM
ejpam-5339	98	2	b1ηη	b1ηη	X
ejpam-5339	98	3	′η′′	′η′′	NOUN
ejpam-5339	98	4	+	+	CCONJ
ejpam-5339	98	5	c1η	c1η	NOUN
ejpam-5339	98	6	2η′′	2η′′	NUM
ejpam-5339	98	7	+	+	CCONJ
ejpam-5339	98	8	d1η	d1η	X
ejpam-5339	98	9	′3	′3	NOUN
ejpam-5339	98	10	+	+	CCONJ
ejpam-5339	98	11	e1η	e1η	PROPN
ejpam-5339	98	12	′′η′	′′η′	PROPN
ejpam-5339	98	13	2	2	NUM
ejpam-5339	98	14	g(η	g(η	VERB
ejpam-5339	98	15	,	,	PUNCT
ejpam-5339	98	16	η′	η′	NOUN
ejpam-5339	98	17	,	,	PUNCT
ejpam-5339	98	18	η′′	η′′	NOUN
ejpam-5339	98	19	)	)	PUNCT
ejpam-5339	98	20	=	=	SYM
ejpam-5339	99	1	ω2η	ω2η	PROPN
ejpam-5339	99	2	+	+	CCONJ
ejpam-5339	99	3	b2η	b2η	NOUN
ejpam-5339	99	4	2η′	2η′	NUM
ejpam-5339	100	1	+	+	CCONJ
ejpam-5339	100	2	c2ηη	c2ηη	X
ejpam-5339	100	3	′2	′2	X
ejpam-5339	100	4	+	+	CCONJ
ejpam-5339	100	5	d2η	d2η	VERB
ejpam-5339	100	6	3	3	NUM
ejpam-5339	100	7	+	+	CCONJ
ejpam-5339	100	8	e2η	e2η	ADJ
ejpam-5339	100	9	′′η	′′η	NOUN
ejpam-5339	100	10	2	2	NUM
ejpam-5339	100	11	h(η	h(η	NOUN
ejpam-5339	100	12	,	,	PUNCT
ejpam-5339	100	13	η′	η′	NOUN
ejpam-5339	100	14	,	,	PUNCT
ejpam-5339	100	15	η′′	η′′	NOUN
ejpam-5339	100	16	)	)	PUNCT
ejpam-5339	100	17	=	=	X
ejpam-5339	100	18	a3ηη	a3ηη	PUNCT
ejpam-5339	101	1	′	′	NOUN
ejpam-5339	102	1	+	+	CCONJ
ejpam-5339	102	2	b3η	b3η	NOUN
ejpam-5339	102	3	′2	′2	NOUN
ejpam-5339	102	4	+	+	CCONJ
ejpam-5339	102	5	c3η	c3η	ADP
ejpam-5339	102	6	2	2	NUM
ejpam-5339	102	7	+	+	NUM
ejpam-5339	102	8	d3η	d3η	NOUN
ejpam-5339	102	9	′η′′	′η′′	NOUN
ejpam-5339	102	10	+	+	CCONJ
ejpam-5339	102	11	e3ηη	e3ηη	PUNCT
ejpam-5339	103	1	′′	′′	PROPN
ejpam-5339	103	2			NOUN
ejpam-5339	103	3	,	,	PUNCT
ejpam-5339	103	4	(	(	PUNCT
ejpam-5339	103	5	2	2	X
ejpam-5339	103	6	)	)	PUNCT
ejpam-5339	103	7	where	where	SCONJ
ejpam-5339	103	8	aj	aj	PROPN
ejpam-5339	103	9	,	,	PUNCT
ejpam-5339	103	10	bj	bj	VERB
ejpam-5339	103	11	,	,	PUNCT
ejpam-5339	103	12	cj	cj	INTJ
ejpam-5339	103	13	,	,	PUNCT
ejpam-5339	103	14	dj	dj	X
ejpam-5339	103	15	,	,	PUNCT
ejpam-5339	103	16	ej	ej	X
ejpam-5339	103	17	(	(	PUNCT
ejpam-5339	103	18	j	j	NOUN
ejpam-5339	103	19	=	=	SYM
ejpam-5339	103	20	1	1	NUM
ejpam-5339	103	21	,	,	PUNCT
ejpam-5339	103	22	2	2	NUM
ejpam-5339	103	23	,	,	PUNCT
ejpam-5339	103	24	3	3	NUM
ejpam-5339	103	25	)	)	PUNCT
ejpam-5339	103	26	are	be	AUX
ejpam-5339	103	27	constant	constant	ADJ
ejpam-5339	103	28	coefficients	coefficient	NOUN
ejpam-5339	103	29	,	,	PUNCT
ejpam-5339	103	30	and	and	CCONJ
ejpam-5339	103	31	ω	ω	NOUN
ejpam-5339	103	32	represents	represent	VERB
ejpam-5339	103	33	the	the	DET
ejpam-5339	103	34	natural	natural	ADJ
ejpam-5339	103	35	frequency	frequency	NOUN
ejpam-5339	103	36	of	of	ADP
ejpam-5339	103	37	the	the	DET
ejpam-5339	103	38	given	give	VERB
ejpam-5339	103	39	structure	structure	NOUN
ejpam-5339	103	40	.	.	PUNCT
ejpam-5339	104	1	as	as	SCONJ
ejpam-5339	104	2	previously	previously	ADV
ejpam-5339	104	3	demonstrated	demonstrate	VERB
ejpam-5339	104	4	throughout	throughout	ADP
ejpam-5339	104	5	the	the	DET
ejpam-5339	104	6	conventional	conventional	ADJ
ejpam-5339	104	7	perturbation	perturbation	NOUN
ejpam-5339	104	8	techniques	technique	NOUN
ejpam-5339	104	9	[	[	X
ejpam-5339	104	10	37	37	NUM
ejpam-5339	104	11	]	]	PUNCT
ejpam-5339	104	12	,	,	PUNCT
ejpam-5339	104	13	the	the	DET
ejpam-5339	104	14	first	first	ADJ
ejpam-5339	104	15	two	two	NUM
ejpam-5339	104	16	functions	function	NOUN
ejpam-5339	104	17	yield	yield	VERB
ejpam-5339	104	18	secular	secular	ADJ
ejpam-5339	104	19	terms	term	NOUN
ejpam-5339	104	20	,	,	PUNCT
ejpam-5339	104	21	but	but	CCONJ
ejpam-5339	104	22	the	the	DET
ejpam-5339	104	23	third	third	ADJ
ejpam-5339	104	24	function	function	NOUN
ejpam-5339	104	25	does	do	AUX
ejpam-5339	104	26	not	not	PART
ejpam-5339	104	27	generate	generate	VERB
ejpam-5339	104	28	secular	secular	ADJ
ejpam-5339	104	29	terms	term	NOUN
ejpam-5339	104	30	.	.	PUNCT
ejpam-5339	105	1	now	now	ADV
ejpam-5339	105	2	,	,	PUNCT
ejpam-5339	105	3	as	as	ADV
ejpam-5339	105	4	well	well	ADV
ejpam-5339	105	5	-	-	PUNCT
ejpam-5339	105	6	known	know	VERB
ejpam-5339	105	7	,	,	PUNCT
ejpam-5339	105	8	the	the	DET
ejpam-5339	105	9	npa	npa	NOUN
ejpam-5339	105	10	aims	aim	VERB
ejpam-5339	105	11	mainly	mainly	ADV
ejpam-5339	105	12	to	to	ADP
ejpam-5339	105	13	obtaining	obtain	VERB
ejpam-5339	105	14	an	an	DET
ejpam-5339	105	15	alternative	alternative	ADJ
ejpam-5339	105	16	linear	linear	ADJ
ejpam-5339	105	17	ode	ode	PROPN
ejpam-5339	105	18	.	.	PUNCT
ejpam-5339	106	1	three	three	NUM
ejpam-5339	106	2	constants	constant	NOUN
ejpam-5339	106	3	will	will	AUX
ejpam-5339	106	4	be	be	AUX
ejpam-5339	106	5	established	establish	VERB
ejpam-5339	106	6	in	in	ADP
ejpam-5339	106	7	order	order	NOUN
ejpam-5339	106	8	to	to	PART
ejpam-5339	106	9	create	create	VERB
ejpam-5339	106	10	the	the	DET
ejpam-5339	106	11	necessary	necessary	ADJ
ejpam-5339	106	12	linear	linear	ADJ
ejpam-5339	106	13	differential	differential	NOUN
ejpam-5339	106	14	equation	equation	NOUN
ejpam-5339	106	15	for	for	ADP
ejpam-5339	106	16	this	this	DET
ejpam-5339	106	17	objective	objective	NOUN
ejpam-5339	106	18	.	.	PUNCT
ejpam-5339	107	1	it	it	PRON
ejpam-5339	107	2	should	should	AUX
ejpam-5339	107	3	be	be	AUX
ejpam-5339	107	4	noted	note	VERB
ejpam-5339	107	5	that	that	SCONJ
ejpam-5339	107	6	the	the	DET
ejpam-5339	107	7	intention	intention	NOUN
ejpam-5339	107	8	in	in	ADP
ejpam-5339	107	9	generating	generate	VERB
ejpam-5339	107	10	the	the	DET
ejpam-5339	107	11	linear	linear	ADJ
ejpam-5339	107	12	ode	ode	NOUN
ejpam-5339	107	13	is	be	AUX
ejpam-5339	107	14	to	to	PART
ejpam-5339	107	15	behave	behave	VERB
ejpam-5339	107	16	similar	similar	ADJ
ejpam-5339	107	17	to	to	ADP
ejpam-5339	107	18	the	the	DET
ejpam-5339	107	19	simple	simple	ADJ
ejpam-5339	107	20	harmonic	harmonic	ADJ
ejpam-5339	107	21	motion	motion	NOUN
ejpam-5339	107	22	.	.	PUNCT
ejpam-5339	108	1	to	to	PART
ejpam-5339	108	2	accomplish	accomplish	VERB
ejpam-5339	108	3	this	this	DET
ejpam-5339	108	4	aim	aim	NOUN
ejpam-5339	108	5	,	,	PUNCT
ejpam-5339	108	6	following	follow	VERB
ejpam-5339	108	7	he	he	PRON
ejpam-5339	109	1	[	[	X
ejpam-5339	109	2	4	4	NUM
ejpam-5339	109	3	]	]	PUNCT
ejpam-5339	109	4	,	,	PUNCT
ejpam-5339	109	5	where	where	SCONJ
ejpam-5339	109	6	a	a	DET
ejpam-5339	109	7	guessing	guess	VERB
ejpam-5339	109	8	solution	solution	NOUN
ejpam-5339	109	9	of	of	ADP
ejpam-5339	109	10	the	the	DET
ejpam-5339	109	11	given	give	VERB
ejpam-5339	109	12	nonlinear	nonlinear	ADJ
ejpam-5339	109	13	ode	ode	NOUN
ejpam-5339	109	14	in	in	ADP
ejpam-5339	109	15	the	the	DET
ejpam-5339	109	16	form	form	NOUN
ejpam-5339	109	17	:	:	PUNCT
ejpam-5339	109	18	x	x	X
ejpam-5339	109	19	=	=	PUNCT
ejpam-5339	109	20	a	a	DET
ejpam-5339	109	21	cosωt	cosωt	NOUN
ejpam-5339	109	22	,	,	PUNCT
ejpam-5339	109	23	(	(	PUNCT
ejpam-5339	109	24	3	3	X
ejpam-5339	109	25	)	)	PUNCT
ejpam-5339	109	26	the	the	DET
ejpam-5339	109	27	initial	initial	ADJ
ejpam-5339	109	28	conditions	condition	NOUN
ejpam-5339	109	29	(	(	PUNCT
ejpam-5339	109	30	ics	ics	NOUN
ejpam-5339	109	31	)	)	PUNCT
ejpam-5339	109	32	are	be	AUX
ejpam-5339	109	33	given	give	VERB
ejpam-5339	109	34	as	as	ADP
ejpam-5339	109	35	:	:	PUNCT
ejpam-5339	109	36	x(0	x(0	PROPN
ejpam-5339	109	37	)	)	PUNCT
ejpam-5339	109	38	=	=	SYM
ejpam-5339	110	1	a	a	PRON
ejpam-5339	110	2	,	,	PUNCT
ejpam-5339	110	3	and	and	CCONJ
ejpam-5339	110	4	x′(0	x′(0	PROPN
ejpam-5339	110	5	)	)	PUNCT
ejpam-5339	110	6	=	=	SYM
ejpam-5339	110	7	0	0	X
ejpam-5339	110	8	.	.	PUNCT
ejpam-5339	110	9	g.	g.	PROPN
ejpam-5339	110	10	m.	m.	PROPN
ejpam-5339	110	11	ismail	ismail	PROPN
ejpam-5339	110	12	,	,	PUNCT
ejpam-5339	110	13	g.	g.	PROPN
ejpam-5339	110	14	m.	m.	PROPN
ejpam-5339	110	15	moatimid	moatimid	PROPN
ejpam-5339	110	16	,	,	PUNCT
ejpam-5339	110	17	m.	m.	NOUN
ejpam-5339	110	18	i.	i.	PROPN
ejpam-5339	110	19	yamani	yamani	PROPN
ejpam-5339	110	20	/	/	SYM
ejpam-5339	110	21	eur	eur	PROPN
ejpam-5339	110	22	.	.	PUNCT
ejpam-5339	111	1	j.	j.	PROPN
ejpam-5339	111	2	pure	pure	PROPN
ejpam-5339	111	3	appl	appl	PROPN
ejpam-5339	111	4	.	.	PROPN
ejpam-5339	111	5	math	math	PROPN
ejpam-5339	111	6	,	,	PUNCT
ejpam-5339	111	7	17	17	NUM
ejpam-5339	111	8	(	(	PUNCT
ejpam-5339	111	9	3	3	NUM
ejpam-5339	111	10	)	)	PUNCT
ejpam-5339	111	11	(	(	PUNCT
ejpam-5339	111	12	2024	2024	NUM
ejpam-5339	111	13	)	)	PUNCT
ejpam-5339	111	14	,	,	PUNCT
ejpam-5339	111	15	2155	2155	NUM
ejpam-5339	111	16	-	-	SYM
ejpam-5339	111	17	2172	2172	NUM
ejpam-5339	111	18	2159	2159	NUM
ejpam-5339	111	19	the	the	DET
ejpam-5339	111	20	parameter	parameter	PROPN
ejpam-5339	111	21	ω	ω	PROPN
ejpam-5339	111	22	represents	represent	VERB
ejpam-5339	111	23	the	the	DET
ejpam-5339	111	24	overall	overall	ADJ
ejpam-5339	111	25	frequency	frequency	NOUN
ejpam-5339	111	26	,	,	PUNCT
ejpam-5339	111	27	which	which	PRON
ejpam-5339	111	28	will	will	AUX
ejpam-5339	111	29	be	be	AUX
ejpam-5339	111	30	specified	specify	VERB
ejpam-5339	111	31	at	at	ADP
ejpam-5339	111	32	a	a	DET
ejpam-5339	111	33	later	later	ADJ
ejpam-5339	111	34	time	time	NOUN
ejpam-5339	111	35	.	.	PUNCT
ejpam-5339	112	1	the	the	DET
ejpam-5339	112	2	required	require	VERB
ejpam-5339	112	3	linear	linear	PROPN
ejpam-5339	112	4	differential	differential	NOUN
ejpam-5339	112	5	equation	equation	NOUN
ejpam-5339	112	6	may	may	AUX
ejpam-5339	112	7	be	be	AUX
ejpam-5339	112	8	expressed	express	VERB
ejpam-5339	112	9	as	as	ADP
ejpam-5339	112	10	:	:	PUNCT
ejpam-5339	112	11	x′′	x′′	PROPN
ejpam-5339	112	12	+	+	CCONJ
ejpam-5339	113	1	σeqvx	σeqvx	ADJ
ejpam-5339	113	2	′	′	NOUN
ejpam-5339	114	1	+	+	CCONJ
ejpam-5339	114	2	ω2	ω2	ADJ
ejpam-5339	114	3	eqvx	eqvx	NOUN
ejpam-5339	115	1	=	=	SYM
ejpam-5339	115	2	λ	λ	PROPN
ejpam-5339	115	3	,	,	PUNCT
ejpam-5339	115	4	(	(	PUNCT
ejpam-5339	115	5	4	4	NUM
ejpam-5339	115	6	)	)	PUNCT
ejpam-5339	115	7	as	as	SCONJ
ejpam-5339	115	8	previously	previously	ADV
ejpam-5339	115	9	shown	show	VERB
ejpam-5339	115	10	[	[	PUNCT
ejpam-5339	115	11	1	1	NUM
ejpam-5339	115	12	]	]	PUNCT
ejpam-5339	115	13	,	,	PUNCT
ejpam-5339	115	14	the	the	DET
ejpam-5339	115	15	above	above	ADJ
ejpam-5339	115	16	three	three	NUM
ejpam-5339	115	17	parameters	parameter	NOUN
ejpam-5339	115	18	may	may	AUX
ejpam-5339	115	19	be	be	AUX
ejpam-5339	115	20	evaluated	evaluate	VERB
ejpam-5339	115	21	as	as	SCONJ
ejpam-5339	115	22	follows	follow	VERB
ejpam-5339	115	23	:	:	PUNCT
ejpam-5339	115	24	σeqv	σeqv	NOUN
ejpam-5339	115	25	=	=	SYM
ejpam-5339	115	26	2π	2π	NOUN
ejpam-5339	115	27	/	/	SYM
ejpam-5339	116	1	ω∫	ω∫	NOUN
ejpam-5339	116	2	0	0	NUM
ejpam-5339	116	3	x′f	x′f	NOUN
ejpam-5339	116	4	(	(	PUNCT
ejpam-5339	116	5	x	x	X
ejpam-5339	116	6	,	,	PUNCT
ejpam-5339	116	7	x′	x′	PROPN
ejpam-5339	116	8	,	,	PUNCT
ejpam-5339	116	9	x′′	x′′	PROPN
ejpam-5339	116	10	)	)	PUNCT
ejpam-5339	116	11	dt/	dt/	VERB
ejpam-5339	116	12	2π	2π	NOUN
ejpam-5339	116	13	/	/	SYM
ejpam-5339	116	14	ω∫	ω∫	NOUN
ejpam-5339	116	15	0	0	NUM
ejpam-5339	116	16	x′2dt	x′2dt	NOUN
ejpam-5339	117	1	=	=	SYM
ejpam-5339	117	2	σeqv(ω	σeqv(ω	PROPN
ejpam-5339	117	3	)	)	PUNCT
ejpam-5339	117	4	.	.	PUNCT
ejpam-5339	118	1	(	(	PUNCT
ejpam-5339	118	2	5	5	X
ejpam-5339	118	3	)	)	PUNCT
ejpam-5339	118	4	consider	consider	VERB
ejpam-5339	118	5	a	a	DET
ejpam-5339	118	6	comparable	comparable	ADJ
ejpam-5339	118	7	frequency	frequency	NOUN
ejpam-5339	118	8	ω2	ω2	ADJ
ejpam-5339	118	9	eqv	eqv	NOUN
ejpam-5339	118	10	,	,	PUNCT
ejpam-5339	118	11	which	which	PRON
ejpam-5339	118	12	can	can	AUX
ejpam-5339	118	13	be	be	AUX
ejpam-5339	118	14	calculated	calculate	VERB
ejpam-5339	118	15	using	use	VERB
ejpam-5339	118	16	the	the	DET
ejpam-5339	118	17	total	total	ADJ
ejpam-5339	118	18	frequency	frequency	NOUN
ejpam-5339	118	19	according	accord	VERB
ejpam-5339	118	20	to	to	ADP
ejpam-5339	118	21	the	the	DET
ejpam-5339	118	22	following	follow	VERB
ejpam-5339	118	23	function	function	NOUN
ejpam-5339	118	24	:	:	PUNCT
ejpam-5339	118	25	ω2	ω2	ADJ
ejpam-5339	118	26	eqv	eqv	NOUN
ejpam-5339	118	27	=	=	PUNCT
ejpam-5339	118	28	2π	2π	NOUN
ejpam-5339	118	29	/	/	SYM
ejpam-5339	118	30	ω∫	ω∫	NOUN
ejpam-5339	118	31	0	0	NUM
ejpam-5339	118	32	x	x	SYM
ejpam-5339	118	33	g	g	PROPN
ejpam-5339	118	34	(	(	PUNCT
ejpam-5339	118	35	x	x	PROPN
ejpam-5339	118	36	,	,	PUNCT
ejpam-5339	118	37	x′	x′	PROPN
ejpam-5339	118	38	,	,	PUNCT
ejpam-5339	118	39	x′′	x′′	PROPN
ejpam-5339	118	40	)	)	PUNCT
ejpam-5339	118	41	dt/	dt/	VERB
ejpam-5339	118	42	2π	2π	NOUN
ejpam-5339	118	43	/	/	SYM
ejpam-5339	118	44	ω∫	ω∫	NOUN
ejpam-5339	118	45	0	0	NUM
ejpam-5339	118	46	x2dt	x2dt	PUNCT
ejpam-5339	119	1	=	=	PUNCT
ejpam-5339	120	1	ω2	ω2	NUM
ejpam-5339	120	2	eqv(ω	eqv(ω	NUM
ejpam-5339	120	3	)	)	PUNCT
ejpam-5339	120	4	.	.	PUNCT
ejpam-5339	121	1	(	(	PUNCT
ejpam-5339	121	2	6	6	X
ejpam-5339	121	3	)	)	PUNCT
ejpam-5339	121	4	it	it	PRON
ejpam-5339	121	5	should	should	AUX
ejpam-5339	121	6	be	be	AUX
ejpam-5339	121	7	understood	understand	VERB
ejpam-5339	121	8	that	that	SCONJ
ejpam-5339	121	9	the	the	DET
ejpam-5339	121	10	non	non	ADJ
ejpam-5339	121	11	-	-	ADJ
ejpam-5339	121	12	secular	secular	ADJ
ejpam-5339	121	13	portion	portion	NOUN
ejpam-5339	121	14	includes	include	VERB
ejpam-5339	121	15	the	the	DET
ejpam-5339	121	16	quadratic	quadratic	ADJ
ejpam-5339	121	17	formula	formula	NOUN
ejpam-5339	121	18	.	.	PUNCT
ejpam-5339	122	1	therefore	therefore	ADV
ejpam-5339	122	2	,	,	PUNCT
ejpam-5339	122	3	the	the	DET
ejpam-5339	122	4	inhomogeneity	inhomogeneity	NOUN
ejpam-5339	122	5	will	will	AUX
ejpam-5339	122	6	be	be	AUX
ejpam-5339	122	7	computed	compute	VERB
ejpam-5339	122	8	by	by	ADP
ejpam-5339	122	9	replacing	replace	VERB
ejpam-5339	122	10	:	:	PUNCT
ejpam-5339	122	11	η	η	PROPN
ejpam-5339	122	12	→	→	SYM
ejpam-5339	122	13	ka	ka	PROPN
ejpam-5339	122	14	,	,	PUNCT
ejpam-5339	122	15	η′	η′	PROPN
ejpam-5339	122	16	→	→	SYM
ejpam-5339	122	17	kaω	kaω	PROPN
ejpam-5339	122	18	,	,	PUNCT
ejpam-5339	122	19	and	and	CCONJ
ejpam-5339	122	20	η′′	η′′	PROPN
ejpam-5339	122	21	→	→	SYM
ejpam-5339	122	22	kaω2	kaω2	PROPN
ejpam-5339	122	23	in	in	ADP
ejpam-5339	122	24	the	the	DET
ejpam-5339	122	25	even	even	ADJ
ejpam-5339	122	26	non	non	ADJ
ejpam-5339	122	27	-	-	ADJ
ejpam-5339	122	28	secular	secular	ADJ
ejpam-5339	122	29	function	function	NOUN
ejpam-5339	122	30	h	h	NOUN
ejpam-5339	122	31	(	(	PUNCT
ejpam-5339	122	32	η	η	PROPN
ejpam-5339	122	33	,	,	PUNCT
ejpam-5339	122	34	η′	η′	NOUN
ejpam-5339	122	35	,	,	PUNCT
ejpam-5339	122	36	η′′	η′′	PROPN
ejpam-5339	122	37	)	)	PUNCT
ejpam-5339	122	38	.	.	PUNCT
ejpam-5339	123	1	as	as	SCONJ
ejpam-5339	123	2	shown	show	VERB
ejpam-5339	123	3	by	by	ADP
ejpam-5339	123	4	el	el	PROPN
ejpam-5339	123	5	-	-	PROPN
ejpam-5339	123	6	dib	dib	PROPN
ejpam-5339	123	7	[	[	X
ejpam-5339	123	8	1	1	NUM
ejpam-5339	123	9	]	]	PUNCT
ejpam-5339	123	10	,	,	PUNCT
ejpam-5339	123	11	the	the	DET
ejpam-5339	123	12	parameter	parameter	NOUN
ejpam-5339	123	13	k	k	PROPN
ejpam-5339	123	14	is	be	AUX
ejpam-5339	123	15	defined	define	VERB
ejpam-5339	123	16	as	as	ADP
ejpam-5339	123	17	k	k	PROPN
ejpam-5339	123	18	=	=	PROPN
ejpam-5339	123	19	1/2	1/2	NUM
ejpam-5339	123	20	√	√	NUM
ejpam-5339	123	21	n−	n−	PROPN
ejpam-5339	123	22	r	r	NOUN
ejpam-5339	123	23	,	,	PUNCT
ejpam-5339	123	24	where	where	SCONJ
ejpam-5339	123	25	n	n	PRON
ejpam-5339	123	26	indicates	indicate	VERB
ejpam-5339	123	27	the	the	DET
ejpam-5339	123	28	order	order	NOUN
ejpam-5339	123	29	of	of	ADP
ejpam-5339	123	30	the	the	DET
ejpam-5339	123	31	system	system	NOUN
ejpam-5339	123	32	and	and	CCONJ
ejpam-5339	123	33	r	r	NOUN
ejpam-5339	123	34	signifies	signify	VERB
ejpam-5339	123	35	the	the	DET
ejpam-5339	123	36	degree	degree	NOUN
ejpam-5339	123	37	of	of	ADP
ejpam-5339	123	38	freedom	freedom	NOUN
ejpam-5339	123	39	of	of	ADP
ejpam-5339	123	40	the	the	DET
ejpam-5339	123	41	system	system	NOUN
ejpam-5339	123	42	.	.	PUNCT
ejpam-5339	124	1	therefore	therefore	ADV
ejpam-5339	124	2	,	,	PUNCT
ejpam-5339	124	3	in	in	ADP
ejpam-5339	124	4	the	the	DET
ejpam-5339	124	5	present	present	ADJ
ejpam-5339	124	6	case	case	NOUN
ejpam-5339	124	7	,	,	PUNCT
ejpam-5339	124	8	one	one	PRON
ejpam-5339	124	9	gets	get	VERB
ejpam-5339	124	10	n	n	NOUN
ejpam-5339	124	11	=	=	SYM
ejpam-5339	124	12	2	2	NUM
ejpam-5339	124	13	and	and	CCONJ
ejpam-5339	124	14	,	,	PUNCT
ejpam-5339	124	15	r	r	NOUN
ejpam-5339	124	16	=	=	NOUN
ejpam-5339	124	17	1	1	NUM
ejpam-5339	124	18	then	then	ADV
ejpam-5339	124	19	the	the	DET
ejpam-5339	124	20	value	value	NOUN
ejpam-5339	124	21	of	of	ADP
ejpam-5339	124	22	k	k	PROPN
ejpam-5339	124	23	becomes	become	VERB
ejpam-5339	124	24	k	k	NOUN
ejpam-5339	124	25	=	=	SYM
ejpam-5339	124	26	1/2	1/2	NUM
ejpam-5339	124	27	.	.	PUNCT
ejpam-5339	125	1	it	it	PRON
ejpam-5339	125	2	follows	follow	VERB
ejpam-5339	125	3	that	that	SCONJ
ejpam-5339	125	4	the	the	DET
ejpam-5339	125	5	value	value	NOUN
ejpam-5339	125	6	of	of	ADP
ejpam-5339	125	7	the	the	DET
ejpam-5339	125	8	quadratic	quadratic	ADJ
ejpam-5339	125	9	(	(	PUNCT
ejpam-5339	125	10	non	non	ADJ
ejpam-5339	125	11	-	-	ADJ
ejpam-5339	125	12	secular	secular	ADJ
ejpam-5339	125	13	term	term	NOUN
ejpam-5339	125	14	)	)	PUNCT
ejpam-5339	125	15	.	.	PUNCT
ejpam-5339	126	1	consequently	consequently	ADV
ejpam-5339	126	2	,	,	PUNCT
ejpam-5339	126	3	the	the	DET
ejpam-5339	126	4	inhomogeneity	inhomogeneity	NOUN
ejpam-5339	126	5	part	part	NOUN
ejpam-5339	126	6	will	will	AUX
ejpam-5339	126	7	be	be	AUX
ejpam-5339	126	8	computed	compute	VERB
ejpam-5339	126	9	by	by	ADP
ejpam-5339	126	10	replacing	replace	VERB
ejpam-5339	126	11	:	:	PUNCT
ejpam-5339	126	12	η	η	PROPN
ejpam-5339	126	13	→	→	PROPN
ejpam-5339	126	14	a	a	DET
ejpam-5339	126	15	2	2	NUM
ejpam-5339	126	16	,	,	PUNCT
ejpam-5339	126	17	η′	η′	PROPN
ejpam-5339	126	18	→	→	SYM
ejpam-5339	126	19	aω	aω	PROPN
ejpam-5339	126	20	2	2	NUM
ejpam-5339	126	21	,	,	PUNCT
ejpam-5339	126	22	and	and	CCONJ
ejpam-5339	126	23	η′′	η′′	PROPN
ejpam-5339	126	24	→	→	SYM
ejpam-5339	126	25	aω2	aω2	PROPN
ejpam-5339	126	26	2	2	NUM
ejpam-5339	126	27	.	.	PUNCT
ejpam-5339	127	1	for	for	ADP
ejpam-5339	127	2	simplicity	simplicity	NOUN
ejpam-5339	127	3	,	,	PUNCT
ejpam-5339	127	4	eq	eq	NOUN
ejpam-5339	127	5	.	.	PUNCT
ejpam-5339	128	1	(	(	PUNCT
ejpam-5339	128	2	4	4	X
ejpam-5339	128	3	)	)	PUNCT
ejpam-5339	128	4	can	can	AUX
ejpam-5339	128	5	be	be	AUX
ejpam-5339	128	6	stated	state	VERB
ejpam-5339	128	7	in	in	ADP
ejpam-5339	128	8	the	the	DET
ejpam-5339	128	9	ordinary	ordinary	ADJ
ejpam-5339	128	10	normal	normal	ADJ
ejpam-5339	128	11	form	form	NOUN
ejpam-5339	128	12	using	use	VERB
ejpam-5339	128	13	the	the	DET
ejpam-5339	128	14	following	follow	VERB
ejpam-5339	128	15	substitution	substitution	NOUN
ejpam-5339	128	16	:	:	PUNCT
ejpam-5339	128	17	x(t	x(t	PROPN
ejpam-5339	128	18	)	)	PUNCT
ejpam-5339	129	1	=	=	SYM
ejpam-5339	129	2	f(t)exp	f(t)exp	NOUN
ejpam-5339	129	3	(	(	PUNCT
ejpam-5339	129	4	−σeqvt/2	−σeqvt/2	PROPN
ejpam-5339	129	5	)	)	PUNCT
ejpam-5339	129	6	.	.	PUNCT
ejpam-5339	130	1	(	(	PUNCT
ejpam-5339	130	2	7	7	X
ejpam-5339	130	3	)	)	PUNCT
ejpam-5339	130	4	putting	put	VERB
ejpam-5339	130	5	eq	eq	NOUN
ejpam-5339	130	6	.	.	PUNCT
ejpam-5339	131	1	(	(	PUNCT
ejpam-5339	131	2	7	7	NUM
ejpam-5339	131	3	)	)	PUNCT
ejpam-5339	131	4	into	into	ADP
ejpam-5339	131	5	eq	eq	NOUN
ejpam-5339	131	6	.	.	PUNCT
ejpam-5339	132	1	(	(	PUNCT
ejpam-5339	132	2	4	4	X
ejpam-5339	132	3	)	)	PUNCT
ejpam-5339	132	4	yields	yield	NOUN
ejpam-5339	132	5	f	f	PROPN
ejpam-5339	133	1	′′	′′	PROPN
ejpam-5339	133	2	+	+	CCONJ
ejpam-5339	133	3	(	(	PUNCT
ejpam-5339	133	4	ω2	ω2	ADJ
ejpam-5339	133	5	eqv	eqv	NOUN
ejpam-5339	133	6	−	−	PROPN
ejpam-5339	133	7	1	1	NUM
ejpam-5339	133	8	4	4	NUM
ejpam-5339	133	9	σ2	σ2	NOUN
ejpam-5339	133	10	eqv	eqv	NOUN
ejpam-5339	133	11	)	)	PUNCT
ejpam-5339	133	12	f	f	X
ejpam-5339	133	13	=	=	SYM
ejpam-5339	133	14	λ	λ	X
ejpam-5339	133	15	exp	exp	X
ejpam-5339	133	16	(	(	PUNCT
ejpam-5339	133	17	σeqvt/2	σeqvt/2	NOUN
ejpam-5339	133	18	)	)	PUNCT
ejpam-5339	133	19	.	.	PUNCT
ejpam-5339	134	1	(	(	PUNCT
ejpam-5339	134	2	8)	8)	NUM
ejpam-5339	134	3	finally	finally	ADV
ejpam-5339	134	4	,	,	PUNCT
ejpam-5339	134	5	the	the	DET
ejpam-5339	134	6	overall	overall	ADJ
ejpam-5339	134	7	frequency	frequency	NOUN
ejpam-5339	134	8	is	be	AUX
ejpam-5339	134	9	expressed	express	VERB
ejpam-5339	134	10	as	as	ADP
ejpam-5339	134	11	ω2	ω2	ADJ
ejpam-5339	134	12	=	=	SYM
ejpam-5339	134	13	ω2	ω2	ADJ
ejpam-5339	134	14	eqv	eqv	NOUN
ejpam-5339	134	15	−	−	PROPN
ejpam-5339	134	16	1	1	NUM
ejpam-5339	134	17	4σ	4σ	NUM
ejpam-5339	134	18	2	2	NUM
ejpam-5339	134	19	eqv	eqv	NOUN
ejpam-5339	134	20	.	.	PUNCT
ejpam-5339	135	1	3	3	X
ejpam-5339	135	2	.	.	X
ejpam-5339	135	3	applications	application	NOUN
ejpam-5339	135	4	in	in	ADP
ejpam-5339	135	5	this	this	DET
ejpam-5339	135	6	section	section	NOUN
ejpam-5339	135	7	,	,	PUNCT
ejpam-5339	135	8	we	we	PRON
ejpam-5339	135	9	will	will	AUX
ejpam-5339	135	10	test	test	VERB
ejpam-5339	135	11	the	the	DET
ejpam-5339	135	12	validity	validity	NOUN
ejpam-5339	135	13	of	of	ADP
ejpam-5339	135	14	the	the	DET
ejpam-5339	135	15	npa	npa	NOUN
ejpam-5339	135	16	as	as	SCONJ
ejpam-5339	135	17	previously	previously	ADV
ejpam-5339	135	18	indicated	indicate	VERB
ejpam-5339	135	19	to	to	PART
ejpam-5339	135	20	analyze	analyze	VERB
ejpam-5339	135	21	some	some	DET
ejpam-5339	135	22	different	different	ADJ
ejpam-5339	135	23	illustrations	illustration	NOUN
ejpam-5339	135	24	that	that	PRON
ejpam-5339	135	25	characterize	characterize	VERB
ejpam-5339	135	26	some	some	DET
ejpam-5339	135	27	highly	highly	ADV
ejpam-5339	135	28	nonlinear	nonlinear	ADJ
ejpam-5339	135	29	constructions	construction	NOUN
ejpam-5339	135	30	.	.	PUNCT
ejpam-5339	136	1	the	the	DET
ejpam-5339	136	2	physical	physical	ADJ
ejpam-5339	136	3	interpretation	interpretation	NOUN
ejpam-5339	136	4	with	with	ADP
ejpam-5339	136	5	plot	plot	NOUN
ejpam-5339	136	6	structure	structure	NOUN
ejpam-5339	136	7	agrees	agree	VERB
ejpam-5339	136	8	well	well	ADV
ejpam-5339	136	9	with	with	ADP
ejpam-5339	136	10	the	the	DET
ejpam-5339	136	11	proposed	propose	VERB
ejpam-5339	136	12	technique	technique	NOUN
ejpam-5339	136	13	.	.	PUNCT
ejpam-5339	137	1	g.	g.	PROPN
ejpam-5339	137	2	m.	m.	PROPN
ejpam-5339	137	3	ismail	ismail	PROPN
ejpam-5339	137	4	,	,	PUNCT
ejpam-5339	137	5	g.	g.	PROPN
ejpam-5339	137	6	m.	m.	PROPN
ejpam-5339	137	7	moatimid	moatimid	PROPN
ejpam-5339	137	8	,	,	PUNCT
ejpam-5339	137	9	m.	m.	NOUN
ejpam-5339	137	10	i.	i.	PROPN
ejpam-5339	137	11	yamani	yamani	PROPN
ejpam-5339	137	12	/	/	SYM
ejpam-5339	137	13	eur	eur	PROPN
ejpam-5339	137	14	.	.	PUNCT
ejpam-5339	138	1	j.	j.	PROPN
ejpam-5339	138	2	pure	pure	PROPN
ejpam-5339	138	3	appl	appl	PROPN
ejpam-5339	138	4	.	.	PROPN
ejpam-5339	138	5	math	math	PROPN
ejpam-5339	138	6	,	,	PUNCT
ejpam-5339	138	7	17	17	NUM
ejpam-5339	138	8	(	(	PUNCT
ejpam-5339	138	9	3	3	NUM
ejpam-5339	138	10	)	)	PUNCT
ejpam-5339	138	11	(	(	PUNCT
ejpam-5339	138	12	2024	2024	NUM
ejpam-5339	138	13	)	)	PUNCT
ejpam-5339	138	14	,	,	PUNCT
ejpam-5339	138	15	2155	2155	NUM
ejpam-5339	138	16	-	-	SYM
ejpam-5339	138	17	2172	2172	NUM
ejpam-5339	138	18	2160	2160	NUM
ejpam-5339	138	19	3.1	3.1	NUM
ejpam-5339	138	20	.	.	PUNCT
ejpam-5339	139	1	application	application	NOUN
ejpam-5339	139	2	1	1	NUM
ejpam-5339	139	3	consider	consider	VERB
ejpam-5339	139	4	the	the	DET
ejpam-5339	139	5	motion	motion	NOUN
ejpam-5339	139	6	of	of	ADP
ejpam-5339	139	7	a	a	DET
ejpam-5339	139	8	particle	particle	NOUN
ejpam-5339	139	9	of	of	ADP
ejpam-5339	139	10	mass	mass	NOUN
ejpam-5339	139	11	m	m	AUX
ejpam-5339	139	12	moving	move	VERB
ejpam-5339	139	13	without	without	ADP
ejpam-5339	139	14	friction	friction	NOUN
ejpam-5339	139	15	along	along	ADP
ejpam-5339	139	16	a	a	DET
ejpam-5339	139	17	circle	circle	NOUN
ejpam-5339	139	18	of	of	ADP
ejpam-5339	139	19	radius	radius	NOUN
ejpam-5339	139	20	r	r	NOUN
ejpam-5339	139	21	and	and	CCONJ
ejpam-5339	139	22	center	center	NOUN
ejpam-5339	139	23	,	,	PUNCT
ejpam-5339	139	24	which	which	PRON
ejpam-5339	139	25	is	be	AUX
ejpam-5339	139	26	located	locate	VERB
ejpam-5339	139	27	at	at	ADP
ejpam-5339	139	28	the	the	DET
ejpam-5339	139	29	origin	origin	NOUN
ejpam-5339	139	30	0	0	PUNCT
ejpam-5339	139	31	and	and	CCONJ
ejpam-5339	139	32	rotating	rotate	VERB
ejpam-5339	139	33	with	with	ADP
ejpam-5339	139	34	uniform	uniform	ADJ
ejpam-5339	139	35	angular	angular	ADJ
ejpam-5339	139	36	velocity	velocity	NOUN
ejpam-5339	139	37	ω	ω	PROPN
ejpam-5339	139	38	about	about	ADP
ejpam-5339	139	39	its	its	PRON
ejpam-5339	139	40	vertical	vertical	ADJ
ejpam-5339	139	41	diameter	diameter	NOUN
ejpam-5339	140	1	[	[	X
ejpam-5339	140	2	37	37	NUM
ejpam-5339	140	3	]	]	PUNCT
ejpam-5339	140	4	.	.	PUNCT
ejpam-5339	141	1	the	the	DET
ejpam-5339	141	2	forces	force	NOUN
ejpam-5339	141	3	acting	act	VERB
ejpam-5339	141	4	on	on	ADP
ejpam-5339	141	5	the	the	DET
ejpam-5339	141	6	particle	particle	NOUN
ejpam-5339	141	7	are	be	AUX
ejpam-5339	141	8	the	the	DET
ejpam-5339	141	9	gravitational	gravitational	ADJ
ejpam-5339	141	10	force	force	NOUN
ejpam-5339	141	11	mg	mg	PROPN
ejpam-5339	141	12	,	,	PUNCT
ejpam-5339	141	13	the	the	DET
ejpam-5339	141	14	centrifugal	centrifugal	ADJ
ejpam-5339	141	15	force	force	NOUN
ejpam-5339	141	16	becomes	become	VERB
ejpam-5339	141	17	mω2r	mω2r	NOUN
ejpam-5339	141	18	sin	sin	NOUN
ejpam-5339	141	19	θ	θ	PROPN
ejpam-5339	141	20	,	,	PUNCT
ejpam-5339	141	21	where	where	SCONJ
ejpam-5339	141	22	θ	θ	PROPN
ejpam-5339	141	23	is	be	AUX
ejpam-5339	141	24	the	the	DET
ejpam-5339	141	25	central	central	ADJ
ejpam-5339	141	26	angle	angle	NOUN
ejpam-5339	141	27	between	between	ADP
ejpam-5339	141	28	the	the	DET
ejpam-5339	141	29	radius	radius	NOUN
ejpam-5339	141	30	that	that	PRON
ejpam-5339	141	31	containing	contain	VERB
ejpam-5339	141	32	the	the	DET
ejpam-5339	141	33	particle	particle	NOUN
ejpam-5339	141	34	and	and	CCONJ
ejpam-5339	141	35	the	the	DET
ejpam-5339	141	36	vertically	vertically	ADJ
ejpam-5339	141	37	downwards	downward	NOUN
ejpam-5339	141	38	.	.	PUNCT
ejpam-5339	142	1	the	the	DET
ejpam-5339	142	2	moments	moment	NOUN
ejpam-5339	142	3	about	about	ADP
ejpam-5339	142	4	the	the	DET
ejpam-5339	142	5	origin	origin	NOUN
ejpam-5339	142	6	and	and	CCONJ
ejpam-5339	142	7	equation	equation	NOUN
ejpam-5339	142	8	their	their	PRON
ejpam-5339	142	9	sum	sum	NOUN
ejpam-5339	142	10	to	to	ADP
ejpam-5339	142	11	the	the	DET
ejpam-5339	142	12	rate	rate	NOUN
ejpam-5339	142	13	of	of	ADP
ejpam-5339	142	14	change	change	NOUN
ejpam-5339	142	15	of	of	ADP
ejpam-5339	142	16	the	the	DET
ejpam-5339	142	17	angular	angular	ADJ
ejpam-5339	142	18	momentum	momentum	NOUN
ejpam-5339	142	19	of	of	ADP
ejpam-5339	142	20	the	the	DET
ejpam-5339	142	21	particle	particle	NOUN
ejpam-5339	142	22	about	about	ADP
ejpam-5339	142	23	the	the	DET
ejpam-5339	142	24	origin	origin	NOUN
ejpam-5339	142	25	0	0	NUM
ejpam-5339	142	26	are	be	AUX
ejpam-5339	142	27	reflected	reflect	VERB
ejpam-5339	142	28	.	.	PUNCT
ejpam-5339	143	1	following	follow	VERB
ejpam-5339	143	2	nayfeh	nayfeh	NOUN
ejpam-5339	143	3	and	and	CCONJ
ejpam-5339	143	4	mook	mook	NOUN
ejpam-5339	144	1	[	[	X
ejpam-5339	144	2	37	37	NUM
ejpam-5339	144	3	]	]	PUNCT
ejpam-5339	144	4	,	,	PUNCT
ejpam-5339	144	5	the	the	DET
ejpam-5339	144	6	equation	equation	NOUN
ejpam-5339	144	7	that	that	PRON
ejpam-5339	144	8	governs	govern	VERB
ejpam-5339	144	9	motion	motion	NOUN
ejpam-5339	144	10	can	can	AUX
ejpam-5339	144	11	be	be	AUX
ejpam-5339	144	12	simplified	simplify	VERB
ejpam-5339	144	13	as	as	SCONJ
ejpam-5339	144	14	follows	follow	VERB
ejpam-5339	144	15	:	:	PUNCT
ejpam-5339	145	1	θ̈	θ̈	NOUN
ejpam-5339	145	2	−	−	ADP
ejpam-5339	145	3	ω2	ω2	ADJ
ejpam-5339	145	4	sin	sin	NOUN
ejpam-5339	145	5	θ	θ	PROPN
ejpam-5339	145	6	cos	cos	PROPN
ejpam-5339	145	7	θ	θ	PROPN
ejpam-5339	146	1	+	+	CCONJ
ejpam-5339	146	2	g	g	PROPN
ejpam-5339	146	3	sin	sin	NOUN
ejpam-5339	146	4	θ	θ	PROPN
ejpam-5339	146	5	/	/	SYM
ejpam-5339	146	6	r	r	NOUN
ejpam-5339	146	7	=	=	SYM
ejpam-5339	146	8	0	0	NUM
ejpam-5339	146	9	.	.	PUNCT
ejpam-5339	147	1	(	(	PUNCT
ejpam-5339	147	2	9	9	NUM
ejpam-5339	147	3	)	)	PUNCT
ejpam-5339	147	4	in	in	ADP
ejpam-5339	147	5	the	the	DET
ejpam-5339	147	6	previous	previous	ADJ
ejpam-5339	147	7	example	example	NOUN
ejpam-5339	147	8	,	,	PUNCT
ejpam-5339	147	9	the	the	DET
ejpam-5339	147	10	nonlinearity	nonlinearity	NOUN
ejpam-5339	147	11	comes	come	VERB
ejpam-5339	147	12	due	due	ADJ
ejpam-5339	147	13	to	to	ADP
ejpam-5339	147	14	both	both	CCONJ
ejpam-5339	147	15	the	the	DET
ejpam-5339	147	16	inertia	inertia	NOUN
ejpam-5339	147	17	and	and	CCONJ
ejpam-5339	147	18	large	large	ADJ
ejpam-5339	147	19	deformation	deformation	NOUN
ejpam-5339	147	20	.	.	PUNCT
ejpam-5339	148	1	eq	eq	ADJ
ejpam-5339	148	2	.	.	PUNCT
ejpam-5339	149	1	(	(	PUNCT
ejpam-5339	149	2	9	9	X
ejpam-5339	149	3	)	)	PUNCT
ejpam-5339	149	4	can	can	AUX
ejpam-5339	149	5	be	be	AUX
ejpam-5339	149	6	written	write	VERB
ejpam-5339	149	7	as	as	SCONJ
ejpam-5339	149	8	follows	follow	VERB
ejpam-5339	149	9	:	:	PUNCT
ejpam-5339	150	1	θ̈	θ̈	CCONJ
ejpam-5339	150	2	+	+	SYM
ejpam-5339	150	3	f(θ	f(θ	PROPN
ejpam-5339	150	4	)	)	PUNCT
ejpam-5339	150	5	=	=	SYM
ejpam-5339	150	6	0	0	NUM
ejpam-5339	150	7	,	,	PUNCT
ejpam-5339	150	8	(	(	PUNCT
ejpam-5339	150	9	10	10	NUM
ejpam-5339	150	10	)	)	PUNCT
ejpam-5339	150	11	where	where	SCONJ
ejpam-5339	150	12	f(θ	f(θ	NOUN
ejpam-5339	150	13	)	)	PUNCT
ejpam-5339	150	14	=	=	PUNCT
ejpam-5339	151	1	−ω2	−ω2	ADP
ejpam-5339	151	2	sin	sin	VERB
ejpam-5339	151	3	θ	θ	PROPN
ejpam-5339	151	4	cos	cos	PROPN
ejpam-5339	151	5	θ	θ	PROPN
ejpam-5339	151	6	+	+	CCONJ
ejpam-5339	151	7	g	g	PROPN
ejpam-5339	151	8	sin	sin	NOUN
ejpam-5339	151	9	θ	θ	PROPN
ejpam-5339	151	10	/	/	SYM
ejpam-5339	151	11	r.	r.	PROPN
ejpam-5339	151	12	it	it	PRON
ejpam-5339	151	13	should	should	AUX
ejpam-5339	151	14	be	be	AUX
ejpam-5339	151	15	noted	note	VERB
ejpam-5339	151	16	that	that	SCONJ
ejpam-5339	151	17	the	the	DET
ejpam-5339	151	18	previous	previous	ADJ
ejpam-5339	151	19	function	function	NOUN
ejpam-5339	151	20	represent	represent	VERB
ejpam-5339	151	21	an	an	DET
ejpam-5339	151	22	odd	odd	ADJ
ejpam-5339	151	23	function	function	NOUN
ejpam-5339	151	24	without	without	ADP
ejpam-5339	151	25	any	any	DET
ejpam-5339	151	26	damping	damp	VERB
ejpam-5339	151	27	terms	term	NOUN
ejpam-5339	151	28	.	.	PUNCT
ejpam-5339	152	1	as	as	SCONJ
ejpam-5339	152	2	previously	previously	ADV
ejpam-5339	152	3	seen	see	VERB
ejpam-5339	152	4	,	,	PUNCT
ejpam-5339	152	5	assuming	assume	VERB
ejpam-5339	152	6	a	a	DET
ejpam-5339	152	7	predicting	predict	VERB
ejpam-5339	152	8	solution	solution	NOUN
ejpam-5339	152	9	,	,	PUNCT
ejpam-5339	152	10	where	where	SCONJ
ejpam-5339	152	11	the	the	DET
ejpam-5339	152	12	guessing	guess	VERB
ejpam-5339	152	13	solution	solution	NOUN
ejpam-5339	152	14	is	be	AUX
ejpam-5339	152	15	given	give	VERB
ejpam-5339	152	16	by	by	ADP
ejpam-5339	152	17	u	u	NOUN
ejpam-5339	152	18	=	=	PROPN
ejpam-5339	152	19	a	a	DET
ejpam-5339	152	20	cosωt	cosωt	NOUN
ejpam-5339	152	21	,	,	PUNCT
ejpam-5339	152	22	ics	ics	PROPN
ejpam-5339	152	23	u(0	u(0	PROPN
ejpam-5339	152	24	)	)	PUNCT
ejpam-5339	152	25	=	=	SYM
ejpam-5339	153	1	a	a	PRON
ejpam-5339	153	2	,	,	PUNCT
ejpam-5339	153	3	and	and	CCONJ
ejpam-5339	153	4	u̇(0	u̇(0	NOUN
ejpam-5339	153	5	)	)	PUNCT
ejpam-5339	153	6	=	=	SYM
ejpam-5339	153	7	0	0	X
ejpam-5339	153	8	.	.	PUNCT
ejpam-5339	154	1	(	(	PUNCT
ejpam-5339	154	2	11	11	NUM
ejpam-5339	154	3	)	)	PUNCT
ejpam-5339	154	4	the	the	DET
ejpam-5339	154	5	equivalent	equivalent	ADJ
ejpam-5339	154	6	frequency	frequency	NOUN
ejpam-5339	154	7	may	may	AUX
ejpam-5339	154	8	be	be	AUX
ejpam-5339	154	9	determined	determine	VERB
ejpam-5339	154	10	from	from	ADP
ejpam-5339	154	11	the	the	DET
ejpam-5339	154	12	following	follow	VERB
ejpam-5339	154	13	integration	integration	NOUN
ejpam-5339	154	14	:	:	PUNCT
ejpam-5339	154	15	ω2	ω2	ADJ
ejpam-5339	154	16	eqv	eqv	NOUN
ejpam-5339	154	17	=	=	PUNCT
ejpam-5339	154	18	2π	2π	NOUN
ejpam-5339	154	19	/	/	SYM
ejpam-5339	154	20	ω∫	ω∫	NOUN
ejpam-5339	154	21	0	0	NUM
ejpam-5339	154	22	uf(u	uf(u	NUM
ejpam-5339	154	23	)	)	PUNCT
ejpam-5339	154	24	dt	dt	X
ejpam-5339	155	1	/	/	SYM
ejpam-5339	155	2	2π	2π	NOUN
ejpam-5339	155	3	/	/	SYM
ejpam-5339	155	4	ω∫	ω∫	NOUN
ejpam-5339	155	5	0	0	NUM
ejpam-5339	155	6	u2dt	u2dt	NUM
ejpam-5339	155	7	.	.	PUNCT
ejpam-5339	156	1	(	(	PUNCT
ejpam-5339	156	2	12	12	NUM
ejpam-5339	156	3	)	)	PUNCT
ejpam-5339	156	4	by	by	ADP
ejpam-5339	156	5	means	mean	NOUN
ejpam-5339	156	6	of	of	ADP
ejpam-5339	156	7	the	the	DET
ejpam-5339	156	8	ms	ms	NOUN
ejpam-5339	156	9	,	,	PUNCT
ejpam-5339	156	10	eq	eq	NOUN
ejpam-5339	156	11	.	.	PUNCT
ejpam-5339	157	1	(	(	PUNCT
ejpam-5339	157	2	12	12	NUM
ejpam-5339	157	3	)	)	PUNCT
ejpam-5339	157	4	yields	yield	NOUN
ejpam-5339	157	5	ω2	ω2	ADJ
ejpam-5339	157	6	eqv	eqv	NOUN
ejpam-5339	157	7	=	=	SYM
ejpam-5339	157	8	1	1	NUM
ejpam-5339	157	9	ar	ar	NOUN
ejpam-5339	157	10	(	(	PUNCT
ejpam-5339	157	11	2gj1(a)−rω2j1(2a	2gj1(a)−rω2j1(2a	NUM
ejpam-5339	157	12	)	)	PUNCT
ejpam-5339	157	13	)	)	PUNCT
ejpam-5339	157	14	,	,	PUNCT
ejpam-5339	157	15	(	(	PUNCT
ejpam-5339	157	16	13	13	NUM
ejpam-5339	157	17	)	)	PUNCT
ejpam-5339	157	18	where	where	SCONJ
ejpam-5339	157	19	j1(a	j1(a	NOUN
ejpam-5339	157	20	)	)	PUNCT
ejpam-5339	157	21	,	,	PUNCT
ejpam-5339	157	22	and	and	CCONJ
ejpam-5339	157	23	j1(2a	j1(2a	ADJ
ejpam-5339	157	24	)	)	PUNCT
ejpam-5339	157	25	are	be	AUX
ejpam-5339	157	26	the	the	DET
ejpam-5339	157	27	bessel	bessel	ADJ
ejpam-5339	157	28	function	function	NOUN
ejpam-5339	157	29	in	in	ADP
ejpam-5339	157	30	the	the	DET
ejpam-5339	157	31	arguments	argument	NOUN
ejpam-5339	157	32	a	a	PRON
ejpam-5339	157	33	,	,	PUNCT
ejpam-5339	157	34	and	and	CCONJ
ejpam-5339	157	35	2a	2a	NUM
ejpam-5339	157	36	respectively	respectively	ADV
ejpam-5339	157	37	.	.	PUNCT
ejpam-5339	158	1	since	since	SCONJ
ejpam-5339	158	2	there	there	PRON
ejpam-5339	158	3	is	be	VERB
ejpam-5339	158	4	no	no	DET
ejpam-5339	158	5	equivalent	equivalent	ADJ
ejpam-5339	158	6	damping	damping	NOUN
ejpam-5339	158	7	,	,	PUNCT
ejpam-5339	158	8	in	in	ADP
ejpam-5339	158	9	considered	consider	VERB
ejpam-5339	158	10	problem	problem	NOUN
ejpam-5339	158	11	,	,	PUNCT
ejpam-5339	158	12	it	it	PRON
ejpam-5339	158	13	follows	follow	VERB
ejpam-5339	158	14	that	that	SCONJ
ejpam-5339	158	15	the	the	DET
ejpam-5339	158	16	total	total	ADJ
ejpam-5339	158	17	frequency	frequency	NOUN
ejpam-5339	158	18	becomes	become	VERB
ejpam-5339	158	19	ω2	ω2	ADJ
ejpam-5339	158	20	=	=	SYM
ejpam-5339	158	21	1	1	NUM
ejpam-5339	158	22	ar	ar	NOUN
ejpam-5339	158	23	(	(	PUNCT
ejpam-5339	158	24	2gj1(a)−rω2j1(2a	2gj1(a)−rω2j1(2a	NUM
ejpam-5339	158	25	)	)	PUNCT
ejpam-5339	158	26	)	)	PUNCT
ejpam-5339	158	27	.	.	PUNCT
ejpam-5339	159	1	(	(	PUNCT
ejpam-5339	159	2	14	14	NUM
ejpam-5339	159	3	)	)	PUNCT
ejpam-5339	159	4	the	the	DET
ejpam-5339	159	5	equivalent	equivalent	ADJ
ejpam-5339	159	6	linear	linear	PROPN
ejpam-5339	159	7	differential	differential	NOUN
ejpam-5339	159	8	equation	equation	NOUN
ejpam-5339	159	9	is	be	AUX
ejpam-5339	159	10	then	then	ADV
ejpam-5339	159	11	given	give	VERB
ejpam-5339	159	12	as	as	ADP
ejpam-5339	159	13	:	:	PUNCT
ejpam-5339	159	14	ü	ü	PART
ejpam-5339	159	15	+	+	NOUN
ejpam-5339	159	16	ω2u	ω2u	NOUN
ejpam-5339	159	17	=	=	SYM
ejpam-5339	159	18	0	0	X
ejpam-5339	159	19	.	.	PUNCT
ejpam-5339	160	1	(	(	PUNCT
ejpam-5339	160	2	15	15	NUM
ejpam-5339	160	3	)	)	PUNCT
ejpam-5339	160	4	the	the	DET
ejpam-5339	160	5	stability	stability	NOUN
ejpam-5339	160	6	criterion	criterion	NOUN
ejpam-5339	160	7	requires	require	VERB
ejpam-5339	160	8	that	that	SCONJ
ejpam-5339	161	1	ω2	ω2	ADV
ejpam-5339	161	2	>	>	X
ejpam-5339	161	3	0	0	PROPN
ejpam-5339	161	4	.	.	PUNCT
ejpam-5339	162	1	the	the	DET
ejpam-5339	162	2	following	follow	VERB
ejpam-5339	162	3	figure	figure	NOUN
ejpam-5339	162	4	displays	display	VERB
ejpam-5339	162	5	this	this	DET
ejpam-5339	162	6	criterion	criterion	NOUN
ejpam-5339	162	7	for	for	ADP
ejpam-5339	162	8	various	various	ADJ
ejpam-5339	162	9	values	value	NOUN
ejpam-5339	162	10	of	of	ADP
ejpam-5339	162	11	the	the	DET
ejpam-5339	162	12	radius	radius	NOUN
ejpam-5339	162	13	of	of	ADP
ejpam-5339	162	14	the	the	DET
ejpam-5339	162	15	circle	circle	NOUN
ejpam-5339	162	16	.	.	PUNCT
ejpam-5339	163	1	g.	g.	PROPN
ejpam-5339	163	2	m.	m.	PROPN
ejpam-5339	163	3	ismail	ismail	PROPN
ejpam-5339	163	4	,	,	PUNCT
ejpam-5339	163	5	g.	g.	PROPN
ejpam-5339	163	6	m.	m.	PROPN
ejpam-5339	163	7	moatimid	moatimid	PROPN
ejpam-5339	163	8	,	,	PUNCT
ejpam-5339	163	9	m.	m.	NOUN
ejpam-5339	163	10	i.	i.	PROPN
ejpam-5339	163	11	yamani	yamani	PROPN
ejpam-5339	163	12	/	/	SYM
ejpam-5339	163	13	eur	eur	PROPN
ejpam-5339	163	14	.	.	PUNCT
ejpam-5339	164	1	j.	j.	PROPN
ejpam-5339	164	2	pure	pure	PROPN
ejpam-5339	164	3	appl	appl	PROPN
ejpam-5339	164	4	.	.	PROPN
ejpam-5339	164	5	math	math	PROPN
ejpam-5339	164	6	,	,	PUNCT
ejpam-5339	164	7	17	17	NUM
ejpam-5339	164	8	(	(	PUNCT
ejpam-5339	164	9	3	3	NUM
ejpam-5339	164	10	)	)	PUNCT
ejpam-5339	164	11	(	(	PUNCT
ejpam-5339	164	12	2024	2024	NUM
ejpam-5339	164	13	)	)	PUNCT
ejpam-5339	164	14	,	,	PUNCT
ejpam-5339	164	15	2155	2155	NUM
ejpam-5339	164	16	-	-	SYM
ejpam-5339	164	17	2172	2172	NUM
ejpam-5339	164	18	2161	2161	NUM
ejpam-5339	164	19	fig	fig	NOUN
ejpam-5339	164	20	.	.	PUNCT
ejpam-5339	164	21	1	1	NUM
ejpam-5339	164	22	shows	show	VERB
ejpam-5339	164	23	that	that	SCONJ
ejpam-5339	164	24	the	the	DET
ejpam-5339	164	25	increasing	increasing	NOUN
ejpam-5339	164	26	of	of	ADP
ejpam-5339	164	27	the	the	DET
ejpam-5339	164	28	radius	radius	NOUN
ejpam-5339	164	29	has	have	VERB
ejpam-5339	164	30	a	a	DET
ejpam-5339	164	31	destabilizing	destabilizing	ADJ
ejpam-5339	164	32	influence	influence	NOUN
ejpam-5339	164	33	.	.	PUNCT
ejpam-5339	165	1	as	as	SCONJ
ejpam-5339	165	2	seen	see	VERB
ejpam-5339	165	3	,	,	PUNCT
ejpam-5339	165	4	the	the	DET
ejpam-5339	165	5	small	small	ADJ
ejpam-5339	165	6	values	value	NOUN
ejpam-5339	165	7	of	of	ADP
ejpam-5339	165	8	the	the	DET
ejpam-5339	165	9	radius	radius	NOUN
ejpam-5339	165	10	of	of	ADP
ejpam-5339	165	11	the	the	DET
ejpam-5339	165	12	circle	circle	NOUN
ejpam-5339	165	13	improvement	improvement	NOUN
ejpam-5339	165	14	a	a	DET
ejpam-5339	165	15	larger	large	ADJ
ejpam-5339	165	16	stability	stability	NOUN
ejpam-5339	165	17	zones	zone	NOUN
ejpam-5339	165	18	.	.	PUNCT
ejpam-5339	166	1	for	for	ADP
ejpam-5339	166	2	more	more	ADJ
ejpam-5339	166	3	convenience	convenience	NOUN
ejpam-5339	166	4	,	,	PUNCT
ejpam-5339	166	5	with	with	ADP
ejpam-5339	166	6	the	the	DET
ejpam-5339	166	7	aid	aid	NOUN
ejpam-5339	166	8	of	of	ADP
ejpam-5339	166	9	the	the	DET
ejpam-5339	166	10	ms	ms	PROPN
ejpam-5339	166	11	,	,	PUNCT
ejpam-5339	166	12	a	a	DET
ejpam-5339	166	13	matching	matching	NOUN
ejpam-5339	166	14	between	between	ADP
ejpam-5339	166	15	the	the	DET
ejpam-5339	166	16	original	original	ADJ
ejpam-5339	166	17	nonlinear	nonlinear	ADJ
ejpam-5339	166	18	differential	differential	ADJ
ejpam-5339	166	19	equation	equation	NOUN
ejpam-5339	166	20	as	as	SCONJ
ejpam-5339	166	21	given	give	VERB
ejpam-5339	166	22	in	in	ADP
ejpam-5339	166	23	eq	eq	ADP
ejpam-5339	166	24	.	.	PUNCT
ejpam-5339	167	1	(	(	PUNCT
ejpam-5339	167	2	9	9	NUM
ejpam-5339	167	3	)	)	PUNCT
ejpam-5339	167	4	with	with	ADP
ejpam-5339	167	5	the	the	DET
ejpam-5339	167	6	equivalent	equivalent	ADJ
ejpam-5339	167	7	linear	linear	ADJ
ejpam-5339	167	8	ode	ode	NOUN
ejpam-5339	167	9	as	as	SCONJ
ejpam-5339	167	10	given	give	VERB
ejpam-5339	167	11	in	in	ADP
ejpam-5339	167	12	eq	eq	ADP
ejpam-5339	167	13	.	.	PUNCT
ejpam-5339	168	1	(	(	PUNCT
ejpam-5339	168	2	15	15	NUM
ejpam-5339	168	3	)	)	PUNCT
ejpam-5339	168	4	can	can	AUX
ejpam-5339	168	5	be	be	AUX
ejpam-5339	168	6	drawn	draw	VERB
ejpam-5339	168	7	for	for	ADP
ejpam-5339	168	8	the	the	DET
ejpam-5339	168	9	sample	sample	NOUN
ejpam-5339	168	10	chosen	choose	VERB
ejpam-5339	168	11	system	system	NOUN
ejpam-5339	168	12	ω	ω	X
ejpam-5339	168	13	=	=	SYM
ejpam-5339	168	14	0.5	0.5	NUM
ejpam-5339	168	15	,	,	PUNCT
ejpam-5339	168	16	g	g	NOUN
ejpam-5339	168	17	=	=	PROPN
ejpam-5339	168	18	12	12	NUM
ejpam-5339	168	19	,	,	PUNCT
ejpam-5339	168	20	r	r	NOUN
ejpam-5339	168	21	=	=	SYM
ejpam-5339	168	22	14	14	NUM
ejpam-5339	168	23	,	,	PUNCT
ejpam-5339	168	24	and	and	CCONJ
ejpam-5339	168	25	a	a	DET
ejpam-5339	168	26	=	=	SYM
ejpam-5339	168	27	0.5	0.5	NUM
ejpam-5339	168	28	:	:	PUNCT
ejpam-5339	168	29	from	from	ADP
ejpam-5339	168	30	the	the	DET
ejpam-5339	168	31	ns	ns	NOUN
ejpam-5339	168	32	in	in	ADP
ejpam-5339	168	33	fig	fig	NOUN
ejpam-5339	168	34	.	.	PUNCT
ejpam-5339	169	1	2	2	NUM
ejpam-5339	169	2	,	,	PUNCT
ejpam-5339	169	3	it	it	PRON
ejpam-5339	169	4	is	be	AUX
ejpam-5339	169	5	found	find	VERB
ejpam-5339	169	6	that	that	SCONJ
ejpam-5339	169	7	the	the	DET
ejpam-5339	169	8	absolute	absolute	ADJ
ejpam-5339	169	9	error	error	NOUN
ejpam-5339	169	10	between	between	ADP
ejpam-5339	169	11	the	the	DET
ejpam-5339	169	12	two	two	NUM
ejpam-5339	169	13	solutions	solution	NOUN
ejpam-5339	169	14	is	be	AUX
ejpam-5339	169	15	0.00367	0.00367	NUM
ejpam-5339	169	16	.	.	PUNCT
ejpam-5339	170	1	it	it	PRON
ejpam-5339	170	2	should	should	AUX
ejpam-5339	170	3	be	be	AUX
ejpam-5339	170	4	noted	note	VERB
ejpam-5339	170	5	that	that	SCONJ
ejpam-5339	170	6	,	,	PUNCT
ejpam-5339	170	7	in	in	ADP
ejpam-5339	170	8	contrast	contrast	NOUN
ejpam-5339	170	9	with	with	ADP
ejpam-5339	170	10	the	the	DET
ejpam-5339	170	11	traditional	traditional	ADJ
ejpam-5339	170	12	perturbation	perturbation	NOUN
ejpam-5339	170	13	techniques	technique	NOUN
ejpam-5339	170	14	,	,	PUNCT
ejpam-5339	170	15	the	the	DET
ejpam-5339	170	16	present	present	ADJ
ejpam-5339	170	17	npa	npa	NOUN
ejpam-5339	170	18	does	do	AUX
ejpam-5339	170	19	not	not	PART
ejpam-5339	170	20	use	use	VERB
ejpam-5339	170	21	the	the	DET
ejpam-5339	170	22	taylor	taylor	PROPN
ejpam-5339	170	23	expansion	expansion	NOUN
ejpam-5339	170	24	for	for	ADP
ejpam-5339	170	25	the	the	DET
ejpam-5339	170	26	restoring	restore	VERB
ejpam-5339	170	27	forces	force	NOUN
ejpam-5339	170	28	.	.	PUNCT
ejpam-5339	171	1	additionally	additionally	ADV
ejpam-5339	171	2	,	,	PUNCT
ejpam-5339	171	3	it	it	PRON
ejpam-5339	171	4	enables	enable	VERB
ejpam-5339	171	5	us	we	PRON
ejpam-5339	171	6	to	to	PART
ejpam-5339	171	7	discuss	discuss	VERB
ejpam-5339	171	8	the	the	DET
ejpam-5339	171	9	stability	stability	NOUN
ejpam-5339	171	10	criterion	criterion	NOUN
ejpam-5339	171	11	.	.	PUNCT
ejpam-5339	172	1	3.2	3.2	NUM
ejpam-5339	172	2	.	.	PUNCT
ejpam-5339	172	3	application	application	NOUN
ejpam-5339	172	4	2	2	NUM
ejpam-5339	172	5	a	a	DET
ejpam-5339	172	6	simple	simple	ADJ
ejpam-5339	172	7	pendulum	pendulum	NOUN
ejpam-5339	172	8	with	with	ADP
ejpam-5339	172	9	viscous	viscous	ADJ
ejpam-5339	172	10	damping	damping	NOUN
ejpam-5339	172	11	,	,	PUNCT
ejpam-5339	172	12	the	the	DET
ejpam-5339	172	13	governing	govern	VERB
ejpam-5339	172	14	equation	equation	NOUN
ejpam-5339	172	15	of	of	ADP
ejpam-5339	172	16	motion	motion	NOUN
ejpam-5339	172	17	is	be	AUX
ejpam-5339	172	18	given	give	VERB
ejpam-5339	172	19	by	by	ADP
ejpam-5339	172	20	[	[	PUNCT
ejpam-5339	172	21	37	37	NUM
ejpam-5339	172	22	]	]	PUNCT
ejpam-5339	172	23	:	:	PUNCT
ejpam-5339	172	24	θ̈	θ̈	X
ejpam-5339	172	25	+	+	CCONJ
ejpam-5339	172	26	2µθ̇	2µθ̇	NUM
ejpam-5339	172	27	+	+	CCONJ
ejpam-5339	172	28	ω2	ω2	ADJ
ejpam-5339	172	29	sin	sin	NOUN
ejpam-5339	172	30	θ	θ	NOUN
ejpam-5339	172	31	=	=	SYM
ejpam-5339	172	32	0	0	NUM
ejpam-5339	172	33	.	.	PUNCT
ejpam-5339	173	1	(	(	PUNCT
ejpam-5339	173	2	16	16	NUM
ejpam-5339	173	3	)	)	PUNCT
ejpam-5339	173	4	eq	eq	NOUN
ejpam-5339	173	5	.	.	PUNCT
ejpam-5339	174	1	(	(	PUNCT
ejpam-5339	174	2	16	16	NUM
ejpam-5339	174	3	)	)	PUNCT
ejpam-5339	174	4	can	can	AUX
ejpam-5339	174	5	be	be	AUX
ejpam-5339	174	6	rewritten	rewrite	VERB
ejpam-5339	174	7	as	as	SCONJ
ejpam-5339	174	8	follows	follow	VERB
ejpam-5339	174	9	:	:	PUNCT
ejpam-5339	174	10	θ̈	θ̈	X
ejpam-5339	174	11	+	+	CCONJ
ejpam-5339	174	12	f1(θ̇	f1(θ̇	ADJ
ejpam-5339	174	13	)	)	PUNCT
ejpam-5339	174	14	+	+	PUNCT
ejpam-5339	174	15	f2(θ	f2(θ	X
ejpam-5339	174	16	)	)	PUNCT
ejpam-5339	174	17	=	=	SYM
ejpam-5339	174	18	0	0	NUM
ejpam-5339	174	19	,	,	PUNCT
ejpam-5339	174	20	(	(	PUNCT
ejpam-5339	174	21	17	17	NUM
ejpam-5339	174	22	)	)	PUNCT
ejpam-5339	174	23	where	where	SCONJ
ejpam-5339	174	24	f1(θ̇	f1(θ̇	NOUN
ejpam-5339	174	25	)	)	PUNCT
ejpam-5339	174	26	=	=	SYM
ejpam-5339	174	27	2µθ̇	2µθ̇	NOUN
ejpam-5339	174	28	,	,	PUNCT
ejpam-5339	174	29	and	and	CCONJ
ejpam-5339	174	30	f2(θ	f2(θ	NOUN
ejpam-5339	174	31	)	)	PUNCT
ejpam-5339	174	32	=	=	SYM
ejpam-5339	174	33	ω2	ω2	ADJ
ejpam-5339	174	34	sin	sin	NOUN
ejpam-5339	174	35	θ	θ	PROPN
ejpam-5339	174	36	assuming	assume	VERB
ejpam-5339	174	37	that	that	SCONJ
ejpam-5339	174	38	the	the	DET
ejpam-5339	174	39	guessing	guess	VERB
ejpam-5339	174	40	solution	solution	NOUN
ejpam-5339	174	41	is	be	AUX
ejpam-5339	174	42	given	give	VERB
ejpam-5339	174	43	by	by	ADP
ejpam-5339	174	44	w	w	PROPN
ejpam-5339	174	45	=	=	PUNCT
ejpam-5339	174	46	a	a	DET
ejpam-5339	174	47	cosωt	cosωt	NOUN
ejpam-5339	174	48	,	,	PUNCT
ejpam-5339	174	49	ics	ics	PROPN
ejpam-5339	174	50	w(0	w(0	PROPN
ejpam-5339	174	51	)	)	PUNCT
ejpam-5339	174	52	=	=	SYM
ejpam-5339	174	53	a	a	PRON
ejpam-5339	174	54	,	,	PUNCT
ejpam-5339	174	55	and	and	CCONJ
ejpam-5339	174	56	ẇ(0	ẇ(0	ADV
ejpam-5339	174	57	)	)	PUNCT
ejpam-5339	174	58	=	=	SYM
ejpam-5339	175	1	0	0	X
ejpam-5339	175	2	.	.	PUNCT
ejpam-5339	176	1	(	(	PUNCT
ejpam-5339	176	2	18	18	NUM
ejpam-5339	176	3	)	)	PUNCT
ejpam-5339	176	4	the	the	DET
ejpam-5339	176	5	equivalent	equivalent	ADJ
ejpam-5339	176	6	frequency	frequency	NOUN
ejpam-5339	176	7	may	may	AUX
ejpam-5339	176	8	be	be	AUX
ejpam-5339	176	9	determined	determine	VERB
ejpam-5339	176	10	from	from	ADP
ejpam-5339	176	11	the	the	DET
ejpam-5339	176	12	following	follow	VERB
ejpam-5339	176	13	integration	integration	NOUN
ejpam-5339	176	14	:	:	PUNCT
ejpam-5339	176	15	ω2	ω2	ADJ
ejpam-5339	176	16	eqv	eqv	NOUN
ejpam-5339	176	17	=	=	PUNCT
ejpam-5339	176	18	2π	2π	NOUN
ejpam-5339	176	19	/	/	SYM
ejpam-5339	176	20	ω∫	ω∫	NOUN
ejpam-5339	176	21	0	0	NUM
ejpam-5339	176	22	wf2(w	wf2(w	NOUN
ejpam-5339	176	23	)	)	PUNCT
ejpam-5339	176	24	dt	dt	NOUN
ejpam-5339	176	25	/	/	SYM
ejpam-5339	177	1	2π	2π	NOUN
ejpam-5339	177	2	/	/	SYM
ejpam-5339	177	3	ω∫	ω∫	NOUN
ejpam-5339	177	4	0	0	NUM
ejpam-5339	177	5	w2dt	w2dt	NUM
ejpam-5339	177	6	.	.	PUNCT
ejpam-5339	178	1	(	(	PUNCT
ejpam-5339	178	2	19	19	NUM
ejpam-5339	178	3	)	)	PUNCT
ejpam-5339	178	4	by	by	ADP
ejpam-5339	178	5	means	mean	NOUN
ejpam-5339	178	6	of	of	ADP
ejpam-5339	178	7	the	the	DET
ejpam-5339	178	8	ms	ms	NOUN
ejpam-5339	178	9	,	,	PUNCT
ejpam-5339	178	10	eq	eq	NOUN
ejpam-5339	178	11	.	.	PUNCT
ejpam-5339	179	1	(	(	PUNCT
ejpam-5339	179	2	19	19	NUM
ejpam-5339	179	3	)	)	PUNCT
ejpam-5339	179	4	yields	yield	NOUN
ejpam-5339	179	5	ω2	ω2	ADJ
ejpam-5339	179	6	eqv	eqv	NOUN
ejpam-5339	179	7	=	=	PUNCT
ejpam-5339	179	8	2ω2	2ω2	NUM
ejpam-5339	179	9	a	a	DET
ejpam-5339	179	10	j1(a	j1(a	NOUN
ejpam-5339	179	11	)	)	PUNCT
ejpam-5339	179	12	.	.	PUNCT
ejpam-5339	180	1	(	(	PUNCT
ejpam-5339	180	2	20	20	NUM
ejpam-5339	180	3	)	)	PUNCT
ejpam-5339	180	4	the	the	DET
ejpam-5339	180	5	equivalent	equivalent	ADJ
ejpam-5339	180	6	damping	damp	VERB
ejpam-5339	180	7	may	may	AUX
ejpam-5339	180	8	be	be	AUX
ejpam-5339	180	9	evaluated	evaluate	VERB
ejpam-5339	180	10	from	from	ADP
ejpam-5339	180	11	the	the	DET
ejpam-5339	180	12	integral	integral	ADJ
ejpam-5339	180	13	form	form	NOUN
ejpam-5339	180	14	:	:	PUNCT
ejpam-5339	180	15	σeqv	σeqv	NOUN
ejpam-5339	180	16	=	=	SYM
ejpam-5339	180	17	2π	2π	NOUN
ejpam-5339	180	18	/	/	SYM
ejpam-5339	180	19	ω∫	ω∫	NOUN
ejpam-5339	180	20	0	0	NUM
ejpam-5339	180	21	ẇ	ẇ	NOUN
ejpam-5339	180	22	f1	f1	NOUN
ejpam-5339	180	23	(	(	PUNCT
ejpam-5339	180	24	ẇ	ẇ	PROPN
ejpam-5339	180	25	)	)	PUNCT
ejpam-5339	180	26	dt/	dt/	VERB
ejpam-5339	180	27	2π	2π	NOUN
ejpam-5339	180	28	/	/	SYM
ejpam-5339	180	29	ω∫	ω∫	NOUN
ejpam-5339	180	30	0	0	NUM
ejpam-5339	180	31	ẇ2dt	ẇ2dt	NUM
ejpam-5339	180	32	=	=	SYM
ejpam-5339	180	33	2µ.	2µ.	NUM
ejpam-5339	180	34	(	(	PUNCT
ejpam-5339	180	35	21	21	NUM
ejpam-5339	180	36	)	)	PUNCT
ejpam-5339	180	37	from	from	ADP
ejpam-5339	180	38	eqs	eqs	PROPN
ejpam-5339	180	39	.	.	PUNCT
ejpam-5339	181	1	(	(	PUNCT
ejpam-5339	181	2	20	20	NUM
ejpam-5339	181	3	)	)	PUNCT
ejpam-5339	181	4	and	and	CCONJ
ejpam-5339	181	5	(	(	PUNCT
ejpam-5339	181	6	21	21	NUM
ejpam-5339	181	7	)	)	PUNCT
ejpam-5339	181	8	,	,	PUNCT
ejpam-5339	181	9	it	it	PRON
ejpam-5339	181	10	follows	follow	VERB
ejpam-5339	181	11	that	that	SCONJ
ejpam-5339	181	12	the	the	DET
ejpam-5339	181	13	equivalent	equivalent	ADJ
ejpam-5339	181	14	linear	linear	ADJ
ejpam-5339	181	15	ode	ode	NOUN
ejpam-5339	181	16	may	may	AUX
ejpam-5339	181	17	be	be	AUX
ejpam-5339	181	18	written	write	VERB
ejpam-5339	181	19	as	as	SCONJ
ejpam-5339	181	20	follows	follow	VERB
ejpam-5339	181	21	:	:	PUNCT
ejpam-5339	181	22	ẅ	ẅ	PROPN
ejpam-5339	182	1	+	+	CCONJ
ejpam-5339	182	2	2µẇ	2µẇ	NUM
ejpam-5339	182	3	+	+	CCONJ
ejpam-5339	182	4	ω2	ω2	ADJ
ejpam-5339	182	5	eqv	eqv	NOUN
ejpam-5339	182	6	=	=	NOUN
ejpam-5339	182	7	0	0	NUM
ejpam-5339	182	8	.	.	PUNCT
ejpam-5339	182	9	(	(	PUNCT
ejpam-5339	182	10	22	22	NUM
ejpam-5339	182	11	)	)	PUNCT
ejpam-5339	182	12	g.	g.	PROPN
ejpam-5339	182	13	m.	m.	PROPN
ejpam-5339	182	14	ismail	ismail	PROPN
ejpam-5339	182	15	,	,	PUNCT
ejpam-5339	182	16	g.	g.	PROPN
ejpam-5339	182	17	m.	m.	PROPN
ejpam-5339	182	18	moatimid	moatimid	PROPN
ejpam-5339	182	19	,	,	PUNCT
ejpam-5339	182	20	m.	m.	NOUN
ejpam-5339	182	21	i.	i.	PROPN
ejpam-5339	182	22	yamani	yamani	PROPN
ejpam-5339	182	23	/	/	SYM
ejpam-5339	182	24	eur	eur	PROPN
ejpam-5339	182	25	.	.	PUNCT
ejpam-5339	183	1	j.	j.	PROPN
ejpam-5339	183	2	pure	pure	PROPN
ejpam-5339	183	3	appl	appl	PROPN
ejpam-5339	183	4	.	.	PROPN
ejpam-5339	183	5	math	math	PROPN
ejpam-5339	183	6	,	,	PUNCT
ejpam-5339	183	7	17	17	NUM
ejpam-5339	183	8	(	(	PUNCT
ejpam-5339	183	9	3	3	NUM
ejpam-5339	183	10	)	)	PUNCT
ejpam-5339	183	11	(	(	PUNCT
ejpam-5339	183	12	2024	2024	NUM
ejpam-5339	183	13	)	)	PUNCT
ejpam-5339	183	14	,	,	PUNCT
ejpam-5339	183	15	2155	2155	NUM
ejpam-5339	183	16	-	-	SYM
ejpam-5339	183	17	2172	2172	NUM
ejpam-5339	183	18	2162	2162	NUM
ejpam-5339	183	19	from	from	ADP
ejpam-5339	183	20	the	the	DET
ejpam-5339	183	21	standard	standard	ADJ
ejpam-5339	183	22	normal	normal	ADJ
ejpam-5339	183	23	form	form	NOUN
ejpam-5339	184	1	,	,	PUNCT
ejpam-5339	184	2	it	it	PRON
ejpam-5339	184	3	follows	follow	VERB
ejpam-5339	184	4	that	that	SCONJ
ejpam-5339	184	5	the	the	DET
ejpam-5339	184	6	equivalent	equivalent	ADJ
ejpam-5339	184	7	linear	linear	ADJ
ejpam-5339	184	8	ode	ode	NOUN
ejpam-5339	184	9	is	be	AUX
ejpam-5339	184	10	then	then	ADV
ejpam-5339	184	11	given	give	VERB
ejpam-5339	184	12	as	as	ADP
ejpam-5339	184	13	ẅ	ẅ	ADJ
ejpam-5339	184	14	+	+	NOUN
ejpam-5339	184	15	ω2w	ω2w	NOUN
ejpam-5339	184	16	=	=	SYM
ejpam-5339	184	17	0	0	NUM
ejpam-5339	184	18	.	.	PUNCT
ejpam-5339	185	1	(	(	PUNCT
ejpam-5339	185	2	23	23	NUM
ejpam-5339	185	3	)	)	PUNCT
ejpam-5339	185	4	the	the	DET
ejpam-5339	185	5	stability	stability	NOUN
ejpam-5339	185	6	criterion	criterion	NOUN
ejpam-5339	185	7	requires	require	VERB
ejpam-5339	185	8	that	that	SCONJ
ejpam-5339	185	9	ω2	ω2	ADJ
ejpam-5339	185	10	=	=	SYM
ejpam-5339	185	11	2ω2	2ω2	NUM
ejpam-5339	185	12	a	a	DET
ejpam-5339	185	13	j1(a	j1(a	NOUN
ejpam-5339	185	14	)	)	PUNCT
ejpam-5339	185	15	−	−	NOUN
ejpam-5339	185	16	µ2	µ2	PROPN
ejpam-5339	185	17	.	.	PUNCT
ejpam-5339	186	1	this	this	PRON
ejpam-5339	186	2	means	mean	VERB
ejpam-5339	186	3	that	that	SCONJ
ejpam-5339	186	4	2ω2	2ω2	NUM
ejpam-5339	186	5	a	a	DET
ejpam-5339	186	6	j1(a	j1(a	NOUN
ejpam-5339	186	7	)	)	PUNCT
ejpam-5339	186	8	−	−	NOUN
ejpam-5339	186	9	µ2	µ2	PROPN
ejpam-5339	186	10	>	>	X
ejpam-5339	186	11	0	0	NUM
ejpam-5339	186	12	,	,	PUNCT
ejpam-5339	186	13	or	or	CCONJ
ejpam-5339	186	14	µ2	µ2	VERB
ejpam-5339	186	15	<	<	X
ejpam-5339	186	16	2ω2	2ω2	NUM
ejpam-5339	186	17	a	a	DET
ejpam-5339	186	18	j1(a	j1(a	NOUN
ejpam-5339	186	19	)	)	PUNCT
ejpam-5339	186	20	.	.	PUNCT
ejpam-5339	187	1	for	for	ADP
ejpam-5339	187	2	more	more	ADJ
ejpam-5339	187	3	convenience	convenience	NOUN
ejpam-5339	187	4	,	,	PUNCT
ejpam-5339	187	5	with	with	ADP
ejpam-5339	187	6	the	the	DET
ejpam-5339	187	7	aid	aid	NOUN
ejpam-5339	187	8	of	of	ADP
ejpam-5339	187	9	the	the	DET
ejpam-5339	187	10	ms	ms	PROPN
ejpam-5339	187	11	,	,	PUNCT
ejpam-5339	187	12	a	a	DET
ejpam-5339	187	13	matching	matching	NOUN
ejpam-5339	187	14	between	between	ADP
ejpam-5339	187	15	the	the	DET
ejpam-5339	187	16	original	original	ADJ
ejpam-5339	187	17	non	non	ADJ
ejpam-5339	187	18	-	-	ADJ
ejpam-5339	187	19	linear	linear	ADJ
ejpam-5339	187	20	ode	ode	NOUN
ejpam-5339	187	21	as	as	SCONJ
ejpam-5339	187	22	given	give	VERB
ejpam-5339	187	23	in	in	ADP
ejpam-5339	187	24	eq	eq	ADP
ejpam-5339	187	25	.	.	PUNCT
ejpam-5339	188	1	(	(	PUNCT
ejpam-5339	188	2	16	16	NUM
ejpam-5339	188	3	)	)	PUNCT
ejpam-5339	188	4	with	with	ADP
ejpam-5339	188	5	the	the	DET
ejpam-5339	188	6	equivalent	equivalent	ADJ
ejpam-5339	188	7	linear	linear	PROPN
ejpam-5339	188	8	differential	differential	NOUN
ejpam-5339	188	9	equation	equation	NOUN
ejpam-5339	188	10	as	as	SCONJ
ejpam-5339	188	11	given	give	VERB
ejpam-5339	188	12	in	in	ADP
ejpam-5339	188	13	eq	eq	ADP
ejpam-5339	188	14	.	.	PUNCT
ejpam-5339	189	1	(	(	PUNCT
ejpam-5339	189	2	22	22	NUM
ejpam-5339	189	3	)	)	PUNCT
ejpam-5339	189	4	can	can	AUX
ejpam-5339	189	5	be	be	AUX
ejpam-5339	189	6	drawn	draw	VERB
ejpam-5339	189	7	for	for	ADP
ejpam-5339	189	8	the	the	DET
ejpam-5339	189	9	sample	sample	NOUN
ejpam-5339	189	10	chosen	choose	VERB
ejpam-5339	189	11	system	system	NOUN
ejpam-5339	189	12	ω	ω	PROPN
ejpam-5339	189	13	=	=	SYM
ejpam-5339	189	14	2.0	2.0	NUM
ejpam-5339	189	15	,	,	PUNCT
ejpam-5339	189	16	µ	µ	X
ejpam-5339	189	17	=	=	SYM
ejpam-5339	189	18	0.1,and	0.1,and	NOUN
ejpam-5339	190	1	a	a	DET
ejpam-5339	190	2	=	=	SYM
ejpam-5339	190	3	0.5	0.5	NUM
ejpam-5339	190	4	:	:	PUNCT
ejpam-5339	190	5	from	from	ADP
ejpam-5339	190	6	the	the	DET
ejpam-5339	190	7	ns	ns	NOUN
ejpam-5339	190	8	in	in	ADP
ejpam-5339	190	9	fig	fig	NOUN
ejpam-5339	190	10	.	.	PUNCT
ejpam-5339	191	1	3	3	NUM
ejpam-5339	191	2	,	,	PUNCT
ejpam-5339	191	3	it	it	PRON
ejpam-5339	191	4	is	be	AUX
ejpam-5339	191	5	found	find	VERB
ejpam-5339	191	6	that	that	SCONJ
ejpam-5339	191	7	the	the	DET
ejpam-5339	191	8	absolute	absolute	ADJ
ejpam-5339	191	9	error	error	NOUN
ejpam-5339	191	10	between	between	ADP
ejpam-5339	191	11	the	the	DET
ejpam-5339	191	12	two	two	NUM
ejpam-5339	191	13	solutions	solution	NOUN
ejpam-5339	191	14	is	be	AUX
ejpam-5339	191	15	0.0345	0.0345	NUM
ejpam-5339	191	16	.	.	PUNCT
ejpam-5339	192	1	it	it	PRON
ejpam-5339	192	2	should	should	AUX
ejpam-5339	192	3	be	be	AUX
ejpam-5339	192	4	noted	note	VERB
ejpam-5339	192	5	that	that	SCONJ
ejpam-5339	192	6	,	,	PUNCT
ejpam-5339	192	7	in	in	ADP
ejpam-5339	192	8	contrast	contrast	NOUN
ejpam-5339	192	9	with	with	ADP
ejpam-5339	192	10	the	the	DET
ejpam-5339	192	11	traditional	traditional	ADJ
ejpam-5339	192	12	perturbation	perturbation	NOUN
ejpam-5339	192	13	techniques	technique	NOUN
ejpam-5339	192	14	,	,	PUNCT
ejpam-5339	192	15	the	the	DET
ejpam-5339	192	16	present	present	ADJ
ejpam-5339	192	17	npa	npa	NOUN
ejpam-5339	192	18	enables	enable	VERB
ejpam-5339	192	19	us	we	PRON
ejpam-5339	192	20	to	to	PART
ejpam-5339	192	21	discuss	discuss	VERB
ejpam-5339	192	22	the	the	DET
ejpam-5339	192	23	stability	stability	NOUN
ejpam-5339	192	24	criterion	criterion	NOUN
ejpam-5339	192	25	.	.	PUNCT
ejpam-5339	193	1	the	the	DET
ejpam-5339	193	2	stability	stability	NOUN
ejpam-5339	193	3	criterion	criterion	NOUN
ejpam-5339	193	4	may	may	AUX
ejpam-5339	193	5	be	be	AUX
ejpam-5339	193	6	plotted	plot	VERB
ejpam-5339	193	7	as	as	SCONJ
ejpam-5339	193	8	follows	follow	VERB
ejpam-5339	193	9	:	:	PUNCT
ejpam-5339	193	10	from	from	ADP
ejpam-5339	193	11	fig	fig	NOUN
ejpam-5339	193	12	.	.	PUNCT
ejpam-5339	194	1	4	4	NUM
ejpam-5339	194	2	,	,	PUNCT
ejpam-5339	194	3	it	it	PRON
ejpam-5339	194	4	is	be	AUX
ejpam-5339	194	5	found	find	VERB
ejpam-5339	194	6	that	that	SCONJ
ejpam-5339	194	7	the	the	DET
ejpam-5339	194	8	stable	stable	ADJ
ejpam-5339	194	9	regions	region	NOUN
ejpam-5339	194	10	increase	increase	VERB
ejpam-5339	194	11	as	as	ADP
ejpam-5339	194	12	the	the	DET
ejpam-5339	194	13	frequency	frequency	NOUN
ejpam-5339	194	14	ω	ω	NOUN
ejpam-5339	194	15	increases	increase	NOUN
ejpam-5339	194	16	.	.	PUNCT
ejpam-5339	195	1	therefore	therefore	ADV
ejpam-5339	195	2	,	,	PUNCT
ejpam-5339	195	3	this	this	DET
ejpam-5339	195	4	parameter	parameter	NOUN
ejpam-5339	195	5	has	have	VERB
ejpam-5339	195	6	a	a	DET
ejpam-5339	195	7	stabilizing	stabilize	VERB
ejpam-5339	195	8	influence	influence	NOUN
ejpam-5339	195	9	.	.	PUNCT
ejpam-5339	196	1	3.3	3.3	NUM
ejpam-5339	196	2	.	.	PUNCT
ejpam-5339	197	1	application	application	NOUN
ejpam-5339	197	2	3	3	NUM
ejpam-5339	197	3	a	a	DET
ejpam-5339	197	4	system	system	NOUN
ejpam-5339	197	5	composed	compose	VERB
ejpam-5339	197	6	of	of	ADP
ejpam-5339	197	7	a	a	DET
ejpam-5339	197	8	mass	mass	NOUN
ejpam-5339	197	9	on	on	ADP
ejpam-5339	197	10	a	a	DET
ejpam-5339	197	11	spring	spring	NOUN
ejpam-5339	197	12	with	with	ADP
ejpam-5339	197	13	cubic	cubic	ADJ
ejpam-5339	197	14	and	and	CCONJ
ejpam-5339	197	15	quantic	quantic	ADJ
ejpam-5339	197	16	nonlinearity	nonlinearity	NOUN
ejpam-5339	197	17	is	be	AUX
ejpam-5339	197	18	described	describe	VERB
ejpam-5339	197	19	by	by	ADP
ejpam-5339	197	20	a	a	DET
ejpam-5339	197	21	strongly	strongly	ADV
ejpam-5339	197	22	non	non	ADJ
ejpam-5339	197	23	-	-	ADJ
ejpam-5339	197	24	linear	linear	ADJ
ejpam-5339	197	25	oscillator	oscillator	NOUN
ejpam-5339	197	26	with	with	ADP
ejpam-5339	197	27	a	a	DET
ejpam-5339	197	28	cubic	cubic	ADJ
ejpam-5339	197	29	and	and	CCONJ
ejpam-5339	197	30	harmonic	harmonic	ADJ
ejpam-5339	197	31	restoring	restore	VERB
ejpam-5339	197	32	force	force	NOUN
ejpam-5339	197	33	equation	equation	NOUN
ejpam-5339	197	34	,	,	PUNCT
ejpam-5339	197	35	as	as	SCONJ
ejpam-5339	197	36	illustrated	illustrate	VERB
ejpam-5339	197	37	in	in	ADP
ejpam-5339	197	38	figure	figure	NOUN
ejpam-5339	197	39	5	5	NUM
ejpam-5339	197	40	,	,	PUNCT
ejpam-5339	197	41	where	where	SCONJ
ejpam-5339	197	42	k	k	PROPN
ejpam-5339	197	43	is	be	AUX
ejpam-5339	197	44	the	the	DET
ejpam-5339	197	45	linear	linear	ADJ
ejpam-5339	197	46	stiffness	stiffness	ADJ
ejpam-5339	197	47	coefficients	coefficient	NOUN
ejpam-5339	197	48	,	,	PUNCT
ejpam-5339	197	49	m	m	VERB
ejpam-5339	197	50	is	be	AUX
ejpam-5339	197	51	the	the	DET
ejpam-5339	197	52	mass	mass	PROPN
ejpam-5339	197	53	,	,	PUNCT
ejpam-5339	197	54	b	b	PROPN
ejpam-5339	197	55	sinx	sinx	PROPN
ejpam-5339	197	56	is	be	AUX
ejpam-5339	197	57	the	the	DET
ejpam-5339	197	58	driving	drive	VERB
ejpam-5339	197	59	force	force	NOUN
ejpam-5339	197	60	and	and	CCONJ
ejpam-5339	197	61	x(t	x(t	PROPN
ejpam-5339	197	62	)	)	PUNCT
ejpam-5339	197	63	is	be	AUX
ejpam-5339	197	64	the	the	DET
ejpam-5339	197	65	system	system	NOUN
ejpam-5339	197	66	response	response	NOUN
ejpam-5339	197	67	.	.	PUNCT
ejpam-5339	198	1	the	the	DET
ejpam-5339	198	2	strongly	strongly	ADV
ejpam-5339	198	3	non	non	ADJ
ejpam-5339	198	4	-	-	ADJ
ejpam-5339	198	5	linear	linear	ADJ
ejpam-5339	198	6	oscillator	oscillator	NOUN
ejpam-5339	198	7	with	with	ADP
ejpam-5339	198	8	cubic	cubic	ADJ
ejpam-5339	198	9	/	/	SYM
ejpam-5339	198	10	quantic	quantic	ADJ
ejpam-5339	198	11	and	and	CCONJ
ejpam-5339	198	12	harmonic	harmonic	ADJ
ejpam-5339	198	13	restoring	restore	VERB
ejpam-5339	198	14	force	force	NOUN
ejpam-5339	198	15	is	be	AUX
ejpam-5339	198	16	modeled	model	VERB
ejpam-5339	198	17	mathematically	mathematically	ADV
ejpam-5339	198	18	by	by	ADP
ejpam-5339	198	19	the	the	DET
ejpam-5339	198	20	following	follow	VERB
ejpam-5339	198	21	non	non	ADJ
ejpam-5339	198	22	-	-	ADJ
ejpam-5339	198	23	linear	linear	ADJ
ejpam-5339	198	24	ode	ode	NOUN
ejpam-5339	199	1	[	[	X
ejpam-5339	199	2	8	8	NUM
ejpam-5339	199	3	]	]	SYM
ejpam-5339	199	4	:	:	PUNCT
ejpam-5339	199	5	ẍ+	ẍ+	PROPN
ejpam-5339	199	6	x+	x+	ADJ
ejpam-5339	199	7	ax3	ax3	NOUN
ejpam-5339	200	1	+	+	CCONJ
ejpam-5339	200	2	cx5	cx5	NOUN
ejpam-5339	200	3	+	+	CCONJ
ejpam-5339	200	4	b	b	X
ejpam-5339	200	5	sinx	sinx	X
ejpam-5339	200	6	=	=	SYM
ejpam-5339	200	7	0	0	NUM
ejpam-5339	200	8	,	,	PUNCT
ejpam-5339	200	9	(	(	PUNCT
ejpam-5339	200	10	24	24	NUM
ejpam-5339	200	11	)	)	PUNCT
ejpam-5339	200	12	where	where	SCONJ
ejpam-5339	200	13	a	a	DET
ejpam-5339	200	14	,	,	PUNCT
ejpam-5339	200	15	b	b	NOUN
ejpam-5339	200	16	,	,	PUNCT
ejpam-5339	200	17	and	and	CCONJ
ejpam-5339	200	18	c	c	PROPN
ejpam-5339	200	19	are	be	AUX
ejpam-5339	200	20	constants	constant	NOUN
ejpam-5339	200	21	and	and	CCONJ
ejpam-5339	200	22	the	the	DET
ejpam-5339	200	23	dot	dot	NOUN
ejpam-5339	200	24	denotes	denote	NOUN
ejpam-5339	200	25	to	to	ADP
ejpam-5339	200	26	the	the	DET
ejpam-5339	200	27	time	time	NOUN
ejpam-5339	200	28	derivative	derivative	ADJ
ejpam-5339	200	29	.	.	PUNCT
ejpam-5339	201	1	the	the	DET
ejpam-5339	201	2	ics	ics	PROPN
ejpam-5339	201	3	are	be	AUX
ejpam-5339	201	4	assumed	assume	VERB
ejpam-5339	201	5	as	as	SCONJ
ejpam-5339	201	6	follows	follow	VERB
ejpam-5339	201	7	:	:	PUNCT
ejpam-5339	201	8	x(0	x(0	PROPN
ejpam-5339	201	9	)	)	PUNCT
ejpam-5339	202	1	=	=	SYM
ejpam-5339	202	2	a	a	PRON
ejpam-5339	202	3	,	,	PUNCT
ejpam-5339	202	4	and	and	CCONJ
ejpam-5339	202	5	ẋ(0	ẋ(0	NOUN
ejpam-5339	202	6	)	)	PUNCT
ejpam-5339	202	7	=	=	SYM
ejpam-5339	203	1	0	0	X
ejpam-5339	203	2	.	.	PUNCT
ejpam-5339	204	1	eq	eq	NOUN
ejpam-5339	204	2	.	.	PUNCT
ejpam-5339	205	1	(	(	PUNCT
ejpam-5339	205	2	24	24	NUM
ejpam-5339	205	3	)	)	PUNCT
ejpam-5339	205	4	can	can	AUX
ejpam-5339	205	5	be	be	AUX
ejpam-5339	205	6	rewritten	rewrite	VERB
ejpam-5339	205	7	as	as	SCONJ
ejpam-5339	205	8	follows	follow	VERB
ejpam-5339	205	9	:	:	PUNCT
ejpam-5339	205	10	ẍ+	ẍ+	PROPN
ejpam-5339	205	11	f(x	f(x	PROPN
ejpam-5339	205	12	)	)	PUNCT
ejpam-5339	206	1	=	=	SYM
ejpam-5339	206	2	0	0	NUM
ejpam-5339	206	3	,	,	PUNCT
ejpam-5339	206	4	(	(	PUNCT
ejpam-5339	206	5	25	25	NUM
ejpam-5339	206	6	)	)	PUNCT
ejpam-5339	206	7	where	where	SCONJ
ejpam-5339	206	8	f(x	f(x	NOUN
ejpam-5339	206	9	)	)	PUNCT
ejpam-5339	207	1	=	=	PUNCT
ejpam-5339	208	1	x+	x+	PUNCT
ejpam-5339	208	2	ax3	ax3	NOUN
ejpam-5339	208	3	+	+	CCONJ
ejpam-5339	208	4	cx5	cx5	NOUN
ejpam-5339	209	1	+	+	CCONJ
ejpam-5339	209	2	b	b	NOUN
ejpam-5339	209	3	sinx	sinx	NOUN
ejpam-5339	209	4	assuming	assume	VERB
ejpam-5339	209	5	that	that	SCONJ
ejpam-5339	209	6	the	the	DET
ejpam-5339	209	7	guessing	guess	VERB
ejpam-5339	209	8	solution	solution	NOUN
ejpam-5339	209	9	is	be	AUX
ejpam-5339	209	10	given	give	VERB
ejpam-5339	209	11	by	by	ADP
ejpam-5339	209	12	h	h	NOUN
ejpam-5339	209	13	=	=	NOUN
ejpam-5339	209	14	a	a	DET
ejpam-5339	209	15	cosωt	cosωt	NOUN
ejpam-5339	209	16	,	,	PUNCT
ejpam-5339	209	17	ics	ics	PROPN
ejpam-5339	209	18	h(0	h(0	PROPN
ejpam-5339	209	19	)	)	PUNCT
ejpam-5339	209	20	=	=	SYM
ejpam-5339	209	21	a	a	PRON
ejpam-5339	209	22	,	,	PUNCT
ejpam-5339	209	23	and	and	CCONJ
ejpam-5339	209	24	ḣ(0	ḣ(0	NOUN
ejpam-5339	209	25	)	)	PUNCT
ejpam-5339	210	1	=	=	SYM
ejpam-5339	210	2	0	0	X
ejpam-5339	210	3	.	.	PUNCT
ejpam-5339	211	1	(	(	PUNCT
ejpam-5339	211	2	26	26	NUM
ejpam-5339	211	3	)	)	PUNCT
ejpam-5339	211	4	the	the	DET
ejpam-5339	211	5	equivalent	equivalent	ADJ
ejpam-5339	211	6	frequency	frequency	NOUN
ejpam-5339	211	7	may	may	AUX
ejpam-5339	211	8	be	be	AUX
ejpam-5339	211	9	determined	determine	VERB
ejpam-5339	211	10	from	from	ADP
ejpam-5339	211	11	the	the	DET
ejpam-5339	211	12	following	follow	VERB
ejpam-5339	211	13	integration	integration	NOUN
ejpam-5339	211	14	:	:	PUNCT
ejpam-5339	211	15	ω2	ω2	ADJ
ejpam-5339	211	16	eqv	eqv	NOUN
ejpam-5339	211	17	=	=	PUNCT
ejpam-5339	211	18	2π	2π	NOUN
ejpam-5339	211	19	/	/	SYM
ejpam-5339	211	20	ω∫	ω∫	NOUN
ejpam-5339	211	21	0	0	NUM
ejpam-5339	211	22	hf(h)dt	hf(h)dt	NOUN
ejpam-5339	211	23	/	/	PUNCT
ejpam-5339	212	1	2π	2π	NOUN
ejpam-5339	212	2	/	/	SYM
ejpam-5339	212	3	ω∫	ω∫	NOUN
ejpam-5339	212	4	0	0	NUM
ejpam-5339	212	5	h2dt	h2dt	PUNCT
ejpam-5339	212	6	.	.	PUNCT
ejpam-5339	213	1	(	(	PUNCT
ejpam-5339	213	2	27	27	NUM
ejpam-5339	213	3	)	)	PUNCT
ejpam-5339	213	4	by	by	ADP
ejpam-5339	213	5	means	mean	NOUN
ejpam-5339	213	6	of	of	ADP
ejpam-5339	213	7	the	the	DET
ejpam-5339	213	8	ms	ms	NOUN
ejpam-5339	213	9	,	,	PUNCT
ejpam-5339	213	10	eq	eq	NOUN
ejpam-5339	213	11	.	.	PUNCT
ejpam-5339	214	1	(	(	PUNCT
ejpam-5339	214	2	27	27	NUM
ejpam-5339	214	3	)	)	PUNCT
ejpam-5339	214	4	yields	yield	NOUN
ejpam-5339	214	5	ω2	ω2	ADJ
ejpam-5339	214	6	eqv	eqv	NOUN
ejpam-5339	214	7	=	=	SYM
ejpam-5339	214	8	1	1	NUM
ejpam-5339	214	9	+	+	NUM
ejpam-5339	214	10	3	3	NUM
ejpam-5339	214	11	4	4	NUM
ejpam-5339	214	12	aa2	aa2	NOUN
ejpam-5339	215	1	+	+	CCONJ
ejpam-5339	215	2	5	5	NUM
ejpam-5339	215	3	8	8	NUM
ejpam-5339	215	4	ca4	ca4	NOUN
ejpam-5339	215	5	+	+	NOUN
ejpam-5339	215	6	2b	2b	NUM
ejpam-5339	215	7	a	a	DET
ejpam-5339	215	8	j1(a	j1(a	NOUN
ejpam-5339	215	9	)	)	PUNCT
ejpam-5339	215	10	.	.	PUNCT
ejpam-5339	216	1	(	(	PUNCT
ejpam-5339	216	2	28	28	NUM
ejpam-5339	216	3	)	)	PUNCT
ejpam-5339	216	4	g.	g.	PROPN
ejpam-5339	216	5	m.	m.	PROPN
ejpam-5339	216	6	ismail	ismail	PROPN
ejpam-5339	216	7	,	,	PUNCT
ejpam-5339	216	8	g.	g.	PROPN
ejpam-5339	216	9	m.	m.	PROPN
ejpam-5339	216	10	moatimid	moatimid	PROPN
ejpam-5339	216	11	,	,	PUNCT
ejpam-5339	216	12	m.	m.	NOUN
ejpam-5339	216	13	i.	i.	PROPN
ejpam-5339	216	14	yamani	yamani	PROPN
ejpam-5339	216	15	/	/	SYM
ejpam-5339	216	16	eur	eur	PROPN
ejpam-5339	216	17	.	.	PUNCT
ejpam-5339	217	1	j.	j.	PROPN
ejpam-5339	217	2	pure	pure	PROPN
ejpam-5339	217	3	appl	appl	PROPN
ejpam-5339	217	4	.	.	PROPN
ejpam-5339	217	5	math	math	PROPN
ejpam-5339	217	6	,	,	PUNCT
ejpam-5339	217	7	17	17	NUM
ejpam-5339	217	8	(	(	PUNCT
ejpam-5339	217	9	3	3	NUM
ejpam-5339	217	10	)	)	PUNCT
ejpam-5339	217	11	(	(	PUNCT
ejpam-5339	217	12	2024	2024	NUM
ejpam-5339	217	13	)	)	PUNCT
ejpam-5339	217	14	,	,	PUNCT
ejpam-5339	217	15	2155	2155	NUM
ejpam-5339	217	16	-	-	SYM
ejpam-5339	217	17	2172	2172	NUM
ejpam-5339	217	18	2163	2163	NUM
ejpam-5339	217	19	since	since	SCONJ
ejpam-5339	217	20	the	the	DET
ejpam-5339	217	21	original	original	ADJ
ejpam-5339	217	22	nonlinear	nonlinear	ADJ
ejpam-5339	217	23	differential	differential	NOUN
ejpam-5339	217	24	is	be	AUX
ejpam-5339	217	25	independent	independent	ADJ
ejpam-5339	217	26	of	of	ADP
ejpam-5339	217	27	damping	damp	VERB
ejpam-5339	217	28	terms	term	NOUN
ejpam-5339	217	29	,	,	PUNCT
ejpam-5339	217	30	the	the	DET
ejpam-5339	217	31	forgoing	forgoing	ADJ
ejpam-5339	217	32	equivalent	equivalent	ADJ
ejpam-5339	217	33	frequency	frequency	NOUN
ejpam-5339	217	34	represents	represent	VERB
ejpam-5339	217	35	the	the	DET
ejpam-5339	217	36	same	same	ADJ
ejpam-5339	217	37	total	total	ADJ
ejpam-5339	217	38	frequency	frequency	NOUN
ejpam-5339	217	39	.	.	PUNCT
ejpam-5339	218	1	therefore	therefore	ADV
ejpam-5339	218	2	,	,	PUNCT
ejpam-5339	218	3	the	the	DET
ejpam-5339	218	4	stability	stability	NOUN
ejpam-5339	218	5	criterion	criterion	NOUN
ejpam-5339	218	6	becomes	become	VERB
ejpam-5339	218	7	:	:	PUNCT
ejpam-5339	218	8	ω2	ω2	ADJ
ejpam-5339	218	9	=	=	SYM
ejpam-5339	218	10	1	1	NUM
ejpam-5339	218	11	+	+	NUM
ejpam-5339	218	12	3	3	NUM
ejpam-5339	218	13	4	4	NUM
ejpam-5339	218	14	aa2	aa2	NOUN
ejpam-5339	218	15	+	+	CCONJ
ejpam-5339	218	16	5	5	NUM
ejpam-5339	218	17	8	8	NUM
ejpam-5339	218	18	ca4	ca4	NOUN
ejpam-5339	218	19	+	+	NOUN
ejpam-5339	218	20	2b	2b	NUM
ejpam-5339	218	21	a	a	DET
ejpam-5339	218	22	j1(a	j1(a	NOUN
ejpam-5339	218	23	)	)	PUNCT
ejpam-5339	218	24	>	>	X
ejpam-5339	218	25	0	0	PUNCT
ejpam-5339	218	26	(	(	PUNCT
ejpam-5339	218	27	29	29	NUM
ejpam-5339	218	28	)	)	PUNCT
ejpam-5339	218	29	the	the	DET
ejpam-5339	218	30	equivalent	equivalent	ADJ
ejpam-5339	218	31	linear	linear	ADJ
ejpam-5339	218	32	ode	ode	NOUN
ejpam-5339	218	33	becomes	become	VERB
ejpam-5339	218	34	:	:	PUNCT
ejpam-5339	218	35	ḧ+ω2h	ḧ+ω2h	PROPN
ejpam-5339	218	36	=	=	PUNCT
ejpam-5339	218	37	0	0	PROPN
ejpam-5339	218	38	.	.	PUNCT
ejpam-5339	219	1	(	(	PUNCT
ejpam-5339	219	2	30	30	NUM
ejpam-5339	219	3	)	)	PUNCT
ejpam-5339	219	4	for	for	ADP
ejpam-5339	219	5	more	more	ADJ
ejpam-5339	219	6	convenience	convenience	NOUN
ejpam-5339	219	7	,	,	PUNCT
ejpam-5339	219	8	with	with	ADP
ejpam-5339	219	9	the	the	DET
ejpam-5339	219	10	aid	aid	NOUN
ejpam-5339	219	11	of	of	ADP
ejpam-5339	219	12	the	the	DET
ejpam-5339	219	13	ms	ms	PROPN
ejpam-5339	219	14	,	,	PUNCT
ejpam-5339	219	15	a	a	DET
ejpam-5339	219	16	matching	matching	NOUN
ejpam-5339	219	17	between	between	ADP
ejpam-5339	219	18	the	the	DET
ejpam-5339	219	19	original	original	ADJ
ejpam-5339	219	20	non	non	ADJ
ejpam-5339	219	21	-	-	ADJ
ejpam-5339	219	22	linear	linear	ADJ
ejpam-5339	219	23	ode	ode	NOUN
ejpam-5339	219	24	as	as	SCONJ
ejpam-5339	219	25	given	give	VERB
ejpam-5339	219	26	in	in	ADP
ejpam-5339	219	27	eq	eq	ADP
ejpam-5339	219	28	.	.	PUNCT
ejpam-5339	220	1	(	(	PUNCT
ejpam-5339	220	2	24	24	NUM
ejpam-5339	220	3	)	)	PUNCT
ejpam-5339	220	4	with	with	ADP
ejpam-5339	220	5	the	the	DET
ejpam-5339	220	6	equivalent	equivalent	ADJ
ejpam-5339	220	7	linear	linear	ADJ
ejpam-5339	220	8	ode	ode	NOUN
ejpam-5339	220	9	as	as	SCONJ
ejpam-5339	220	10	given	give	VERB
ejpam-5339	220	11	in	in	ADP
ejpam-5339	220	12	eq	eq	ADP
ejpam-5339	220	13	.	.	PUNCT
ejpam-5339	221	1	(	(	PUNCT
ejpam-5339	221	2	30	30	NUM
ejpam-5339	221	3	)	)	PUNCT
ejpam-5339	221	4	can	can	AUX
ejpam-5339	221	5	be	be	AUX
ejpam-5339	221	6	drawn	draw	VERB
ejpam-5339	221	7	for	for	ADP
ejpam-5339	221	8	the	the	DET
ejpam-5339	221	9	sample	sample	NOUN
ejpam-5339	221	10	chosen	choose	VERB
ejpam-5339	221	11	system	system	NOUN
ejpam-5339	221	12	a	a	PRON
ejpam-5339	221	13	=	=	SYM
ejpam-5339	221	14	1	1	NUM
ejpam-5339	221	15	,	,	PUNCT
ejpam-5339	221	16	b	b	NOUN
ejpam-5339	221	17	=	=	SYM
ejpam-5339	221	18	1	1	NUM
ejpam-5339	221	19	,	,	PUNCT
ejpam-5339	221	20	c	c	NOUN
ejpam-5339	221	21	=	=	SYM
ejpam-5339	221	22	1	1	NUM
ejpam-5339	221	23	,	,	PUNCT
ejpam-5339	221	24	and	and	CCONJ
ejpam-5339	221	25	a	a	DET
ejpam-5339	221	26	=	=	SYM
ejpam-5339	221	27	0.5	0.5	NUM
ejpam-5339	221	28	:	:	PUNCT
ejpam-5339	221	29	from	from	ADP
ejpam-5339	221	30	the	the	DET
ejpam-5339	221	31	ns	ns	NOUN
ejpam-5339	221	32	in	in	ADP
ejpam-5339	221	33	fig	fig	NOUN
ejpam-5339	221	34	.	.	PUNCT
ejpam-5339	222	1	6	6	NUM
ejpam-5339	222	2	,	,	PUNCT
ejpam-5339	222	3	it	it	PRON
ejpam-5339	222	4	is	be	AUX
ejpam-5339	222	5	found	find	VERB
ejpam-5339	222	6	that	that	SCONJ
ejpam-5339	222	7	the	the	DET
ejpam-5339	222	8	absolute	absolute	ADJ
ejpam-5339	222	9	error	error	NOUN
ejpam-5339	222	10	between	between	ADP
ejpam-5339	222	11	the	the	DET
ejpam-5339	222	12	two	two	NUM
ejpam-5339	222	13	solutions	solution	NOUN
ejpam-5339	222	14	is	be	AUX
ejpam-5339	222	15	0.00948421	0.00948421	NUM
ejpam-5339	222	16	.	.	PUNCT
ejpam-5339	223	1	it	it	PRON
ejpam-5339	223	2	should	should	AUX
ejpam-5339	223	3	be	be	AUX
ejpam-5339	223	4	noted	note	VERB
ejpam-5339	223	5	that	that	SCONJ
ejpam-5339	223	6	,	,	PUNCT
ejpam-5339	223	7	in	in	ADP
ejpam-5339	223	8	contrast	contrast	NOUN
ejpam-5339	223	9	with	with	ADP
ejpam-5339	223	10	the	the	DET
ejpam-5339	223	11	traditional	traditional	ADJ
ejpam-5339	223	12	perturbation	perturbation	NOUN
ejpam-5339	223	13	techniques	technique	NOUN
ejpam-5339	223	14	,	,	PUNCT
ejpam-5339	223	15	the	the	DET
ejpam-5339	223	16	present	present	ADJ
ejpam-5339	223	17	npa	npa	NOUN
ejpam-5339	223	18	enables	enable	VERB
ejpam-5339	223	19	us	we	PRON
ejpam-5339	223	20	to	to	PART
ejpam-5339	223	21	discuss	discuss	VERB
ejpam-5339	223	22	the	the	DET
ejpam-5339	223	23	stability	stability	NOUN
ejpam-5339	223	24	criterion	criterion	NOUN
ejpam-5339	223	25	.	.	PUNCT
ejpam-5339	224	1	table	table	NOUN
ejpam-5339	224	2	1	1	NUM
ejpam-5339	224	3	:	:	PUNCT
ejpam-5339	224	4	validates	validate	VERB
ejpam-5339	224	5	the	the	DET
ejpam-5339	224	6	convergence	convergence	NOUN
ejpam-5339	224	7	of	of	ADP
ejpam-5339	224	8	the	the	DET
ejpam-5339	224	9	numerical	numerical	ADJ
ejpam-5339	224	10	and	and	CCONJ
ejpam-5339	224	11	npa	npa	NOUN
ejpam-5339	224	12	solutions	solution	NOUN
ejpam-5339	224	13	.	.	PUNCT
ejpam-5339	225	1	t	t	PROPN
ejpam-5339	225	2	numerical	numerical	PROPN
ejpam-5339	225	3	approximate	approximate	ADJ
ejpam-5339	225	4	absolute	absolute	ADJ
ejpam-5339	225	5	error	error	NOUN
ejpam-5339	225	6	0	0	NUM
ejpam-5339	225	7	0.5	0.5	NUM
ejpam-5339	225	8	0.5	0.5	NUM
ejpam-5339	225	9	0	0	NUM
ejpam-5339	225	10	5	5	NUM
ejpam-5339	225	11	0.21334	0.21334	NUM
ejpam-5339	225	12	0.215293	0.215293	NUM
ejpam-5339	225	13	0.00215861	0.00215861	NUM
ejpam-5339	225	14	10	10	NUM
ejpam-5339	225	15	-0.31025	-0.31025	NOUN
ejpam-5339	225	16	-0.314596	-0.314596	NOUN
ejpam-5339	226	1	0.00434554	0.00434554	NUM
ejpam-5339	226	2	15	15	NUM
ejpam-5339	226	3	-0.486305	-0.486305	NOUN
ejpam-5339	226	4	-0.486214	-0.486214	NOUN
ejpam-5339	226	5	0.00009056	0.00009056	NUM
ejpam-5339	226	6	20	20	NUM
ejpam-5339	226	7	-0.105488	-0.105488	NOUN
ejpam-5339	226	8	-0.104118	-0.104118	VERB
ejpam-5339	227	1	0.00137032	0.00137032	NUM
ejpam-5339	227	2	25	25	NUM
ejpam-5339	227	3	0.391676	0.391676	NUM
ejpam-5339	227	4	0.396551	0.396551	NUM
ejpam-5339	227	5	0.00487468	0.00487468	NUM
ejpam-5339	227	6	30	30	NUM
ejpam-5339	227	7	0.446169	0.446169	NUM
ejpam-5339	227	8	0.445617	0.445617	NUM
ejpam-5339	227	9	0.000552448	0.000552448	NUM
ejpam-5339	227	10	35	35	NUM
ejpam-5339	227	11	-0.0072927	-0.0072927	NOUN
ejpam-5339	227	12	-0.0127984	-0.0127984	NOUN
ejpam-5339	228	1	0.00550568	0.00550568	NUM
ejpam-5339	228	2	40	40	NUM
ejpam-5339	228	3	-0.452727	-0.452727	NOUN
ejpam-5339	228	4	-0.456639	-0.456639	NOUN
ejpam-5339	228	5	0.0039112	0.0039112	NUM
ejpam-5339	228	6	45	45	NUM
ejpam-5339	228	7	-0.382264	-0.382264	PROPN
ejpam-5339	228	8	-0.380446	-0.380446	NOUN
ejpam-5339	228	9	0.00181781	0.00181781	NUM
ejpam-5339	228	10	50	50	NUM
ejpam-5339	228	11	0.119721	0.119721	NUM
ejpam-5339	228	12	0.129009	0.129009	NUM
ejpam-5339	228	13	0.00928869	0.00928869	NUM
ejpam-5339	228	14	additionally	additionally	ADV
ejpam-5339	228	15	,	,	PUNCT
ejpam-5339	228	16	table	table	NOUN
ejpam-5339	228	17	1	1	NUM
ejpam-5339	228	18	displays	display	VERB
ejpam-5339	228	19	the	the	DET
ejpam-5339	228	20	absolute	absolute	ADJ
ejpam-5339	228	21	error	error	NOUN
ejpam-5339	228	22	between	between	ADP
ejpam-5339	228	23	the	the	DET
ejpam-5339	228	24	numerical	numerical	ADJ
ejpam-5339	228	25	and	and	CCONJ
ejpam-5339	228	26	approximate	approximate	ADJ
ejpam-5339	228	27	solutions	solution	NOUN
ejpam-5339	228	28	.	.	PUNCT
ejpam-5339	229	1	as	as	SCONJ
ejpam-5339	229	2	seen	see	VERB
ejpam-5339	229	3	,	,	PUNCT
ejpam-5339	229	4	this	this	DET
ejpam-5339	229	5	table	table	NOUN
ejpam-5339	229	6	demonstrates	demonstrate	VERB
ejpam-5339	229	7	that	that	SCONJ
ejpam-5339	229	8	the	the	DET
ejpam-5339	229	9	changes	change	NOUN
ejpam-5339	229	10	between	between	ADP
ejpam-5339	229	11	the	the	DET
ejpam-5339	229	12	two	two	NUM
ejpam-5339	229	13	solutions	solution	NOUN
ejpam-5339	229	14	are	be	AUX
ejpam-5339	229	15	very	very	ADV
ejpam-5339	229	16	small	small	ADJ
ejpam-5339	229	17	.	.	PUNCT
ejpam-5339	230	1	3.4	3.4	NUM
ejpam-5339	230	2	.	.	PUNCT
ejpam-5339	230	3	application	application	NOUN
ejpam-5339	230	4	4	4	NUM
ejpam-5339	230	5	consider	consider	VERB
ejpam-5339	230	6	the	the	DET
ejpam-5339	230	7	system	system	NOUN
ejpam-5339	230	8	generated	generate	VERB
ejpam-5339	230	9	by	by	ADP
ejpam-5339	230	10	nayfeh	nayfeh	PROPN
ejpam-5339	230	11	and	and	CCONJ
ejpam-5339	230	12	mook	mook	NOUN
ejpam-5339	231	1	[	[	X
ejpam-5339	231	2	37	37	NUM
ejpam-5339	231	3	]	]	PUNCT
ejpam-5339	231	4	,	,	PUNCT
ejpam-5339	231	5	the	the	DET
ejpam-5339	231	6	governing	govern	VERB
ejpam-5339	231	7	equation	equation	NOUN
ejpam-5339	231	8	of	of	ADP
ejpam-5339	231	9	motion	motion	NOUN
ejpam-5339	231	10	is	be	AUX
ejpam-5339	231	11	may	may	AUX
ejpam-5339	231	12	be	be	AUX
ejpam-5339	231	13	simplified	simplify	VERB
ejpam-5339	231	14	as	as	SCONJ
ejpam-5339	231	15	follows	follow	VERB
ejpam-5339	231	16	:	:	PUNCT
ejpam-5339	231	17	ü+	ü+	NUM
ejpam-5339	232	1	µ	µ	PRON
ejpam-5339	232	2	sin	sin	NOUN
ejpam-5339	232	3	u̇+	u̇+	PROPN
ejpam-5339	232	4	u	u	NOUN
ejpam-5339	232	5	=	=	PROPN
ejpam-5339	232	6	0	0	PROPN
ejpam-5339	232	7	.	.	PUNCT
ejpam-5339	233	1	(	(	PUNCT
ejpam-5339	233	2	31	31	NUM
ejpam-5339	233	3	)	)	PUNCT
ejpam-5339	233	4	in	in	ADP
ejpam-5339	233	5	the	the	DET
ejpam-5339	233	6	abovementioned	abovementioned	ADJ
ejpam-5339	233	7	example	example	NOUN
ejpam-5339	233	8	,	,	PUNCT
ejpam-5339	233	9	the	the	DET
ejpam-5339	233	10	nonlinearity	nonlinearity	NOUN
ejpam-5339	233	11	arises	arise	VERB
ejpam-5339	233	12	from	from	ADP
ejpam-5339	233	13	inertia	inertia	NOUN
ejpam-5339	233	14	and	and	CCONJ
ejpam-5339	233	15	significant	significant	ADJ
ejpam-5339	233	16	deformation	deformation	NOUN
ejpam-5339	233	17	.	.	PUNCT
ejpam-5339	234	1	g.	g.	PROPN
ejpam-5339	234	2	m.	m.	PROPN
ejpam-5339	234	3	ismail	ismail	PROPN
ejpam-5339	234	4	,	,	PUNCT
ejpam-5339	234	5	g.	g.	PROPN
ejpam-5339	234	6	m.	m.	PROPN
ejpam-5339	234	7	moatimid	moatimid	PROPN
ejpam-5339	234	8	,	,	PUNCT
ejpam-5339	234	9	m.	m.	NOUN
ejpam-5339	234	10	i.	i.	PROPN
ejpam-5339	234	11	yamani	yamani	PROPN
ejpam-5339	234	12	/	/	SYM
ejpam-5339	234	13	eur	eur	PROPN
ejpam-5339	234	14	.	.	PUNCT
ejpam-5339	235	1	j.	j.	PROPN
ejpam-5339	235	2	pure	pure	PROPN
ejpam-5339	235	3	appl	appl	PROPN
ejpam-5339	235	4	.	.	PROPN
ejpam-5339	235	5	math	math	PROPN
ejpam-5339	235	6	,	,	PUNCT
ejpam-5339	235	7	17	17	NUM
ejpam-5339	235	8	(	(	PUNCT
ejpam-5339	235	9	3	3	NUM
ejpam-5339	235	10	)	)	PUNCT
ejpam-5339	235	11	(	(	PUNCT
ejpam-5339	235	12	2024	2024	NUM
ejpam-5339	235	13	)	)	PUNCT
ejpam-5339	235	14	,	,	PUNCT
ejpam-5339	235	15	2155	2155	NUM
ejpam-5339	235	16	-	-	SYM
ejpam-5339	235	17	2172	2172	NUM
ejpam-5339	235	18	2164	2164	NUM
ejpam-5339	235	19	eq	eq	ADP
ejpam-5339	235	20	.	.	PUNCT
ejpam-5339	236	1	(	(	PUNCT
ejpam-5339	236	2	31	31	NUM
ejpam-5339	236	3	)	)	PUNCT
ejpam-5339	236	4	can	can	AUX
ejpam-5339	236	5	be	be	AUX
ejpam-5339	236	6	written	write	VERB
ejpam-5339	236	7	as	as	SCONJ
ejpam-5339	236	8	follows	follow	VERB
ejpam-5339	236	9	:	:	PUNCT
ejpam-5339	236	10	ü+	ü+	VERB
ejpam-5339	236	11	f1(u̇	f1(u̇	PROPN
ejpam-5339	236	12	)	)	PUNCT
ejpam-5339	237	1	+	+	PUNCT
ejpam-5339	237	2	f2(u	f2(u	NOUN
ejpam-5339	237	3	)	)	PUNCT
ejpam-5339	237	4	=	=	SYM
ejpam-5339	237	5	0	0	NUM
ejpam-5339	237	6	,	,	PUNCT
ejpam-5339	237	7	(	(	PUNCT
ejpam-5339	237	8	32	32	NUM
ejpam-5339	237	9	)	)	PUNCT
ejpam-5339	237	10	where	where	SCONJ
ejpam-5339	237	11	f1(u̇	f1(u̇	ADV
ejpam-5339	237	12	)	)	PUNCT
ejpam-5339	237	13	=	=	SYM
ejpam-5339	237	14	µ	µ	X
ejpam-5339	237	15	sin	sin	NOUN
ejpam-5339	237	16	u̇	u̇	PROPN
ejpam-5339	237	17	,	,	PUNCT
ejpam-5339	237	18	and	and	CCONJ
ejpam-5339	237	19	f2(u	f2(u	NOUN
ejpam-5339	237	20	)	)	PUNCT
ejpam-5339	237	21	=	=	SYM
ejpam-5339	237	22	u	u	NOUN
ejpam-5339	237	23	assuming	assume	VERB
ejpam-5339	237	24	that	that	SCONJ
ejpam-5339	237	25	the	the	DET
ejpam-5339	237	26	guessing	guess	VERB
ejpam-5339	237	27	solution	solution	NOUN
ejpam-5339	237	28	is	be	AUX
ejpam-5339	237	29	given	give	VERB
ejpam-5339	237	30	by	by	ADP
ejpam-5339	237	31	p	p	NOUN
ejpam-5339	237	32	=	=	PROPN
ejpam-5339	237	33	a	a	DET
ejpam-5339	237	34	cosωt	cosωt	NOUN
ejpam-5339	237	35	,	,	PUNCT
ejpam-5339	237	36	ics	ics	PROPN
ejpam-5339	237	37	p(0	p(0	PROPN
ejpam-5339	237	38	)	)	PUNCT
ejpam-5339	237	39	=	=	SYM
ejpam-5339	237	40	a	a	PRON
ejpam-5339	237	41	,	,	PUNCT
ejpam-5339	237	42	and	and	CCONJ
ejpam-5339	237	43	ṗ(0	ṗ(0	NOUN
ejpam-5339	237	44	)	)	PUNCT
ejpam-5339	237	45	=	=	SYM
ejpam-5339	238	1	0	0	X
ejpam-5339	238	2	.	.	PUNCT
ejpam-5339	239	1	(	(	PUNCT
ejpam-5339	239	2	33	33	NUM
ejpam-5339	239	3	)	)	PUNCT
ejpam-5339	239	4	the	the	DET
ejpam-5339	239	5	equivalent	equivalent	ADJ
ejpam-5339	239	6	frequency	frequency	NOUN
ejpam-5339	239	7	may	may	AUX
ejpam-5339	239	8	be	be	AUX
ejpam-5339	239	9	determined	determine	VERB
ejpam-5339	239	10	from	from	ADP
ejpam-5339	239	11	the	the	DET
ejpam-5339	239	12	following	follow	VERB
ejpam-5339	239	13	integration	integration	NOUN
ejpam-5339	239	14	:	:	PUNCT
ejpam-5339	239	15	ω2	ω2	ADJ
ejpam-5339	239	16	eqv	eqv	NOUN
ejpam-5339	239	17	=	=	PUNCT
ejpam-5339	239	18	2π	2π	NOUN
ejpam-5339	239	19	/	/	SYM
ejpam-5339	239	20	ω∫	ω∫	NOUN
ejpam-5339	239	21	0	0	NUM
ejpam-5339	239	22	pf2(p)dt	pf2(p)dt	NOUN
ejpam-5339	239	23	/	/	SYM
ejpam-5339	240	1	2π	2π	NOUN
ejpam-5339	240	2	/	/	SYM
ejpam-5339	240	3	ω∫	ω∫	NOUN
ejpam-5339	240	4	0	0	NUM
ejpam-5339	240	5	p2dt	p2dt	NOUN
ejpam-5339	240	6	=	=	SYM
ejpam-5339	240	7	1	1	X
ejpam-5339	240	8	.	.	PUNCT
ejpam-5339	241	1	(	(	PUNCT
ejpam-5339	241	2	34	34	NUM
ejpam-5339	241	3	)	)	PUNCT
ejpam-5339	241	4	the	the	DET
ejpam-5339	241	5	equivalent	equivalent	ADJ
ejpam-5339	241	6	damping	damp	VERB
ejpam-5339	241	7	may	may	AUX
ejpam-5339	241	8	be	be	AUX
ejpam-5339	241	9	determined	determine	VERB
ejpam-5339	241	10	from	from	ADP
ejpam-5339	241	11	the	the	DET
ejpam-5339	241	12	following	follow	VERB
ejpam-5339	241	13	integral	integral	ADJ
ejpam-5339	241	14	σeqv	σeqv	NOUN
ejpam-5339	241	15	=	=	SYM
ejpam-5339	241	16	2π	2π	NOUN
ejpam-5339	241	17	/	/	SYM
ejpam-5339	241	18	ω∫	ω∫	NOUN
ejpam-5339	241	19	0	0	NUM
ejpam-5339	241	20	f1(ṗ)dt	f1(ṗ)dt	NOUN
ejpam-5339	241	21	/	/	SYM
ejpam-5339	241	22	2π	2π	NOUN
ejpam-5339	241	23	/	/	SYM
ejpam-5339	241	24	ω∫	ω∫	NOUN
ejpam-5339	241	25	0	0	NUM
ejpam-5339	241	26	ṗ2dt	ṗ2dt	NUM
ejpam-5339	241	27	.	.	PUNCT
ejpam-5339	242	1	(	(	PUNCT
ejpam-5339	242	2	35	35	NUM
ejpam-5339	242	3	)	)	PUNCT
ejpam-5339	242	4	by	by	ADP
ejpam-5339	242	5	means	mean	NOUN
ejpam-5339	242	6	of	of	ADP
ejpam-5339	242	7	the	the	DET
ejpam-5339	242	8	ms	ms	NOUN
ejpam-5339	242	9	,	,	PUNCT
ejpam-5339	242	10	eq	eq	NOUN
ejpam-5339	242	11	.	.	PUNCT
ejpam-5339	243	1	(	(	PUNCT
ejpam-5339	243	2	35	35	NUM
ejpam-5339	243	3	)	)	PUNCT
ejpam-5339	243	4	yields	yield	VERB
ejpam-5339	243	5	σeqv	σeqv	NOUN
ejpam-5339	243	6	=	=	SYM
ejpam-5339	243	7	2µ	2µ	NUM
ejpam-5339	243	8	aω	aω	PROPN
ejpam-5339	243	9	j1(aω	j1(aω	PROPN
ejpam-5339	243	10	)	)	PUNCT
ejpam-5339	243	11	.	.	PUNCT
ejpam-5339	244	1	(	(	PUNCT
ejpam-5339	244	2	36	36	NUM
ejpam-5339	244	3	)	)	PUNCT
ejpam-5339	244	4	as	as	SCONJ
ejpam-5339	244	5	previously	previously	ADV
ejpam-5339	244	6	seen	see	VERB
ejpam-5339	244	7	,	,	PUNCT
ejpam-5339	244	8	the	the	DET
ejpam-5339	244	9	equivalent	equivalent	ADJ
ejpam-5339	244	10	linear	linear	ADJ
ejpam-5339	244	11	equation	equation	NOUN
ejpam-5339	244	12	may	may	AUX
ejpam-5339	244	13	be	be	AUX
ejpam-5339	244	14	written	write	VERB
ejpam-5339	244	15	as	as	SCONJ
ejpam-5339	244	16	follows	follow	VERB
ejpam-5339	244	17	:	:	PUNCT
ejpam-5339	245	1	p̈+	p̈+	NOUN
ejpam-5339	245	2	σeqvṗ+	σeqvṗ+	PROPN
ejpam-5339	245	3	p	p	NOUN
ejpam-5339	245	4	=	=	NOUN
ejpam-5339	245	5	0	0	PROPN
ejpam-5339	245	6	.	.	PUNCT
ejpam-5339	246	1	(	(	PUNCT
ejpam-5339	246	2	37	37	NUM
ejpam-5339	246	3	)	)	PUNCT
ejpam-5339	246	4	by	by	ADP
ejpam-5339	246	5	making	make	VERB
ejpam-5339	246	6	use	use	NOUN
ejpam-5339	246	7	of	of	ADP
ejpam-5339	246	8	the	the	DET
ejpam-5339	246	9	standard	standard	ADJ
ejpam-5339	246	10	normal	normal	ADJ
ejpam-5339	246	11	form	form	NOUN
ejpam-5339	246	12	,	,	PUNCT
ejpam-5339	246	13	the	the	DET
ejpam-5339	246	14	total	total	ADJ
ejpam-5339	246	15	frequency	frequency	NOUN
ejpam-5339	246	16	of	of	ADP
ejpam-5339	246	17	the	the	DET
ejpam-5339	246	18	considered	consider	VERB
ejpam-5339	246	19	system	system	NOUN
ejpam-5339	246	20	can	can	AUX
ejpam-5339	246	21	be	be	AUX
ejpam-5339	246	22	written	write	VERB
ejpam-5339	246	23	as	as	ADP
ejpam-5339	246	24	:	:	PUNCT
ejpam-5339	246	25	ω2	ω2	PROPN
ejpam-5339	246	26	=	=	SYM
ejpam-5339	246	27	1−	1−	NUM
ejpam-5339	246	28	(	(	PUNCT
ejpam-5339	246	29	µ	µ	X
ejpam-5339	246	30	aω	aω	X
ejpam-5339	246	31	j1(aω	j1(aω	PROPN
ejpam-5339	246	32	)	)	PUNCT
ejpam-5339	246	33	)	)	PUNCT
ejpam-5339	246	34	2	2	X
ejpam-5339	246	35	.	.	PUNCT
ejpam-5339	247	1	(	(	PUNCT
ejpam-5339	247	2	38	38	NUM
ejpam-5339	247	3	)	)	PUNCT
ejpam-5339	247	4	the	the	DET
ejpam-5339	247	5	stability	stability	NOUN
ejpam-5339	247	6	criterion	criterion	NOUN
ejpam-5339	247	7	requires	require	VERB
ejpam-5339	247	8	that	that	SCONJ
ejpam-5339	247	9	ω2	ω2	ADV
ejpam-5339	247	10	>	>	X
ejpam-5339	247	11	0	0	PUNCT
ejpam-5339	247	12	or	or	CCONJ
ejpam-5339	247	13	(	(	PUNCT
ejpam-5339	247	14	µ	µ	X
ejpam-5339	247	15	aωj1(aω	aωj1(aω	ADV
ejpam-5339	247	16	)	)	PUNCT
ejpam-5339	247	17	)	)	PUNCT
ejpam-5339	248	1	<	<	X
ejpam-5339	248	2	1	1	X
ejpam-5339	248	3	.	.	PUNCT
ejpam-5339	248	4	it	it	PRON
ejpam-5339	248	5	should	should	AUX
ejpam-5339	248	6	be	be	AUX
ejpam-5339	248	7	noted	note	VERB
ejpam-5339	248	8	that	that	SCONJ
ejpam-5339	248	9	eq	eq	ADP
ejpam-5339	248	10	.	.	PUNCT
ejpam-5339	248	11	(	(	PUNCT
ejpam-5339	248	12	30	30	NUM
ejpam-5339	248	13	)	)	PUNCT
ejpam-5339	248	14	is	be	AUX
ejpam-5339	248	15	a	a	DET
ejpam-5339	248	16	transcendental	transcendental	ADJ
ejpam-5339	248	17	equation	equation	NOUN
ejpam-5339	248	18	in	in	ADP
ejpam-5339	248	19	the	the	DET
ejpam-5339	248	20	total	total	ADJ
ejpam-5339	248	21	frequency	frequency	NOUN
ejpam-5339	248	22	ω	ω	NOUN
ejpam-5339	248	23	.	.	PUNCT
ejpam-5339	248	24	by	by	ADP
ejpam-5339	248	25	making	make	VERB
ejpam-5339	248	26	use	use	NOUN
ejpam-5339	248	27	of	of	ADP
ejpam-5339	248	28	the	the	DET
ejpam-5339	248	29	ms	ms	NOUN
ejpam-5339	248	30	,	,	PUNCT
ejpam-5339	248	31	through	through	ADP
ejpam-5339	248	32	the	the	DET
ejpam-5339	248	33	command	command	NOUN
ejpam-5339	248	34	findroot	findroot	NOUN
ejpam-5339	248	35	,	,	PUNCT
ejpam-5339	248	36	for	for	ADP
ejpam-5339	248	37	the	the	DET
ejpam-5339	248	38	data	datum	NOUN
ejpam-5339	248	39	µ	µ	X
ejpam-5339	248	40	=	=	SYM
ejpam-5339	248	41	0.05	0.05	NUM
ejpam-5339	248	42	and	and	CCONJ
ejpam-5339	248	43	,	,	PUNCT
ejpam-5339	248	44	a	a	DET
ejpam-5339	248	45	=	=	SYM
ejpam-5339	248	46	0.5	0.5	NUM
ejpam-5339	248	47	utilizing	utilize	VERB
ejpam-5339	248	48	the	the	DET
ejpam-5339	248	49	ns	ns	NOUN
ejpam-5339	248	50	,	,	PUNCT
ejpam-5339	248	51	it	it	PRON
ejpam-5339	248	52	follows	follow	VERB
ejpam-5339	248	53	that	that	SCONJ
ejpam-5339	248	54	the	the	DET
ejpam-5339	248	55	approximate	approximate	ADJ
ejpam-5339	248	56	root	root	NOUN
ejpam-5339	248	57	of	of	ADP
ejpam-5339	248	58	the	the	DET
ejpam-5339	248	59	frequency	frequency	NOUN
ejpam-5339	248	60	becomes	become	VERB
ejpam-5339	248	61	:	:	PUNCT
ejpam-5339	249	1	0.999706	0.999706	NUM
ejpam-5339	249	2	.	.	PUNCT
ejpam-5339	250	1	it	it	PRON
ejpam-5339	250	2	should	should	AUX
ejpam-5339	250	3	be	be	AUX
ejpam-5339	250	4	noted	note	VERB
ejpam-5339	250	5	that	that	SCONJ
ejpam-5339	250	6	the	the	DET
ejpam-5339	250	7	total	total	ADJ
ejpam-5339	250	8	frequency	frequency	NOUN
ejpam-5339	250	9	is	be	AUX
ejpam-5339	250	10	very	very	ADV
ejpam-5339	250	11	close	close	ADJ
ejpam-5339	250	12	with	with	ADP
ejpam-5339	250	13	nature	nature	NOUN
ejpam-5339	250	14	frequency	frequency	NOUN
ejpam-5339	250	15	of	of	ADP
ejpam-5339	250	16	the	the	DET
ejpam-5339	250	17	system	system	NOUN
ejpam-5339	250	18	.	.	PUNCT
ejpam-5339	251	1	for	for	ADP
ejpam-5339	251	2	more	more	ADJ
ejpam-5339	251	3	convenience	convenience	NOUN
ejpam-5339	251	4	,	,	PUNCT
ejpam-5339	251	5	with	with	ADP
ejpam-5339	251	6	the	the	DET
ejpam-5339	251	7	aid	aid	NOUN
ejpam-5339	251	8	of	of	ADP
ejpam-5339	251	9	the	the	DET
ejpam-5339	251	10	ms	ms	PROPN
ejpam-5339	251	11	,	,	PUNCT
ejpam-5339	251	12	a	a	DET
ejpam-5339	251	13	matching	matching	NOUN
ejpam-5339	251	14	between	between	ADP
ejpam-5339	251	15	the	the	DET
ejpam-5339	251	16	original	original	ADJ
ejpam-5339	251	17	non	non	ADJ
ejpam-5339	251	18	-	-	ADJ
ejpam-5339	251	19	linear	linear	ADJ
ejpam-5339	251	20	ode	ode	NOUN
ejpam-5339	251	21	as	as	SCONJ
ejpam-5339	251	22	given	give	VERB
ejpam-5339	251	23	in	in	ADP
ejpam-5339	251	24	eq	eq	ADP
ejpam-5339	251	25	.	.	PUNCT
ejpam-5339	252	1	(	(	PUNCT
ejpam-5339	252	2	31	31	NUM
ejpam-5339	252	3	)	)	PUNCT
ejpam-5339	252	4	with	with	ADP
ejpam-5339	252	5	the	the	DET
ejpam-5339	252	6	equivalent	equivalent	ADJ
ejpam-5339	252	7	linear	linear	ADJ
ejpam-5339	252	8	ode	ode	NOUN
ejpam-5339	252	9	as	as	SCONJ
ejpam-5339	252	10	given	give	VERB
ejpam-5339	252	11	in	in	ADP
ejpam-5339	252	12	eq	eq	ADP
ejpam-5339	252	13	.	.	PUNCT
ejpam-5339	253	1	(	(	PUNCT
ejpam-5339	253	2	37	37	NUM
ejpam-5339	253	3	)	)	PUNCT
ejpam-5339	253	4	can	can	AUX
ejpam-5339	253	5	be	be	AUX
ejpam-5339	253	6	drawn	draw	VERB
ejpam-5339	253	7	for	for	ADP
ejpam-5339	253	8	the	the	DET
ejpam-5339	253	9	previous	previous	ADJ
ejpam-5339	253	10	data	data	NOUN
ejpam-5339	253	11	system	system	NOUN
ejpam-5339	253	12	:	:	PUNCT
ejpam-5339	253	13	from	from	ADP
ejpam-5339	253	14	the	the	DET
ejpam-5339	253	15	ns	ns	NOUN
ejpam-5339	253	16	in	in	ADP
ejpam-5339	253	17	fig	fig	NOUN
ejpam-5339	253	18	.	.	PUNCT
ejpam-5339	254	1	7	7	NUM
ejpam-5339	254	2	,	,	PUNCT
ejpam-5339	254	3	it	it	PRON
ejpam-5339	254	4	is	be	AUX
ejpam-5339	254	5	found	find	VERB
ejpam-5339	254	6	that	that	SCONJ
ejpam-5339	254	7	the	the	DET
ejpam-5339	254	8	absolute	absolute	ADJ
ejpam-5339	254	9	error	error	NOUN
ejpam-5339	254	10	between	between	ADP
ejpam-5339	254	11	the	the	DET
ejpam-5339	254	12	two	two	NUM
ejpam-5339	254	13	solutions	solution	NOUN
ejpam-5339	254	14	is	be	AUX
ejpam-5339	254	15	0.00347	0.00347	NUM
ejpam-5339	254	16	.	.	PUNCT
ejpam-5339	255	1	it	it	PRON
ejpam-5339	255	2	should	should	AUX
ejpam-5339	255	3	be	be	AUX
ejpam-5339	255	4	renowned	renowne	VERB
ejpam-5339	255	5	that	that	SCONJ
ejpam-5339	255	6	,	,	PUNCT
ejpam-5339	255	7	in	in	ADP
ejpam-5339	255	8	contrast	contrast	NOUN
ejpam-5339	255	9	with	with	ADP
ejpam-5339	255	10	the	the	DET
ejpam-5339	255	11	traditional	traditional	ADJ
ejpam-5339	255	12	perturbation	perturbation	NOUN
ejpam-5339	255	13	techniques	technique	NOUN
ejpam-5339	255	14	,	,	PUNCT
ejpam-5339	255	15	the	the	DET
ejpam-5339	255	16	present	present	ADJ
ejpam-5339	255	17	npa	npa	NOUN
ejpam-5339	255	18	does	do	AUX
ejpam-5339	255	19	not	not	PART
ejpam-5339	255	20	use	use	VERB
ejpam-5339	255	21	the	the	DET
ejpam-5339	255	22	taylor	taylor	PROPN
ejpam-5339	255	23	expansion	expansion	NOUN
ejpam-5339	255	24	for	for	ADP
ejpam-5339	255	25	the	the	DET
ejpam-5339	255	26	restoring	restore	VERB
ejpam-5339	255	27	forces	force	NOUN
ejpam-5339	255	28	.	.	PUNCT
ejpam-5339	256	1	additionally	additionally	ADV
ejpam-5339	256	2	,	,	PUNCT
ejpam-5339	256	3	it	it	PRON
ejpam-5339	256	4	enables	enable	VERB
ejpam-5339	256	5	us	we	PRON
ejpam-5339	256	6	to	to	PART
ejpam-5339	256	7	discuss	discuss	VERB
ejpam-5339	256	8	the	the	DET
ejpam-5339	256	9	stability	stability	NOUN
ejpam-5339	256	10	criterion	criterion	NOUN
ejpam-5339	256	11	.	.	PUNCT
ejpam-5339	257	1	g.	g.	PROPN
ejpam-5339	257	2	m.	m.	PROPN
ejpam-5339	257	3	ismail	ismail	PROPN
ejpam-5339	257	4	,	,	PUNCT
ejpam-5339	257	5	g.	g.	PROPN
ejpam-5339	257	6	m.	m.	PROPN
ejpam-5339	257	7	moatimid	moatimid	PROPN
ejpam-5339	257	8	,	,	PUNCT
ejpam-5339	257	9	m.	m.	NOUN
ejpam-5339	257	10	i.	i.	PROPN
ejpam-5339	257	11	yamani	yamani	PROPN
ejpam-5339	257	12	/	/	SYM
ejpam-5339	257	13	eur	eur	PROPN
ejpam-5339	257	14	.	.	PUNCT
ejpam-5339	258	1	j.	j.	PROPN
ejpam-5339	258	2	pure	pure	PROPN
ejpam-5339	258	3	appl	appl	PROPN
ejpam-5339	258	4	.	.	PROPN
ejpam-5339	258	5	math	math	PROPN
ejpam-5339	258	6	,	,	PUNCT
ejpam-5339	258	7	17	17	NUM
ejpam-5339	258	8	(	(	PUNCT
ejpam-5339	258	9	3	3	NUM
ejpam-5339	258	10	)	)	PUNCT
ejpam-5339	258	11	(	(	PUNCT
ejpam-5339	258	12	2024	2024	NUM
ejpam-5339	258	13	)	)	PUNCT
ejpam-5339	258	14	,	,	PUNCT
ejpam-5339	258	15	2155	2155	NUM
ejpam-5339	258	16	-	-	SYM
ejpam-5339	258	17	2172	2172	NUM
ejpam-5339	258	18	2165	2165	NUM
ejpam-5339	258	19	4	4	NUM
ejpam-5339	258	20	.	.	PUNCT
ejpam-5339	258	21	discussion	discussion	NOUN
ejpam-5339	258	22	and	and	CCONJ
ejpam-5339	258	23	results	result	VERB
ejpam-5339	258	24	the	the	DET
ejpam-5339	258	25	solutions	solution	NOUN
ejpam-5339	258	26	from	from	ADP
ejpam-5339	258	27	the	the	DET
ejpam-5339	258	28	npa	npa	NOUN
ejpam-5339	258	29	are	be	AUX
ejpam-5339	258	30	compared	compare	VERB
ejpam-5339	258	31	to	to	ADP
ejpam-5339	258	32	the	the	DET
ejpam-5339	258	33	fourth	fourth	ADJ
ejpam-5339	258	34	order	order	NOUN
ejpam-5339	258	35	runge	runge	NOUN
ejpam-5339	258	36	-	-	PUNCT
ejpam-5339	258	37	kutta	kutta	NOUN
ejpam-5339	258	38	approximations	approximation	NOUN
ejpam-5339	258	39	illustrated	illustrate	VERB
ejpam-5339	258	40	in	in	ADP
ejpam-5339	258	41	figs	fig	NOUN
ejpam-5339	258	42	.	.	PUNCT
ejpam-5339	259	1	2	2	NUM
ejpam-5339	259	2	,	,	PUNCT
ejpam-5339	259	3	3	3	NUM
ejpam-5339	259	4	,	,	PUNCT
ejpam-5339	259	5	6	6	NUM
ejpam-5339	259	6	and	and	CCONJ
ejpam-5339	259	7	7	7	NUM
ejpam-5339	259	8	.	.	PUNCT
ejpam-5339	260	1	the	the	DET
ejpam-5339	260	2	precisions	precision	NOUN
ejpam-5339	260	3	of	of	ADP
ejpam-5339	260	4	all	all	DET
ejpam-5339	260	5	derived	derived	ADJ
ejpam-5339	260	6	analytical	analytical	ADJ
ejpam-5339	260	7	approximations	approximation	NOUN
ejpam-5339	260	8	using	use	VERB
ejpam-5339	260	9	the	the	DET
ejpam-5339	260	10	npa	npa	NOUN
ejpam-5339	260	11	and	and	CCONJ
ejpam-5339	260	12	rk4	rk4	NOUN
ejpam-5339	260	13	are	be	AUX
ejpam-5339	260	14	remarkably	remarkably	ADV
ejpam-5339	260	15	compatible	compatible	ADJ
ejpam-5339	260	16	.	.	PUNCT
ejpam-5339	261	1	based	base	VERB
ejpam-5339	261	2	on	on	ADP
ejpam-5339	261	3	these	these	DET
ejpam-5339	261	4	comparisons	comparison	NOUN
ejpam-5339	261	5	,	,	PUNCT
ejpam-5339	261	6	the	the	DET
ejpam-5339	261	7	current	current	ADJ
ejpam-5339	261	8	study	study	NOUN
ejpam-5339	261	9	gives	give	VERB
ejpam-5339	261	10	assurance	assurance	NOUN
ejpam-5339	261	11	in	in	ADP
ejpam-5339	261	12	the	the	DET
ejpam-5339	261	13	approach	approach	NOUN
ejpam-5339	261	14	used	use	VERB
ejpam-5339	261	15	to	to	PART
ejpam-5339	261	16	discover	discover	VERB
ejpam-5339	261	17	a	a	DET
ejpam-5339	261	18	quick	quick	ADJ
ejpam-5339	261	19	and	and	CCONJ
ejpam-5339	261	20	efficient	efficient	ADJ
ejpam-5339	261	21	analytical	analytical	ADJ
ejpam-5339	261	22	solution	solution	NOUN
ejpam-5339	261	23	of	of	ADP
ejpam-5339	261	24	the	the	DET
ejpam-5339	261	25	previous	previous	ADJ
ejpam-5339	261	26	odes	ode	NOUN
ejpam-5339	261	27	.	.	PUNCT
ejpam-5339	262	1	furthermore	furthermore	ADV
ejpam-5339	262	2	,	,	PUNCT
ejpam-5339	262	3	the	the	DET
ejpam-5339	262	4	accuracy	accuracy	NOUN
ejpam-5339	262	5	of	of	ADP
ejpam-5339	262	6	the	the	DET
ejpam-5339	262	7	npa	npa	NOUN
ejpam-5339	262	8	is	be	AUX
ejpam-5339	262	9	sometimes	sometimes	ADV
ejpam-5339	262	10	better	well	ADJ
ejpam-5339	262	11	than	than	ADP
ejpam-5339	262	12	that	that	PRON
ejpam-5339	262	13	of	of	ADP
ejpam-5339	262	14	traditional	traditional	ADJ
ejpam-5339	262	15	perturbation	perturbation	NOUN
ejpam-5339	262	16	techniques	technique	NOUN
ejpam-5339	262	17	,	,	PUNCT
ejpam-5339	262	18	and	and	CCONJ
ejpam-5339	262	19	there	there	PRON
ejpam-5339	262	20	is	be	VERB
ejpam-5339	262	21	a	a	DET
ejpam-5339	262	22	high	high	ADJ
ejpam-5339	262	23	degree	degree	NOUN
ejpam-5339	262	24	of	of	ADP
ejpam-5339	262	25	harmony	harmony	NOUN
ejpam-5339	262	26	and	and	CCONJ
ejpam-5339	262	27	agreement	agreement	NOUN
ejpam-5339	262	28	between	between	ADP
ejpam-5339	262	29	the	the	DET
ejpam-5339	262	30	analytical	analytical	ADJ
ejpam-5339	262	31	and	and	CCONJ
ejpam-5339	262	32	numerical	numerical	ADJ
ejpam-5339	262	33	approximations	approximation	NOUN
ejpam-5339	262	34	,	,	PUNCT
ejpam-5339	262	35	which	which	PRON
ejpam-5339	262	36	contributes	contribute	VERB
ejpam-5339	262	37	to	to	ADP
ejpam-5339	262	38	the	the	DET
ejpam-5339	262	39	exceptional	exceptional	ADJ
ejpam-5339	262	40	accuracy	accuracy	NOUN
ejpam-5339	262	41	of	of	ADP
ejpam-5339	262	42	all	all	DET
ejpam-5339	262	43	derived	derived	ADJ
ejpam-5339	262	44	analytic	analytic	ADJ
ejpam-5339	262	45	approximations	approximation	NOUN
ejpam-5339	262	46	.	.	PUNCT
ejpam-5339	263	1	figure	figure	NOUN
ejpam-5339	263	2	1	1	NUM
ejpam-5339	263	3	:	:	PUNCT
ejpam-5339	263	4	displays	display	VERB
ejpam-5339	263	5	the	the	DET
ejpam-5339	263	6	stability	stability	NOUN
ejpam-5339	263	7	profile	profile	NOUN
ejpam-5339	263	8	for	for	ADP
ejpam-5339	263	9	ω	ω	PROPN
ejpam-5339	263	10	via	via	ADP
ejpam-5339	263	11	a	a	PRON
ejpam-5339	263	12	at	at	ADP
ejpam-5339	263	13	g	g	NOUN
ejpam-5339	263	14	=	=	SYM
ejpam-5339	263	15	12	12	NUM
ejpam-5339	263	16	.	.	PUNCT
ejpam-5339	264	1	figure	figure	NOUN
ejpam-5339	264	2	2	2	NUM
ejpam-5339	264	3	:	:	PUNCT
ejpam-5339	264	4	a	a	DET
ejpam-5339	264	5	matching	matching	NOUN
ejpam-5339	264	6	between	between	ADP
ejpam-5339	264	7	the	the	DET
ejpam-5339	264	8	nonlinear	nonlinear	ADJ
ejpam-5339	264	9	/	/	SYM
ejpam-5339	264	10	linear	linear	ADJ
ejpam-5339	264	11	odes	ode	NOUN
ejpam-5339	264	12	as	as	SCONJ
ejpam-5339	264	13	given	give	VERB
ejpam-5339	264	14	in	in	ADP
ejpam-5339	264	15	eqs	eqs	PROPN
ejpam-5339	264	16	.	.	PUNCT
ejpam-5339	265	1	(	(	PUNCT
ejpam-5339	265	2	9	9	NUM
ejpam-5339	265	3	)	)	PUNCT
ejpam-5339	265	4	and	and	CCONJ
ejpam-5339	265	5	(	(	PUNCT
ejpam-5339	265	6	15	15	NUM
ejpam-5339	265	7	)	)	PUNCT
ejpam-5339	265	8	,	,	PUNCT
ejpam-5339	265	9	respectively	respectively	ADV
ejpam-5339	265	10	.	.	PUNCT
ejpam-5339	266	1	g.	g.	PROPN
ejpam-5339	266	2	m.	m.	PROPN
ejpam-5339	266	3	ismail	ismail	PROPN
ejpam-5339	266	4	,	,	PUNCT
ejpam-5339	266	5	g.	g.	PROPN
ejpam-5339	266	6	m.	m.	PROPN
ejpam-5339	266	7	moatimid	moatimid	PROPN
ejpam-5339	266	8	,	,	PUNCT
ejpam-5339	266	9	m.	m.	NOUN
ejpam-5339	266	10	i.	i.	PROPN
ejpam-5339	266	11	yamani	yamani	PROPN
ejpam-5339	266	12	/	/	SYM
ejpam-5339	266	13	eur	eur	PROPN
ejpam-5339	266	14	.	.	PUNCT
ejpam-5339	267	1	j.	j.	PROPN
ejpam-5339	267	2	pure	pure	PROPN
ejpam-5339	267	3	appl	appl	PROPN
ejpam-5339	267	4	.	.	PROPN
ejpam-5339	267	5	math	math	PROPN
ejpam-5339	267	6	,	,	PUNCT
ejpam-5339	267	7	17	17	NUM
ejpam-5339	267	8	(	(	PUNCT
ejpam-5339	267	9	3	3	NUM
ejpam-5339	267	10	)	)	PUNCT
ejpam-5339	267	11	(	(	PUNCT
ejpam-5339	267	12	2024	2024	NUM
ejpam-5339	267	13	)	)	PUNCT
ejpam-5339	267	14	,	,	PUNCT
ejpam-5339	267	15	2155	2155	NUM
ejpam-5339	267	16	-	-	SYM
ejpam-5339	267	17	2172	2172	NUM
ejpam-5339	267	18	2166	2166	NUM
ejpam-5339	267	19	figure	figure	NOUN
ejpam-5339	267	20	3	3	NUM
ejpam-5339	267	21	:	:	PUNCT
ejpam-5339	267	22	a	a	DET
ejpam-5339	267	23	matching	matching	NOUN
ejpam-5339	267	24	between	between	ADP
ejpam-5339	267	25	the	the	DET
ejpam-5339	267	26	two	two	NUM
ejpam-5339	267	27	nonlinear	nonlinear	ADJ
ejpam-5339	267	28	/	/	SYM
ejpam-5339	267	29	linear	linear	ADJ
ejpam-5339	267	30	odes	ode	NOUN
ejpam-5339	267	31	as	as	SCONJ
ejpam-5339	267	32	given	give	VERB
ejpam-5339	267	33	in	in	ADP
ejpam-5339	267	34	eqs	eqs	PROPN
ejpam-5339	267	35	.	.	PUNCT
ejpam-5339	268	1	(	(	PUNCT
ejpam-5339	268	2	16	16	NUM
ejpam-5339	268	3	)	)	PUNCT
ejpam-5339	268	4	and	and	CCONJ
ejpam-5339	268	5	(	(	PUNCT
ejpam-5339	268	6	22	22	NUM
ejpam-5339	268	7	)	)	PUNCT
ejpam-5339	268	8	,	,	PUNCT
ejpam-5339	268	9	respectively	respectively	ADV
ejpam-5339	268	10	.	.	PUNCT
ejpam-5339	269	1	figure	figure	VERB
ejpam-5339	269	2	4	4	NUM
ejpam-5339	269	3	:	:	PUNCT
ejpam-5339	269	4	sketches	sketch	VERB
ejpam-5339	269	5	the	the	DET
ejpam-5339	269	6	stability	stability	NOUN
ejpam-5339	269	7	/	/	SYM
ejpam-5339	269	8	instability	instability	NOUN
ejpam-5339	269	9	zones	zone	NOUN
ejpam-5339	269	10	.	.	PUNCT
ejpam-5339	270	1	g.	g.	PROPN
ejpam-5339	270	2	m.	m.	PROPN
ejpam-5339	270	3	ismail	ismail	PROPN
ejpam-5339	270	4	,	,	PUNCT
ejpam-5339	270	5	g.	g.	PROPN
ejpam-5339	270	6	m.	m.	PROPN
ejpam-5339	270	7	moatimid	moatimid	PROPN
ejpam-5339	270	8	,	,	PUNCT
ejpam-5339	270	9	m.	m.	NOUN
ejpam-5339	270	10	i.	i.	PROPN
ejpam-5339	270	11	yamani	yamani	PROPN
ejpam-5339	270	12	/	/	SYM
ejpam-5339	270	13	eur	eur	PROPN
ejpam-5339	270	14	.	.	PUNCT
ejpam-5339	271	1	j.	j.	PROPN
ejpam-5339	271	2	pure	pure	PROPN
ejpam-5339	271	3	appl	appl	PROPN
ejpam-5339	271	4	.	.	PROPN
ejpam-5339	271	5	math	math	PROPN
ejpam-5339	271	6	,	,	PUNCT
ejpam-5339	271	7	17	17	NUM
ejpam-5339	271	8	(	(	PUNCT
ejpam-5339	271	9	3	3	NUM
ejpam-5339	271	10	)	)	PUNCT
ejpam-5339	271	11	(	(	PUNCT
ejpam-5339	271	12	2024	2024	NUM
ejpam-5339	271	13	)	)	PUNCT
ejpam-5339	271	14	,	,	PUNCT
ejpam-5339	271	15	2155	2155	NUM
ejpam-5339	271	16	-	-	SYM
ejpam-5339	271	17	2172	2172	NUM
ejpam-5339	271	18	2167	2167	NUM
ejpam-5339	271	19	figure	figure	NOUN
ejpam-5339	271	20	5	5	NUM
ejpam-5339	271	21	:	:	PUNCT
ejpam-5339	271	22	geometric	geometric	ADJ
ejpam-5339	271	23	structure	structure	NOUN
ejpam-5339	271	24	of	of	ADP
ejpam-5339	271	25	the	the	DET
ejpam-5339	271	26	problem	problem	NOUN
ejpam-5339	271	27	.	.	PUNCT
ejpam-5339	272	1	figure	figure	VERB
ejpam-5339	272	2	6	6	NUM
ejpam-5339	272	3	:	:	PUNCT
ejpam-5339	272	4	a	a	DET
ejpam-5339	272	5	matching	matching	NOUN
ejpam-5339	272	6	between	between	ADP
ejpam-5339	272	7	the	the	DET
ejpam-5339	272	8	two	two	NUM
ejpam-5339	272	9	solutions	solution	NOUN
ejpam-5339	272	10	of	of	ADP
ejpam-5339	272	11	nonlinear	nonlinear	ADJ
ejpam-5339	272	12	/	/	SYM
ejpam-5339	272	13	linear	linear	ADJ
ejpam-5339	272	14	odes	ode	NOUN
ejpam-5339	272	15	as	as	SCONJ
ejpam-5339	272	16	given	give	VERB
ejpam-5339	272	17	in	in	ADP
ejpam-5339	272	18	eqs	eqs	PROPN
ejpam-5339	272	19	.	.	PUNCT
ejpam-5339	273	1	(	(	PUNCT
ejpam-5339	273	2	24	24	NUM
ejpam-5339	273	3	)	)	PUNCT
ejpam-5339	273	4	and	and	CCONJ
ejpam-5339	273	5	(	(	PUNCT
ejpam-5339	273	6	30	30	NUM
ejpam-5339	273	7	)	)	PUNCT
ejpam-5339	273	8	,	,	PUNCT
ejpam-5339	273	9	respectively	respectively	ADV
ejpam-5339	273	10	.	.	PUNCT
ejpam-5339	274	1	g.	g.	PROPN
ejpam-5339	274	2	m.	m.	PROPN
ejpam-5339	274	3	ismail	ismail	PROPN
ejpam-5339	274	4	,	,	PUNCT
ejpam-5339	274	5	g.	g.	PROPN
ejpam-5339	274	6	m.	m.	PROPN
ejpam-5339	274	7	moatimid	moatimid	PROPN
ejpam-5339	274	8	,	,	PUNCT
ejpam-5339	274	9	m.	m.	NOUN
ejpam-5339	274	10	i.	i.	PROPN
ejpam-5339	274	11	yamani	yamani	PROPN
ejpam-5339	274	12	/	/	SYM
ejpam-5339	274	13	eur	eur	PROPN
ejpam-5339	274	14	.	.	PUNCT
ejpam-5339	275	1	j.	j.	PROPN
ejpam-5339	275	2	pure	pure	PROPN
ejpam-5339	275	3	appl	appl	PROPN
ejpam-5339	275	4	.	.	PROPN
ejpam-5339	275	5	math	math	PROPN
ejpam-5339	275	6	,	,	PUNCT
ejpam-5339	275	7	17	17	NUM
ejpam-5339	275	8	(	(	PUNCT
ejpam-5339	275	9	3	3	NUM
ejpam-5339	275	10	)	)	PUNCT
ejpam-5339	275	11	(	(	PUNCT
ejpam-5339	275	12	2024	2024	NUM
ejpam-5339	275	13	)	)	PUNCT
ejpam-5339	275	14	,	,	PUNCT
ejpam-5339	275	15	2155	2155	NUM
ejpam-5339	275	16	-	-	SYM
ejpam-5339	275	17	2172	2172	NUM
ejpam-5339	275	18	2168	2168	NUM
ejpam-5339	275	19	figure	figure	NOUN
ejpam-5339	275	20	7	7	NUM
ejpam-5339	275	21	:	:	PUNCT
ejpam-5339	275	22	a	a	DET
ejpam-5339	275	23	matching	matching	NOUN
ejpam-5339	275	24	between	between	ADP
ejpam-5339	275	25	the	the	DET
ejpam-5339	275	26	two	two	NUM
ejpam-5339	275	27	solutions	solution	NOUN
ejpam-5339	275	28	nonlinear	nonlinear	ADJ
ejpam-5339	275	29	/	/	SYM
ejpam-5339	275	30	linear	linear	ADJ
ejpam-5339	275	31	odes	ode	NOUN
ejpam-5339	275	32	as	as	SCONJ
ejpam-5339	275	33	given	give	VERB
ejpam-5339	275	34	in	in	ADP
ejpam-5339	275	35	eqs	eqs	PROPN
ejpam-5339	275	36	.	.	PUNCT
ejpam-5339	276	1	(	(	PUNCT
ejpam-5339	276	2	31	31	NUM
ejpam-5339	276	3	)	)	PUNCT
ejpam-5339	276	4	and	and	CCONJ
ejpam-5339	276	5	(	(	PUNCT
ejpam-5339	276	6	37	37	NUM
ejpam-5339	276	7	)	)	PUNCT
ejpam-5339	276	8	,	,	PUNCT
ejpam-5339	276	9	respectively	respectively	ADV
ejpam-5339	276	10	.	.	PUNCT
ejpam-5339	277	1	finally	finally	ADV
ejpam-5339	277	2	,	,	PUNCT
ejpam-5339	277	3	we	we	PRON
ejpam-5339	277	4	can	can	AUX
ejpam-5339	277	5	say	say	VERB
ejpam-5339	277	6	that	that	SCONJ
ejpam-5339	277	7	the	the	DET
ejpam-5339	277	8	npa	npa	NOUN
ejpam-5339	277	9	is	be	AUX
ejpam-5339	277	10	appropriate	appropriate	ADJ
ejpam-5339	277	11	for	for	ADP
ejpam-5339	277	12	obtaining	obtain	VERB
ejpam-5339	277	13	an	an	DET
ejpam-5339	277	14	accurate	accurate	ADJ
ejpam-5339	277	15	solution	solution	NOUN
ejpam-5339	277	16	for	for	ADP
ejpam-5339	277	17	the	the	DET
ejpam-5339	277	18	strong	strong	ADJ
ejpam-5339	277	19	nonlinear	nonlinear	ADJ
ejpam-5339	277	20	oscillator	oscillator	NOUN
ejpam-5339	277	21	.	.	PUNCT
ejpam-5339	278	1	5	5	NUM
ejpam-5339	278	2	.	.	X
ejpam-5339	278	3	conclusion	conclusion	VERB
ejpam-5339	278	4	the	the	DET
ejpam-5339	278	5	primary	primary	ADJ
ejpam-5339	278	6	goal	goal	NOUN
ejpam-5339	278	7	of	of	ADP
ejpam-5339	278	8	the	the	DET
ejpam-5339	278	9	current	current	ADJ
ejpam-5339	278	10	study	study	NOUN
ejpam-5339	278	11	is	be	AUX
ejpam-5339	278	12	to	to	PART
ejpam-5339	278	13	employ	employ	VERB
ejpam-5339	278	14	the	the	DET
ejpam-5339	278	15	npa	npa	NOUN
ejpam-5339	278	16	in	in	ADP
ejpam-5339	278	17	order	order	NOUN
ejpam-5339	278	18	to	to	PART
ejpam-5339	278	19	realize	realize	VERB
ejpam-5339	278	20	the	the	DET
ejpam-5339	278	21	analytical	analytical	ADJ
ejpam-5339	278	22	explanations	explanation	NOUN
ejpam-5339	278	23	for	for	ADP
ejpam-5339	278	24	many	many	ADJ
ejpam-5339	278	25	different	different	ADJ
ejpam-5339	278	26	types	type	NOUN
ejpam-5339	278	27	of	of	ADP
ejpam-5339	278	28	exceedingly	exceedingly	ADV
ejpam-5339	278	29	nonlinear	nonlinear	ADJ
ejpam-5339	278	30	oscillators	oscillator	NOUN
ejpam-5339	278	31	,	,	PUNCT
ejpam-5339	278	32	where	where	SCONJ
ejpam-5339	278	33	the	the	DET
ejpam-5339	278	34	nonlinear	nonlinear	ADJ
ejpam-5339	278	35	oscillators	oscillator	NOUN
ejpam-5339	278	36	are	be	AUX
ejpam-5339	278	37	growing	grow	VERB
ejpam-5339	278	38	more	more	ADV
ejpam-5339	278	39	and	and	CCONJ
ejpam-5339	278	40	more	more	ADV
ejpam-5339	278	41	corporate	corporate	ADJ
ejpam-5339	278	42	.	.	PUNCT
ejpam-5339	279	1	we	we	PRON
ejpam-5339	279	2	scrutinize	scrutinize	VERB
ejpam-5339	279	3	the	the	DET
ejpam-5339	279	4	relationship	relationship	NOUN
ejpam-5339	279	5	involving	involve	VERB
ejpam-5339	279	6	elastic	elastic	ADJ
ejpam-5339	279	7	forces	force	NOUN
ejpam-5339	279	8	and	and	CCONJ
ejpam-5339	279	9	the	the	DET
ejpam-5339	279	10	solution	solution	NOUN
ejpam-5339	279	11	of	of	ADP
ejpam-5339	279	12	a	a	DET
ejpam-5339	279	13	certain	certain	ADJ
ejpam-5339	279	14	type	type	NOUN
ejpam-5339	279	15	of	of	ADP
ejpam-5339	279	16	oscillators	oscillator	NOUN
ejpam-5339	279	17	with	with	ADP
ejpam-5339	279	18	large	large	ADJ
ejpam-5339	279	19	nonlinear	nonlinear	ADJ
ejpam-5339	279	20	damping	damp	VERB
ejpam-5339	279	21	both	both	CCONJ
ejpam-5339	279	22	mathematically	mathematically	ADV
ejpam-5339	279	23	and	and	CCONJ
ejpam-5339	279	24	numerically	numerically	ADV
ejpam-5339	279	25	.	.	PUNCT
ejpam-5339	280	1	it	it	PRON
ejpam-5339	280	2	is	be	AUX
ejpam-5339	280	3	supposed	suppose	VERB
ejpam-5339	280	4	that	that	SCONJ
ejpam-5339	280	5	the	the	DET
ejpam-5339	280	6	suitable	suitable	ADJ
ejpam-5339	280	7	sum	sum	NOUN
ejpam-5339	280	8	of	of	ADP
ejpam-5339	280	9	the	the	DET
ejpam-5339	280	10	trigonometric	trigonometric	ADJ
ejpam-5339	280	11	functions	function	NOUN
ejpam-5339	280	12	equals	equal	VERB
ejpam-5339	280	13	the	the	DET
ejpam-5339	280	14	solution	solution	NOUN
ejpam-5339	280	15	of	of	ADP
ejpam-5339	280	16	a	a	DET
ejpam-5339	280	17	powerful	powerful	ADJ
ejpam-5339	280	18	nonlinear	nonlinear	ADJ
ejpam-5339	280	19	ode	ode	NOUN
ejpam-5339	280	20	that	that	PRON
ejpam-5339	280	21	represents	represent	VERB
ejpam-5339	280	22	motion	motion	NOUN
ejpam-5339	280	23	.	.	PUNCT
ejpam-5339	281	1	we	we	PRON
ejpam-5339	281	2	give	give	VERB
ejpam-5339	281	3	several	several	ADJ
ejpam-5339	281	4	instances	instance	NOUN
ejpam-5339	281	5	from	from	ADP
ejpam-5339	281	6	diverse	diverse	ADJ
ejpam-5339	281	7	arenas	arena	NOUN
ejpam-5339	281	8	of	of	ADP
ejpam-5339	281	9	science	science	NOUN
ejpam-5339	281	10	and	and	CCONJ
ejpam-5339	281	11	technology	technology	NOUN
ejpam-5339	281	12	.	.	PUNCT
ejpam-5339	282	1	the	the	DET
ejpam-5339	282	2	novel	novel	ADJ
ejpam-5339	282	3	approach	approach	NOUN
ejpam-5339	282	4	clearly	clearly	ADV
ejpam-5339	282	5	requires	require	VERB
ejpam-5339	282	6	less	less	ADJ
ejpam-5339	282	7	processing	processing	NOUN
ejpam-5339	282	8	time	time	NOUN
ejpam-5339	282	9	and	and	CCONJ
ejpam-5339	282	10	is	be	AUX
ejpam-5339	282	11	less	less	ADV
ejpam-5339	282	12	difficult	difficult	ADJ
ejpam-5339	282	13	than	than	ADP
ejpam-5339	282	14	the	the	DET
ejpam-5339	282	15	conventional	conventional	ADJ
ejpam-5339	282	16	perturbation	perturbation	NOUN
ejpam-5339	282	17	methods	method	NOUN
ejpam-5339	282	18	that	that	PRON
ejpam-5339	282	19	were	be	AUX
ejpam-5339	282	20	widely	widely	ADV
ejpam-5339	282	21	employed	employ	VERB
ejpam-5339	282	22	in	in	ADP
ejpam-5339	282	23	the	the	DET
ejpam-5339	282	24	field	field	NOUN
ejpam-5339	282	25	of	of	ADP
ejpam-5339	282	26	the	the	DET
ejpam-5339	282	27	dynamical	dynamical	ADJ
ejpam-5339	282	28	systems	system	NOUN
ejpam-5339	282	29	.	.	PUNCT
ejpam-5339	283	1	this	this	DET
ejpam-5339	283	2	new	new	ADJ
ejpam-5339	283	3	method	method	NOUN
ejpam-5339	283	4	,	,	PUNCT
ejpam-5339	283	5	which	which	PRON
ejpam-5339	283	6	is	be	AUX
ejpam-5339	283	7	essentially	essentially	ADV
ejpam-5339	283	8	a	a	DET
ejpam-5339	283	9	linear	linear	ADJ
ejpam-5339	283	10	transformation	transformation	NOUN
ejpam-5339	283	11	of	of	ADP
ejpam-5339	283	12	the	the	DET
ejpam-5339	283	13	nonlinear	nonlinear	ADJ
ejpam-5339	283	14	ode	ode	NOUN
ejpam-5339	283	15	,	,	PUNCT
ejpam-5339	283	16	is	be	AUX
ejpam-5339	283	17	characterized	characterize	VERB
ejpam-5339	283	18	by	by	ADP
ejpam-5339	283	19	the	the	DET
ejpam-5339	283	20	npa	npa	NOUN
ejpam-5339	283	21	.	.	PUNCT
ejpam-5339	284	1	this	this	DET
ejpam-5339	284	2	process	process	NOUN
ejpam-5339	284	3	yields	yield	VERB
ejpam-5339	284	4	a	a	DET
ejpam-5339	284	5	new	new	ADJ
ejpam-5339	284	6	frequency	frequency	NOUN
ejpam-5339	284	7	that	that	PRON
ejpam-5339	284	8	is	be	AUX
ejpam-5339	284	9	analogous	analogous	ADJ
ejpam-5339	284	10	to	to	ADP
ejpam-5339	284	11	a	a	DET
ejpam-5339	284	12	linear	linear	ADJ
ejpam-5339	284	13	ode	ode	NOUN
ejpam-5339	284	14	,	,	PUNCT
ejpam-5339	284	15	similar	similar	ADJ
ejpam-5339	284	16	to	to	ADP
ejpam-5339	284	17	a	a	DET
ejpam-5339	284	18	situation	situation	NOUN
ejpam-5339	284	19	involving	involve	VERB
ejpam-5339	284	20	simple	simple	ADJ
ejpam-5339	284	21	harmonic	harmonic	ADJ
ejpam-5339	284	22	motion	motion	NOUN
ejpam-5339	284	23	.	.	PUNCT
ejpam-5339	285	1	when	when	SCONJ
ejpam-5339	285	2	evaluated	evaluate	VERB
ejpam-5339	285	3	for	for	ADP
ejpam-5339	285	4	physiologically	physiologically	ADV
ejpam-5339	285	5	significant	significant	ADJ
ejpam-5339	285	6	expert	expert	ADJ
ejpam-5339	285	7	examples	example	NOUN
ejpam-5339	285	8	,	,	PUNCT
ejpam-5339	285	9	this	this	DET
ejpam-5339	285	10	simple	simple	ADJ
ejpam-5339	285	11	methodology	methodology	NOUN
ejpam-5339	285	12	produces	produce	VERB
ejpam-5339	285	13	results	result	NOUN
ejpam-5339	285	14	that	that	SCONJ
ejpam-5339	285	15	not	not	PART
ejpam-5339	285	16	only	only	ADV
ejpam-5339	285	17	correspond	correspond	VERB
ejpam-5339	285	18	well	well	ADV
ejpam-5339	285	19	with	with	ADP
ejpam-5339	285	20	the	the	DET
ejpam-5339	285	21	ns	ns	ADJ
ejpam-5339	285	22	,	,	PUNCT
ejpam-5339	285	23	but	but	CCONJ
ejpam-5339	285	24	also	also	ADV
ejpam-5339	285	25	prove	prove	VERB
ejpam-5339	285	26	to	to	PART
ejpam-5339	285	27	be	be	AUX
ejpam-5339	285	28	more	more	ADV
ejpam-5339	285	29	accurate	accurate	ADJ
ejpam-5339	285	30	than	than	ADP
ejpam-5339	285	31	the	the	DET
ejpam-5339	285	32	results	result	NOUN
ejpam-5339	285	33	obtained	obtain	VERB
ejpam-5339	285	34	with	with	ADP
ejpam-5339	285	35	many	many	ADJ
ejpam-5339	285	36	well	well	ADV
ejpam-5339	285	37	-	-	PUNCT
ejpam-5339	285	38	known	know	VERB
ejpam-5339	285	39	traditional	traditional	ADJ
ejpam-5339	285	40	approximate	approximate	ADJ
ejpam-5339	285	41	methodologies	methodology	NOUN
ejpam-5339	285	42	.	.	PUNCT
ejpam-5339	286	1	for	for	ADP
ejpam-5339	286	2	the	the	DET
ejpam-5339	286	3	advantage	advantage	NOUN
ejpam-5339	286	4	of	of	ADP
ejpam-5339	286	5	the	the	DET
ejpam-5339	286	6	readers	reader	NOUN
ejpam-5339	286	7	,	,	PUNCT
ejpam-5339	286	8	a	a	DET
ejpam-5339	286	9	detailed	detailed	ADJ
ejpam-5339	286	10	description	description	NOUN
ejpam-5339	286	11	of	of	ADP
ejpam-5339	286	12	the	the	DET
ejpam-5339	286	13	npa	npa	NOUN
ejpam-5339	286	14	is	be	AUX
ejpam-5339	286	15	provided	provide	VERB
ejpam-5339	286	16	.	.	PUNCT
ejpam-5339	287	1	the	the	DET
ejpam-5339	287	2	theoretical	theoretical	ADJ
ejpam-5339	287	3	conclusions	conclusion	NOUN
ejpam-5339	287	4	are	be	AUX
ejpam-5339	287	5	validated	validate	VERB
ejpam-5339	287	6	by	by	ADP
ejpam-5339	287	7	a	a	DET
ejpam-5339	287	8	numerical	numerical	ADJ
ejpam-5339	287	9	comparison	comparison	NOUN
ejpam-5339	287	10	with	with	ADP
ejpam-5339	287	11	the	the	DET
ejpam-5339	287	12	ms	ms	PROPN
ejpam-5339	287	13	.	.	PROPN
ejpam-5339	288	1	the	the	DET
ejpam-5339	288	2	ns	ns	ADJ
ejpam-5339	288	3	test	test	NOUN
ejpam-5339	288	4	results	result	NOUN
ejpam-5339	288	5	and	and	CCONJ
ejpam-5339	288	6	the	the	DET
ejpam-5339	288	7	theories	theory	NOUN
ejpam-5339	288	8	were	be	AUX
ejpam-5339	288	9	remarkably	remarkably	ADV
ejpam-5339	288	10	consistent	consistent	ADJ
ejpam-5339	288	11	.	.	PUNCT
ejpam-5339	289	1	it	it	PRON
ejpam-5339	289	2	is	be	AUX
ejpam-5339	289	3	commonly	commonly	ADV
ejpam-5339	289	4	known	know	VERB
ejpam-5339	289	5	that	that	SCONJ
ejpam-5339	289	6	all	all	DET
ejpam-5339	289	7	traditional	traditional	ADJ
ejpam-5339	289	8	perturbation	perturbation	NOUN
ejpam-5339	289	9	techniques	technique	NOUN
ejpam-5339	289	10	use	use	VERB
ejpam-5339	289	11	the	the	DET
ejpam-5339	289	12	taylor	taylor	PROPN
ejpam-5339	289	13	expansion	expansion	NOUN
ejpam-5339	289	14	to	to	PART
ejpam-5339	289	15	enlarge	enlarge	VERB
ejpam-5339	289	16	the	the	DET
ejpam-5339	289	17	restoring	restore	VERB
ejpam-5339	289	18	forces	force	NOUN
ejpam-5339	289	19	when	when	SCONJ
ejpam-5339	289	20	they	they	PRON
ejpam-5339	289	21	exist	exist	VERB
ejpam-5339	289	22	,	,	PUNCT
ejpam-5339	289	23	therefore	therefore	ADV
ejpam-5339	289	24	simplifying	simplify	VERB
ejpam-5339	289	25	the	the	DET
ejpam-5339	289	26	current	current	ADJ
ejpam-5339	289	27	situation	situation	NOUN
ejpam-5339	289	28	.	.	PUNCT
ejpam-5339	290	1	using	use	VERB
ejpam-5339	290	2	the	the	DET
ejpam-5339	290	3	npa	npa	NOUN
ejpam-5339	290	4	eliminates	eliminate	NOUN
ejpam-5339	290	5	this	this	DET
ejpam-5339	290	6	susceptibility	susceptibility	NOUN
ejpam-5339	290	7	.	.	PUNCT
ejpam-5339	291	1	additionally	additionally	ADV
ejpam-5339	291	2	,	,	PUNCT
ejpam-5339	291	3	the	the	DET
ejpam-5339	291	4	stability	stability	NOUN
ejpam-5339	291	5	analysis	analysis	NOUN
ejpam-5339	291	6	of	of	ADP
ejpam-5339	291	7	the	the	DET
ejpam-5339	291	8	problems	problem	NOUN
ejpam-5339	291	9	may	may	AUX
ejpam-5339	291	10	be	be	AUX
ejpam-5339	291	11	fully	fully	ADV
ejpam-5339	291	12	examined	examine	VERB
ejpam-5339	291	13	agrees	agree	VERB
ejpam-5339	291	14	to	to	ADP
ejpam-5339	291	15	the	the	DET
ejpam-5339	291	16	references	reference	NOUN
ejpam-5339	291	17	2169	2169	NUM
ejpam-5339	291	18	npa	npa	NOUN
ejpam-5339	291	19	,	,	PUNCT
ejpam-5339	291	20	which	which	PRON
ejpam-5339	291	21	was	be	AUX
ejpam-5339	291	22	not	not	PART
ejpam-5339	291	23	achievable	achievable	ADJ
ejpam-5339	291	24	with	with	ADP
ejpam-5339	291	25	previous	previous	ADJ
ejpam-5339	291	26	conventional	conventional	ADJ
ejpam-5339	291	27	methodologies	methodology	NOUN
ejpam-5339	291	28	.	.	PUNCT
ejpam-5339	292	1	consequently	consequently	ADV
ejpam-5339	292	2	,	,	PUNCT
ejpam-5339	292	3	the	the	DET
ejpam-5339	292	4	npa	npa	NOUN
ejpam-5339	292	5	is	be	AUX
ejpam-5339	292	6	a	a	DET
ejpam-5339	292	7	more	more	ADV
ejpam-5339	292	8	helpful	helpful	ADJ
ejpam-5339	292	9	accountability	accountability	NOUN
ejpam-5339	292	10	tool	tool	NOUN
ejpam-5339	292	11	when	when	SCONJ
ejpam-5339	292	12	analyzing	analyze	VERB
ejpam-5339	292	13	approximations	approximation	NOUN
ejpam-5339	292	14	for	for	ADP
ejpam-5339	292	15	very	very	ADV
ejpam-5339	292	16	nonlinear	nonlinear	ADJ
ejpam-5339	292	17	oscillators	oscillator	NOUN
ejpam-5339	292	18	in	in	ADP
ejpam-5339	292	19	ms	ms	PROPN
ejpam-5339	292	20	.	.	PROPN
ejpam-5339	292	21	because	because	SCONJ
ejpam-5339	292	22	the	the	DET
ejpam-5339	292	23	npa	npa	NOUN
ejpam-5339	292	24	is	be	AUX
ejpam-5339	292	25	easily	easily	ADV
ejpam-5339	292	26	adaptable	adaptable	ADJ
ejpam-5339	292	27	to	to	PART
ejpam-5339	292	28	address	address	VERB
ejpam-5339	292	29	a	a	DET
ejpam-5339	292	30	wide	wide	ADJ
ejpam-5339	292	31	range	range	NOUN
ejpam-5339	292	32	of	of	ADP
ejpam-5339	292	33	nonlinear	nonlinear	ADJ
ejpam-5339	292	34	challenges	challenge	NOUN
ejpam-5339	292	35	,	,	PUNCT
ejpam-5339	292	36	it	it	PRON
ejpam-5339	292	37	is	be	AUX
ejpam-5339	292	38	a	a	DET
ejpam-5339	292	39	valuable	valuable	ADJ
ejpam-5339	292	40	tool	tool	NOUN
ejpam-5339	292	41	in	in	ADP
ejpam-5339	292	42	the	the	DET
ejpam-5339	292	43	fields	field	NOUN
ejpam-5339	292	44	of	of	ADP
ejpam-5339	292	45	science	science	NOUN
ejpam-5339	292	46	and	and	CCONJ
ejpam-5339	292	47	technology	technology	NOUN
ejpam-5339	292	48	as	as	ADV
ejpam-5339	292	49	well	well	ADV
ejpam-5339	292	50	as	as	ADP
ejpam-5339	292	51	applied	apply	VERB
ejpam-5339	292	52	studies	study	NOUN
ejpam-5339	292	53	.	.	PUNCT
ejpam-5339	293	1	it	it	PRON
ejpam-5339	293	2	should	should	AUX
ejpam-5339	293	3	be	be	AUX
ejpam-5339	293	4	noted	note	VERB
ejpam-5339	293	5	that	that	SCONJ
ejpam-5339	293	6	the	the	DET
ejpam-5339	293	7	understanding	understanding	NOUN
ejpam-5339	293	8	the	the	DET
ejpam-5339	293	9	periodic	periodic	ADJ
ejpam-5339	293	10	solutions	solution	NOUN
ejpam-5339	293	11	of	of	ADP
ejpam-5339	293	12	strongly	strongly	ADV
ejpam-5339	293	13	nonlinear	nonlinear	ADJ
ejpam-5339	293	14	oscillators	oscillator	NOUN
ejpam-5339	293	15	have	have	VERB
ejpam-5339	293	16	important	important	ADJ
ejpam-5339	293	17	applications	application	NOUN
ejpam-5339	293	18	in	in	ADP
ejpam-5339	293	19	various	various	ADJ
ejpam-5339	293	20	fields	field	NOUN
ejpam-5339	293	21	:	:	PUNCT
ejpam-5339	293	22	improve	improve	VERB
ejpam-5339	293	23	stability	stability	NOUN
ejpam-5339	293	24	and	and	CCONJ
ejpam-5339	293	25	comfort	comfort	NOUN
ejpam-5339	293	26	in	in	ADP
ejpam-5339	293	27	buildings	building	NOUN
ejpam-5339	293	28	,	,	PUNCT
ejpam-5339	293	29	automobiles	automobile	NOUN
ejpam-5339	293	30	,	,	PUNCT
ejpam-5339	293	31	and	and	CCONJ
ejpam-5339	293	32	marine	marine	ADJ
ejpam-5339	293	33	engines	engine	NOUN
ejpam-5339	293	34	.	.	PUNCT
ejpam-5339	294	1	prevent	prevent	VERB
ejpam-5339	294	2	resonance	resonance	NOUN
ejpam-5339	294	3	and	and	CCONJ
ejpam-5339	294	4	potential	potential	ADJ
ejpam-5339	294	5	damage	damage	NOUN
ejpam-5339	294	6	in	in	ADP
ejpam-5339	294	7	turbines	turbine	NOUN
ejpam-5339	294	8	and	and	CCONJ
ejpam-5339	294	9	engines	engine	NOUN
ejpam-5339	294	10	.	.	PUNCT
ejpam-5339	295	1	protect	protect	VERB
ejpam-5339	295	2	buildings	building	NOUN
ejpam-5339	295	3	and	and	CCONJ
ejpam-5339	295	4	bridges	bridge	NOUN
ejpam-5339	295	5	during	during	ADP
ejpam-5339	295	6	earthquakes	earthquake	NOUN
ejpam-5339	295	7	.	.	PUNCT
ejpam-5339	296	1	mitigate	mitigate	VERB
ejpam-5339	296	2	impacts	impact	NOUN
ejpam-5339	296	3	of	of	ADP
ejpam-5339	296	4	wind	wind	NOUN
ejpam-5339	296	5	and	and	CCONJ
ejpam-5339	296	6	traffic	traffic	NOUN
ejpam-5339	296	7	loads	load	NOUN
ejpam-5339	296	8	on	on	ADP
ejpam-5339	296	9	structures	structure	NOUN
ejpam-5339	296	10	.	.	PUNCT
ejpam-5339	297	1	ensure	ensure	VERB
ejpam-5339	297	2	effective	effective	ADJ
ejpam-5339	297	3	operation	operation	NOUN
ejpam-5339	297	4	of	of	ADP
ejpam-5339	297	5	devices	device	NOUN
ejpam-5339	297	6	like	like	ADP
ejpam-5339	297	7	pacemakers	pacemaker	NOUN
ejpam-5339	297	8	and	and	CCONJ
ejpam-5339	297	9	respiratory	respiratory	ADJ
ejpam-5339	297	10	machines	machine	NOUN
ejpam-5339	297	11	.	.	PUNCT
ejpam-5339	298	1	as	as	ADP
ejpam-5339	298	2	a	a	DET
ejpam-5339	298	3	progress	progress	NOUN
ejpam-5339	298	4	work	work	NOUN
ejpam-5339	298	5	,	,	PUNCT
ejpam-5339	298	6	the	the	DET
ejpam-5339	298	7	npa	npa	NOUN
ejpam-5339	298	8	can	can	AUX
ejpam-5339	298	9	be	be	AUX
ejpam-5339	298	10	developed	develop	VERB
ejpam-5339	298	11	to	to	ADP
ejpam-5339	298	12	handling	handle	VERB
ejpam-5339	298	13	the	the	DET
ejpam-5339	298	14	coupled	couple	VERB
ejpam-5339	298	15	dynamical	dynamical	ADJ
ejpam-5339	298	16	system	system	NOUN
ejpam-5339	298	17	.	.	PUNCT
ejpam-5339	299	1	coupled	couple	VERB
ejpam-5339	299	2	dynamic	dynamic	ADJ
ejpam-5339	299	3	systems	system	NOUN
ejpam-5339	299	4	,	,	PUNCT
ejpam-5339	299	5	characterized	characterize	VERB
ejpam-5339	299	6	by	by	ADP
ejpam-5339	299	7	the	the	DET
ejpam-5339	299	8	mutual	mutual	ADJ
ejpam-5339	299	9	interaction	interaction	NOUN
ejpam-5339	299	10	of	of	ADP
ejpam-5339	299	11	numerous	numerous	ADJ
ejpam-5339	299	12	interacting	interacting	ADJ
ejpam-5339	299	13	subsystems	subsystem	NOUN
ejpam-5339	299	14	,	,	PUNCT
ejpam-5339	299	15	find	find	VERB
ejpam-5339	299	16	extensive	extensive	ADJ
ejpam-5339	299	17	applications	application	NOUN
ejpam-5339	299	18	across	across	ADP
ejpam-5339	299	19	many	many	ADJ
ejpam-5339	299	20	fields	field	NOUN
ejpam-5339	299	21	:	:	PUNCT
ejpam-5339	299	22	improves	improve	VERB
ejpam-5339	299	23	the	the	DET
ejpam-5339	299	24	efficiency	efficiency	NOUN
ejpam-5339	299	25	of	of	ADP
ejpam-5339	299	26	design	design	NOUN
ejpam-5339	299	27	and	and	CCONJ
ejpam-5339	299	28	maintenance	maintenance	NOUN
ejpam-5339	299	29	processes	process	NOUN
ejpam-5339	299	30	by	by	ADP
ejpam-5339	299	31	analyzing	analyze	VERB
ejpam-5339	299	32	the	the	DET
ejpam-5339	299	33	interactions	interaction	NOUN
ejpam-5339	299	34	within	within	ADP
ejpam-5339	299	35	machines	machine	NOUN
ejpam-5339	299	36	.	.	PUNCT
ejpam-5339	300	1	acknowledgements	acknowledgement	NOUN
ejpam-5339	300	2	the	the	DET
ejpam-5339	300	3	researchers	researcher	NOUN
ejpam-5339	300	4	wish	wish	VERB
ejpam-5339	300	5	to	to	PART
ejpam-5339	300	6	extend	extend	VERB
ejpam-5339	300	7	their	their	PRON
ejpam-5339	300	8	sincere	sincere	ADJ
ejpam-5339	300	9	gratitude	gratitude	NOUN
ejpam-5339	300	10	to	to	ADP
ejpam-5339	300	11	the	the	DET
ejpam-5339	300	12	deanship	deanship	NOUN
ejpam-5339	300	13	of	of	ADP
ejpam-5339	300	14	scientific	scientific	ADJ
ejpam-5339	300	15	research	research	NOUN
ejpam-5339	300	16	at	at	ADP
ejpam-5339	300	17	the	the	DET
ejpam-5339	300	18	islamic	islamic	PROPN
ejpam-5339	300	19	university	university	PROPN
ejpam-5339	300	20	of	of	ADP
ejpam-5339	300	21	madinah	madinah	PROPN
ejpam-5339	300	22	for	for	ADP
ejpam-5339	300	23	the	the	DET
ejpam-5339	300	24	support	support	NOUN
ejpam-5339	300	25	provided	provide	VERB
ejpam-5339	300	26	to	to	ADP
ejpam-5339	300	27	the	the	DET
ejpam-5339	300	28	postpublishing	postpublishe	VERB
ejpam-5339	300	29	program	program	NOUN
ejpam-5339	300	30	.	.	PUNCT
ejpam-5339	301	1	references	reference	NOUN
ejpam-5339	301	2	[	[	X
ejpam-5339	301	3	1	1	X
ejpam-5339	301	4	]	]	X
ejpam-5339	301	5	y.	y.	PROPN
ejpam-5339	301	6	o.	o.	PROPN
ejpam-5339	301	7	el	el	PROPN
ejpam-5339	301	8	-	-	PROPN
ejpam-5339	301	9	dib	dib	PROPN
ejpam-5339	301	10	.	.	PROPN
ejpam-5339	302	1	insightful	insightful	ADJ
ejpam-5339	302	2	and	and	CCONJ
ejpam-5339	302	3	comprehensive	comprehensive	ADJ
ejpam-5339	302	4	formularization	formularization	NOUN
ejpam-5339	302	5	of	of	ADP
ejpam-5339	302	6	frequency	frequency	NOUN
ejpam-5339	302	7	-	-	PUNCT
ejpam-5339	302	8	amplitude	amplitude	NOUN
ejpam-5339	302	9	formula	formula	NOUN
ejpam-5339	302	10	for	for	ADP
ejpam-5339	302	11	strong	strong	ADJ
ejpam-5339	302	12	or	or	CCONJ
ejpam-5339	302	13	singular	singular	ADJ
ejpam-5339	302	14	nonlinear	nonlinear	ADJ
ejpam-5339	302	15	oscillators	oscillator	NOUN
ejpam-5339	302	16	.	.	PUNCT
ejpam-5339	303	1	journal	journal	NOUN
ejpam-5339	303	2	of	of	ADP
ejpam-5339	303	3	low	low	ADJ
ejpam-5339	303	4	frequency	frequency	NOUN
ejpam-5339	303	5	noise	noise	NOUN
ejpam-5339	303	6	,	,	PUNCT
ejpam-5339	303	7	vibration	vibration	NOUN
ejpam-5339	303	8	and	and	CCONJ
ejpam-5339	303	9	active	active	ADJ
ejpam-5339	303	10	control	control	NOUN
ejpam-5339	303	11	,	,	PUNCT
ejpam-5339	303	12	42(1):89–109	42(1):89–109	NUM
ejpam-5339	303	13	,	,	PUNCT
ejpam-5339	303	14	2023	2023	NUM
ejpam-5339	303	15	.	.	PUNCT
ejpam-5339	304	1	[	[	X
ejpam-5339	304	2	2	2	NUM
ejpam-5339	304	3	]	]	PUNCT
ejpam-5339	304	4	c.	c.	PROPN
ejpam-5339	304	5	h.	h.	PROPN
ejpam-5339	304	6	he	he	PRON
ejpam-5339	304	7	and	and	CCONJ
ejpam-5339	304	8	c.	c.	PROPN
ejpam-5339	304	9	liu	liu	PROPN
ejpam-5339	304	10	.	.	PUNCT
ejpam-5339	305	1	a	a	DET
ejpam-5339	305	2	modified	modify	VERB
ejpam-5339	305	3	frequency	frequency	NOUN
ejpam-5339	305	4	-	-	PUNCT
ejpam-5339	305	5	amplitude	amplitude	NOUN
ejpam-5339	305	6	formulation	formulation	NOUN
ejpam-5339	305	7	for	for	ADP
ejpam-5339	305	8	fractal	fractal	ADJ
ejpam-5339	305	9	vibration	vibration	NOUN
ejpam-5339	305	10	systems	system	NOUN
ejpam-5339	305	11	.	.	PUNCT
ejpam-5339	306	1	fractals	fractal	NOUN
ejpam-5339	306	2	,	,	PUNCT
ejpam-5339	306	3	30(03):2250046	30(03):2250046	NUM
ejpam-5339	306	4	,	,	PUNCT
ejpam-5339	306	5	2022	2022	NUM
ejpam-5339	306	6	.	.	PUNCT
ejpam-5339	307	1	[	[	X
ejpam-5339	307	2	3	3	X
ejpam-5339	307	3	]	]	PUNCT
ejpam-5339	307	4	j.	j.	PROPN
ejpam-5339	307	5	h.	h.	PROPN
ejpam-5339	307	6	he	he	PRON
ejpam-5339	307	7	.	.	PUNCT
ejpam-5339	308	1	homotopy	homotopy	VERB
ejpam-5339	308	2	perturbation	perturbation	NOUN
ejpam-5339	308	3	technique	technique	NOUN
ejpam-5339	308	4	.	.	PUNCT
ejpam-5339	309	1	computer	computer	NOUN
ejpam-5339	309	2	methods	method	NOUN
ejpam-5339	309	3	in	in	ADP
ejpam-5339	309	4	applied	applied	ADJ
ejpam-5339	309	5	mechanics	mechanic	NOUN
ejpam-5339	309	6	and	and	CCONJ
ejpam-5339	309	7	engineering	engineering	NOUN
ejpam-5339	309	8	,	,	PUNCT
ejpam-5339	309	9	178:257–262	178:257–262	NUM
ejpam-5339	309	10	,	,	PUNCT
ejpam-5339	309	11	1999	1999	NUM
ejpam-5339	309	12	.	.	PUNCT
ejpam-5339	310	1	[	[	X
ejpam-5339	310	2	4	4	X
ejpam-5339	310	3	]	]	PUNCT
ejpam-5339	310	4	j.	j.	PROPN
ejpam-5339	310	5	h.	h.	PROPN
ejpam-5339	310	6	he	he	PRON
ejpam-5339	310	7	.	.	PUNCT
ejpam-5339	311	1	an	an	DET
ejpam-5339	311	2	improved	improve	VERB
ejpam-5339	311	3	amplitude	amplitude	NOUN
ejpam-5339	311	4	-	-	PUNCT
ejpam-5339	311	5	frequency	frequency	NOUN
ejpam-5339	311	6	formulation	formulation	NOUN
ejpam-5339	311	7	for	for	ADP
ejpam-5339	311	8	nonlinear	nonlinear	ADJ
ejpam-5339	311	9	oscillators	oscillator	NOUN
ejpam-5339	311	10	.	.	PUNCT
ejpam-5339	312	1	international	international	ADJ
ejpam-5339	312	2	journal	journal	PROPN
ejpam-5339	312	3	of	of	ADP
ejpam-5339	312	4	nonlinear	nonlinear	PROPN
ejpam-5339	312	5	sciences	sciences	PROPN
ejpam-5339	312	6	and	and	CCONJ
ejpam-5339	312	7	numerical	numerical	PROPN
ejpam-5339	312	8	simulation	simulation	PROPN
ejpam-5339	312	9	,	,	PUNCT
ejpam-5339	312	10	9:211–212	9:211–212	NUM
ejpam-5339	312	11	,	,	PUNCT
ejpam-5339	312	12	2008	2008	NUM
ejpam-5339	312	13	.	.	PUNCT
ejpam-5339	313	1	[	[	X
ejpam-5339	313	2	5	5	X
ejpam-5339	313	3	]	]	PUNCT
ejpam-5339	313	4	j.	j.	PROPN
ejpam-5339	313	5	h.	h.	PROPN
ejpam-5339	313	6	he	he	PRON
ejpam-5339	313	7	.	.	PUNCT
ejpam-5339	314	1	the	the	DET
ejpam-5339	314	2	simplest	simple	ADJ
ejpam-5339	314	3	approach	approach	NOUN
ejpam-5339	314	4	to	to	ADP
ejpam-5339	314	5	nonlinear	nonlinear	ADJ
ejpam-5339	314	6	oscillators	oscillator	NOUN
ejpam-5339	314	7	.	.	PUNCT
ejpam-5339	315	1	results	result	NOUN
ejpam-5339	315	2	in	in	ADP
ejpam-5339	315	3	physics	physics	NOUN
ejpam-5339	315	4	,	,	PUNCT
ejpam-5339	315	5	15:102546	15:102546	NUM
ejpam-5339	315	6	,	,	PUNCT
ejpam-5339	315	7	2019	2019	NUM
ejpam-5339	315	8	.	.	PUNCT
ejpam-5339	316	1	[	[	X
ejpam-5339	316	2	6	6	NUM
ejpam-5339	316	3	]	]	PUNCT
ejpam-5339	316	4	j.	j.	PROPN
ejpam-5339	316	5	h.	h.	PROPN
ejpam-5339	316	6	he	he	PRON
ejpam-5339	316	7	,	,	PUNCT
ejpam-5339	316	8	t.	t.	PROPN
ejpam-5339	316	9	s.	s.	PROPN
ejpam-5339	316	10	amer	amer	PROPN
ejpam-5339	316	11	,	,	PUNCT
ejpam-5339	316	12	s.	s.	PROPN
ejpam-5339	316	13	elnaggar	elnaggar	PROPN
ejpam-5339	316	14	,	,	PUNCT
ejpam-5339	316	15	and	and	CCONJ
ejpam-5339	316	16	a.	a.	NOUN
ejpam-5339	316	17	a.	a.	PROPN
ejpam-5339	316	18	galal	galal	PROPN
ejpam-5339	316	19	.	.	PUNCT
ejpam-5339	317	1	periodic	periodic	ADJ
ejpam-5339	317	2	property	property	NOUN
ejpam-5339	317	3	and	and	CCONJ
ejpam-5339	317	4	instability	instability	NOUN
ejpam-5339	317	5	of	of	ADP
ejpam-5339	317	6	a	a	DET
ejpam-5339	317	7	rotating	rotate	VERB
ejpam-5339	317	8	pendulum	pendulum	NOUN
ejpam-5339	317	9	system	system	NOUN
ejpam-5339	317	10	.	.	PUNCT
ejpam-5339	318	1	axioms	axiom	NOUN
ejpam-5339	318	2	,	,	PUNCT
ejpam-5339	318	3	10:191	10:191	NUM
ejpam-5339	318	4	,	,	PUNCT
ejpam-5339	318	5	2021	2021	NUM
ejpam-5339	318	6	.	.	PUNCT
ejpam-5339	319	1	references	reference	NOUN
ejpam-5339	319	2	2170	2170	NUM
ejpam-5339	320	1	[	[	X
ejpam-5339	320	2	7	7	X
ejpam-5339	320	3	]	]	PUNCT
ejpam-5339	320	4	j.	j.	PROPN
ejpam-5339	320	5	h.	h.	PROPN
ejpam-5339	320	6	he	he	PRON
ejpam-5339	320	7	,	,	PUNCT
ejpam-5339	320	8	m.	m.	PROPN
ejpam-5339	320	9	l.	l.	PROPN
ejpam-5339	320	10	jlao	jlao	PROPN
ejpam-5339	320	11	,	,	PUNCT
ejpam-5339	320	12	and	and	CCONJ
ejpam-5339	320	13	c.	c.	PROPN
ejpam-5339	320	14	h.	h.	PROPN
ejpam-5339	321	1	he	he	PRON
ejpam-5339	321	2	.	.	PUNCT
ejpam-5339	322	1	homotopy	homotopy	VERB
ejpam-5339	322	2	perturbation	perturbation	NOUN
ejpam-5339	322	3	method	method	NOUN
ejpam-5339	322	4	for	for	ADP
ejpam-5339	322	5	fractal	fractal	ADJ
ejpam-5339	322	6	duffing	duffing	NOUN
ejpam-5339	322	7	oscillator	oscillator	NOUN
ejpam-5339	322	8	with	with	ADP
ejpam-5339	322	9	arbitrary	arbitrary	ADJ
ejpam-5339	322	10	constants	constant	NOUN
ejpam-5339	322	11	.	.	PUNCT
ejpam-5339	323	1	fractals	fractal	NOUN
ejpam-5339	323	2	,	,	PUNCT
ejpam-5339	323	3	30:2250165–346	30:2250165–346	NUM
ejpam-5339	323	4	,	,	PUNCT
ejpam-5339	323	5	2022	2022	NUM
ejpam-5339	323	6	.	.	PUNCT
ejpam-5339	324	1	[	[	X
ejpam-5339	324	2	8	8	NUM
ejpam-5339	324	3	]	]	X
ejpam-5339	324	4	md	md	PROPN
ejpam-5339	324	5	.	.	PUNCT
ejpam-5339	324	6	a.	a.	PROPN
ejpam-5339	324	7	hosen	hosen	PROPN
ejpam-5339	324	8	,	,	PUNCT
ejpam-5339	324	9	g.	g.	PROPN
ejpam-5339	324	10	m.	m.	PROPN
ejpam-5339	324	11	ismail	ismail	PROPN
ejpam-5339	324	12	,	,	PUNCT
ejpam-5339	324	13	a.	a.	PROPN
ejpam-5339	324	14	yildirim	yildirim	PROPN
ejpam-5339	324	15	,	,	PUNCT
ejpam-5339	324	16	and	and	CCONJ
ejpam-5339	324	17	m.	m.	PROPN
ejpam-5339	324	18	a.	a.	PROPN
ejpam-5339	324	19	s.	s.	PROPN
ejpam-5339	324	20	kamal	kamal	PROPN
ejpam-5339	324	21	.	.	PUNCT
ejpam-5339	325	1	a	a	DET
ejpam-5339	325	2	modified	modify	VERB
ejpam-5339	325	3	energy	energy	NOUN
ejpam-5339	325	4	balance	balance	NOUN
ejpam-5339	325	5	method	method	NOUN
ejpam-5339	325	6	to	to	PART
ejpam-5339	325	7	obtain	obtain	VERB
ejpam-5339	325	8	higher	high	ADJ
ejpam-5339	325	9	-	-	PUNCT
ejpam-5339	325	10	order	order	NOUN
ejpam-5339	325	11	approximations	approximation	NOUN
ejpam-5339	325	12	to	to	ADP
ejpam-5339	325	13	the	the	DET
ejpam-5339	325	14	oscillators	oscillator	NOUN
ejpam-5339	325	15	with	with	ADP
ejpam-5339	325	16	cubic	cubic	ADJ
ejpam-5339	325	17	and	and	CCONJ
ejpam-5339	325	18	harmonic	harmonic	ADJ
ejpam-5339	325	19	restoring	restore	VERB
ejpam-5339	325	20	force	force	NOUN
ejpam-5339	325	21	.	.	PUNCT
ejpam-5339	326	1	journal	journal	NOUN
ejpam-5339	326	2	of	of	ADP
ejpam-5339	326	3	applied	applied	ADJ
ejpam-5339	326	4	and	and	CCONJ
ejpam-5339	326	5	computational	computational	ADJ
ejpam-5339	326	6	mechanics	mechanic	NOUN
ejpam-5339	326	7	,	,	PUNCT
ejpam-5339	326	8	6(2):320–331	6(2):320–331	NUM
ejpam-5339	326	9	,	,	PUNCT
ejpam-5339	326	10	2020	2020	NUM
ejpam-5339	326	11	.	.	PUNCT
ejpam-5339	327	1	[	[	X
ejpam-5339	327	2	9	9	NUM
ejpam-5339	327	3	]	]	X
ejpam-5339	327	4	g.	g.	PROPN
ejpam-5339	327	5	m.	m.	PROPN
ejpam-5339	327	6	ismail	ismail	PROPN
ejpam-5339	327	7	,	,	PUNCT
ejpam-5339	327	8	m.	m.	NOUN
ejpam-5339	327	9	m.	m.	PROPN
ejpam-5339	327	10	el	el	PROPN
ejpam-5339	327	11	-	-	PUNCT
ejpam-5339	327	12	moshneb	moshneb	ADJ
ejpam-5339	327	13	,	,	PUNCT
ejpam-5339	327	14	and	and	CCONJ
ejpam-5339	327	15	m.	m.	NOUN
ejpam-5339	327	16	zayed	zaye	VERB
ejpam-5339	327	17	.	.	PUNCT
ejpam-5339	328	1	analytical	analytical	ADJ
ejpam-5339	328	2	technique	technique	NOUN
ejpam-5339	328	3	for	for	ADP
ejpam-5339	328	4	solving	solve	VERB
ejpam-5339	328	5	strongly	strongly	ADV
ejpam-5339	328	6	nonlinear	nonlinear	ADJ
ejpam-5339	328	7	oscillator	oscillator	NOUN
ejpam-5339	328	8	differential	differential	NOUN
ejpam-5339	328	9	equations	equation	NOUN
ejpam-5339	328	10	.	.	PUNCT
ejpam-5339	329	1	alexandria	alexandria	PROPN
ejpam-5339	329	2	engineering	engineering	PROPN
ejpam-5339	329	3	journal	journal	PROPN
ejpam-5339	329	4	,	,	PUNCT
ejpam-5339	329	5	74:547–557	74:547–557	PROPN
ejpam-5339	329	6	,	,	PUNCT
ejpam-5339	329	7	2023	2023	NUM
ejpam-5339	329	8	.	.	PUNCT
ejpam-5339	330	1	[	[	X
ejpam-5339	330	2	10	10	NUM
ejpam-5339	330	3	]	]	X
ejpam-5339	330	4	g.	g.	PROPN
ejpam-5339	330	5	m.	m.	PROPN
ejpam-5339	330	6	ismail	ismail	PROPN
ejpam-5339	330	7	,	,	PUNCT
ejpam-5339	330	8	m.	m.	NOUN
ejpam-5339	330	9	m.	m.	PROPN
ejpam-5339	330	10	el	el	PROPN
ejpam-5339	330	11	-	-	PUNCT
ejpam-5339	330	12	moshneb	moshneb	ADJ
ejpam-5339	330	13	,	,	PUNCT
ejpam-5339	330	14	and	and	CCONJ
ejpam-5339	330	15	m.	m.	NOUN
ejpam-5339	330	16	zayed	zayed	PROPN
ejpam-5339	330	17	.	.	PUNCT
ejpam-5339	331	1	a	a	DET
ejpam-5339	331	2	modified	modify	VERB
ejpam-5339	331	3	global	global	ADJ
ejpam-5339	331	4	error	error	NOUN
ejpam-5339	331	5	minimization	minimization	NOUN
ejpam-5339	331	6	method	method	NOUN
ejpam-5339	331	7	for	for	ADP
ejpam-5339	331	8	solving	solve	VERB
ejpam-5339	331	9	nonlinear	nonlinear	ADJ
ejpam-5339	331	10	duffing	duffing	NOUN
ejpam-5339	331	11	-	-	PUNCT
ejpam-5339	331	12	harmonic	harmonic	ADJ
ejpam-5339	331	13	oscillators	oscillator	NOUN
ejpam-5339	331	14	.	.	PUNCT
ejpam-5339	332	1	aims	aim	VERB
ejpam-5339	332	2	mathematics	mathematic	NOUN
ejpam-5339	332	3	,	,	PUNCT
ejpam-5339	332	4	8(1):484–500	8(1):484–500	NUM
ejpam-5339	332	5	,	,	PUNCT
ejpam-5339	332	6	2023	2023	NUM
ejpam-5339	332	7	.	.	PUNCT
ejpam-5339	333	1	[	[	X
ejpam-5339	333	2	11	11	NUM
ejpam-5339	333	3	]	]	X
ejpam-5339	333	4	g.	g.	PROPN
ejpam-5339	333	5	m.	m.	PROPN
ejpam-5339	333	6	ismail	ismail	PROPN
ejpam-5339	333	7	,	,	PUNCT
ejpam-5339	333	8	m.	m.	PROPN
ejpam-5339	333	9	d.	d.	PROPN
ejpam-5339	333	10	hosen	hosen	PROPN
ejpam-5339	333	11	,	,	PUNCT
ejpam-5339	333	12	m.	m.	NOUN
ejpam-5339	333	13	mohammadian	mohammadian	NOUN
ejpam-5339	333	14	,	,	PUNCT
ejpam-5339	333	15	m.	m.	NOUN
ejpam-5339	333	16	m.	m.	PROPN
ejpam-5339	333	17	el	el	PROPN
ejpam-5339	333	18	-	-	PUNCT
ejpam-5339	333	19	moshneb	moshneb	ADJ
ejpam-5339	333	20	,	,	PUNCT
ejpam-5339	333	21	and	and	CCONJ
ejpam-5339	333	22	m.	m.	NOUN
ejpam-5339	333	23	bayat	bayat	PROPN
ejpam-5339	333	24	.	.	PUNCT
ejpam-5339	334	1	nonlinear	nonlinear	ADJ
ejpam-5339	334	2	vibration	vibration	NOUN
ejpam-5339	334	3	of	of	ADP
ejpam-5339	334	4	electrostatically	electrostatically	ADV
ejpam-5339	334	5	actuated	actuate	VERB
ejpam-5339	334	6	microbeam	microbeam	NOUN
ejpam-5339	334	7	.	.	PUNCT
ejpam-5339	335	1	mathematics	mathematic	NOUN
ejpam-5339	335	2	,	,	PUNCT
ejpam-5339	335	3	10:4762	10:4762	NUM
ejpam-5339	335	4	,	,	PUNCT
ejpam-5339	335	5	2022	2022	NUM
ejpam-5339	335	6	.	.	PUNCT
ejpam-5339	336	1	[	[	X
ejpam-5339	336	2	12	12	NUM
ejpam-5339	336	3	]	]	X
ejpam-5339	336	4	w.	w.	PROPN
ejpam-5339	336	5	m.	m.	PROPN
ejpam-5339	336	6	ji	ji	PROPN
ejpam-5339	336	7	,	,	PUNCT
ejpam-5339	336	8	h.	h.	PROPN
ejpam-5339	336	9	wang	wang	PROPN
ejpam-5339	336	10	,	,	PUNCT
ejpam-5339	336	11	and	and	CCONJ
ejpam-5339	336	12	m.	m.	PROPN
ejpam-5339	336	13	liu	liu	PROPN
ejpam-5339	336	14	.	.	PUNCT
ejpam-5339	337	1	dynamics	dynamic	VERB
ejpam-5339	337	2	analysis	analysis	NOUN
ejpam-5339	337	3	of	of	ADP
ejpam-5339	337	4	an	an	DET
ejpam-5339	337	5	impulsive	impulsive	ADJ
ejpam-5339	337	6	stochastic	stochastic	ADJ
ejpam-5339	337	7	model	model	NOUN
ejpam-5339	337	8	for	for	ADP
ejpam-5339	337	9	spruce	spruce	NOUN
ejpam-5339	337	10	budworm	budworm	NOUN
ejpam-5339	337	11	growth	growth	NOUN
ejpam-5339	337	12	.	.	PUNCT
ejpam-5339	338	1	applied	apply	VERB
ejpam-5339	338	2	mathematics	mathematic	NOUN
ejpam-5339	338	3	and	and	CCONJ
ejpam-5339	338	4	computations	computation	NOUN
ejpam-5339	338	5	,	,	PUNCT
ejpam-5339	338	6	19:336–359	19:336–359	NUM
ejpam-5339	338	7	,	,	PUNCT
ejpam-5339	338	8	2021	2021	NUM
ejpam-5339	338	9	.	.	PUNCT
ejpam-5339	339	1	[	[	X
ejpam-5339	339	2	13	13	NUM
ejpam-5339	339	3	]	]	X
ejpam-5339	339	4	d.	d.	PROPN
ejpam-5339	339	5	kumar	kumar	PROPN
ejpam-5339	339	6	,	,	PUNCT
ejpam-5339	339	7	j.	j.	PROPN
ejpam-5339	339	8	singh	singh	PROPN
ejpam-5339	339	9	,	,	PUNCT
ejpam-5339	339	10	and	and	CCONJ
ejpam-5339	339	11	d.	d.	PROPN
ejpam-5339	339	12	baleanu	baleanu	PROPN
ejpam-5339	339	13	.	.	PUNCT
ejpam-5339	340	1	a	a	DET
ejpam-5339	340	2	hybrid	hybrid	ADJ
ejpam-5339	340	3	computational	computational	ADJ
ejpam-5339	340	4	approach	approach	NOUN
ejpam-5339	340	5	for	for	ADP
ejpam-5339	340	6	kleingordon	kleingordon	PROPN
ejpam-5339	340	7	equations	equation	NOUN
ejpam-5339	340	8	on	on	ADP
ejpam-5339	340	9	cantor	cantor	NOUN
ejpam-5339	340	10	sets	set	NOUN
ejpam-5339	340	11	.	.	PUNCT
ejpam-5339	341	1	nonlinear	nonlinear	ADJ
ejpam-5339	341	2	dynamics	dynamic	NOUN
ejpam-5339	341	3	,	,	PUNCT
ejpam-5339	341	4	87:511–517	87:511–517	PROPN
ejpam-5339	341	5	,	,	PUNCT
ejpam-5339	341	6	2017	2017	NUM
ejpam-5339	341	7	.	.	PUNCT
ejpam-5339	342	1	[	[	X
ejpam-5339	342	2	14	14	NUM
ejpam-5339	342	3	]	]	X
ejpam-5339	342	4	c.	c.	PROPN
ejpam-5339	342	5	s.	s.	PROPN
ejpam-5339	342	6	liu	liu	PROPN
ejpam-5339	342	7	and	and	CCONJ
ejpam-5339	342	8	y.	y.	PROPN
ejpam-5339	342	9	w.	w.	PROPN
ejpam-5339	342	10	chen	chen	PROPN
ejpam-5339	342	11	.	.	PUNCT
ejpam-5339	343	1	a	a	DET
ejpam-5339	343	2	simplified	simplified	ADJ
ejpam-5339	343	3	lindstedt	lindstedt	VERB
ejpam-5339	343	4	-	-	PUNCT
ejpam-5339	343	5	poincare	poincare	PROPN
ejpam-5339	343	6	method	method	NOUN
ejpam-5339	343	7	for	for	ADP
ejpam-5339	343	8	saving	save	VERB
ejpam-5339	343	9	computational	computational	ADJ
ejpam-5339	343	10	cost	cost	NOUN
ejpam-5339	343	11	to	to	PART
ejpam-5339	343	12	determine	determine	VERB
ejpam-5339	343	13	higher	high	ADJ
ejpam-5339	343	14	order	order	NOUN
ejpam-5339	343	15	nonlinear	nonlinear	ADJ
ejpam-5339	343	16	free	free	ADJ
ejpam-5339	343	17	vibrations	vibration	NOUN
ejpam-5339	343	18	.	.	PUNCT
ejpam-5339	344	1	mathematics	mathematic	NOUN
ejpam-5339	344	2	,	,	PUNCT
ejpam-5339	344	3	9:3070	9:3070	NUM
ejpam-5339	344	4	,	,	PUNCT
ejpam-5339	344	5	2021	2021	NUM
ejpam-5339	344	6	.	.	PUNCT
ejpam-5339	345	1	[	[	X
ejpam-5339	345	2	15	15	NUM
ejpam-5339	345	3	]	]	X
ejpam-5339	345	4	h.	h.	PROPN
ejpam-5339	345	5	ma	ma	PROPN
ejpam-5339	345	6	.	.	PROPN
ejpam-5339	346	1	a	a	DET
ejpam-5339	346	2	short	short	ADJ
ejpam-5339	346	3	remark	remark	NOUN
ejpam-5339	346	4	on	on	ADP
ejpam-5339	346	5	he	he	PRON
ejpam-5339	346	6	’s	’s	PART
ejpam-5339	346	7	frequency	frequency	NOUN
ejpam-5339	346	8	formulation	formulation	NOUN
ejpam-5339	346	9	.	.	PUNCT
ejpam-5339	347	1	journal	journal	NOUN
ejpam-5339	347	2	of	of	ADP
ejpam-5339	347	3	low	low	ADJ
ejpam-5339	347	4	frequency	frequency	NOUN
ejpam-5339	347	5	noise	noise	NOUN
ejpam-5339	347	6	,	,	PUNCT
ejpam-5339	347	7	vibration	vibration	NOUN
ejpam-5339	347	8	and	and	CCONJ
ejpam-5339	347	9	active	active	ADJ
ejpam-5339	347	10	control	control	NOUN
ejpam-5339	347	11	,	,	PUNCT
ejpam-5339	347	12	41(4):1380–1385	41(4):1380–1385	PROPN
ejpam-5339	347	13	,	,	PUNCT
ejpam-5339	347	14	2022	2022	NUM
ejpam-5339	347	15	.	.	PUNCT
ejpam-5339	348	1	[	[	X
ejpam-5339	348	2	16	16	NUM
ejpam-5339	348	3	]	]	X
ejpam-5339	348	4	h.	h.	PROPN
ejpam-5339	348	5	ma	ma	PROPN
ejpam-5339	348	6	.	.	PROPN
ejpam-5339	348	7	simplified	simplify	VERB
ejpam-5339	348	8	hamiltonian	hamiltonian	NOUN
ejpam-5339	348	9	-	-	PUNCT
ejpam-5339	348	10	based	base	VERB
ejpam-5339	348	11	frequency	frequency	NOUN
ejpam-5339	348	12	-	-	PUNCT
ejpam-5339	348	13	amplitude	amplitude	NOUN
ejpam-5339	348	14	formulation	formulation	NOUN
ejpam-5339	348	15	for	for	ADP
ejpam-5339	348	16	nonlinear	nonlinear	ADJ
ejpam-5339	348	17	vibration	vibration	NOUN
ejpam-5339	348	18	systems	system	NOUN
ejpam-5339	348	19	.	.	PUNCT
ejpam-5339	349	1	facta	facta	PROPN
ejpam-5339	349	2	universitatis	universitatis	PROPN
ejpam-5339	349	3	series	series	PROPN
ejpam-5339	349	4	mechanical	mechanical	ADJ
ejpam-5339	349	5	engineering	engineering	NOUN
ejpam-5339	349	6	,	,	PUNCT
ejpam-5339	349	7	20(2):445–455	20(2):445–455	NUM
ejpam-5339	349	8	,	,	PUNCT
ejpam-5339	349	9	2022	2022	NUM
ejpam-5339	349	10	.	.	PUNCT
ejpam-5339	350	1	[	[	X
ejpam-5339	350	2	17	17	NUM
ejpam-5339	350	3	]	]	X
ejpam-5339	350	4	r.	r.	PROPN
ejpam-5339	350	5	e.	e.	PROPN
ejpam-5339	350	6	mickens	mickens	PROPN
ejpam-5339	350	7	.	.	PUNCT
ejpam-5339	351	1	oscillations	oscillation	NOUN
ejpam-5339	351	2	in	in	ADP
ejpam-5339	351	3	planner	planner	NOUN
ejpam-5339	351	4	dynamic	dynamic	ADJ
ejpam-5339	351	5	systems	system	NOUN
ejpam-5339	351	6	.	.	PUNCT
ejpam-5339	352	1	world	world	PROPN
ejpam-5339	352	2	scientific	scientific	PROPN
ejpam-5339	352	3	,	,	PUNCT
ejpam-5339	352	4	singapore	singapore	PROPN
ejpam-5339	352	5	,	,	PUNCT
ejpam-5339	352	6	1996	1996	NUM
ejpam-5339	352	7	.	.	PUNCT
ejpam-5339	353	1	[	[	X
ejpam-5339	353	2	18	18	NUM
ejpam-5339	353	3	]	]	X
ejpam-5339	353	4	g.	g.	PROPN
ejpam-5339	353	5	m.	m.	PROPN
ejpam-5339	353	6	moatimid	moatimid	PROPN
ejpam-5339	353	7	and	and	CCONJ
ejpam-5339	353	8	t.	t.	PROPN
ejpam-5339	353	9	s.	s.	PROPN
ejpam-5339	353	10	amer	amer	PROPN
ejpam-5339	353	11	.	.	PUNCT
ejpam-5339	354	1	analytical	analytical	ADJ
ejpam-5339	354	2	solution	solution	NOUN
ejpam-5339	354	3	for	for	ADP
ejpam-5339	354	4	the	the	DET
ejpam-5339	354	5	motion	motion	NOUN
ejpam-5339	354	6	of	of	ADP
ejpam-5339	354	7	a	a	DET
ejpam-5339	354	8	pendulum	pendulum	NOUN
ejpam-5339	354	9	with	with	ADP
ejpam-5339	354	10	rolling	rolling	ADJ
ejpam-5339	354	11	wheel	wheel	NOUN
ejpam-5339	354	12	:	:	PUNCT
ejpam-5339	354	13	stability	stability	NOUN
ejpam-5339	354	14	analysis	analysis	NOUN
ejpam-5339	354	15	.	.	PUNCT
ejpam-5339	355	1	scientific	scientific	ADJ
ejpam-5339	355	2	reports	report	NOUN
ejpam-5339	355	3	,	,	PUNCT
ejpam-5339	355	4	12:12628	12:12628	NUM
ejpam-5339	355	5	,	,	PUNCT
ejpam-5339	355	6	2022	2022	NUM
ejpam-5339	355	7	.	.	PUNCT
ejpam-5339	356	1	[	[	X
ejpam-5339	356	2	19	19	NUM
ejpam-5339	356	3	]	]	X
ejpam-5339	356	4	g.	g.	PROPN
ejpam-5339	356	5	m.	m.	PROPN
ejpam-5339	356	6	moatimid	moatimid	PROPN
ejpam-5339	356	7	and	and	CCONJ
ejpam-5339	356	8	t.	t.	PROPN
ejpam-5339	356	9	s.	s.	PROPN
ejpam-5339	356	10	amer	amer	PROPN
ejpam-5339	356	11	.	.	PUNCT
ejpam-5339	357	1	nonlinear	nonlinear	ADJ
ejpam-5339	357	2	suppression	suppression	NOUN
ejpam-5339	357	3	using	use	VERB
ejpam-5339	357	4	time	time	NOUN
ejpam-5339	357	5	-	-	PUNCT
ejpam-5339	357	6	delayed	delay	VERB
ejpam-5339	357	7	controller	controller	NOUN
ejpam-5339	357	8	to	to	ADP
ejpam-5339	357	9	excited	excited	ADJ
ejpam-5339	357	10	van	van	PROPN
ejpam-5339	357	11	der	der	ADJ
ejpam-5339	357	12	pol	pol	PROPN
ejpam-5339	357	13	-	-	PUNCT
ejpam-5339	357	14	duffing	duffing	NOUN
ejpam-5339	357	15	oscillator	oscillator	NOUN
ejpam-5339	357	16	:	:	PUNCT
ejpam-5339	357	17	analytical	analytical	ADJ
ejpam-5339	357	18	solution	solution	NOUN
ejpam-5339	357	19	techniques	technique	NOUN
ejpam-5339	357	20	.	.	PUNCT
ejpam-5339	358	1	archive	archive	NOUN
ejpam-5339	358	2	of	of	ADP
ejpam-5339	358	3	applied	apply	VERB
ejpam-5339	358	4	mechanics	mechanic	NOUN
ejpam-5339	358	5	,	,	PUNCT
ejpam-5339	358	6	92:3515–3531	92:3515–3531	NUM
ejpam-5339	358	7	,	,	PUNCT
ejpam-5339	358	8	2022	2022	NUM
ejpam-5339	358	9	.	.	PUNCT
ejpam-5339	359	1	references	reference	NOUN
ejpam-5339	359	2	2171	2171	NUM
ejpam-5339	360	1	[	[	X
ejpam-5339	360	2	20	20	NUM
ejpam-5339	360	3	]	]	PUNCT
ejpam-5339	360	4	g.	g.	PROPN
ejpam-5339	360	5	m.	m.	PROPN
ejpam-5339	360	6	moatimid	moatimid	PROPN
ejpam-5339	360	7	and	and	CCONJ
ejpam-5339	360	8	t.	t.	PROPN
ejpam-5339	360	9	s.	s.	PROPN
ejpam-5339	360	10	amer	amer	PROPN
ejpam-5339	360	11	.	.	PUNCT
ejpam-5339	361	1	analytical	analytical	ADJ
ejpam-5339	361	2	approximate	approximate	ADJ
ejpam-5339	361	3	solutions	solution	NOUN
ejpam-5339	361	4	of	of	ADP
ejpam-5339	361	5	a	a	DET
ejpam-5339	361	6	magnetic	magnetic	ADJ
ejpam-5339	361	7	spherical	spherical	ADJ
ejpam-5339	361	8	pendulum	pendulum	NOUN
ejpam-5339	361	9	:	:	PUNCT
ejpam-5339	361	10	stability	stability	NOUN
ejpam-5339	361	11	analysis	analysis	NOUN
ejpam-5339	361	12	.	.	PUNCT
ejpam-5339	362	1	journal	journal	NOUN
ejpam-5339	362	2	of	of	ADP
ejpam-5339	362	3	vibration	vibration	NOUN
ejpam-5339	362	4	engineering	engineering	NOUN
ejpam-5339	362	5	&	&	CCONJ
ejpam-5339	362	6	technologies	technologies	PROPN
ejpam-5339	362	7	,	,	PUNCT
ejpam-5339	362	8	11:2155–2165	11:2155–2165	NUM
ejpam-5339	362	9	,	,	PUNCT
ejpam-5339	362	10	2023	2023	NUM
ejpam-5339	362	11	.	.	PUNCT
ejpam-5339	363	1	[	[	X
ejpam-5339	363	2	21	21	NUM
ejpam-5339	363	3	]	]	X
ejpam-5339	363	4	g.	g.	PROPN
ejpam-5339	363	5	m.	m.	PROPN
ejpam-5339	363	6	moatimid	moatimid	PROPN
ejpam-5339	363	7	and	and	CCONJ
ejpam-5339	363	8	t.	t.	PROPN
ejpam-5339	363	9	s.	s.	PROPN
ejpam-5339	363	10	amer	amer	PROPN
ejpam-5339	363	11	.	.	PUNCT
ejpam-5339	364	1	dynamical	dynamical	ADJ
ejpam-5339	364	2	system	system	NOUN
ejpam-5339	364	3	of	of	ADP
ejpam-5339	364	4	a	a	DET
ejpam-5339	364	5	time	time	NOUN
ejpam-5339	364	6	-	-	PUNCT
ejpam-5339	364	7	delayed	delay	VERB
ejpam-5339	364	8	of	of	ADP
ejpam-5339	364	9	rigid	rigid	ADJ
ejpam-5339	364	10	rocking	rocking	NOUN
ejpam-5339	364	11	rod	rod	NOUN
ejpam-5339	364	12	:	:	PUNCT
ejpam-5339	364	13	analytical	analytical	ADJ
ejpam-5339	364	14	approximate	approximate	ADJ
ejpam-5339	364	15	solution	solution	NOUN
ejpam-5339	364	16	.	.	PUNCT
ejpam-5339	365	1	scientific	scientific	ADJ
ejpam-5339	365	2	reports	report	NOUN
ejpam-5339	365	3	,	,	PUNCT
ejpam-5339	365	4	13:5570	13:5570	NUM
ejpam-5339	365	5	,	,	PUNCT
ejpam-5339	365	6	2023	2023	NUM
ejpam-5339	365	7	.	.	PUNCT
ejpam-5339	366	1	[	[	X
ejpam-5339	366	2	22	22	NUM
ejpam-5339	366	3	]	]	X
ejpam-5339	366	4	g.	g.	PROPN
ejpam-5339	366	5	m.	m.	PROPN
ejpam-5339	366	6	moatimid	moatimid	PROPN
ejpam-5339	366	7	and	and	CCONJ
ejpam-5339	366	8	t.	t.	PROPN
ejpam-5339	366	9	s.	s.	PROPN
ejpam-5339	366	10	amer	amer	PROPN
ejpam-5339	366	11	.	.	PUNCT
ejpam-5339	367	1	dynamical	dynamical	ADJ
ejpam-5339	367	2	system	system	NOUN
ejpam-5339	367	3	of	of	ADP
ejpam-5339	367	4	a	a	DET
ejpam-5339	367	5	time	time	NOUN
ejpam-5339	367	6	-	-	PUNCT
ejpam-5339	367	7	delayed	delay	VERB
ejpam-5339	367	8	ϕ6	ϕ6	PROPN
ejpam-5339	367	9	-	-	PUNCT
ejpam-5339	367	10	van	van	PROPN
ejpam-5339	367	11	der	der	PROPN
ejpam-5339	367	12	pole	pole	NOUN
ejpam-5339	367	13	oscillator	oscillator	NOUN
ejpam-5339	367	14	:	:	PUNCT
ejpam-5339	367	15	a	a	DET
ejpam-5339	367	16	non	non	ADJ
ejpam-5339	367	17	-	-	ADJ
ejpam-5339	367	18	perturbative	perturbative	ADJ
ejpam-5339	367	19	approach	approach	NOUN
ejpam-5339	367	20	.	.	PUNCT
ejpam-5339	368	1	scientific	scientific	ADJ
ejpam-5339	368	2	reports	report	NOUN
ejpam-5339	368	3	,	,	PUNCT
ejpam-5339	368	4	13:11942	13:11942	NUM
ejpam-5339	368	5	,	,	PUNCT
ejpam-5339	368	6	2023	2023	NUM
ejpam-5339	368	7	.	.	PUNCT
ejpam-5339	369	1	[	[	X
ejpam-5339	369	2	23	23	NUM
ejpam-5339	369	3	]	]	X
ejpam-5339	369	4	g.	g.	PROPN
ejpam-5339	369	5	m.	m.	PROPN
ejpam-5339	369	6	moatimid	moatimid	PROPN
ejpam-5339	369	7	,	,	PUNCT
ejpam-5339	369	8	t.	t.	PROPN
ejpam-5339	369	9	s.	s.	PROPN
ejpam-5339	369	10	amer	amer	PROPN
ejpam-5339	369	11	,	,	PUNCT
ejpam-5339	369	12	and	and	CCONJ
ejpam-5339	369	13	w.	w.	PROPN
ejpam-5339	369	14	s.	s.	PROPN
ejpam-5339	369	15	amer	amer	PROPN
ejpam-5339	369	16	.	.	PUNCT
ejpam-5339	370	1	dynamical	dynamical	ADJ
ejpam-5339	370	2	analysis	analysis	NOUN
ejpam-5339	370	3	of	of	ADP
ejpam-5339	370	4	a	a	DET
ejpam-5339	370	5	damped	damped	ADJ
ejpam-5339	370	6	harmonic	harmonic	NOUN
ejpam-5339	370	7	forced	force	VERB
ejpam-5339	370	8	duffing	duffe	VERB
ejpam-5339	370	9	oscillator	oscillator	NOUN
ejpam-5339	370	10	with	with	ADP
ejpam-5339	370	11	time	time	NOUN
ejpam-5339	370	12	delay	delay	NOUN
ejpam-5339	370	13	.	.	PUNCT
ejpam-5339	371	1	scientific	scientific	ADJ
ejpam-5339	371	2	reports	report	NOUN
ejpam-5339	371	3	,	,	PUNCT
ejpam-5339	371	4	13:6507	13:6507	NUM
ejpam-5339	371	5	,	,	PUNCT
ejpam-5339	371	6	2023	2023	NUM
ejpam-5339	371	7	.	.	PUNCT
ejpam-5339	372	1	[	[	X
ejpam-5339	372	2	24	24	NUM
ejpam-5339	372	3	]	]	X
ejpam-5339	372	4	g.	g.	PROPN
ejpam-5339	372	5	m.	m.	PROPN
ejpam-5339	372	6	moatimid	moatimid	PROPN
ejpam-5339	372	7	,	,	PUNCT
ejpam-5339	372	8	t.	t.	PROPN
ejpam-5339	372	9	s.	s.	PROPN
ejpam-5339	372	10	amer	amer	PROPN
ejpam-5339	372	11	,	,	PUNCT
ejpam-5339	372	12	and	and	CCONJ
ejpam-5339	372	13	w.	w.	PROPN
ejpam-5339	372	14	s.	s.	PROPN
ejpam-5339	372	15	amer	amer	PROPN
ejpam-5339	372	16	.	.	PUNCT
ejpam-5339	373	1	dynamical	dynamical	ADJ
ejpam-5339	373	2	stability	stability	NOUN
ejpam-5339	373	3	of	of	ADP
ejpam-5339	373	4	a	a	DET
ejpam-5339	373	5	3	3	NUM
ejpam-5339	373	6	-	-	PUNCT
ejpam-5339	373	7	dof	dof	NOUN
ejpam-5339	373	8	auto	auto	NOUN
ejpam-5339	373	9	-	-	PUNCT
ejpam-5339	373	10	parametric	parametric	ADJ
ejpam-5339	373	11	vibrating	vibrating	NOUN
ejpam-5339	373	12	system	system	NOUN
ejpam-5339	373	13	.	.	PUNCT
ejpam-5339	374	1	journal	journal	NOUN
ejpam-5339	374	2	of	of	ADP
ejpam-5339	374	3	vibration	vibration	NOUN
ejpam-5339	374	4	engineering	engineering	NOUN
ejpam-5339	374	5	&	&	CCONJ
ejpam-5339	374	6	technologies	technology	NOUN
ejpam-5339	374	7	,	,	PUNCT
ejpam-5339	374	8	11:4151–4186	11:4151–4186	NUM
ejpam-5339	374	9	,	,	PUNCT
ejpam-5339	374	10	2023	2023	NUM
ejpam-5339	374	11	.	.	PUNCT
ejpam-5339	375	1	[	[	X
ejpam-5339	375	2	25	25	NUM
ejpam-5339	375	3	]	]	X
ejpam-5339	375	4	g.	g.	PROPN
ejpam-5339	375	5	m.	m.	PROPN
ejpam-5339	375	6	moatimid	moatimid	PROPN
ejpam-5339	375	7	,	,	PUNCT
ejpam-5339	375	8	t.	t.	PROPN
ejpam-5339	375	9	s.	s.	PROPN
ejpam-5339	375	10	amer	amer	PROPN
ejpam-5339	375	11	,	,	PUNCT
ejpam-5339	375	12	and	and	CCONJ
ejpam-5339	375	13	y.	y.	PROPN
ejpam-5339	375	14	y.	y.	PROPN
ejpam-5339	375	15	ellabban	ellabban	PROPN
ejpam-5339	375	16	.	.	PUNCT
ejpam-5339	376	1	a	a	DET
ejpam-5339	376	2	novel	novel	ADJ
ejpam-5339	376	3	methodology	methodology	NOUN
ejpam-5339	376	4	for	for	ADP
ejpam-5339	376	5	a	a	DET
ejpam-5339	376	6	timedelayed	timedelayed	ADJ
ejpam-5339	376	7	controller	controller	NOUN
ejpam-5339	376	8	to	to	PART
ejpam-5339	376	9	prevent	prevent	VERB
ejpam-5339	376	10	nonlinear	nonlinear	ADJ
ejpam-5339	376	11	system	system	NOUN
ejpam-5339	376	12	oscillations	oscillation	NOUN
ejpam-5339	376	13	.	.	PUNCT
ejpam-5339	377	1	journal	journal	NOUN
ejpam-5339	377	2	of	of	ADP
ejpam-5339	377	3	low	low	ADJ
ejpam-5339	377	4	frequency	frequency	NOUN
ejpam-5339	377	5	noise	noise	NOUN
ejpam-5339	377	6	,	,	PUNCT
ejpam-5339	377	7	vibration	vibration	NOUN
ejpam-5339	377	8	and	and	CCONJ
ejpam-5339	377	9	active	active	ADJ
ejpam-5339	377	10	control	control	NOUN
ejpam-5339	377	11	,	,	PUNCT
ejpam-5339	377	12	43(1):525–542	43(1):525–542	PROPN
ejpam-5339	377	13	,	,	PUNCT
ejpam-5339	377	14	2024	2024	NUM
ejpam-5339	377	15	.	.	PUNCT
ejpam-5339	378	1	[	[	X
ejpam-5339	378	2	26	26	NUM
ejpam-5339	378	3	]	]	X
ejpam-5339	378	4	g.	g.	PROPN
ejpam-5339	378	5	m.	m.	PROPN
ejpam-5339	378	6	moatimid	moatimid	PROPN
ejpam-5339	378	7	,	,	PUNCT
ejpam-5339	378	8	t.	t.	PROPN
ejpam-5339	378	9	s.	s.	PROPN
ejpam-5339	378	10	amer	amer	PROPN
ejpam-5339	378	11	,	,	PUNCT
ejpam-5339	378	12	and	and	CCONJ
ejpam-5339	378	13	a.	a.	NOUN
ejpam-5339	378	14	a.	a.	PROPN
ejpam-5339	378	15	galal	galal	PROPN
ejpam-5339	378	16	.	.	PUNCT
ejpam-5339	379	1	studying	study	VERB
ejpam-5339	379	2	highly	highly	ADV
ejpam-5339	379	3	nonlinear	nonlinear	ADJ
ejpam-5339	379	4	oscillators	oscillator	NOUN
ejpam-5339	379	5	using	use	VERB
ejpam-5339	379	6	the	the	DET
ejpam-5339	379	7	non	non	ADJ
ejpam-5339	379	8	-	-	ADJ
ejpam-5339	379	9	perturbative	perturbative	ADJ
ejpam-5339	379	10	methodology	methodology	NOUN
ejpam-5339	379	11	.	.	PUNCT
ejpam-5339	380	1	scientific	scientific	ADJ
ejpam-5339	380	2	reports	report	NOUN
ejpam-5339	380	3	,	,	PUNCT
ejpam-5339	380	4	13:20288	13:20288	NUM
ejpam-5339	380	5	,	,	PUNCT
ejpam-5339	380	6	2023	2023	NUM
ejpam-5339	380	7	.	.	PUNCT
ejpam-5339	381	1	[	[	X
ejpam-5339	381	2	27	27	NUM
ejpam-5339	381	3	]	]	X
ejpam-5339	381	4	g.	g.	PROPN
ejpam-5339	381	5	m.	m.	PROPN
ejpam-5339	381	6	moatimid	moatimid	PROPN
ejpam-5339	381	7	,	,	PUNCT
ejpam-5339	381	8	t.	t.	PROPN
ejpam-5339	381	9	s.	s.	PROPN
ejpam-5339	381	10	amer	amer	PROPN
ejpam-5339	381	11	,	,	PUNCT
ejpam-5339	381	12	and	and	CCONJ
ejpam-5339	381	13	a.	a.	NOUN
ejpam-5339	381	14	a.	a.	PROPN
ejpam-5339	381	15	galal	galal	PROPN
ejpam-5339	381	16	.	.	PUNCT
ejpam-5339	382	1	inspection	inspection	NOUN
ejpam-5339	382	2	of	of	ADP
ejpam-5339	382	3	some	some	DET
ejpam-5339	382	4	extremely	extremely	ADV
ejpam-5339	382	5	nonlinear	nonlinear	ADJ
ejpam-5339	382	6	oscillators	oscillator	NOUN
ejpam-5339	382	7	using	use	VERB
ejpam-5339	382	8	an	an	DET
ejpam-5339	382	9	inventive	inventive	ADJ
ejpam-5339	382	10	approach	approach	NOUN
ejpam-5339	382	11	.	.	PUNCT
ejpam-5339	383	1	journal	journal	NOUN
ejpam-5339	383	2	of	of	ADP
ejpam-5339	383	3	vibration	vibration	NOUN
ejpam-5339	383	4	engineering	engineering	NOUN
ejpam-5339	383	5	&	&	CCONJ
ejpam-5339	383	6	technologies	technology	NOUN
ejpam-5339	383	7	,	,	PUNCT
ejpam-5339	383	8	2024	2024	NUM
ejpam-5339	383	9	.	.	PUNCT
ejpam-5339	384	1	published	publish	VERB
ejpam-5339	384	2	online	online	ADV
ejpam-5339	384	3	:	:	PUNCT
ejpam-5339	384	4	06	06	NUM
ejpam-5339	384	5	july	july	NOUN
ejpam-5339	384	6	.	.	PUNCT
ejpam-5339	385	1	[	[	X
ejpam-5339	385	2	28	28	NUM
ejpam-5339	385	3	]	]	X
ejpam-5339	385	4	g.	g.	PROPN
ejpam-5339	385	5	m.	m.	PROPN
ejpam-5339	385	6	moatimid	moatimid	PROPN
ejpam-5339	385	7	,	,	PUNCT
ejpam-5339	385	8	t.	t.	PROPN
ejpam-5339	385	9	s.	s.	PROPN
ejpam-5339	385	10	amer	amer	PROPN
ejpam-5339	385	11	,	,	PUNCT
ejpam-5339	385	12	and	and	CCONJ
ejpam-5339	385	13	m.	m.	PROPN
ejpam-5339	385	14	h.	h.	PROPN
ejpam-5339	385	15	zekry	zekry	PROPN
ejpam-5339	385	16	.	.	PROPN
ejpam-5339	386	1	analytical	analytical	ADJ
ejpam-5339	386	2	and	and	CCONJ
ejpam-5339	386	3	numerical	numerical	ADJ
ejpam-5339	386	4	study	study	NOUN
ejpam-5339	386	5	of	of	ADP
ejpam-5339	386	6	a	a	DET
ejpam-5339	386	7	vibrating	vibrate	VERB
ejpam-5339	386	8	magnetic	magnetic	ADJ
ejpam-5339	386	9	inverted	invert	VERB
ejpam-5339	386	10	pendulum	pendulum	NOUN
ejpam-5339	386	11	.	.	PUNCT
ejpam-5339	387	1	archive	archive	NOUN
ejpam-5339	387	2	of	of	ADP
ejpam-5339	387	3	applied	apply	VERB
ejpam-5339	387	4	mechanics	mechanic	NOUN
ejpam-5339	387	5	,	,	PUNCT
ejpam-5339	387	6	93:2533–2547	93:2533–2547	NUM
ejpam-5339	387	7	,	,	PUNCT
ejpam-5339	387	8	2023	2023	NUM
ejpam-5339	387	9	.	.	PUNCT
ejpam-5339	388	1	[	[	X
ejpam-5339	388	2	29	29	NUM
ejpam-5339	388	3	]	]	X
ejpam-5339	388	4	g.	g.	PROPN
ejpam-5339	388	5	m.	m.	PROPN
ejpam-5339	388	6	moatimid	moatimid	PROPN
ejpam-5339	388	7	,	,	PUNCT
ejpam-5339	388	8	m.	m.	PROPN
ejpam-5339	388	9	a.	a.	PROPN
ejpam-5339	388	10	a.	a.	PROPN
ejpam-5339	388	11	mohamed	mohamed	PROPN
ejpam-5339	388	12	,	,	PUNCT
ejpam-5339	388	13	and	and	CCONJ
ejpam-5339	388	14	kh	kh	PROPN
ejpam-5339	388	15	.	.	PROPN
ejpam-5339	388	16	elagamy	elagamy	PROPN
ejpam-5339	388	17	.	.	PUNCT
ejpam-5339	389	1	nonlinear	nonlinear	PROPN
ejpam-5339	389	2	kelvin	kelvin	PROPN
ejpam-5339	389	3	-	-	PUNCT
ejpam-5339	389	4	helmholtz	helmholtz	PROPN
ejpam-5339	389	5	instability	instability	NOUN
ejpam-5339	389	6	of	of	ADP
ejpam-5339	389	7	a	a	DET
ejpam-5339	389	8	horizontal	horizontal	ADJ
ejpam-5339	389	9	interface	interface	NOUN
ejpam-5339	389	10	separating	separate	VERB
ejpam-5339	389	11	two	two	NUM
ejpam-5339	389	12	electrified	electrify	VERB
ejpam-5339	389	13	walters	walter	NOUN
ejpam-5339	389	14	’	'	PUNCT
ejpam-5339	389	15	b	b	PROPN
ejpam-5339	389	16	liquids	liquid	NOUN
ejpam-5339	389	17	:	:	PUNCT
ejpam-5339	389	18	a	a	DET
ejpam-5339	389	19	new	new	ADJ
ejpam-5339	389	20	approach	approach	NOUN
ejpam-5339	389	21	.	.	PUNCT
ejpam-5339	390	1	chinese	chinese	ADJ
ejpam-5339	390	2	journal	journal	PROPN
ejpam-5339	390	3	of	of	ADP
ejpam-5339	390	4	physics	physics	PROPN
ejpam-5339	390	5	,	,	PUNCT
ejpam-5339	390	6	85:629–648	85:629–648	PROPN
ejpam-5339	390	7	,	,	PUNCT
ejpam-5339	390	8	2023	2023	NUM
ejpam-5339	390	9	.	.	PUNCT
ejpam-5339	391	1	[	[	X
ejpam-5339	391	2	30	30	NUM
ejpam-5339	391	3	]	]	X
ejpam-5339	391	4	g.	g.	PROPN
ejpam-5339	391	5	m.	m.	PROPN
ejpam-5339	391	6	moatimid	moatimid	PROPN
ejpam-5339	391	7	,	,	PUNCT
ejpam-5339	391	8	m.	m.	PROPN
ejpam-5339	391	9	a.	a.	PROPN
ejpam-5339	391	10	a.	a.	PROPN
ejpam-5339	391	11	mohamed	mohamed	PROPN
ejpam-5339	391	12	,	,	PUNCT
ejpam-5339	391	13	and	and	CCONJ
ejpam-5339	391	14	kh	kh	PROPN
ejpam-5339	391	15	.	.	PROPN
ejpam-5339	391	16	elagamy	elagamy	PROPN
ejpam-5339	391	17	.	.	PUNCT
ejpam-5339	392	1	insightful	insightful	ADJ
ejpam-5339	392	2	inspection	inspection	NOUN
ejpam-5339	392	3	of	of	ADP
ejpam-5339	392	4	the	the	DET
ejpam-5339	392	5	nonlinear	nonlinear	ADJ
ejpam-5339	392	6	instability	instability	NOUN
ejpam-5339	392	7	of	of	ADP
ejpam-5339	392	8	an	an	DET
ejpam-5339	392	9	azimuthal	azimuthal	ADJ
ejpam-5339	392	10	disturbance	disturbance	NOUN
ejpam-5339	392	11	separating	separate	VERB
ejpam-5339	392	12	two	two	NUM
ejpam-5339	392	13	rotating	rotate	VERB
ejpam-5339	392	14	magnetic	magnetic	ADJ
ejpam-5339	392	15	liquid	liquid	ADJ
ejpam-5339	392	16	columns	column	NOUN
ejpam-5339	392	17	.	.	PUNCT
ejpam-5339	393	1	the	the	DET
ejpam-5339	393	2	european	european	PROPN
ejpam-5339	393	3	physical	physical	PROPN
ejpam-5339	393	4	journal	journal	PROPN
ejpam-5339	393	5	plus	plus	CCONJ
ejpam-5339	393	6	,	,	PUNCT
ejpam-5339	393	7	139:590	139:590	NOUN
ejpam-5339	393	8	,	,	PUNCT
ejpam-5339	393	9	2024	2024	NUM
ejpam-5339	393	10	.	.	PUNCT
ejpam-5339	394	1	[	[	X
ejpam-5339	394	2	31	31	NUM
ejpam-5339	394	3	]	]	PUNCT
ejpam-5339	394	4	g.	g.	PROPN
ejpam-5339	394	5	m.	m.	PROPN
ejpam-5339	394	6	moatimid	moatimid	PROPN
ejpam-5339	394	7	and	and	CCONJ
ejpam-5339	394	8	y.	y.	PROPN
ejpam-5339	394	9	m.	m.	PROPN
ejpam-5339	394	10	mohamed	mohamed	PROPN
ejpam-5339	394	11	.	.	PUNCT
ejpam-5339	395	1	nonlinear	nonlinear	ADJ
ejpam-5339	395	2	electro	electro	ADJ
ejpam-5339	395	3	-	-	PUNCT
ejpam-5339	395	4	rheological	rheological	ADJ
ejpam-5339	395	5	instability	instability	NOUN
ejpam-5339	395	6	of	of	ADP
ejpam-5339	395	7	two	two	NUM
ejpam-5339	395	8	moving	move	VERB
ejpam-5339	395	9	cylindrical	cylindrical	ADJ
ejpam-5339	395	10	fluids	fluid	NOUN
ejpam-5339	395	11	:	:	PUNCT
ejpam-5339	395	12	an	an	DET
ejpam-5339	395	13	innovative	innovative	ADJ
ejpam-5339	395	14	approach	approach	NOUN
ejpam-5339	395	15	.	.	PUNCT
ejpam-5339	396	1	physics	physics	NOUN
ejpam-5339	396	2	of	of	ADP
ejpam-5339	396	3	fluids	fluid	NOUN
ejpam-5339	396	4	,	,	PUNCT
ejpam-5339	396	5	36:024110	36:024110	NUM
ejpam-5339	396	6	,	,	PUNCT
ejpam-5339	396	7	2024	2024	NUM
ejpam-5339	396	8	.	.	PUNCT
ejpam-5339	397	1	[	[	X
ejpam-5339	397	2	32	32	NUM
ejpam-5339	397	3	]	]	PUNCT
ejpam-5339	397	4	g.	g.	PROPN
ejpam-5339	397	5	m.	m.	PROPN
ejpam-5339	397	6	moatimid	moatimid	PROPN
ejpam-5339	397	7	and	and	CCONJ
ejpam-5339	397	8	y.	y.	PROPN
ejpam-5339	397	9	m.	m.	PROPN
ejpam-5339	397	10	mohamed	mohamed	PROPN
ejpam-5339	397	11	.	.	PUNCT
ejpam-5339	398	1	a	a	DET
ejpam-5339	398	2	novel	novel	ADJ
ejpam-5339	398	3	methodology	methodology	NOUN
ejpam-5339	398	4	in	in	ADP
ejpam-5339	398	5	analyzing	analyze	VERB
ejpam-5339	398	6	nonlinear	nonlinear	ADJ
ejpam-5339	398	7	stability	stability	NOUN
ejpam-5339	398	8	of	of	ADP
ejpam-5339	398	9	two	two	NUM
ejpam-5339	398	10	electrified	electrify	VERB
ejpam-5339	398	11	viscoelastic	viscoelastic	ADJ
ejpam-5339	398	12	liquids	liquid	NOUN
ejpam-5339	398	13	.	.	PUNCT
ejpam-5339	399	1	chinese	chinese	ADJ
ejpam-5339	399	2	journal	journal	PROPN
ejpam-5339	399	3	of	of	ADP
ejpam-5339	399	4	physics	physics	PROPN
ejpam-5339	399	5	,	,	PUNCT
ejpam-5339	399	6	89:679–706	89:679–706	PROPN
ejpam-5339	399	7	,	,	PUNCT
ejpam-5339	399	8	2024	2024	NUM
ejpam-5339	399	9	.	.	PUNCT
ejpam-5339	400	1	references	reference	NOUN
ejpam-5339	400	2	2172	2172	NUM
ejpam-5339	400	3	[	[	X
ejpam-5339	400	4	33	33	NUM
ejpam-5339	400	5	]	]	PUNCT
ejpam-5339	400	6	g.	g.	PROPN
ejpam-5339	400	7	m.	m.	PROPN
ejpam-5339	400	8	moatimid	moatimid	PROPN
ejpam-5339	400	9	and	and	CCONJ
ejpam-5339	400	10	d.	d.	PROPN
ejpam-5339	400	11	m.	m.	PROPN
ejpam-5339	400	12	mostafa	mostafa	PROPN
ejpam-5339	400	13	.	.	PUNCT
ejpam-5339	401	1	nonlinear	nonlinear	ADJ
ejpam-5339	401	2	stability	stability	NOUN
ejpam-5339	401	3	of	of	ADP
ejpam-5339	401	4	two	two	NUM
ejpam-5339	401	5	superimposed	superimpose	VERB
ejpam-5339	401	6	electrified	electrified	ADJ
ejpam-5339	401	7	dusty	dusty	ADJ
ejpam-5339	401	8	fluids	fluid	NOUN
ejpam-5339	401	9	of	of	ADP
ejpam-5339	401	10	type	type	NOUN
ejpam-5339	401	11	rivlin	rivlin	PROPN
ejpam-5339	401	12	-	-	PUNCT
ejpam-5339	401	13	ericksen	ericksen	ADJ
ejpam-5339	401	14	:	:	PUNCT
ejpam-5339	401	15	non	non	ADJ
ejpam-5339	401	16	-	-	ADJ
ejpam-5339	401	17	perturbative	perturbative	ADJ
ejpam-5339	401	18	approach	approach	NOUN
ejpam-5339	401	19	.	.	PUNCT
ejpam-5339	402	1	partial	partial	ADJ
ejpam-5339	402	2	differential	differential	ADJ
ejpam-5339	402	3	equations	equation	NOUN
ejpam-5339	402	4	in	in	ADP
ejpam-5339	402	5	applied	applied	ADJ
ejpam-5339	402	6	mathematics	mathematic	NOUN
ejpam-5339	402	7	,	,	PUNCT
ejpam-5339	402	8	10:100745	10:100745	NUM
ejpam-5339	402	9	,	,	PUNCT
ejpam-5339	402	10	2024	2024	NUM
ejpam-5339	402	11	.	.	PUNCT
ejpam-5339	403	1	[	[	X
ejpam-5339	403	2	34	34	NUM
ejpam-5339	403	3	]	]	X
ejpam-5339	403	4	g.	g.	PROPN
ejpam-5339	403	5	m.	m.	PROPN
ejpam-5339	403	6	moatimid	moatimid	PROPN
ejpam-5339	403	7	,	,	PUNCT
ejpam-5339	403	8	d.	d.	PROPN
ejpam-5339	403	9	m.	m.	PROPN
ejpam-5339	403	10	mostafa	mostafa	PROPN
ejpam-5339	403	11	,	,	PUNCT
ejpam-5339	403	12	and	and	CCONJ
ejpam-5339	403	13	m.	m.	PROPN
ejpam-5339	403	14	h.	h.	PROPN
ejpam-5339	403	15	zekry	zekry	PROPN
ejpam-5339	403	16	.	.	PUNCT
ejpam-5339	404	1	a	a	DET
ejpam-5339	404	2	new	new	ADJ
ejpam-5339	404	3	methodology	methodology	NOUN
ejpam-5339	404	4	in	in	ADP
ejpam-5339	404	5	evaluating	evaluate	VERB
ejpam-5339	404	6	nonlinear	nonlinear	ADJ
ejpam-5339	404	7	electrohydrodynamic	electrohydrodynamic	ADJ
ejpam-5339	404	8	azimuthal	azimuthal	NOUN
ejpam-5339	404	9	stability	stability	NOUN
ejpam-5339	404	10	between	between	ADP
ejpam-5339	404	11	two	two	NUM
ejpam-5339	404	12	dusty	dusty	ADJ
ejpam-5339	404	13	viscous	viscous	ADJ
ejpam-5339	404	14	fluids	fluid	NOUN
ejpam-5339	404	15	.	.	PUNCT
ejpam-5339	405	1	chinese	chinese	ADJ
ejpam-5339	405	2	journal	journal	PROPN
ejpam-5339	405	3	of	of	ADP
ejpam-5339	405	4	physics	physics	PROPN
ejpam-5339	405	5	,	,	PUNCT
ejpam-5339	405	6	90:134–154	90:134–154	NUM
ejpam-5339	405	7	,	,	PUNCT
ejpam-5339	405	8	2024	2024	NUM
ejpam-5339	405	9	.	.	PUNCT
ejpam-5339	406	1	[	[	X
ejpam-5339	406	2	35	35	NUM
ejpam-5339	406	3	]	]	X
ejpam-5339	406	4	g.	g.	PROPN
ejpam-5339	406	5	m.	m.	PROPN
ejpam-5339	406	6	moatimid	moatimid	PROPN
ejpam-5339	406	7	and	and	CCONJ
ejpam-5339	406	8	a.	a.	PROPN
ejpam-5339	406	9	sayed	say	VERB
ejpam-5339	406	10	.	.	PUNCT
ejpam-5339	407	1	nonlinear	nonlinear	ADJ
ejpam-5339	407	2	ehd	ehd	NOUN
ejpam-5339	407	3	stability	stability	NOUN
ejpam-5339	407	4	of	of	ADP
ejpam-5339	407	5	a	a	DET
ejpam-5339	407	6	cylindrical	cylindrical	ADJ
ejpam-5339	407	7	interface	interface	NOUN
ejpam-5339	407	8	separating	separate	VERB
ejpam-5339	407	9	two	two	NUM
ejpam-5339	407	10	rivlin	rivlin	ADJ
ejpam-5339	407	11	-	-	PUNCT
ejpam-5339	407	12	ericksen	ericksen	ADJ
ejpam-5339	407	13	fluids	fluid	NOUN
ejpam-5339	407	14	:	:	PUNCT
ejpam-5339	407	15	a	a	DET
ejpam-5339	407	16	novel	novel	ADJ
ejpam-5339	407	17	analysis	analysis	NOUN
ejpam-5339	407	18	.	.	PUNCT
ejpam-5339	408	1	chinese	chinese	ADJ
ejpam-5339	408	2	journal	journal	PROPN
ejpam-5339	408	3	of	of	ADP
ejpam-5339	408	4	physics	physics	PROPN
ejpam-5339	408	5	,	,	PUNCT
ejpam-5339	408	6	87:379–397	87:379–397	NUM
ejpam-5339	408	7	,	,	PUNCT
ejpam-5339	408	8	2024	2024	NUM
ejpam-5339	408	9	.	.	PUNCT
ejpam-5339	409	1	[	[	X
ejpam-5339	409	2	36	36	NUM
ejpam-5339	409	3	]	]	PUNCT
ejpam-5339	409	4	m.	m.	NOUN
ejpam-5339	409	5	mohammadian	mohammadian	NOUN
ejpam-5339	409	6	and	and	CCONJ
ejpam-5339	409	7	g.	g.	PROPN
ejpam-5339	409	8	m.	m.	PROPN
ejpam-5339	409	9	ismail	ismail	PROPN
ejpam-5339	409	10	.	.	PUNCT
ejpam-5339	410	1	improved	improve	VERB
ejpam-5339	410	2	harmonic	harmonic	ADJ
ejpam-5339	410	3	balance	balance	NOUN
ejpam-5339	410	4	method	method	NOUN
ejpam-5339	410	5	for	for	ADP
ejpam-5339	410	6	analyzing	analyze	VERB
ejpam-5339	410	7	asymmetric	asymmetric	ADJ
ejpam-5339	410	8	restoring	restore	VERB
ejpam-5339	410	9	force	force	NOUN
ejpam-5339	410	10	functions	function	NOUN
ejpam-5339	410	11	in	in	ADP
ejpam-5339	410	12	nonlinear	nonlinear	ADJ
ejpam-5339	410	13	vibration	vibration	NOUN
ejpam-5339	410	14	of	of	ADP
ejpam-5339	410	15	mechanical	mechanical	ADJ
ejpam-5339	410	16	systems	system	NOUN
ejpam-5339	410	17	.	.	PUNCT
ejpam-5339	411	1	physica	physica	PROPN
ejpam-5339	411	2	scripta	scripta	PROPN
ejpam-5339	411	3	,	,	PUNCT
ejpam-5339	411	4	99:075280	99:075280	NUM
ejpam-5339	411	5	,	,	PUNCT
ejpam-5339	411	6	2024	2024	NUM
ejpam-5339	411	7	.	.	PUNCT
ejpam-5339	412	1	[	[	X
ejpam-5339	412	2	37	37	NUM
ejpam-5339	412	3	]	]	PUNCT
ejpam-5339	412	4	a.	a.	NOUN
ejpam-5339	412	5	h.	h.	PROPN
ejpam-5339	412	6	nayfeh	nayfeh	PROPN
ejpam-5339	412	7	and	and	CCONJ
ejpam-5339	412	8	d.	d.	PROPN
ejpam-5339	412	9	t.	t.	PROPN
ejpam-5339	412	10	mook	mook	PROPN
ejpam-5339	412	11	.	.	PUNCT
ejpam-5339	413	1	nonlinear	nonlinear	ADJ
ejpam-5339	413	2	oscillations	oscillation	NOUN
ejpam-5339	413	3	.	.	PUNCT
ejpam-5339	414	1	john	john	PROPN
ejpam-5339	414	2	wiley	wiley	PROPN
ejpam-5339	414	3	&	&	CCONJ
ejpam-5339	414	4	sons	son	NOUN
ejpam-5339	414	5	,	,	PUNCT
ejpam-5339	414	6	new	new	PROPN
ejpam-5339	414	7	york	york	PROPN
ejpam-5339	414	8	,	,	PUNCT
ejpam-5339	414	9	1979	1979	NUM
ejpam-5339	414	10	.	.	PUNCT
ejpam-5339	415	1	[	[	X
ejpam-5339	415	2	38	38	NUM
ejpam-5339	415	3	]	]	PUNCT
ejpam-5339	415	4	j.-y	j.-y	NOUN
ejpam-5339	415	5	.	.	PUNCT
ejpam-5339	415	6	niu	niu	PROPN
ejpam-5339	415	7	,	,	PUNCT
ejpam-5339	415	8	g.-q	g.-q	PROPN
ejpam-5339	415	9	.	.	PUNCT
ejpam-5339	416	1	feng	feng	PROPN
ejpam-5339	416	2	,	,	PUNCT
ejpam-5339	416	3	and	and	CCONJ
ejpam-5339	416	4	k.	k.	PROPN
ejpam-5339	416	5	a.	a.	PROPN
ejpam-5339	416	6	gepreel	gepreel	PROPN
ejpam-5339	416	7	.	.	PUNCT
ejpam-5339	417	1	a	a	DET
ejpam-5339	417	2	simple	simple	ADJ
ejpam-5339	417	3	frequency	frequency	NOUN
ejpam-5339	417	4	formulation	formulation	NOUN
ejpam-5339	417	5	for	for	ADP
ejpam-5339	417	6	fractalfractional	fractalfractional	ADJ
ejpam-5339	417	7	non	non	ADJ
ejpam-5339	417	8	-	-	ADJ
ejpam-5339	417	9	linear	linear	ADJ
ejpam-5339	417	10	oscillators	oscillator	NOUN
ejpam-5339	417	11	:	:	PUNCT
ejpam-5339	417	12	a	a	DET
ejpam-5339	417	13	promising	promising	ADJ
ejpam-5339	417	14	tool	tool	NOUN
ejpam-5339	417	15	and	and	CCONJ
ejpam-5339	417	16	its	its	PRON
ejpam-5339	417	17	future	future	ADJ
ejpam-5339	417	18	challenge	challenge	NOUN
ejpam-5339	417	19	.	.	PUNCT
ejpam-5339	418	1	frontiers	frontier	NOUN
ejpam-5339	418	2	in	in	ADP
ejpam-5339	418	3	physics	physics	PROPN
ejpam-5339	418	4	,	,	PUNCT
ejpam-5339	418	5	11:1158121	11:1158121	NUM
ejpam-5339	418	6	,	,	PUNCT
ejpam-5339	418	7	2023	2023	NUM
ejpam-5339	418	8	.	.	PUNCT
ejpam-5339	419	1	[	[	X
ejpam-5339	419	2	39	39	NUM
ejpam-5339	419	3	]	]	PUNCT
ejpam-5339	419	4	s.	s.	PROPN
ejpam-5339	419	5	telli	telli	PROPN
ejpam-5339	419	6	and	and	CCONJ
ejpam-5339	419	7	o.	o.	PROPN
ejpam-5339	419	8	kopmaz	kopmaz	PROPN
ejpam-5339	419	9	.	.	PUNCT
ejpam-5339	420	1	free	free	ADJ
ejpam-5339	420	2	vibrations	vibration	NOUN
ejpam-5339	420	3	of	of	ADP
ejpam-5339	420	4	a	a	DET
ejpam-5339	420	5	mass	mass	NOUN
ejpam-5339	420	6	grounded	ground	VERB
ejpam-5339	420	7	by	by	ADP
ejpam-5339	420	8	linear	linear	ADJ
ejpam-5339	420	9	and	and	CCONJ
ejpam-5339	420	10	nonlinear	nonlinear	ADJ
ejpam-5339	420	11	springs	spring	NOUN
ejpam-5339	420	12	in	in	ADP
ejpam-5339	420	13	series	series	PROPN
ejpam-5339	420	14	.	.	PUNCT
ejpam-5339	421	1	journal	journal	PROPN
ejpam-5339	421	2	of	of	ADP
ejpam-5339	421	3	sound	sound	NOUN
ejpam-5339	421	4	and	and	CCONJ
ejpam-5339	421	5	vibrations	vibration	NOUN
ejpam-5339	421	6	,	,	PUNCT
ejpam-5339	421	7	289:689–710	289:689–710	NUM
ejpam-5339	421	8	,	,	PUNCT
ejpam-5339	421	9	2006	2006	NUM
ejpam-5339	421	10	.	.	PUNCT
ejpam-5339	422	1	[	[	X
ejpam-5339	422	2	40	40	NUM
ejpam-5339	422	3	]	]	PUNCT
ejpam-5339	422	4	j.-g	j.-g	PROPN
ejpam-5339	422	5	.	.	PUNCT
ejpam-5339	423	1	zhang	zhang	PROPN
ejpam-5339	423	2	,	,	PUNCT
ejpam-5339	423	3	q.-r	q.-r	PROPN
ejpam-5339	423	4	.	.	PUNCT
ejpam-5339	424	1	song	song	PROPN
ejpam-5339	424	2	,	,	PUNCT
ejpam-5339	424	3	j.-q	j.-q	PROPN
ejpam-5339	424	4	.	.	PUNCT
ejpam-5339	425	1	zhang	zhang	PROPN
ejpam-5339	425	2	,	,	PUNCT
ejpam-5339	425	3	and	and	CCONJ
ejpam-5339	425	4	f.	f.	PROPN
ejpam-5339	425	5	wang	wang	PROPN
ejpam-5339	425	6	.	.	PUNCT
ejpam-5339	426	1	application	application	NOUN
ejpam-5339	426	2	of	of	ADP
ejpam-5339	426	3	he	he	PRON
ejpam-5339	426	4	’s	’s	PART
ejpam-5339	426	5	frequency	frequency	NOUN
ejpam-5339	426	6	formula	formula	NOUN
ejpam-5339	426	7	to	to	PART
ejpam-5339	426	8	nonlinear	nonlinear	ADJ
ejpam-5339	426	9	oscillators	oscillator	NOUN
ejpam-5339	426	10	with	with	ADP
ejpam-5339	426	11	generalized	generalized	ADJ
ejpam-5339	426	12	initial	initial	ADJ
ejpam-5339	426	13	conditions	condition	NOUN
ejpam-5339	426	14	.	.	PUNCT
ejpam-5339	427	1	facta	facta	PROPN
ejpam-5339	427	2	universitatis	universitatis	PROPN
ejpam-5339	427	3	series	series	NOUN
ejpam-5339	427	4	:	:	PUNCT
ejpam-5339	427	5	mechanical	mechanical	ADJ
ejpam-5339	427	6	engineering	engineering	NOUN
ejpam-5339	427	7	,	,	PUNCT
ejpam-5339	427	8	21(4):701–712	21(4):701–712	NOUN
ejpam-5339	427	9	,	,	PUNCT
ejpam-5339	427	10	2023	2023	NUM
ejpam-5339	427	11	.	.	PUNCT