id	sid	tid	token	lemma	pos
ejpam-5662	1	1	european	european	PROPN
ejpam-5662	1	2	journal	journal	PROPN
ejpam-5662	1	3	of	of	ADP
ejpam-5662	1	4	pure	pure	ADJ
ejpam-5662	1	5	and	and	CCONJ
ejpam-5662	1	6	applied	applied	ADJ
ejpam-5662	1	7	mathematics	mathematic	NOUN
ejpam-5662	1	8	2025	2025	NUM
ejpam-5662	1	9	,	,	PUNCT
ejpam-5662	1	10	vol	vol	NOUN
ejpam-5662	1	11	.	.	PROPN
ejpam-5662	1	12	18	18	NUM
ejpam-5662	1	13	,	,	PUNCT
ejpam-5662	1	14	issue	issue	NOUN
ejpam-5662	1	15	2	2	NUM
ejpam-5662	1	16	,	,	PUNCT
ejpam-5662	1	17	article	article	NOUN
ejpam-5662	1	18	number	number	NOUN
ejpam-5662	1	19	5662	5662	NUM
ejpam-5662	1	20	issn	issn	PROPN
ejpam-5662	1	21	1307	1307	NUM
ejpam-5662	1	22	-	-	SYM
ejpam-5662	1	23	5543	5543	NUM
ejpam-5662	1	24	–	–	PUNCT
ejpam-5662	1	25	ejpam.com	ejpam.com	X
ejpam-5662	1	26	published	publish	VERB
ejpam-5662	1	27	by	by	ADP
ejpam-5662	1	28	new	new	PROPN
ejpam-5662	1	29	york	york	PROPN
ejpam-5662	1	30	business	business	PROPN
ejpam-5662	1	31	global	global	ADJ
ejpam-5662	1	32	insights	insight	NOUN
ejpam-5662	1	33	in	in	ADP
ejpam-5662	1	34	inspecting	inspect	VERB
ejpam-5662	1	35	two	two	NUM
ejpam-5662	1	36	-	-	PUNCT
ejpam-5662	1	37	degree	degree	NOUN
ejpam-5662	1	38	-	-	PUNCT
ejpam-5662	1	39	of	of	ADP
ejpam-5662	1	40	-	-	PUNCT
ejpam-5662	1	41	freedom	freedom	NOUN
ejpam-5662	1	42	of	of	ADP
ejpam-5662	1	43	mathieu	mathieu	PROPN
ejpam-5662	1	44	-	-	PUNCT
ejpam-5662	1	45	cubic	cubic	ADJ
ejpam-5662	1	46	-	-	PUNCT
ejpam-5662	1	47	quintic	quintic	ADJ
ejpam-5662	1	48	duffing	duffing	NOUN
ejpam-5662	1	49	oscillator	oscillator	NOUN
ejpam-5662	1	50	asma	asma	PROPN
ejpam-5662	1	51	alanazy1	alanazy1	PROPN
ejpam-5662	1	52	,	,	PUNCT
ejpam-5662	1	53	galal	galal	PROPN
ejpam-5662	1	54	m.	m.	NOUN
ejpam-5662	1	55	moatimid2	moatimid2	PROPN
ejpam-5662	1	56	,	,	PUNCT
ejpam-5662	1	57	and	and	CCONJ
ejpam-5662	1	58	mona	mona	PROPN
ejpam-5662	1	59	a.a	a.a	PROPN
ejpam-5662	1	60	.	.	PROPN
ejpam-5662	1	61	mohamed2,∗	mohamed2,∗	ADJ
ejpam-5662	1	62	1	1	NUM
ejpam-5662	1	63	department	department	NOUN
ejpam-5662	1	64	of	of	ADP
ejpam-5662	1	65	mathematics	mathematic	NOUN
ejpam-5662	1	66	,	,	PUNCT
ejpam-5662	1	67	northern	northern	ADJ
ejpam-5662	1	68	border	border	NOUN
ejpam-5662	1	69	university	university	PROPN
ejpam-5662	1	70	,	,	PUNCT
ejpam-5662	1	71	arar	arar	PROPN
ejpam-5662	1	72	,	,	PUNCT
ejpam-5662	1	73	kingdom	kingdom	NOUN
ejpam-5662	1	74	of	of	ADP
ejpam-5662	1	75	saudi	saudi	PROPN
ejpam-5662	1	76	arabia	arabia	PROPN
ejpam-5662	1	77	2	2	NUM
ejpam-5662	1	78	department	department	NOUN
ejpam-5662	1	79	of	of	ADP
ejpam-5662	1	80	mathematics	mathematic	NOUN
ejpam-5662	1	81	,	,	PUNCT
ejpam-5662	1	82	faculty	faculty	NOUN
ejpam-5662	1	83	of	of	ADP
ejpam-5662	1	84	education	education	NOUN
ejpam-5662	1	85	,	,	PUNCT
ejpam-5662	1	86	ain	ain	PROPN
ejpam-5662	1	87	shams	shams	PROPN
ejpam-5662	1	88	university	university	PROPN
ejpam-5662	1	89	,	,	PUNCT
ejpam-5662	1	90	roxy	roxy	PROPN
ejpam-5662	1	91	,	,	PUNCT
ejpam-5662	1	92	cairo	cairo	PROPN
ejpam-5662	1	93	,	,	PUNCT
ejpam-5662	1	94	egypt	egypt	PROPN
ejpam-5662	1	95	abstract	abstract	PROPN
ejpam-5662	1	96	.	.	PUNCT
ejpam-5662	2	1	mathieu	mathieu	PROPN
ejpam-5662	2	2	–	–	PUNCT
ejpam-5662	2	3	cubic	cubic	ADJ
ejpam-5662	2	4	-	-	PUNCT
ejpam-5662	2	5	quintic	quintic	ADJ
ejpam-5662	2	6	duffing	duffing	NOUN
ejpam-5662	2	7	oscillator	oscillator	NOUN
ejpam-5662	2	8	exemplifies	exemplify	VERB
ejpam-5662	2	9	a	a	DET
ejpam-5662	2	10	fundamental	fundamental	ADJ
ejpam-5662	2	11	model	model	NOUN
ejpam-5662	2	12	of	of	ADP
ejpam-5662	2	13	a	a	DET
ejpam-5662	2	14	parametric	parametric	ADJ
ejpam-5662	2	15	stimulated	stimulate	VERB
ejpam-5662	2	16	system	system	NOUN
ejpam-5662	2	17	characterized	characterize	VERB
ejpam-5662	2	18	by	by	ADP
ejpam-5662	2	19	nonlinearities	nonlinearitie	NOUN
ejpam-5662	2	20	.	.	PUNCT
ejpam-5662	3	1	this	this	DET
ejpam-5662	3	2	issue	issue	NOUN
ejpam-5662	3	3	is	be	AUX
ejpam-5662	3	4	essential	essential	ADJ
ejpam-5662	3	5	in	in	ADP
ejpam-5662	3	6	understanding	understand	VERB
ejpam-5662	3	7	intricate	intricate	ADJ
ejpam-5662	3	8	,	,	PUNCT
ejpam-5662	3	9	nonlinear	nonlinear	ADJ
ejpam-5662	3	10	dynamical	dynamical	ADJ
ejpam-5662	3	11	behavior	behavior	NOUN
ejpam-5662	3	12	,	,	PUNCT
ejpam-5662	3	13	including	include	VERB
ejpam-5662	3	14	bifurcations	bifurcation	NOUN
ejpam-5662	3	15	,	,	PUNCT
ejpam-5662	3	16	chaos	chaos	NOUN
ejpam-5662	3	17	,	,	PUNCT
ejpam-5662	3	18	and	and	CCONJ
ejpam-5662	3	19	resonance	resonance	NOUN
ejpam-5662	3	20	phenomena	phenomenon	NOUN
ejpam-5662	3	21	,	,	PUNCT
ejpam-5662	3	22	pertinent	pertinent	ADJ
ejpam-5662	3	23	to	to	ADP
ejpam-5662	3	24	engineering	engineering	NOUN
ejpam-5662	3	25	and	and	CCONJ
ejpam-5662	3	26	physics	physics	NOUN
ejpam-5662	3	27	for	for	ADP
ejpam-5662	3	28	systems	system	NOUN
ejpam-5662	3	29	influenced	influence	VERB
ejpam-5662	3	30	by	by	ADP
ejpam-5662	3	31	periodic	periodic	ADJ
ejpam-5662	3	32	external	external	ADJ
ejpam-5662	3	33	incentives	incentive	NOUN
ejpam-5662	3	34	.	.	PUNCT
ejpam-5662	4	1	a	a	PRON
ejpam-5662	4	2	universal	universal	ADJ
ejpam-5662	4	3	two	two	NUM
ejpam-5662	4	4	-	-	PUNCT
ejpam-5662	4	5	degree	degree	NOUN
ejpam-5662	4	6	-	-	PUNCT
ejpam-5662	4	7	of	of	ADP
ejpam-5662	4	8	-	-	PUNCT
ejpam-5662	4	9	freedom	freedom	NOUN
ejpam-5662	4	10	of	of	ADP
ejpam-5662	4	11	mathieu	mathieu	PROPN
ejpam-5662	4	12	–	–	PUNCT
ejpam-5662	4	13	cubic	cubic	ADJ
ejpam-5662	4	14	-	-	PUNCT
ejpam-5662	4	15	quintic	quintic	ADJ
ejpam-5662	4	16	duffing	duffing	NOUN
ejpam-5662	4	17	oscillator	oscillator	NOUN
ejpam-5662	4	18	is	be	AUX
ejpam-5662	4	19	examined	examine	VERB
ejpam-5662	4	20	.	.	PUNCT
ejpam-5662	5	1	this	this	DET
ejpam-5662	5	2	study	study	NOUN
ejpam-5662	5	3	utilizes	utilize	VERB
ejpam-5662	5	4	an	an	DET
ejpam-5662	5	5	adaptation	adaptation	NOUN
ejpam-5662	5	6	of	of	ADP
ejpam-5662	5	7	the	the	DET
ejpam-5662	5	8	non	non	ADJ
ejpam-5662	5	9	-	-	ADJ
ejpam-5662	5	10	perturbative	perturbative	ADJ
ejpam-5662	5	11	approach	approach	NOUN
ejpam-5662	5	12	,	,	PUNCT
ejpam-5662	5	13	to	to	PART
ejpam-5662	5	14	encompass	encompass	VERB
ejpam-5662	5	15	the	the	DET
ejpam-5662	5	16	coupled	couple	VERB
ejpam-5662	5	17	system	system	NOUN
ejpam-5662	5	18	and	and	CCONJ
ejpam-5662	5	19	inspect	inspect	VERB
ejpam-5662	5	20	a	a	DET
ejpam-5662	5	21	parametric	parametric	ADJ
ejpam-5662	5	22	nonlinear	nonlinear	ADJ
ejpam-5662	5	23	oscillatory	oscillatory	ADJ
ejpam-5662	5	24	system	system	NOUN
ejpam-5662	5	25	and	and	CCONJ
ejpam-5662	5	26	evaluate	evaluate	VERB
ejpam-5662	5	27	its	its	PRON
ejpam-5662	5	28	efficacy	efficacy	NOUN
ejpam-5662	5	29	.	.	PUNCT
ejpam-5662	6	1	the	the	DET
ejpam-5662	6	2	non	non	ADJ
ejpam-5662	6	3	-	-	ADJ
ejpam-5662	6	4	perturbative	perturbative	ADJ
ejpam-5662	6	5	approach	approach	NOUN
ejpam-5662	6	6	is	be	AUX
ejpam-5662	6	7	based	base	VERB
ejpam-5662	6	8	mainly	mainly	ADV
ejpam-5662	6	9	on	on	ADP
ejpam-5662	6	10	the	the	DET
ejpam-5662	6	11	he	he	PRON
ejpam-5662	6	12	’s	’s	PART
ejpam-5662	6	13	frequency	frequency	NOUN
ejpam-5662	6	14	formula	formula	NOUN
ejpam-5662	6	15	.	.	PUNCT
ejpam-5662	7	1	the	the	DET
ejpam-5662	7	2	main	main	ADJ
ejpam-5662	7	3	aim	aim	NOUN
ejpam-5662	7	4	of	of	ADP
ejpam-5662	7	5	this	this	DET
ejpam-5662	7	6	technique	technique	NOUN
ejpam-5662	7	7	is	be	AUX
ejpam-5662	7	8	to	to	PART
ejpam-5662	7	9	convert	convert	VERB
ejpam-5662	7	10	any	any	DET
ejpam-5662	7	11	nonlinear	nonlinear	ADJ
ejpam-5662	7	12	ordinary	ordinary	ADJ
ejpam-5662	7	13	differential	differential	ADJ
ejpam-5662	7	14	equation	equation	NOUN
ejpam-5662	7	15	into	into	ADP
ejpam-5662	7	16	a	a	DET
ejpam-5662	7	17	linear	linear	ADJ
ejpam-5662	7	18	one	one	NUM
ejpam-5662	7	19	.	.	PUNCT
ejpam-5662	8	1	the	the	DET
ejpam-5662	8	2	approximate	approximate	ADJ
ejpam-5662	8	3	solutions	solution	NOUN
ejpam-5662	8	4	are	be	AUX
ejpam-5662	8	5	derived	derive	VERB
ejpam-5662	8	6	independently	independently	ADV
ejpam-5662	8	7	of	of	ADP
ejpam-5662	8	8	conventional	conventional	ADJ
ejpam-5662	8	9	perturbation	perturbation	NOUN
ejpam-5662	8	10	methods	method	NOUN
ejpam-5662	8	11	,	,	PUNCT
ejpam-5662	8	12	excluding	exclude	VERB
ejpam-5662	8	13	the	the	DET
ejpam-5662	8	14	series	series	NOUN
ejpam-5662	8	15	expansion	expansion	NOUN
ejpam-5662	8	16	.	.	PUNCT
ejpam-5662	9	1	consequently	consequently	ADV
ejpam-5662	9	2	,	,	PUNCT
ejpam-5662	9	3	the	the	DET
ejpam-5662	9	4	objective	objective	NOUN
ejpam-5662	9	5	of	of	ADP
ejpam-5662	9	6	this	this	DET
ejpam-5662	9	7	study	study	NOUN
ejpam-5662	9	8	is	be	AUX
ejpam-5662	9	9	to	to	PART
ejpam-5662	9	10	depart	depart	VERB
ejpam-5662	9	11	from	from	ADP
ejpam-5662	9	12	traditional	traditional	ADJ
ejpam-5662	9	13	perturbation	perturbation	NOUN
ejpam-5662	9	14	methods	method	NOUN
ejpam-5662	9	15	and	and	CCONJ
ejpam-5662	9	16	derive	derive	VERB
ejpam-5662	9	17	estimated	estimated	ADJ
ejpam-5662	9	18	solutions	solution	NOUN
ejpam-5662	9	19	for	for	ADP
ejpam-5662	9	20	tiny	tiny	ADJ
ejpam-5662	9	21	amplitude	amplitude	NOUN
ejpam-5662	9	22	parametric	parametric	ADJ
ejpam-5662	9	23	components	component	NOUN
ejpam-5662	9	24	without	without	ADP
ejpam-5662	9	25	restrictions	restriction	NOUN
ejpam-5662	9	26	.	.	PUNCT
ejpam-5662	10	1	furthermore	furthermore	ADV
ejpam-5662	10	2	,	,	PUNCT
ejpam-5662	10	3	this	this	DET
ejpam-5662	10	4	technique	technique	NOUN
ejpam-5662	10	5	is	be	AUX
ejpam-5662	10	6	extended	extend	VERB
ejpam-5662	10	7	to	to	PART
ejpam-5662	10	8	ascertain	ascertain	VERB
ejpam-5662	10	9	optimal	optimal	ADJ
ejpam-5662	10	10	responses	response	NOUN
ejpam-5662	10	11	for	for	ADP
ejpam-5662	10	12	the	the	DET
ejpam-5662	10	13	nonlinear	nonlinear	ADJ
ejpam-5662	10	14	large	large	ADJ
ejpam-5662	10	15	amplitude	amplitude	NOUN
ejpam-5662	10	16	fluctuations	fluctuation	NOUN
ejpam-5662	10	17	.	.	PUNCT
ejpam-5662	11	1	the	the	DET
ejpam-5662	11	2	capacity	capacity	NOUN
ejpam-5662	11	3	to	to	PART
ejpam-5662	11	4	swiftly	swiftly	ADV
ejpam-5662	11	5	assess	assess	VERB
ejpam-5662	11	6	the	the	DET
ejpam-5662	11	7	frequency	frequency	NOUN
ejpam-5662	11	8	-	-	PUNCT
ejpam-5662	11	9	amplitude	amplitude	NOUN
ejpam-5662	11	10	correlation	correlation	NOUN
ejpam-5662	11	11	is	be	AUX
ejpam-5662	11	12	essential	essential	ADJ
ejpam-5662	11	13	for	for	ADP
ejpam-5662	11	14	deriving	derive	VERB
ejpam-5662	11	15	successive	successive	ADJ
ejpam-5662	11	16	estimates	estimate	NOUN
ejpam-5662	11	17	of	of	ADP
ejpam-5662	11	18	the	the	DET
ejpam-5662	11	19	solutions	solution	NOUN
ejpam-5662	11	20	to	to	PART
ejpam-5662	11	21	parametric	parametric	VERB
ejpam-5662	11	22	nonlinear	nonlinear	ADJ
ejpam-5662	11	23	fluctuations	fluctuation	NOUN
ejpam-5662	11	24	.	.	PUNCT
ejpam-5662	12	1	in	in	ADP
ejpam-5662	12	2	addition	addition	NOUN
ejpam-5662	12	3	,	,	PUNCT
ejpam-5662	12	4	the	the	DET
ejpam-5662	12	5	discussion	discussion	NOUN
ejpam-5662	12	6	of	of	ADP
ejpam-5662	12	7	the	the	DET
ejpam-5662	12	8	coupled	couple	VERB
ejpam-5662	12	9	oscillators	oscillator	NOUN
ejpam-5662	12	10	is	be	AUX
ejpam-5662	12	11	considered	consider	VERB
ejpam-5662	12	12	as	as	ADP
ejpam-5662	12	13	a	a	DET
ejpam-5662	12	14	new	new	ADJ
ejpam-5662	12	15	direction	direction	NOUN
ejpam-5662	12	16	in	in	ADP
ejpam-5662	12	17	the	the	DET
ejpam-5662	12	18	usage	usage	NOUN
ejpam-5662	12	19	of	of	ADP
ejpam-5662	12	20	the	the	DET
ejpam-5662	12	21	current	current	ADJ
ejpam-5662	12	22	approach	approach	NOUN
ejpam-5662	12	23	.	.	PUNCT
ejpam-5662	13	1	the	the	DET
ejpam-5662	13	2	mathematica	mathematica	PROPN
ejpam-5662	13	3	software	software	PROPN
ejpam-5662	13	4	is	be	AUX
ejpam-5662	13	5	employed	employ	VERB
ejpam-5662	13	6	to	to	PART
ejpam-5662	13	7	verify	verify	VERB
ejpam-5662	13	8	the	the	DET
ejpam-5662	13	9	agreement	agreement	NOUN
ejpam-5662	13	10	parametric	parametric	ADJ
ejpam-5662	13	11	equation	equation	NOUN
ejpam-5662	13	12	,	,	PUNCT
ejpam-5662	13	13	which	which	PRON
ejpam-5662	13	14	demonstrates	demonstrate	VERB
ejpam-5662	13	15	significant	significant	ADJ
ejpam-5662	13	16	concordance	concordance	NOUN
ejpam-5662	13	17	with	with	ADP
ejpam-5662	13	18	the	the	DET
ejpam-5662	13	19	original	original	ADJ
ejpam-5662	13	20	equation	equation	NOUN
ejpam-5662	13	21	.	.	PUNCT
ejpam-5662	14	1	the	the	DET
ejpam-5662	14	2	stability	stability	NOUN
ejpam-5662	14	3	behavior	behavior	NOUN
ejpam-5662	14	4	is	be	AUX
ejpam-5662	14	5	examined	examine	VERB
ejpam-5662	14	6	in	in	ADP
ejpam-5662	14	7	multiple	multiple	ADJ
ejpam-5662	14	8	instances	instance	NOUN
ejpam-5662	14	9	.	.	PUNCT
ejpam-5662	15	1	the	the	DET
ejpam-5662	15	2	existing	exist	VERB
ejpam-5662	15	3	methodology	methodology	NOUN
ejpam-5662	15	4	is	be	AUX
ejpam-5662	15	5	characterized	characterize	VERB
ejpam-5662	15	6	by	by	ADP
ejpam-5662	15	7	clear	clear	ADJ
ejpam-5662	15	8	principles	principle	NOUN
ejpam-5662	15	9	,	,	PUNCT
ejpam-5662	15	10	appropriateness	appropriateness	NOUN
ejpam-5662	15	11	,	,	PUNCT
ejpam-5662	15	12	user	user	NOUN
ejpam-5662	15	13	-	-	PUNCT
ejpam-5662	15	14	friendliness	friendliness	ADJ
ejpam-5662	15	15	,	,	PUNCT
ejpam-5662	15	16	and	and	CCONJ
ejpam-5662	15	17	exceptional	exceptional	ADJ
ejpam-5662	15	18	numerical	numerical	ADJ
ejpam-5662	15	19	precision	precision	NOUN
ejpam-5662	15	20	.	.	PUNCT
ejpam-5662	16	1	the	the	DET
ejpam-5662	16	2	current	current	ADJ
ejpam-5662	16	3	method	method	NOUN
ejpam-5662	16	4	reduces	reduce	VERB
ejpam-5662	16	5	mathematical	mathematical	ADJ
ejpam-5662	16	6	complexity	complexity	NOUN
ejpam-5662	16	7	,	,	PUNCT
ejpam-5662	16	8	making	make	VERB
ejpam-5662	16	9	it	it	PRON
ejpam-5662	16	10	advantageous	advantageous	ADJ
ejpam-5662	16	11	in	in	ADP
ejpam-5662	16	12	addressing	address	VERB
ejpam-5662	16	13	nonlinear	nonlinear	ADJ
ejpam-5662	16	14	parametric	parametric	ADJ
ejpam-5662	16	15	problems	problem	NOUN
ejpam-5662	16	16	.	.	PUNCT
ejpam-5662	17	1	it	it	PRON
ejpam-5662	17	2	likewise	likewise	ADV
ejpam-5662	17	3	discussed	discuss	VERB
ejpam-5662	17	4	the	the	DET
ejpam-5662	17	5	influence	influence	NOUN
ejpam-5662	17	6	of	of	ADP
ejpam-5662	17	7	multiple	multiple	ADJ
ejpam-5662	17	8	coefficients	coefficient	NOUN
ejpam-5662	17	9	on	on	ADP
ejpam-5662	17	10	solution	solution	NOUN
ejpam-5662	17	11	behavior	behavior	NOUN
ejpam-5662	17	12	,	,	PUNCT
ejpam-5662	17	13	ensuring	ensure	VERB
ejpam-5662	17	14	stability	stability	NOUN
ejpam-5662	17	15	through	through	ADP
ejpam-5662	17	16	time	time	NOUN
ejpam-5662	17	17	-	-	PUNCT
ejpam-5662	17	18	dependent	dependent	ADJ
ejpam-5662	17	19	plots	plot	NOUN
ejpam-5662	17	20	and	and	CCONJ
ejpam-5662	17	21	polarplots	polarplot	NOUN
ejpam-5662	17	22	,	,	PUNCT
ejpam-5662	17	23	and	and	CCONJ
ejpam-5662	17	24	detecting	detect	VERB
ejpam-5662	17	25	periodic	periodic	ADJ
ejpam-5662	17	26	behavior	behavior	NOUN
ejpam-5662	17	27	with	with	ADP
ejpam-5662	17	28	parameter	parameter	NOUN
ejpam-5662	17	29	variations	variation	NOUN
ejpam-5662	17	30	.	.	PUNCT
ejpam-5662	18	1	2020	2020	NUM
ejpam-5662	18	2	mathematics	mathematic	NOUN
ejpam-5662	18	3	subject	subject	NOUN
ejpam-5662	18	4	classifications	classification	NOUN
ejpam-5662	18	5	:	:	PUNCT
ejpam-5662	18	6	34c15	34c15	NUM
ejpam-5662	18	7	,	,	PUNCT
ejpam-5662	18	8	34c25	34c25	NUM
ejpam-5662	18	9	,	,	PUNCT
ejpam-5662	18	10	34d20	34d20	NUM
ejpam-5662	18	11	,	,	PUNCT
ejpam-5662	18	12	37d45	37d45	NUM
ejpam-5662	18	13	,	,	PUNCT
ejpam-5662	18	14	70k30	70k30	NUM
ejpam-5662	18	15	,	,	PUNCT
ejpam-5662	18	16	70h06	70h06	NUM
ejpam-5662	18	17	key	key	ADJ
ejpam-5662	18	18	words	word	NOUN
ejpam-5662	18	19	and	and	CCONJ
ejpam-5662	18	20	phrases	phrase	NOUN
ejpam-5662	18	21	:	:	PUNCT
ejpam-5662	18	22	nonlinear	nonlinear	PROPN
ejpam-5662	18	23	mathieu	mathieu	PROPN
ejpam-5662	18	24	oscillator	oscillator	PROPN
ejpam-5662	18	25	,	,	PUNCT
ejpam-5662	18	26	cubic	cubic	ADJ
ejpam-5662	18	27	-	-	PUNCT
ejpam-5662	18	28	qunitic	qunitic	ADJ
ejpam-5662	18	29	duffing	duffing	NOUN
ejpam-5662	18	30	oscillator	oscillator	NOUN
ejpam-5662	18	31	,	,	PUNCT
ejpam-5662	18	32	coupled	couple	VERB
ejpam-5662	18	33	nonlinear	nonlinear	ADJ
ejpam-5662	18	34	system	system	NOUN
ejpam-5662	18	35	,	,	PUNCT
ejpam-5662	18	36	parametric	parametric	ADJ
ejpam-5662	18	37	excitation	excitation	NOUN
ejpam-5662	18	38	,	,	PUNCT
ejpam-5662	18	39	he	he	PRON
ejpam-5662	18	40	’s	’	VERB
ejpam-5662	18	41	frequency	frequency	NOUN
ejpam-5662	18	42	formula	formula	NOUN
ejpam-5662	18	43	,	,	PUNCT
ejpam-5662	18	44	non	non	ADJ
ejpam-5662	18	45	-	-	ADJ
ejpam-5662	18	46	perturbative	perturbative	ADJ
ejpam-5662	18	47	approach	approach	NOUN
ejpam-5662	18	48	∗corresponding	∗corresponde	VERB
ejpam-5662	18	49	author	author	NOUN
ejpam-5662	18	50	.	.	PUNCT
ejpam-5662	19	1	doi	doi	NOUN
ejpam-5662	19	2	:	:	PUNCT
ejpam-5662	19	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5662	https://doi.org/10.29020/nybg.ejpam.v18i2.5662	NOUN
ejpam-5662	19	4	email	email	NOUN
ejpam-5662	19	5	addresses	address	NOUN
ejpam-5662	19	6	:	:	PUNCT
ejpam-5662	19	7	asma.jazza2@gmail.com	asma.jazza2@gmail.com	X
ejpam-5662	19	8	(	(	PUNCT
ejpam-5662	19	9	a.	a.	NOUN
ejpam-5662	19	10	alanazy	alanazy	PROPN
ejpam-5662	19	11	)	)	PUNCT
ejpam-5662	19	12	,	,	PUNCT
ejpam-5662	19	13	gal	gal	ADJ
ejpam-5662	19	14	moa@edu.asu.edu.eg	moa@edu.asu.edu.eg	PROPN
ejpam-5662	19	15	(	(	PUNCT
ejpam-5662	19	16	g.	g.	PROPN
ejpam-5662	19	17	m.	m.	PROPN
ejpam-5662	19	18	moatimid	moatimid	PROPN
ejpam-5662	19	19	)	)	PUNCT
ejpam-5662	19	20	,	,	PUNCT
ejpam-5662	19	21	monaali@edu.asu.edu.eg	monaali@edu.asu.edu.eg	PROPN
ejpam-5662	19	22	(	(	PUNCT
ejpam-5662	19	23	m.	m.	NOUN
ejpam-5662	19	24	a.	a.	PROPN
ejpam-5662	19	25	a.	a.	PROPN
ejpam-5662	19	26	mohamed	mohamed	PROPN
ejpam-5662	19	27	)	)	PUNCT
ejpam-5662	19	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5662	19	29	1	1	NUM
ejpam-5662	19	30	copyright	copyright	NOUN
ejpam-5662	19	31	:	:	PUNCT
ejpam-5662	19	32	©	©	PROPN
ejpam-5662	19	33	2025	2025	NUM
ejpam-5662	19	34	the	the	DET
ejpam-5662	19	35	author(s	author(s	NOUN
ejpam-5662	19	36	)	)	PUNCT
ejpam-5662	19	37	.	.	PUNCT
ejpam-5662	20	1	(	(	PUNCT
ejpam-5662	20	2	cc	cc	NOUN
ejpam-5662	20	3	by	by	ADP
ejpam-5662	20	4	-	-	PUNCT
ejpam-5662	20	5	nc	nc	PROPN
ejpam-5662	20	6	4.0	4.0	NUM
ejpam-5662	20	7	)	)	PUNCT
ejpam-5662	20	8	a.	a.	NOUN
ejpam-5662	20	9	alanazy	alanazy	NOUN
ejpam-5662	20	10	,	,	PUNCT
ejpam-5662	20	11	g.	g.	PROPN
ejpam-5662	20	12	m.	m.	PROPN
ejpam-5662	20	13	moatimid	moatimid	PROPN
ejpam-5662	20	14	,	,	PUNCT
ejpam-5662	20	15	m.	m.	PROPN
ejpam-5662	20	16	a.	a.	PROPN
ejpam-5662	20	17	a.	a.	PROPN
ejpam-5662	20	18	mohamed	mohamed	PROPN
ejpam-5662	20	19	/	/	SYM
ejpam-5662	20	20	eur	eur	PROPN
ejpam-5662	20	21	.	.	PUNCT
ejpam-5662	21	1	j.	j.	PROPN
ejpam-5662	21	2	pure	pure	PROPN
ejpam-5662	21	3	appl	appl	PROPN
ejpam-5662	21	4	.	.	PROPN
ejpam-5662	21	5	math	math	PROPN
ejpam-5662	21	6	,	,	PUNCT
ejpam-5662	21	7	18	18	NUM
ejpam-5662	21	8	(	(	PUNCT
ejpam-5662	21	9	2	2	NUM
ejpam-5662	21	10	)	)	PUNCT
ejpam-5662	21	11	(	(	PUNCT
ejpam-5662	21	12	2025	2025	NUM
ejpam-5662	21	13	)	)	PUNCT
ejpam-5662	21	14	,	,	PUNCT
ejpam-5662	21	15	5662	5662	NUM
ejpam-5662	21	16	2	2	NUM
ejpam-5662	21	17	of	of	ADP
ejpam-5662	21	18	36	36	NUM
ejpam-5662	21	19	1	1	NUM
ejpam-5662	21	20	.	.	PUNCT
ejpam-5662	22	1	introduction	introduction	NOUN
ejpam-5662	22	2	dynamical	dynamical	ADJ
ejpam-5662	22	3	systems	system	NOUN
ejpam-5662	22	4	with	with	ADP
ejpam-5662	22	5	time	time	NOUN
ejpam-5662	22	6	-	-	PUNCT
ejpam-5662	22	7	periodic	periodic	ADJ
ejpam-5662	22	8	coefficients	coefficient	NOUN
ejpam-5662	22	9	are	be	AUX
ejpam-5662	22	10	commonly	commonly	ADV
ejpam-5662	22	11	considered	consider	VERB
ejpam-5662	22	12	as	as	ADP
ejpam-5662	22	13	parametric	parametric	ADJ
ejpam-5662	22	14	stimulated	stimulate	VERB
ejpam-5662	22	15	systems	system	NOUN
ejpam-5662	22	16	.	.	PUNCT
ejpam-5662	23	1	they	they	PRON
ejpam-5662	23	2	have	have	AUX
ejpam-5662	23	3	been	be	AUX
ejpam-5662	23	4	studied	study	VERB
ejpam-5662	23	5	since	since	SCONJ
ejpam-5662	23	6	the	the	DET
ejpam-5662	23	7	eighteenth	eighteenth	ADJ
ejpam-5662	23	8	century	century	NOUN
ejpam-5662	23	9	to	to	PART
ejpam-5662	23	10	elucidate	elucidate	VERB
ejpam-5662	23	11	various	various	ADJ
ejpam-5662	23	12	wave	wave	NOUN
ejpam-5662	23	13	processes	process	NOUN
ejpam-5662	23	14	in	in	ADP
ejpam-5662	23	15	fluids	fluid	NOUN
ejpam-5662	23	16	and	and	CCONJ
ejpam-5662	23	17	solids	solid	NOUN
ejpam-5662	23	18	.	.	PUNCT
ejpam-5662	24	1	currently	currently	ADV
ejpam-5662	24	2	,	,	PUNCT
ejpam-5662	24	3	parametric	parametric	ADJ
ejpam-5662	24	4	excitation	excitation	NOUN
ejpam-5662	24	5	is	be	AUX
ejpam-5662	24	6	fundamental	fundamental	ADJ
ejpam-5662	24	7	in	in	ADP
ejpam-5662	24	8	numerous	numerous	ADJ
ejpam-5662	24	9	domains	domain	NOUN
ejpam-5662	24	10	of	of	ADP
ejpam-5662	24	11	research	research	NOUN
ejpam-5662	24	12	and	and	CCONJ
ejpam-5662	24	13	engineering	engineering	NOUN
ejpam-5662	24	14	,	,	PUNCT
ejpam-5662	24	15	such	such	ADJ
ejpam-5662	24	16	as	as	ADP
ejpam-5662	24	17	mechanical	mechanical	ADJ
ejpam-5662	24	18	resonators	resonator	NOUN
ejpam-5662	24	19	[	[	X
ejpam-5662	24	20	1	1	NUM
ejpam-5662	24	21	]	]	PUNCT
ejpam-5662	24	22	,	,	PUNCT
ejpam-5662	24	23	optics	optic	NOUN
ejpam-5662	24	24	[	[	X
ejpam-5662	24	25	2	2	NUM
ejpam-5662	24	26	]	]	PUNCT
ejpam-5662	24	27	,	,	PUNCT
ejpam-5662	24	28	microwave	microwave	NOUN
ejpam-5662	24	29	systems	system	NOUN
ejpam-5662	24	30	[	[	X
ejpam-5662	24	31	3	3	NUM
ejpam-5662	24	32	]	]	PUNCT
ejpam-5662	24	33	,	,	PUNCT
ejpam-5662	24	34	and	and	CCONJ
ejpam-5662	24	35	atomic	atomic	ADJ
ejpam-5662	24	36	physics	physics	NOUN
ejpam-5662	25	1	[	[	X
ejpam-5662	25	2	4	4	NUM
ejpam-5662	25	3	]	]	PUNCT
ejpam-5662	25	4	.	.	PUNCT
ejpam-5662	26	1	the	the	DET
ejpam-5662	26	2	prototypical	prototypical	ADJ
ejpam-5662	26	3	and	and	CCONJ
ejpam-5662	26	4	most	most	ADV
ejpam-5662	26	5	fundamental	fundamental	ADJ
ejpam-5662	26	6	mathematical	mathematical	ADJ
ejpam-5662	26	7	representation	representation	NOUN
ejpam-5662	26	8	of	of	ADP
ejpam-5662	26	9	these	these	DET
ejpam-5662	26	10	parametrically	parametrically	ADV
ejpam-5662	26	11	energized	energized	ADJ
ejpam-5662	26	12	systems	system	NOUN
ejpam-5662	26	13	is	be	AUX
ejpam-5662	26	14	found	find	VERB
ejpam-5662	26	15	in	in	ADP
ejpam-5662	26	16	the	the	DET
ejpam-5662	26	17	mathieu	mathieu	PROPN
ejpam-5662	26	18	equation	equation	NOUN
ejpam-5662	26	19	.	.	PUNCT
ejpam-5662	27	1	consequently	consequently	ADV
ejpam-5662	27	2	,	,	PUNCT
ejpam-5662	27	3	considerable	considerable	ADJ
ejpam-5662	27	4	focus	focus	NOUN
ejpam-5662	27	5	was	be	AUX
ejpam-5662	27	6	directed	direct	VERB
ejpam-5662	27	7	towards	towards	ADP
ejpam-5662	27	8	these	these	DET
ejpam-5662	27	9	systems	system	NOUN
ejpam-5662	27	10	in	in	ADP
ejpam-5662	27	11	examining	examine	VERB
ejpam-5662	27	12	the	the	DET
ejpam-5662	27	13	stability	stability	NOUN
ejpam-5662	27	14	of	of	ADP
ejpam-5662	27	15	their	their	PRON
ejpam-5662	27	16	trivial	trivial	ADJ
ejpam-5662	27	17	solutions	solution	NOUN
ejpam-5662	27	18	.	.	PUNCT
ejpam-5662	28	1	in	in	ADP
ejpam-5662	28	2	a	a	DET
ejpam-5662	28	3	nonlinear	nonlinear	ADJ
ejpam-5662	28	4	system	system	NOUN
ejpam-5662	28	5	,	,	PUNCT
ejpam-5662	28	6	parametric	parametric	ADJ
ejpam-5662	28	7	resonance	resonance	NOUN
ejpam-5662	28	8	may	may	AUX
ejpam-5662	28	9	result	result	VERB
ejpam-5662	28	10	in	in	ADP
ejpam-5662	28	11	steady	steady	ADJ
ejpam-5662	28	12	-	-	PUNCT
ejpam-5662	28	13	state	state	NOUN
ejpam-5662	28	14	non	non	ADJ
ejpam-5662	28	15	-	-	ADJ
ejpam-5662	28	16	trivial	trivial	ADJ
ejpam-5662	28	17	solutions	solution	NOUN
ejpam-5662	28	18	and	and	CCONJ
ejpam-5662	28	19	limit	limit	NOUN
ejpam-5662	28	20	cycles	cycle	NOUN
ejpam-5662	28	21	,	,	PUNCT
ejpam-5662	28	22	where	where	SCONJ
ejpam-5662	28	23	the	the	DET
ejpam-5662	28	24	amplitudes	amplitude	NOUN
ejpam-5662	28	25	are	be	AUX
ejpam-5662	28	26	determined	determine	VERB
ejpam-5662	28	27	by	by	ADP
ejpam-5662	28	28	the	the	DET
ejpam-5662	28	29	system	system	NOUN
ejpam-5662	28	30	’s	’s	PART
ejpam-5662	28	31	nonlinear	nonlinear	ADJ
ejpam-5662	28	32	characteristics	characteristic	NOUN
ejpam-5662	28	33	.	.	PUNCT
ejpam-5662	29	1	the	the	DET
ejpam-5662	29	2	duffing	duffing	NOUN
ejpam-5662	29	3	oscillator	oscillator	NOUN
ejpam-5662	29	4	(	(	PUNCT
ejpam-5662	29	5	do	do	AUX
ejpam-5662	29	6	)	)	PUNCT
ejpam-5662	29	7	is	be	AUX
ejpam-5662	29	8	a	a	DET
ejpam-5662	29	9	conspicuous	conspicuous	ADJ
ejpam-5662	29	10	example	example	NOUN
ejpam-5662	29	11	of	of	ADP
ejpam-5662	29	12	nonlinear	nonlinear	ADJ
ejpam-5662	29	13	ordinary	ordinary	ADJ
ejpam-5662	29	14	differential	differential	ADJ
ejpam-5662	29	15	equations	equation	NOUN
ejpam-5662	29	16	(	(	PUNCT
ejpam-5662	29	17	odes	ode	NOUN
ejpam-5662	29	18	)	)	PUNCT
ejpam-5662	29	19	,	,	PUNCT
ejpam-5662	29	20	particularly	particularly	ADV
ejpam-5662	29	21	in	in	ADP
ejpam-5662	29	22	simulating	simulate	VERB
ejpam-5662	29	23	nonlinear	nonlinear	ADJ
ejpam-5662	29	24	systems	system	NOUN
ejpam-5662	29	25	[	[	X
ejpam-5662	29	26	5	5	NUM
ejpam-5662	29	27	]	]	PUNCT
ejpam-5662	29	28	,	,	PUNCT
ejpam-5662	29	29	including	include	VERB
ejpam-5662	29	30	micro	micro	ADJ
ejpam-5662	29	31	and	and	CCONJ
ejpam-5662	29	32	nanomechanical	nanomechanical	ADJ
ejpam-5662	29	33	resonators	resonator	NOUN
ejpam-5662	29	34	.	.	PUNCT
ejpam-5662	30	1	particular	particular	ADJ
ejpam-5662	30	2	attention	attention	NOUN
ejpam-5662	30	3	is	be	AUX
ejpam-5662	30	4	devoted	devote	VERB
ejpam-5662	30	5	to	to	ADP
ejpam-5662	30	6	the	the	DET
ejpam-5662	30	7	parametrically	parametrically	ADV
ejpam-5662	30	8	stimulated	stimulate	VERB
ejpam-5662	30	9	do	do	AUX
ejpam-5662	30	10	,	,	PUNCT
ejpam-5662	30	11	sometimes	sometimes	ADV
ejpam-5662	30	12	referred	refer	VERB
ejpam-5662	30	13	to	to	ADP
ejpam-5662	30	14	as	as	ADP
ejpam-5662	30	15	the	the	DET
ejpam-5662	30	16	mathieu	mathieu	PROPN
ejpam-5662	30	17	–	–	PUNCT
ejpam-5662	30	18	do	do	VERB
ejpam-5662	30	19	[	[	X
ejpam-5662	30	20	6	6	NUM
ejpam-5662	30	21	,	,	PUNCT
ejpam-5662	30	22	7	7	NUM
ejpam-5662	30	23	]	]	PUNCT
ejpam-5662	30	24	.	.	PUNCT
ejpam-5662	31	1	the	the	DET
ejpam-5662	31	2	parametric	parametric	ADJ
ejpam-5662	31	3	odes	ode	NOUN
ejpam-5662	31	4	of	of	ADP
ejpam-5662	31	5	the	the	DET
ejpam-5662	31	6	mathieu	mathieu	PROPN
ejpam-5662	31	7	type	type	NOUN
ejpam-5662	31	8	,	,	PUNCT
ejpam-5662	31	9	whether	whether	SCONJ
ejpam-5662	31	10	nonlinear	nonlinear	ADJ
ejpam-5662	31	11	or	or	CCONJ
ejpam-5662	31	12	linear	linear	ADJ
ejpam-5662	31	13	,	,	PUNCT
ejpam-5662	31	14	have	have	AUX
ejpam-5662	31	15	attracted	attract	VERB
ejpam-5662	31	16	significant	significant	ADJ
ejpam-5662	31	17	attention	attention	NOUN
ejpam-5662	31	18	due	due	ADP
ejpam-5662	31	19	to	to	ADP
ejpam-5662	31	20	their	their	PRON
ejpam-5662	31	21	numerous	numerous	ADJ
ejpam-5662	31	22	potential	potential	ADJ
ejpam-5662	31	23	applications	application	NOUN
ejpam-5662	31	24	.	.	PUNCT
ejpam-5662	32	1	numerous	numerous	ADJ
ejpam-5662	32	2	characteristics	characteristic	NOUN
ejpam-5662	32	3	of	of	ADP
ejpam-5662	32	4	the	the	DET
ejpam-5662	32	5	mathieu	mathieu	PROPN
ejpam-5662	32	6	ode	ode	PROPN
ejpam-5662	32	7	can	can	AUX
ejpam-5662	32	8	be	be	AUX
ejpam-5662	32	9	inferred	infer	VERB
ejpam-5662	32	10	from	from	ADP
ejpam-5662	32	11	the	the	DET
ejpam-5662	32	12	overarching	overarching	ADJ
ejpam-5662	32	13	theory	theory	NOUN
ejpam-5662	32	14	of	of	ADP
ejpam-5662	32	15	odes	ode	NOUN
ejpam-5662	32	16	with	with	ADP
ejpam-5662	32	17	periodic	periodic	ADJ
ejpam-5662	32	18	coefficients	coefficient	NOUN
ejpam-5662	32	19	.	.	PUNCT
ejpam-5662	33	1	mathieu	mathieu	PROPN
ejpam-5662	33	2	’s	’s	PART
ejpam-5662	33	3	odes	ode	NOUN
ejpam-5662	33	4	are	be	AUX
ejpam-5662	33	5	prevalent	prevalent	ADJ
ejpam-5662	33	6	in	in	ADP
ejpam-5662	33	7	various	various	ADJ
ejpam-5662	33	8	domains	domain	NOUN
ejpam-5662	33	9	of	of	ADP
ejpam-5662	33	10	engineering	engineering	NOUN
ejpam-5662	33	11	,	,	PUNCT
ejpam-5662	33	12	physics	physics	NOUN
ejpam-5662	33	13	,	,	PUNCT
ejpam-5662	33	14	and	and	CCONJ
ejpam-5662	33	15	applied	apply	VERB
ejpam-5662	33	16	mathematics	mathematic	NOUN
ejpam-5662	33	17	.	.	PUNCT
ejpam-5662	34	1	this	this	DET
ejpam-5662	34	2	renowned	renowned	ADJ
ejpam-5662	34	3	equation	equation	NOUN
ejpam-5662	34	4	necessitates	necessitate	VERB
ejpam-5662	34	5	careful	careful	ADJ
ejpam-5662	34	6	examination	examination	NOUN
ejpam-5662	34	7	and	and	CCONJ
ejpam-5662	34	8	comprehensive	comprehensive	ADJ
ejpam-5662	34	9	investigation	investigation	NOUN
ejpam-5662	34	10	across	across	ADP
ejpam-5662	34	11	several	several	ADJ
ejpam-5662	34	12	contexts	context	NOUN
ejpam-5662	34	13	due	due	ADP
ejpam-5662	34	14	to	to	ADP
ejpam-5662	34	15	its	its	PRON
ejpam-5662	34	16	extensive	extensive	ADJ
ejpam-5662	34	17	applications	application	NOUN
ejpam-5662	34	18	in	in	ADP
ejpam-5662	34	19	physics	physics	NOUN
ejpam-5662	34	20	and	and	CCONJ
ejpam-5662	34	21	chemistry	chemistry	NOUN
ejpam-5662	34	22	.	.	PUNCT
ejpam-5662	35	1	the	the	DET
ejpam-5662	35	2	theory	theory	NOUN
ejpam-5662	35	3	of	of	ADP
ejpam-5662	35	4	odes	ode	NOUN
ejpam-5662	35	5	with	with	ADP
ejpam-5662	35	6	periodic	periodic	ADJ
ejpam-5662	35	7	coefficients	coefficient	NOUN
ejpam-5662	35	8	,	,	PUNCT
ejpam-5662	35	9	sometimes	sometimes	ADV
ejpam-5662	35	10	referred	refer	VERB
ejpam-5662	35	11	to	to	ADP
ejpam-5662	35	12	as	as	ADP
ejpam-5662	35	13	flux	flux	NOUN
ejpam-5662	35	14	theory	theory	NOUN
ejpam-5662	35	15	,	,	PUNCT
ejpam-5662	35	16	produces	produce	VERB
ejpam-5662	35	17	specific	specific	ADJ
ejpam-5662	35	18	elements	element	NOUN
ejpam-5662	35	19	of	of	ADP
ejpam-5662	35	20	the	the	DET
ejpam-5662	35	21	mathieu	mathieu	PROPN
ejpam-5662	35	22	ode	ode	PROPN
ejpam-5662	35	23	.	.	PUNCT
ejpam-5662	36	1	many	many	ADJ
ejpam-5662	36	2	properties	property	NOUN
ejpam-5662	36	3	of	of	ADP
ejpam-5662	36	4	the	the	DET
ejpam-5662	36	5	mathieu	mathieu	PROPN
ejpam-5662	36	6	ode	ode	PROPN
ejpam-5662	36	7	have	have	AUX
ejpam-5662	36	8	been	be	AUX
ejpam-5662	36	9	established	establish	VERB
ejpam-5662	36	10	through	through	ADP
ejpam-5662	36	11	the	the	DET
ejpam-5662	36	12	general	general	ADJ
ejpam-5662	36	13	theory	theory	NOUN
ejpam-5662	36	14	of	of	ADP
ejpam-5662	36	15	periodic	periodic	ADJ
ejpam-5662	36	16	coefficients	coefficient	NOUN
ejpam-5662	36	17	in	in	ADP
ejpam-5662	36	18	odes	ode	NOUN
ejpam-5662	36	19	.	.	PUNCT
ejpam-5662	37	1	scientists	scientist	NOUN
ejpam-5662	37	2	have	have	AUX
ejpam-5662	37	3	long	long	ADV
ejpam-5662	37	4	employed	employ	VERB
ejpam-5662	37	5	various	various	ADJ
ejpam-5662	37	6	perturbation	perturbation	NOUN
ejpam-5662	37	7	methods	method	NOUN
ejpam-5662	37	8	to	to	PART
ejpam-5662	37	9	investigate	investigate	VERB
ejpam-5662	37	10	the	the	DET
ejpam-5662	37	11	analytical	analytical	ADJ
ejpam-5662	37	12	solutions	solution	NOUN
ejpam-5662	37	13	related	relate	VERB
ejpam-5662	37	14	to	to	ADP
ejpam-5662	37	15	these	these	DET
ejpam-5662	37	16	equations	equation	NOUN
ejpam-5662	37	17	[	[	X
ejpam-5662	37	18	8	8	NUM
ejpam-5662	37	19	-	-	SYM
ejpam-5662	37	20	11	11	NUM
ejpam-5662	37	21	]	]	PUNCT
ejpam-5662	37	22	.	.	PUNCT
ejpam-5662	38	1	the	the	DET
ejpam-5662	38	2	perturbation	perturbation	NOUN
ejpam-5662	38	3	methodology	methodology	NOUN
ejpam-5662	38	4	,	,	PUNCT
ejpam-5662	38	5	according	accord	VERB
ejpam-5662	38	6	to	to	ADP
ejpam-5662	38	7	the	the	DET
ejpam-5662	38	8	many	many	ADJ
ejpam-5662	38	9	-	-	PUNCT
ejpam-5662	38	10	scales	scale	NOUN
ejpam-5662	38	11	approach	approach	NOUN
ejpam-5662	38	12	,	,	PUNCT
ejpam-5662	38	13	is	be	AUX
ejpam-5662	38	14	predicated	predicate	VERB
ejpam-5662	38	15	on	on	ADP
ejpam-5662	38	16	the	the	DET
ejpam-5662	38	17	concept	concept	NOUN
ejpam-5662	38	18	of	of	ADP
ejpam-5662	38	19	a	a	DET
ejpam-5662	38	20	minor	minor	ADJ
ejpam-5662	38	21	parameter	parameter	NOUN
ejpam-5662	38	22	[	[	X
ejpam-5662	38	23	12	12	NUM
ejpam-5662	38	24	]	]	PUNCT
ejpam-5662	38	25	.	.	PUNCT
ejpam-5662	39	1	the	the	DET
ejpam-5662	39	2	pursuit	pursuit	NOUN
ejpam-5662	39	3	of	of	ADP
ejpam-5662	39	4	a	a	DET
ejpam-5662	39	5	correct	correct	ADJ
ejpam-5662	39	6	analytical	analytical	ADJ
ejpam-5662	39	7	solution	solution	NOUN
ejpam-5662	39	8	to	to	ADP
ejpam-5662	39	9	nonlinear	nonlinear	ADJ
ejpam-5662	39	10	problems	problem	NOUN
ejpam-5662	39	11	was	be	AUX
ejpam-5662	39	12	a	a	DET
ejpam-5662	39	13	study	study	NOUN
ejpam-5662	39	14	focus	focus	NOUN
ejpam-5662	39	15	since	since	SCONJ
ejpam-5662	39	16	nonlinear	nonlinear	ADJ
ejpam-5662	39	17	odes	ode	NOUN
ejpam-5662	39	18	proved	prove	VERB
ejpam-5662	39	19	more	more	ADV
ejpam-5662	39	20	challenging	challenging	ADJ
ejpam-5662	39	21	to	to	PART
ejpam-5662	39	22	solve	solve	VERB
ejpam-5662	39	23	than	than	ADP
ejpam-5662	39	24	their	their	PRON
ejpam-5662	39	25	linear	linear	PROPN
ejpam-5662	39	26	counterparts	counterpart	NOUN
ejpam-5662	39	27	.	.	PUNCT
ejpam-5662	40	1	accordingly	accordingly	ADV
ejpam-5662	40	2	,	,	PUNCT
ejpam-5662	40	3	the	the	DET
ejpam-5662	40	4	perturbation	perturbation	NOUN
ejpam-5662	40	5	approach	approach	NOUN
ejpam-5662	40	6	is	be	AUX
ejpam-5662	40	7	the	the	DET
ejpam-5662	40	8	exclusive	exclusive	ADJ
ejpam-5662	40	9	method	method	NOUN
ejpam-5662	40	10	in	in	ADP
ejpam-5662	40	11	analyzing	analyze	VERB
ejpam-5662	40	12	any	any	DET
ejpam-5662	40	13	linear	linear	ADJ
ejpam-5662	40	14	ode	ode	NOUN
ejpam-5662	40	15	subjected	subject	VERB
ejpam-5662	40	16	to	to	ADP
ejpam-5662	40	17	periodic	periodic	ADJ
ejpam-5662	40	18	forces	force	NOUN
ejpam-5662	40	19	.	.	PUNCT
ejpam-5662	41	1	moreover	moreover	ADV
ejpam-5662	41	2	,	,	PUNCT
ejpam-5662	41	3	the	the	DET
ejpam-5662	41	4	existence	existence	NOUN
ejpam-5662	41	5	of	of	ADP
ejpam-5662	41	6	a	a	DET
ejpam-5662	41	7	nonlinear	nonlinear	ADJ
ejpam-5662	41	8	state	state	NOUN
ejpam-5662	41	9	in	in	ADP
ejpam-5662	41	10	odes	ode	NOUN
ejpam-5662	41	11	presents	present	VERB
ejpam-5662	41	12	many	many	ADJ
ejpam-5662	41	13	difficulties	difficulty	NOUN
ejpam-5662	41	14	,	,	PUNCT
ejpam-5662	41	15	especially	especially	ADV
ejpam-5662	41	16	when	when	SCONJ
ejpam-5662	41	17	periodic	periodic	ADJ
ejpam-5662	41	18	components	component	NOUN
ejpam-5662	41	19	are	be	AUX
ejpam-5662	41	20	incorporated	incorporate	VERB
ejpam-5662	41	21	into	into	ADP
ejpam-5662	41	22	the	the	DET
ejpam-5662	41	23	nonlinear	nonlinear	ADJ
ejpam-5662	41	24	state	state	NOUN
ejpam-5662	41	25	.	.	PUNCT
ejpam-5662	42	1	one	one	NUM
ejpam-5662	42	2	of	of	ADP
ejpam-5662	42	3	the	the	DET
ejpam-5662	42	4	primary	primary	ADJ
ejpam-5662	42	5	objectives	objective	NOUN
ejpam-5662	42	6	of	of	ADP
ejpam-5662	42	7	this	this	DET
ejpam-5662	42	8	work	work	NOUN
ejpam-5662	42	9	is	be	AUX
ejpam-5662	42	10	to	to	PART
ejpam-5662	42	11	employ	employ	VERB
ejpam-5662	42	12	an	an	DET
ejpam-5662	42	13	alternative	alternative	ADJ
ejpam-5662	42	14	method	method	NOUN
ejpam-5662	42	15	to	to	PART
ejpam-5662	42	16	attain	attain	VERB
ejpam-5662	42	17	an	an	DET
ejpam-5662	42	18	estimated	estimate	VERB
ejpam-5662	42	19	solution	solution	NOUN
ejpam-5662	42	20	without	without	ADP
ejpam-5662	42	21	utilizing	utilize	VERB
ejpam-5662	42	22	any	any	DET
ejpam-5662	42	23	existing	exist	VERB
ejpam-5662	42	24	perturbation	perturbation	NOUN
ejpam-5662	42	25	techniques	technique	NOUN
ejpam-5662	42	26	.	.	PUNCT
ejpam-5662	43	1	the	the	DET
ejpam-5662	43	2	perturbation	perturbation	NOUN
ejpam-5662	43	3	approaches	approach	NOUN
ejpam-5662	43	4	are	be	AUX
ejpam-5662	43	5	challenging	challenge	VERB
ejpam-5662	43	6	for	for	ADP
ejpam-5662	43	7	obtaining	obtain	VERB
ejpam-5662	43	8	an	an	DET
ejpam-5662	43	9	approximate	approximate	ADJ
ejpam-5662	43	10	solution	solution	NOUN
ejpam-5662	43	11	.	.	PUNCT
ejpam-5662	44	1	this	this	DET
ejpam-5662	44	2	analysis	analysis	NOUN
ejpam-5662	44	3	focuses	focus	VERB
ejpam-5662	44	4	on	on	ADP
ejpam-5662	44	5	mathieu	mathieu	PROPN
ejpam-5662	44	6	’s	’s	PART
ejpam-5662	44	7	nonlinear	nonlinear	ADJ
ejpam-5662	44	8	oscillator	oscillator	NOUN
ejpam-5662	44	9	,	,	PUNCT
ejpam-5662	44	10	with	with	ADP
ejpam-5662	44	11	/	/	SYM
ejpam-5662	44	12	without	without	ADP
ejpam-5662	44	13	damping	damp	VERB
ejpam-5662	44	14	forces	force	NOUN
ejpam-5662	44	15	.	.	PUNCT
ejpam-5662	45	1	disregarding	disregard	VERB
ejpam-5662	45	2	the	the	DET
ejpam-5662	45	3	ramifications	ramification	NOUN
ejpam-5662	45	4	of	of	ADP
ejpam-5662	45	5	nonlinearity	nonlinearity	NOUN
ejpam-5662	45	6	,	,	PUNCT
ejpam-5662	45	7	it	it	PRON
ejpam-5662	45	8	can	can	AUX
ejpam-5662	45	9	be	be	AUX
ejpam-5662	45	10	elucidated	elucidate	VERB
ejpam-5662	45	11	using	use	VERB
ejpam-5662	45	12	perturbation	perturbation	NOUN
ejpam-5662	45	13	systems	system	NOUN
ejpam-5662	45	14	,	,	PUNCT
ejpam-5662	45	15	especially	especially	ADV
ejpam-5662	45	16	due	due	ADP
ejpam-5662	45	17	to	to	ADP
ejpam-5662	45	18	the	the	DET
ejpam-5662	45	19	presence	presence	NOUN
ejpam-5662	45	20	of	of	ADP
ejpam-5662	45	21	periodic	periodic	ADJ
ejpam-5662	45	22	activities	activity	NOUN
ejpam-5662	45	23	.	.	PUNCT
ejpam-5662	46	1	the	the	DET
ejpam-5662	46	2	introduction	introduction	NOUN
ejpam-5662	46	3	of	of	ADP
ejpam-5662	46	4	a	a	DET
ejpam-5662	46	5	unique	unique	ADJ
ejpam-5662	46	6	method	method	NOUN
ejpam-5662	46	7	in	in	ADP
ejpam-5662	46	8	achieving	achieve	VERB
ejpam-5662	46	9	a	a	DET
ejpam-5662	46	10	quasi	quasi	ADJ
ejpam-5662	46	11	-	-	ADJ
ejpam-5662	46	12	perfect	perfect	ADJ
ejpam-5662	46	13	response	response	NOUN
ejpam-5662	46	14	is	be	AUX
ejpam-5662	46	15	regarded	regard	VERB
ejpam-5662	46	16	as	as	ADP
ejpam-5662	46	17	a	a	DET
ejpam-5662	46	18	substantial	substantial	ADJ
ejpam-5662	46	19	achievement	achievement	NOUN
ejpam-5662	46	20	that	that	PRON
ejpam-5662	46	21	advantages	advantage	VERB
ejpam-5662	46	22	both	both	CCONJ
ejpam-5662	46	23	technological	technological	ADJ
ejpam-5662	46	24	and	and	CCONJ
ejpam-5662	46	25	physical	physical	ADJ
ejpam-5662	46	26	fields	field	NOUN
ejpam-5662	46	27	.	.	PUNCT
ejpam-5662	47	1	inspired	inspire	VERB
ejpam-5662	47	2	by	by	ADP
ejpam-5662	47	3	the	the	DET
ejpam-5662	47	4	aforementioned	aforementioned	ADJ
ejpam-5662	47	5	theoretical	theoretical	ADJ
ejpam-5662	47	6	discoveries	discovery	NOUN
ejpam-5662	47	7	and	and	CCONJ
ejpam-5662	47	8	the	the	DET
ejpam-5662	47	9	importance	importance	NOUN
ejpam-5662	47	10	of	of	ADP
ejpam-5662	47	11	parametric	parametric	ADJ
ejpam-5662	47	12	excitation	excitation	NOUN
ejpam-5662	47	13	techniques	technique	NOUN
ejpam-5662	47	14	in	in	ADP
ejpam-5662	47	15	micro	micro	NOUN
ejpam-5662	47	16	-	-	ADJ
ejpam-5662	47	17	and	and	CCONJ
ejpam-5662	47	18	nano	nano	NOUN
ejpam-5662	47	19	-	-	PUNCT
ejpam-5662	47	20	applications	application	NOUN
ejpam-5662	47	21	,	,	PUNCT
ejpam-5662	47	22	the	the	DET
ejpam-5662	47	23	two	two	NUM
ejpam-5662	47	24	-	-	PUNCT
ejpam-5662	47	25	degree	degree	NOUN
ejpam-5662	47	26	-	-	PUNCT
ejpam-5662	47	27	of	of	ADP
ejpam-5662	47	28	-	-	PUNCT
ejpam-5662	47	29	freedom	freedom	NOUN
ejpam-5662	47	30	a.	a.	PROPN
ejpam-5662	47	31	alanazy	alanazy	PROPN
ejpam-5662	47	32	,	,	PUNCT
ejpam-5662	47	33	g.	g.	PROPN
ejpam-5662	47	34	m.	m.	PROPN
ejpam-5662	47	35	moatimid	moatimid	PROPN
ejpam-5662	47	36	,	,	PUNCT
ejpam-5662	47	37	m.	m.	PROPN
ejpam-5662	47	38	a.	a.	PROPN
ejpam-5662	47	39	a.	a.	PROPN
ejpam-5662	47	40	mohamed	mohamed	PROPN
ejpam-5662	47	41	/	/	SYM
ejpam-5662	47	42	eur	eur	PROPN
ejpam-5662	47	43	.	.	PUNCT
ejpam-5662	48	1	j.	j.	PROPN
ejpam-5662	48	2	pure	pure	PROPN
ejpam-5662	48	3	appl	appl	PROPN
ejpam-5662	48	4	.	.	PROPN
ejpam-5662	48	5	math	math	PROPN
ejpam-5662	48	6	,	,	PUNCT
ejpam-5662	48	7	18	18	NUM
ejpam-5662	48	8	(	(	PUNCT
ejpam-5662	48	9	2	2	NUM
ejpam-5662	48	10	)	)	PUNCT
ejpam-5662	48	11	(	(	PUNCT
ejpam-5662	48	12	2025	2025	NUM
ejpam-5662	48	13	)	)	PUNCT
ejpam-5662	48	14	,	,	PUNCT
ejpam-5662	48	15	5662	5662	NUM
ejpam-5662	48	16	3	3	NUM
ejpam-5662	48	17	of	of	ADP
ejpam-5662	48	18	36	36	NUM
ejpam-5662	48	19	(	(	PUNCT
ejpam-5662	48	20	tdof	tdof	NOUN
ejpam-5662	48	21	)	)	PUNCT
ejpam-5662	48	22	of	of	ADP
ejpam-5662	48	23	the	the	DET
ejpam-5662	48	24	mathieu	mathieu	PROPN
ejpam-5662	48	25	–	–	PUNCT
ejpam-5662	48	26	cubic	cubic	ADJ
ejpam-5662	48	27	-	-	PUNCT
ejpam-5662	48	28	quintic	quintic	ADJ
ejpam-5662	48	29	duffing	duffing	NOUN
ejpam-5662	48	30	oscillator	oscillator	NOUN
ejpam-5662	48	31	(	(	PUNCT
ejpam-5662	48	32	mdo	mdo	PROPN
ejpam-5662	48	33	)	)	PUNCT
ejpam-5662	48	34	is	be	AUX
ejpam-5662	48	35	examined	examine	VERB
ejpam-5662	48	36	in	in	ADP
ejpam-5662	48	37	a	a	DET
ejpam-5662	48	38	general	general	ADJ
ejpam-5662	48	39	configuration	configuration	NOUN
ejpam-5662	48	40	,	,	PUNCT
ejpam-5662	48	41	particularly	particularly	ADV
ejpam-5662	48	42	where	where	SCONJ
ejpam-5662	48	43	the	the	DET
ejpam-5662	48	44	broadband	broadband	NOUN
ejpam-5662	48	45	destabilization	destabilization	NOUN
ejpam-5662	48	46	impact	impact	NOUN
ejpam-5662	48	47	is	be	AUX
ejpam-5662	48	48	demonstrated	demonstrate	VERB
ejpam-5662	48	49	.	.	PUNCT
ejpam-5662	49	1	parametric	parametric	PROPN
ejpam-5662	49	2	stimulated	stimulated	ADJ
ejpam-5662	49	3	nonlinear	nonlinear	ADJ
ejpam-5662	49	4	tdof	tdof	ADJ
ejpam-5662	49	5	systems	system	NOUN
ejpam-5662	49	6	were	be	AUX
ejpam-5662	49	7	previously	previously	ADV
ejpam-5662	49	8	examined	examine	VERB
ejpam-5662	49	9	in	in	ADP
ejpam-5662	49	10	various	various	ADJ
ejpam-5662	49	11	configurations	configuration	NOUN
ejpam-5662	49	12	.	.	PUNCT
ejpam-5662	50	1	besides	besides	SCONJ
ejpam-5662	50	2	cubic	cubic	ADJ
ejpam-5662	50	3	nonlinearities	nonlinearitie	NOUN
ejpam-5662	50	4	,	,	PUNCT
ejpam-5662	50	5	certain	certain	ADJ
ejpam-5662	50	6	systems	system	NOUN
ejpam-5662	50	7	featuring	feature	VERB
ejpam-5662	50	8	either	either	CCONJ
ejpam-5662	50	9	quadratic	quadratic	ADJ
ejpam-5662	50	10	or	or	CCONJ
ejpam-5662	50	11	coupling	couple	VERB
ejpam-5662	50	12	nonlinear	nonlinear	ADJ
ejpam-5662	50	13	components	component	NOUN
ejpam-5662	50	14	were	be	AUX
ejpam-5662	50	15	analyzed	analyze	VERB
ejpam-5662	50	16	analytically	analytically	ADV
ejpam-5662	50	17	.	.	PUNCT
ejpam-5662	51	1	the	the	DET
ejpam-5662	51	2	tdof	tdof	NOUN
ejpam-5662	51	3	’s	’s	PART
ejpam-5662	51	4	response	response	NOUN
ejpam-5662	51	5	to	to	ADP
ejpam-5662	51	6	a	a	DET
ejpam-5662	51	7	combination	combination	NOUN
ejpam-5662	51	8	of	of	ADP
ejpam-5662	51	9	parametric	parametric	ADJ
ejpam-5662	51	10	resonance	resonance	NOUN
ejpam-5662	51	11	,	,	PUNCT
ejpam-5662	51	12	influenced	influence	VERB
ejpam-5662	51	13	by	by	ADP
ejpam-5662	51	14	quadratic	quadratic	ADJ
ejpam-5662	51	15	nonlinearity	nonlinearity	NOUN
ejpam-5662	51	16	and	and	CCONJ
ejpam-5662	51	17	two	two	NUM
ejpam-5662	51	18	-	-	PUNCT
ejpam-5662	51	19	to	to	ADP
ejpam-5662	51	20	-	-	PUNCT
ejpam-5662	51	21	one	one	NUM
ejpam-5662	51	22	internal	internal	ADJ
ejpam-5662	51	23	resonances	resonance	NOUN
ejpam-5662	51	24	was	be	AUX
ejpam-5662	51	25	examined	examine	VERB
ejpam-5662	51	26	[	[	PUNCT
ejpam-5662	51	27	13	13	NUM
ejpam-5662	51	28	]	]	PUNCT
ejpam-5662	51	29	.	.	PUNCT
ejpam-5662	52	1	the	the	DET
ejpam-5662	52	2	normal	normal	ADJ
ejpam-5662	52	3	forms	form	NOUN
ejpam-5662	52	4	approach	approach	NOUN
ejpam-5662	52	5	was	be	AUX
ejpam-5662	52	6	employed	employ	VERB
ejpam-5662	52	7	to	to	PART
ejpam-5662	52	8	analyze	analyze	VERB
ejpam-5662	52	9	the	the	DET
ejpam-5662	52	10	nonlinear	nonlinear	ADJ
ejpam-5662	52	11	response	response	NOUN
ejpam-5662	52	12	of	of	ADP
ejpam-5662	52	13	a	a	DET
ejpam-5662	52	14	tdof	tdof	ADJ
ejpam-5662	52	15	system	system	NOUN
ejpam-5662	52	16	exhibiting	exhibit	VERB
ejpam-5662	52	17	recurrent	recurrent	ADJ
ejpam-5662	52	18	natural	natural	ADJ
ejpam-5662	52	19	frequencies	frequency	NOUN
ejpam-5662	52	20	and	and	CCONJ
ejpam-5662	52	21	cubic	cubic	ADJ
ejpam-5662	52	22	nonlinearity	nonlinearity	NOUN
ejpam-5662	52	23	under	under	ADP
ejpam-5662	52	24	principal	principal	ADJ
ejpam-5662	52	25	parametric	parametric	ADJ
ejpam-5662	52	26	excitation	excitation	NOUN
ejpam-5662	52	27	[	[	X
ejpam-5662	52	28	14	14	NUM
ejpam-5662	52	29	]	]	PUNCT
ejpam-5662	52	30	.	.	PUNCT
ejpam-5662	53	1	the	the	DET
ejpam-5662	53	2	linear	linear	PROPN
ejpam-5662	53	3	component	component	NOUN
ejpam-5662	53	4	of	of	ADP
ejpam-5662	53	5	the	the	DET
ejpam-5662	53	6	system	system	NOUN
ejpam-5662	53	7	exhibits	exhibit	VERB
ejpam-5662	53	8	a	a	DET
ejpam-5662	53	9	non	non	ADJ
ejpam-5662	53	10	-	-	ADJ
ejpam-5662	53	11	semi	semi	ADJ
ejpam-5662	53	12	-	-	ADJ
ejpam-5662	53	13	simple	simple	ADJ
ejpam-5662	53	14	one	one	NUM
ejpam-5662	53	15	-	-	PUNCT
ejpam-5662	53	16	to	to	ADP
ejpam-5662	53	17	-	-	PUNCT
ejpam-5662	53	18	one	one	NUM
ejpam-5662	53	19	resonance	resonance	NOUN
ejpam-5662	53	20	.	.	PUNCT
ejpam-5662	54	1	the	the	DET
ejpam-5662	54	2	findings	finding	NOUN
ejpam-5662	54	3	were	be	AUX
ejpam-5662	54	4	utilized	utilize	VERB
ejpam-5662	54	5	for	for	ADP
ejpam-5662	54	6	the	the	DET
ejpam-5662	54	7	interest	interest	NOUN
ejpam-5662	54	8	analysis	analysis	NOUN
ejpam-5662	54	9	of	of	ADP
ejpam-5662	54	10	a	a	DET
ejpam-5662	54	11	simply	simply	ADV
ejpam-5662	54	12	supported	support	VERB
ejpam-5662	54	13	panel	panel	NOUN
ejpam-5662	54	14	in	in	ADP
ejpam-5662	54	15	supersonic	supersonic	ADJ
ejpam-5662	54	16	airflow	airflow	NOUN
ejpam-5662	54	17	.	.	PUNCT
ejpam-5662	55	1	the	the	DET
ejpam-5662	55	2	multiple	multiple	ADJ
ejpam-5662	55	3	timescales	timescale	NOUN
ejpam-5662	55	4	method	method	NOUN
ejpam-5662	55	5	[	[	X
ejpam-5662	55	6	7	7	NUM
ejpam-5662	55	7	,	,	PUNCT
ejpam-5662	55	8	12	12	NUM
ejpam-5662	55	9	]	]	PUNCT
ejpam-5662	55	10	is	be	AUX
ejpam-5662	55	11	employed	employ	VERB
ejpam-5662	55	12	to	to	PART
ejpam-5662	55	13	derive	derive	VERB
ejpam-5662	55	14	a	a	DET
ejpam-5662	55	15	first	first	ADJ
ejpam-5662	55	16	-	-	PUNCT
ejpam-5662	55	17	order	order	NOUN
ejpam-5662	55	18	uniform	uniform	ADJ
ejpam-5662	55	19	expansion	expansion	NOUN
ejpam-5662	55	20	,	,	PUNCT
ejpam-5662	55	21	resulting	result	VERB
ejpam-5662	55	22	in	in	ADP
ejpam-5662	55	23	four	four	NUM
ejpam-5662	55	24	first	first	ADJ
ejpam-5662	55	25	-	-	PUNCT
ejpam-5662	55	26	order	order	NOUN
ejpam-5662	55	27	nonlinear	nonlinear	ADJ
ejpam-5662	55	28	odes	ode	NOUN
ejpam-5662	55	29	that	that	PRON
ejpam-5662	55	30	govern	govern	VERB
ejpam-5662	55	31	the	the	DET
ejpam-5662	55	32	modulation	modulation	NOUN
ejpam-5662	55	33	of	of	ADP
ejpam-5662	55	34	the	the	DET
ejpam-5662	55	35	amplitudes	amplitude	NOUN
ejpam-5662	55	36	and	and	CCONJ
ejpam-5662	55	37	phases	phase	NOUN
ejpam-5662	55	38	of	of	ADP
ejpam-5662	55	39	the	the	DET
ejpam-5662	55	40	two	two	NUM
ejpam-5662	55	41	modes	mode	NOUN
ejpam-5662	55	42	.	.	PUNCT
ejpam-5662	56	1	the	the	DET
ejpam-5662	56	2	steady	steady	ADJ
ejpam-5662	56	3	-	-	PUNCT
ejpam-5662	56	4	state	state	NOUN
ejpam-5662	56	5	responses	response	NOUN
ejpam-5662	56	6	and	and	CCONJ
ejpam-5662	56	7	their	their	PRON
ejpam-5662	56	8	stability	stability	NOUN
ejpam-5662	56	9	are	be	AUX
ejpam-5662	56	10	calculated	calculate	VERB
ejpam-5662	56	11	for	for	ADP
ejpam-5662	56	12	specific	specific	ADJ
ejpam-5662	56	13	values	value	NOUN
ejpam-5662	56	14	of	of	ADP
ejpam-5662	56	15	the	the	DET
ejpam-5662	56	16	system	system	NOUN
ejpam-5662	56	17	parameters	parameter	NOUN
ejpam-5662	56	18	.	.	PUNCT
ejpam-5662	57	1	the	the	DET
ejpam-5662	57	2	impacts	impact	NOUN
ejpam-5662	57	3	of	of	ADP
ejpam-5662	57	4	altering	alter	VERB
ejpam-5662	57	5	the	the	DET
ejpam-5662	57	6	internal	internal	ADJ
ejpam-5662	57	7	resonance	resonance	NOUN
ejpam-5662	57	8	,	,	PUNCT
ejpam-5662	57	9	adjusting	adjust	VERB
ejpam-5662	57	10	the	the	DET
ejpam-5662	57	11	parametric	parametric	ADJ
ejpam-5662	57	12	resonance	resonance	NOUN
ejpam-5662	57	13	,	,	PUNCT
ejpam-5662	57	14	the	the	DET
ejpam-5662	57	15	phase	phase	NOUN
ejpam-5662	57	16	and	and	CCONJ
ejpam-5662	57	17	amplitude	amplitude	NOUN
ejpam-5662	57	18	of	of	ADP
ejpam-5662	57	19	the	the	DET
ejpam-5662	57	20	second	second	ADJ
ejpam-5662	57	21	mode	mode	NOUN
ejpam-5662	57	22	parametric	parametric	ADJ
ejpam-5662	57	23	excitation	excitation	NOUN
ejpam-5662	57	24	,	,	PUNCT
ejpam-5662	57	25	and	and	CCONJ
ejpam-5662	57	26	the	the	DET
ejpam-5662	57	27	beginning	beginning	ADJ
ejpam-5662	57	28	conditions	condition	NOUN
ejpam-5662	57	29	were	be	AUX
ejpam-5662	57	30	examined	examine	VERB
ejpam-5662	57	31	.	.	PUNCT
ejpam-5662	58	1	certain	certain	ADJ
ejpam-5662	58	2	studies	study	NOUN
ejpam-5662	58	3	concentrated	concentrate	VERB
ejpam-5662	58	4	on	on	ADP
ejpam-5662	58	5	tdof	tdof	ADJ
ejpam-5662	58	6	systems	system	NOUN
ejpam-5662	58	7	for	for	ADP
ejpam-5662	58	8	particular	particular	ADJ
ejpam-5662	58	9	applications	application	NOUN
ejpam-5662	58	10	utilizing	utilize	VERB
ejpam-5662	58	11	numerical	numerical	ADJ
ejpam-5662	58	12	or	or	CCONJ
ejpam-5662	58	13	experimental	experimental	ADJ
ejpam-5662	58	14	techniques	technique	NOUN
ejpam-5662	58	15	,	,	PUNCT
ejpam-5662	58	16	incorporating	incorporate	VERB
ejpam-5662	58	17	various	various	ADJ
ejpam-5662	58	18	nonlinear	nonlinear	ADJ
ejpam-5662	58	19	terms	term	NOUN
ejpam-5662	58	20	according	accord	VERB
ejpam-5662	58	21	to	to	ADP
ejpam-5662	58	22	the	the	DET
ejpam-5662	58	23	individual	individual	ADJ
ejpam-5662	58	24	application	application	NOUN
ejpam-5662	58	25	.	.	PUNCT
ejpam-5662	59	1	a	a	DET
ejpam-5662	59	2	novel	novel	ADJ
ejpam-5662	59	3	efficient	efficient	ADJ
ejpam-5662	59	4	numerical	numerical	ADJ
ejpam-5662	59	5	method	method	NOUN
ejpam-5662	59	6	for	for	ADP
ejpam-5662	59	7	the	the	DET
ejpam-5662	59	8	stability	stability	NOUN
ejpam-5662	59	9	analysis	analysis	NOUN
ejpam-5662	59	10	of	of	ADP
ejpam-5662	59	11	linear	linear	PROPN
ejpam-5662	59	12	systems	system	NOUN
ejpam-5662	59	13	with	with	ADP
ejpam-5662	59	14	periodic	periodic	ADJ
ejpam-5662	59	15	parameters	parameter	NOUN
ejpam-5662	59	16	was	be	AUX
ejpam-5662	59	17	proposed	propose	VERB
ejpam-5662	59	18	[	[	X
ejpam-5662	59	19	15	15	NUM
ejpam-5662	59	20	]	]	PUNCT
ejpam-5662	59	21	.	.	PUNCT
ejpam-5662	60	1	the	the	DET
ejpam-5662	60	2	methodology	methodology	NOUN
ejpam-5662	60	3	was	be	AUX
ejpam-5662	60	4	founded	found	VERB
ejpam-5662	60	5	on	on	ADP
ejpam-5662	60	6	the	the	DET
ejpam-5662	60	7	premise	premise	NOUN
ejpam-5662	60	8	that	that	SCONJ
ejpam-5662	60	9	the	the	DET
ejpam-5662	60	10	state	state	NOUN
ejpam-5662	60	11	vector	vector	NOUN
ejpam-5662	60	12	and	and	CCONJ
ejpam-5662	60	13	the	the	DET
ejpam-5662	60	14	periodic	periodic	ADJ
ejpam-5662	60	15	matrix	matrix	NOUN
ejpam-5662	60	16	of	of	ADP
ejpam-5662	60	17	the	the	DET
ejpam-5662	60	18	system	system	NOUN
ejpam-5662	60	19	can	can	AUX
ejpam-5662	60	20	be	be	AUX
ejpam-5662	60	21	expressed	express	VERB
ejpam-5662	60	22	using	use	VERB
ejpam-5662	60	23	chebyshev	chebyshev	NOUN
ejpam-5662	60	24	polynomials	polynomial	NOUN
ejpam-5662	60	25	across	across	ADP
ejpam-5662	60	26	the	the	DET
ejpam-5662	60	27	major	major	ADJ
ejpam-5662	60	28	period	period	NOUN
ejpam-5662	60	29	.	.	PUNCT
ejpam-5662	61	1	the	the	DET
ejpam-5662	61	2	method	method	NOUN
ejpam-5662	61	3	integrates	integrate	VERB
ejpam-5662	61	4	floquet	floquet	NOUN
ejpam-5662	61	5	theory	theory	NOUN
ejpam-5662	61	6	to	to	PART
ejpam-5662	61	7	produce	produce	VERB
ejpam-5662	61	8	the	the	DET
ejpam-5662	61	9	transition	transition	NOUN
ejpam-5662	61	10	matrix	matrix	NOUN
ejpam-5662	61	11	at	at	ADP
ejpam-5662	61	12	the	the	DET
ejpam-5662	61	13	conclusion	conclusion	NOUN
ejpam-5662	61	14	of	of	ADP
ejpam-5662	61	15	one	one	NUM
ejpam-5662	61	16	period	period	NOUN
ejpam-5662	61	17	and	and	CCONJ
ejpam-5662	61	18	establish	establish	VERB
ejpam-5662	61	19	stability	stability	NOUN
ejpam-5662	61	20	requirements	requirement	NOUN
ejpam-5662	61	21	through	through	ADP
ejpam-5662	61	22	an	an	DET
ejpam-5662	61	23	eigenvalue	eigenvalue	ADJ
ejpam-5662	61	24	analysis	analysis	NOUN
ejpam-5662	61	25	procedure	procedure	NOUN
ejpam-5662	61	26	.	.	PUNCT
ejpam-5662	62	1	transient	transient	ADJ
ejpam-5662	62	2	vibrations	vibration	NOUN
ejpam-5662	62	3	in	in	ADP
ejpam-5662	62	4	mechanical	mechanical	ADJ
ejpam-5662	62	5	systems	system	NOUN
ejpam-5662	62	6	represent	represent	VERB
ejpam-5662	62	7	a	a	DET
ejpam-5662	62	8	prevalent	prevalent	ADJ
ejpam-5662	62	9	issue	issue	NOUN
ejpam-5662	62	10	in	in	ADP
ejpam-5662	62	11	engineering	engineering	NOUN
ejpam-5662	62	12	.	.	PUNCT
ejpam-5662	63	1	numerous	numerous	ADJ
ejpam-5662	63	2	theoretical	theoretical	ADJ
ejpam-5662	63	3	investigations	investigation	NOUN
ejpam-5662	63	4	have	have	AUX
ejpam-5662	63	5	demonstrated	demonstrate	VERB
ejpam-5662	63	6	both	both	CCONJ
ejpam-5662	63	7	analytic	analytic	ADJ
ejpam-5662	63	8	and	and	CCONJ
ejpam-5662	63	9	computational	computational	ADJ
ejpam-5662	63	10	analysis	analysis	NOUN
ejpam-5662	63	11	that	that	SCONJ
ejpam-5662	63	12	a	a	DET
ejpam-5662	63	13	vibrating	vibrate	VERB
ejpam-5662	63	14	system	system	NOUN
ejpam-5662	63	15	can	can	AUX
ejpam-5662	63	16	be	be	AUX
ejpam-5662	63	17	stabilized	stabilize	VERB
ejpam-5662	63	18	or	or	CCONJ
ejpam-5662	63	19	its	its	PRON
ejpam-5662	63	20	vibrations	vibration	NOUN
ejpam-5662	63	21	diminished	diminish	VERB
ejpam-5662	63	22	when	when	SCONJ
ejpam-5662	63	23	subjected	subject	VERB
ejpam-5662	63	24	to	to	ADP
ejpam-5662	63	25	excitation	excitation	NOUN
ejpam-5662	63	26	around	around	ADP
ejpam-5662	63	27	a	a	DET
ejpam-5662	63	28	certain	certain	ADJ
ejpam-5662	63	29	parametric	parametric	ADJ
ejpam-5662	63	30	combination	combination	NOUN
ejpam-5662	63	31	resonance	resonance	NOUN
ejpam-5662	63	32	frequency	frequency	NOUN
ejpam-5662	63	33	.	.	PUNCT
ejpam-5662	64	1	in	in	ADP
ejpam-5662	64	2	this	this	DET
ejpam-5662	64	3	procedure	procedure	NOUN
ejpam-5662	64	4	,	,	PUNCT
ejpam-5662	64	5	transitory	transitory	ADJ
ejpam-5662	64	6	vibrations	vibration	NOUN
ejpam-5662	64	7	are	be	AUX
ejpam-5662	64	8	efficiently	efficiently	ADV
ejpam-5662	64	9	mitigated	mitigate	VERB
ejpam-5662	64	10	using	use	VERB
ejpam-5662	64	11	parametric	parametric	ADJ
ejpam-5662	64	12	excitation	excitation	NOUN
ejpam-5662	64	13	.	.	PUNCT
ejpam-5662	65	1	the	the	DET
ejpam-5662	65	2	fundamental	fundamental	ADJ
ejpam-5662	65	3	stage	stage	NOUN
ejpam-5662	65	4	in	in	ADP
ejpam-5662	65	5	utilizing	utilize	VERB
ejpam-5662	65	6	this	this	DET
ejpam-5662	65	7	technology	technology	NOUN
ejpam-5662	65	8	is	be	AUX
ejpam-5662	65	9	its	its	PRON
ejpam-5662	65	10	experimental	experimental	ADJ
ejpam-5662	65	11	application	application	NOUN
ejpam-5662	65	12	in	in	ADP
ejpam-5662	65	13	mechanical	mechanical	ADJ
ejpam-5662	65	14	systems	system	NOUN
ejpam-5662	65	15	.	.	PUNCT
ejpam-5662	66	1	this	this	DET
ejpam-5662	66	2	review	review	NOUN
ejpam-5662	66	3	discusses	discuss	VERB
ejpam-5662	66	4	recent	recent	ADJ
ejpam-5662	66	5	experiments	experiment	NOUN
ejpam-5662	66	6	conducted	conduct	VERB
ejpam-5662	66	7	on	on	ADP
ejpam-5662	66	8	a	a	DET
ejpam-5662	66	9	basic	basic	ADJ
ejpam-5662	66	10	chain	chain	NOUN
ejpam-5662	66	11	mass	mass	NOUN
ejpam-5662	66	12	system	system	NOUN
ejpam-5662	66	13	,	,	PUNCT
ejpam-5662	66	14	a	a	DET
ejpam-5662	66	15	continuous	continuous	ADJ
ejpam-5662	66	16	cantilever	cantilever	NOUN
ejpam-5662	66	17	,	,	PUNCT
ejpam-5662	66	18	and	and	CCONJ
ejpam-5662	66	19	a	a	DET
ejpam-5662	66	20	flexible	flexible	ADJ
ejpam-5662	66	21	rotor	rotor	NOUN
ejpam-5662	66	22	system	system	NOUN
ejpam-5662	66	23	[	[	X
ejpam-5662	66	24	16	16	NUM
ejpam-5662	66	25	,	,	PUNCT
ejpam-5662	66	26	17	17	NUM
ejpam-5662	66	27	]	]	PUNCT
ejpam-5662	66	28	.	.	PUNCT
ejpam-5662	67	1	despite	despite	SCONJ
ejpam-5662	67	2	the	the	DET
ejpam-5662	67	3	nonlinearity	nonlinearity	NOUN
ejpam-5662	67	4	’s	’s	PART
ejpam-5662	67	5	extensive	extensive	ADJ
ejpam-5662	67	6	practical	practical	ADJ
ejpam-5662	67	7	uses	use	NOUN
ejpam-5662	67	8	,	,	PUNCT
ejpam-5662	67	9	researchers	researcher	NOUN
ejpam-5662	67	10	and	and	CCONJ
ejpam-5662	67	11	theoretical	theoretical	ADJ
ejpam-5662	67	12	physicists	physicist	NOUN
ejpam-5662	67	13	have	have	AUX
ejpam-5662	67	14	found	find	VERB
ejpam-5662	67	15	it	it	PRON
ejpam-5662	67	16	difficult	difficult	ADJ
ejpam-5662	67	17	to	to	PART
ejpam-5662	67	18	obtain	obtain	VERB
ejpam-5662	67	19	an	an	DET
ejpam-5662	67	20	exact	exact	ADJ
ejpam-5662	67	21	solution	solution	NOUN
ejpam-5662	67	22	or	or	CCONJ
ejpam-5662	67	23	one	one	NUM
ejpam-5662	67	24	that	that	PRON
ejpam-5662	67	25	closely	closely	ADV
ejpam-5662	67	26	approximates	approximate	VERB
ejpam-5662	67	27	the	the	DET
ejpam-5662	67	28	correct	correct	ADJ
ejpam-5662	67	29	solution	solution	NOUN
ejpam-5662	67	30	.	.	PUNCT
ejpam-5662	68	1	they	they	PRON
ejpam-5662	68	2	typically	typically	ADV
ejpam-5662	68	3	appear	appear	VERB
ejpam-5662	68	4	to	to	PART
ejpam-5662	68	5	possess	possess	VERB
ejpam-5662	68	6	options	option	NOUN
ejpam-5662	68	7	,	,	PUNCT
ejpam-5662	68	8	even	even	ADV
ejpam-5662	68	9	if	if	SCONJ
ejpam-5662	68	10	their	their	PRON
ejpam-5662	68	11	drive	drive	NOUN
ejpam-5662	68	12	stems	stem	VERB
ejpam-5662	68	13	from	from	ADP
ejpam-5662	68	14	their	their	PRON
ejpam-5662	68	15	objectives	objective	NOUN
ejpam-5662	68	16	.	.	PUNCT
ejpam-5662	69	1	as	as	ADP
ejpam-5662	69	2	a	a	DET
ejpam-5662	69	3	consequence	consequence	NOUN
ejpam-5662	69	4	,	,	PUNCT
ejpam-5662	69	5	asymptotic	asymptotic	ADJ
ejpam-5662	69	6	analyses	analysis	NOUN
ejpam-5662	69	7	of	of	ADP
ejpam-5662	69	8	several	several	ADJ
ejpam-5662	69	9	nonlinear	nonlinear	ADJ
ejpam-5662	69	10	odes	ode	NOUN
ejpam-5662	69	11	were	be	AUX
ejpam-5662	69	12	the	the	DET
ejpam-5662	69	13	focus	focus	NOUN
ejpam-5662	69	14	of	of	ADP
ejpam-5662	69	15	numerous	numerous	ADJ
ejpam-5662	69	16	mathematicians	mathematician	NOUN
ejpam-5662	69	17	.	.	PUNCT
ejpam-5662	70	1	the	the	DET
ejpam-5662	70	2	smallest	small	ADJ
ejpam-5662	70	3	factor	factor	NOUN
ejpam-5662	70	4	method	method	NOUN
ejpam-5662	70	5	and	and	CCONJ
ejpam-5662	70	6	the	the	DET
ejpam-5662	70	7	averaging	averaging	NOUN
ejpam-5662	70	8	technique	technique	NOUN
ejpam-5662	70	9	were	be	AUX
ejpam-5662	70	10	employed	employ	VERB
ejpam-5662	70	11	to	to	PART
ejpam-5662	70	12	illustrate	illustrate	VERB
ejpam-5662	70	13	weak	weak	ADJ
ejpam-5662	70	14	nonlinear	nonlinear	ADJ
ejpam-5662	70	15	equations	equation	NOUN
ejpam-5662	70	16	[	[	X
ejpam-5662	70	17	18	18	NUM
ejpam-5662	70	18	]	]	PUNCT
ejpam-5662	70	19	.	.	PUNCT
ejpam-5662	71	1	the	the	DET
ejpam-5662	71	2	homotopy	homotopy	NOUN
ejpam-5662	71	3	perturbation	perturbation	NOUN
ejpam-5662	71	4	method	method	NOUN
ejpam-5662	71	5	(	(	PUNCT
ejpam-5662	71	6	hpm	hpm	NOUN
ejpam-5662	71	7	)	)	PUNCT
ejpam-5662	71	8	is	be	AUX
ejpam-5662	71	9	employed	employ	VERB
ejpam-5662	71	10	to	to	PART
ejpam-5662	71	11	achieve	achieve	VERB
ejpam-5662	71	12	accurate	accurate	ADJ
ejpam-5662	71	13	asymptotic	asymptotic	ADJ
ejpam-5662	71	14	computations	computation	NOUN
ejpam-5662	71	15	in	in	ADP
ejpam-5662	71	16	scenarios	scenario	NOUN
ejpam-5662	71	17	involving	involve	VERB
ejpam-5662	71	18	low	low	ADJ
ejpam-5662	71	19	-	-	PUNCT
ejpam-5662	71	20	intensity	intensity	NOUN
ejpam-5662	71	21	sounds	sound	VERB
ejpam-5662	71	22	.	.	PUNCT
ejpam-5662	72	1	solutions	solution	NOUN
ejpam-5662	72	2	of	of	ADP
ejpam-5662	72	3	oscillation	oscillation	NOUN
ejpam-5662	72	4	systems	system	NOUN
ejpam-5662	72	5	are	be	AUX
ejpam-5662	72	6	also	also	ADV
ejpam-5662	72	7	obtained	obtain	VERB
ejpam-5662	72	8	through	through	ADP
ejpam-5662	72	9	the	the	DET
ejpam-5662	72	10	application	application	NOUN
ejpam-5662	72	11	of	of	ADP
ejpam-5662	72	12	multiple	multiple	ADJ
ejpam-5662	72	13	time	time	NOUN
ejpam-5662	72	14	-	-	PUNCT
ejpam-5662	72	15	scales	scale	NOUN
ejpam-5662	72	16	method	method	NOUN
ejpam-5662	72	17	.	.	PUNCT
ejpam-5662	73	1	regrettably	regrettably	ADV
ejpam-5662	73	2	,	,	PUNCT
ejpam-5662	73	3	utilizing	utilize	VERB
ejpam-5662	73	4	this	this	DET
ejpam-5662	73	5	minimal	minimal	ADJ
ejpam-5662	73	6	quantity	quantity	NOUN
ejpam-5662	73	7	in	in	ADP
ejpam-5662	73	8	both	both	DET
ejpam-5662	73	9	methods	method	NOUN
ejpam-5662	73	10	yielded	yield	VERB
ejpam-5662	73	11	inconsistent	inconsistent	ADJ
ejpam-5662	73	12	results	result	NOUN
ejpam-5662	73	13	[	[	X
ejpam-5662	73	14	12	12	NUM
ejpam-5662	73	15	]	]	PUNCT
ejpam-5662	73	16	.	.	PUNCT
ejpam-5662	74	1	in	in	ADP
ejpam-5662	74	2	any	any	DET
ejpam-5662	74	3	asymptotic	asymptotic	ADJ
ejpam-5662	74	4	or	or	CCONJ
ejpam-5662	74	5	perturbation	perturbation	NOUN
ejpam-5662	74	6	method	method	NOUN
ejpam-5662	74	7	,	,	PUNCT
ejpam-5662	74	8	identifying	identify	VERB
ejpam-5662	74	9	the	the	DET
ejpam-5662	74	10	small	small	ADJ
ejpam-5662	74	11	parameter	parameter	NOUN
ejpam-5662	74	12	necessary	necessary	ADJ
ejpam-5662	74	13	for	for	ADP
ejpam-5662	74	14	a	a	DET
ejpam-5662	74	15	more	more	ADV
ejpam-5662	74	16	practical	practical	ADJ
ejpam-5662	74	17	a.	a.	NOUN
ejpam-5662	74	18	alanazy	alanazy	NOUN
ejpam-5662	74	19	,	,	PUNCT
ejpam-5662	74	20	g.	g.	PROPN
ejpam-5662	74	21	m.	m.	PROPN
ejpam-5662	74	22	moatimid	moatimid	PROPN
ejpam-5662	74	23	,	,	PUNCT
ejpam-5662	74	24	m.	m.	PROPN
ejpam-5662	74	25	a.	a.	PROPN
ejpam-5662	74	26	a.	a.	PROPN
ejpam-5662	74	27	mohamed	mohamed	PROPN
ejpam-5662	74	28	/	/	SYM
ejpam-5662	74	29	eur	eur	PROPN
ejpam-5662	74	30	.	.	PUNCT
ejpam-5662	75	1	j.	j.	PROPN
ejpam-5662	75	2	pure	pure	PROPN
ejpam-5662	75	3	appl	appl	PROPN
ejpam-5662	75	4	.	.	PROPN
ejpam-5662	75	5	math	math	PROPN
ejpam-5662	75	6	,	,	PUNCT
ejpam-5662	75	7	18	18	NUM
ejpam-5662	75	8	(	(	PUNCT
ejpam-5662	75	9	2	2	NUM
ejpam-5662	75	10	)	)	PUNCT
ejpam-5662	75	11	(	(	PUNCT
ejpam-5662	75	12	2025	2025	NUM
ejpam-5662	75	13	)	)	PUNCT
ejpam-5662	75	14	,	,	PUNCT
ejpam-5662	75	15	5662	5662	NUM
ejpam-5662	75	16	4	4	NUM
ejpam-5662	75	17	of	of	ADP
ejpam-5662	75	18	36	36	NUM
ejpam-5662	75	19	and	and	CCONJ
ejpam-5662	75	20	realistic	realistic	ADJ
ejpam-5662	75	21	expression	expression	NOUN
ejpam-5662	75	22	of	of	ADP
ejpam-5662	75	23	the	the	DET
ejpam-5662	75	24	fundamental	fundamental	ADJ
ejpam-5662	75	25	equations	equation	NOUN
ejpam-5662	75	26	is	be	AUX
ejpam-5662	75	27	a	a	DET
ejpam-5662	75	28	crucial	crucial	ADJ
ejpam-5662	75	29	beginning	beginning	NOUN
ejpam-5662	75	30	step	step	NOUN
ejpam-5662	75	31	.	.	PUNCT
ejpam-5662	76	1	there	there	PRON
ejpam-5662	76	2	was	be	VERB
ejpam-5662	76	3	a	a	DET
ejpam-5662	76	4	heightened	heightened	ADJ
ejpam-5662	76	5	appeal	appeal	NOUN
ejpam-5662	76	6	of	of	ADP
ejpam-5662	76	7	numerous	numerous	ADJ
ejpam-5662	76	8	hpm	hpm	NOUN
ejpam-5662	76	9	-	-	PUNCT
ejpam-5662	76	10	based	base	VERB
ejpam-5662	76	11	methodologies	methodology	NOUN
ejpam-5662	76	12	for	for	ADP
ejpam-5662	76	13	forecasting	forecast	VERB
ejpam-5662	76	14	various	various	ADJ
ejpam-5662	76	15	nonlinear	nonlinear	ADJ
ejpam-5662	76	16	odes	ode	NOUN
ejpam-5662	76	17	,	,	PUNCT
ejpam-5662	76	18	hence	hence	ADV
ejpam-5662	76	19	approximating	approximate	VERB
ejpam-5662	76	20	their	their	PRON
ejpam-5662	76	21	solutions	solution	NOUN
ejpam-5662	76	22	more	more	ADV
ejpam-5662	76	23	closely	closely	ADV
ejpam-5662	76	24	[	[	X
ejpam-5662	76	25	19	19	NUM
ejpam-5662	76	26	]	]	PUNCT
ejpam-5662	76	27	.	.	PUNCT
ejpam-5662	77	1	if	if	SCONJ
ejpam-5662	77	2	the	the	DET
ejpam-5662	77	3	beginning	beginning	NOUN
ejpam-5662	77	4	assumption	assumption	NOUN
ejpam-5662	77	5	did	do	AUX
ejpam-5662	77	6	not	not	PART
ejpam-5662	77	7	align	align	VERB
ejpam-5662	77	8	with	with	ADP
ejpam-5662	77	9	the	the	DET
ejpam-5662	77	10	employed	employ	VERB
ejpam-5662	77	11	approach	approach	NOUN
ejpam-5662	77	12	for	for	ADP
ejpam-5662	77	13	the	the	DET
ejpam-5662	77	14	inquiry	inquiry	NOUN
ejpam-5662	77	15	,	,	PUNCT
ejpam-5662	77	16	the	the	DET
ejpam-5662	77	17	procedure	procedure	NOUN
ejpam-5662	77	18	would	would	AUX
ejpam-5662	77	19	diverge	diverge	VERB
ejpam-5662	77	20	and	and	CCONJ
ejpam-5662	77	21	fail	fail	VERB
ejpam-5662	77	22	to	to	PART
ejpam-5662	77	23	yield	yield	VERB
ejpam-5662	77	24	the	the	DET
ejpam-5662	77	25	intended	intend	VERB
ejpam-5662	77	26	results	result	NOUN
ejpam-5662	77	27	.	.	PUNCT
ejpam-5662	78	1	these	these	DET
ejpam-5662	78	2	strategies	strategy	NOUN
ejpam-5662	78	3	depended	depend	VERB
ejpam-5662	78	4	on	on	ADP
ejpam-5662	78	5	the	the	DET
ejpam-5662	78	6	initial	initial	ADJ
ejpam-5662	78	7	estimation	estimation	NOUN
ejpam-5662	78	8	of	of	ADP
ejpam-5662	78	9	the	the	DET
ejpam-5662	78	10	solution	solution	NOUN
ejpam-5662	78	11	.	.	PUNCT
ejpam-5662	79	1	the	the	DET
ejpam-5662	79	2	hpm	hpm	NOUN
ejpam-5662	79	3	is	be	AUX
ejpam-5662	79	4	employed	employ	VERB
ejpam-5662	79	5	in	in	ADP
ejpam-5662	79	6	the	the	DET
ejpam-5662	79	7	analysis	analysis	NOUN
ejpam-5662	79	8	of	of	ADP
ejpam-5662	79	9	analytical	analytical	ADJ
ejpam-5662	79	10	approximations	approximation	NOUN
ejpam-5662	79	11	for	for	ADP
ejpam-5662	79	12	magnetic	magnetic	ADJ
ejpam-5662	79	13	spherical	spherical	ADJ
ejpam-5662	79	14	pendulums	pendulum	NOUN
ejpam-5662	79	15	[	[	X
ejpam-5662	79	16	20	20	NUM
ejpam-5662	79	17	]	]	PUNCT
ejpam-5662	79	18	.	.	PUNCT
ejpam-5662	80	1	moatimid	moatimid	PROPN
ejpam-5662	80	2	et	et	PROPN
ejpam-5662	80	3	al	al	PROPN
ejpam-5662	80	4	.	.	PUNCT
ejpam-5662	81	1	[	[	X
ejpam-5662	81	2	21	21	NUM
ejpam-5662	81	3	-	-	SYM
ejpam-5662	81	4	24	24	NUM
ejpam-5662	81	5	]	]	PUNCT
ejpam-5662	81	6	employed	employ	VERB
ejpam-5662	81	7	the	the	DET
ejpam-5662	81	8	hpm	hpm	NOUN
ejpam-5662	81	9	in	in	ADP
ejpam-5662	81	10	analyzing	analyze	VERB
ejpam-5662	81	11	different	different	ADJ
ejpam-5662	81	12	problems	problem	NOUN
ejpam-5662	81	13	in	in	ADP
ejpam-5662	81	14	fluid	fluid	ADJ
ejpam-5662	81	15	mechanics	mechanic	NOUN
ejpam-5662	81	16	as	as	ADV
ejpam-5662	81	17	well	well	ADV
ejpam-5662	81	18	as	as	ADP
ejpam-5662	81	19	dynamical	dynamical	ADJ
ejpam-5662	81	20	systems	system	NOUN
ejpam-5662	81	21	.	.	PUNCT
ejpam-5662	82	1	despite	despite	SCONJ
ejpam-5662	82	2	the	the	DET
ejpam-5662	82	3	evident	evident	ADJ
ejpam-5662	82	4	advancements	advancement	NOUN
ejpam-5662	82	5	,	,	PUNCT
ejpam-5662	82	6	the	the	DET
ejpam-5662	82	7	hpm	hpm	NOUN
ejpam-5662	82	8	demonstrated	demonstrate	VERB
ejpam-5662	82	9	difficulties	difficulty	NOUN
ejpam-5662	82	10	in	in	ADP
ejpam-5662	82	11	use	use	NOUN
ejpam-5662	82	12	with	with	ADP
ejpam-5662	82	13	non	non	ADJ
ejpam-5662	82	14	-	-	ADJ
ejpam-5662	82	15	conservative	conservative	ADJ
ejpam-5662	82	16	oscillators	oscillator	NOUN
ejpam-5662	82	17	.	.	PUNCT
ejpam-5662	83	1	the	the	DET
ejpam-5662	83	2	enhanced	enhanced	ADJ
ejpam-5662	83	3	analytical	analytical	ADJ
ejpam-5662	83	4	capacity	capacity	NOUN
ejpam-5662	83	5	of	of	ADP
ejpam-5662	83	6	the	the	DET
ejpam-5662	83	7	hpm	hpm	NOUN
ejpam-5662	83	8	for	for	ADP
ejpam-5662	83	9	nonlinear	nonlinear	ADJ
ejpam-5662	83	10	vibration	vibration	NOUN
ejpam-5662	83	11	theory	theory	NOUN
ejpam-5662	83	12	is	be	AUX
ejpam-5662	83	13	assured	assure	VERB
ejpam-5662	83	14	.	.	PUNCT
ejpam-5662	84	1	it	it	PRON
ejpam-5662	84	2	concentrated	concentrate	VERB
ejpam-5662	84	3	on	on	ADP
ejpam-5662	84	4	interconnected	interconnected	ADJ
ejpam-5662	84	5	damping	damp	VERB
ejpam-5662	84	6	nonlinear	nonlinear	ADJ
ejpam-5662	84	7	oscillators	oscillator	NOUN
ejpam-5662	84	8	across	across	ADP
ejpam-5662	84	9	several	several	ADJ
ejpam-5662	84	10	categories	category	NOUN
ejpam-5662	84	11	.	.	PUNCT
ejpam-5662	85	1	the	the	DET
ejpam-5662	85	2	examples	example	NOUN
ejpam-5662	85	3	within	within	ADP
ejpam-5662	85	4	each	each	DET
ejpam-5662	85	5	category	category	NOUN
ejpam-5662	85	6	may	may	AUX
ejpam-5662	85	7	function	function	VERB
ejpam-5662	85	8	as	as	ADP
ejpam-5662	85	9	heuristic	heuristic	ADJ
ejpam-5662	85	10	elucidations	elucidation	NOUN
ejpam-5662	85	11	or	or	CCONJ
ejpam-5662	85	12	as	as	ADP
ejpam-5662	85	13	prototypes	prototype	NOUN
ejpam-5662	85	14	for	for	ADP
ejpam-5662	85	15	further	further	ADJ
ejpam-5662	85	16	applications	application	NOUN
ejpam-5662	85	17	.	.	PUNCT
ejpam-5662	86	1	he	he	PRON
ejpam-5662	86	2	’s	’s	AUX
ejpam-5662	86	3	frequency	frequency	NOUN
ejpam-5662	86	4	formula	formula	NOUN
ejpam-5662	86	5	(	(	PUNCT
ejpam-5662	86	6	hff	hff	NOUN
ejpam-5662	86	7	)	)	PUNCT
ejpam-5662	86	8	is	be	AUX
ejpam-5662	86	9	a	a	DET
ejpam-5662	86	10	straightforward	straightforward	ADJ
ejpam-5662	86	11	and	and	CCONJ
ejpam-5662	86	12	efficient	efficient	ADJ
ejpam-5662	86	13	method	method	NOUN
ejpam-5662	86	14	for	for	ADP
ejpam-5662	86	15	constructing	construct	VERB
ejpam-5662	86	16	a	a	DET
ejpam-5662	86	17	conservation	conservation	NOUN
ejpam-5662	86	18	nonlinear	nonlinear	ADJ
ejpam-5662	86	19	oscillator	oscillator	NOUN
ejpam-5662	86	20	in	in	ADP
ejpam-5662	86	21	the	the	DET
ejpam-5662	86	22	context	context	NOUN
ejpam-5662	86	23	of	of	ADP
ejpam-5662	86	24	nonlinear	nonlinear	ADJ
ejpam-5662	86	25	oscillator	oscillator	NOUN
ejpam-5662	86	26	challenges	challenge	NOUN
ejpam-5662	86	27	[	[	X
ejpam-5662	86	28	25	25	NUM
ejpam-5662	86	29	]	]	PUNCT
ejpam-5662	86	30	.	.	PUNCT
ejpam-5662	87	1	the	the	DET
ejpam-5662	87	2	establishment	establishment	NOUN
ejpam-5662	87	3	of	of	ADP
ejpam-5662	87	4	hff	hff	PROPN
ejpam-5662	87	5	is	be	AUX
ejpam-5662	87	6	credited	credit	VERB
ejpam-5662	87	7	to	to	ADP
ejpam-5662	87	8	the	the	DET
ejpam-5662	87	9	chinese	chinese	ADJ
ejpam-5662	87	10	mathematician	mathematician	ADJ
ejpam-5662	87	11	prof	prof	NOUN
ejpam-5662	87	12	.	.	PUNCT
ejpam-5662	88	1	he	he	PRON
ejpam-5662	88	2	.	.	PUNCT
ejpam-5662	89	1	a	a	DET
ejpam-5662	89	2	study	study	NOUN
ejpam-5662	89	3	of	of	ADP
ejpam-5662	89	4	the	the	DET
ejpam-5662	89	5	do	do	NOUN
ejpam-5662	89	6	in	in	ADP
ejpam-5662	89	7	periodic	periodic	ADJ
ejpam-5662	89	8	vibrational	vibrational	ADJ
ejpam-5662	89	9	behavior	behavior	NOUN
ejpam-5662	89	10	was	be	AUX
ejpam-5662	89	11	conducted	conduct	VERB
ejpam-5662	89	12	under	under	ADP
ejpam-5662	89	13	generalized	generalize	VERB
ejpam-5662	89	14	starting	starting	NOUN
ejpam-5662	89	15	conditions	condition	NOUN
ejpam-5662	89	16	[	[	X
ejpam-5662	89	17	26	26	NUM
ejpam-5662	89	18	]	]	PUNCT
ejpam-5662	89	19	.	.	PUNCT
ejpam-5662	90	1	the	the	DET
ejpam-5662	90	2	hff	hff	PROPN
ejpam-5662	90	3	is	be	AUX
ejpam-5662	90	4	determined	determine	VERB
ejpam-5662	90	5	to	to	PART
ejpam-5662	90	6	be	be	AUX
ejpam-5662	90	7	mathematically	mathematically	ADV
ejpam-5662	90	8	simple	simple	ADJ
ejpam-5662	90	9	,	,	PUNCT
ejpam-5662	90	10	biologically	biologically	ADV
ejpam-5662	90	11	insightful	insightful	ADJ
ejpam-5662	90	12	,	,	PUNCT
ejpam-5662	90	13	and	and	CCONJ
ejpam-5662	90	14	practically	practically	ADV
ejpam-5662	90	15	beneficial	beneficial	ADJ
ejpam-5662	90	16	by	by	ADP
ejpam-5662	90	17	numerical	numerical	ADJ
ejpam-5662	90	18	evaluation	evaluation	NOUN
ejpam-5662	90	19	.	.	PUNCT
ejpam-5662	91	1	engineers	engineer	NOUN
ejpam-5662	91	2	may	may	AUX
ejpam-5662	91	3	swiftly	swiftly	ADV
ejpam-5662	91	4	and	and	CCONJ
ejpam-5662	91	5	precisely	precisely	ADV
ejpam-5662	91	6	assess	assess	VERB
ejpam-5662	91	7	nonlinear	nonlinear	ADJ
ejpam-5662	91	8	vibration	vibration	NOUN
ejpam-5662	91	9	systems	system	NOUN
ejpam-5662	91	10	utilizing	utilize	VERB
ejpam-5662	91	11	the	the	DET
ejpam-5662	91	12	hff	hff	NOUN
ejpam-5662	91	13	through	through	ADP
ejpam-5662	91	14	the	the	DET
ejpam-5662	91	15	distinctive	distinctive	ADJ
ejpam-5662	91	16	methodology	methodology	NOUN
ejpam-5662	91	17	outlined	outline	VERB
ejpam-5662	91	18	in	in	ADP
ejpam-5662	91	19	the	the	DET
ejpam-5662	91	20	research	research	NOUN
ejpam-5662	91	21	.	.	PUNCT
ejpam-5662	92	1	to	to	PART
ejpam-5662	92	2	modify	modify	VERB
ejpam-5662	92	3	the	the	DET
ejpam-5662	92	4	hff	hff	NOUN
ejpam-5662	92	5	creatively	creatively	ADV
ejpam-5662	92	6	,	,	PUNCT
ejpam-5662	92	7	it	it	PRON
ejpam-5662	92	8	is	be	AUX
ejpam-5662	92	9	proposed	propose	VERB
ejpam-5662	92	10	to	to	PART
ejpam-5662	92	11	categorize	categorize	VERB
ejpam-5662	92	12	the	the	DET
ejpam-5662	92	13	oscillators	oscillator	NOUN
ejpam-5662	92	14	into	into	ADP
ejpam-5662	92	15	two	two	NUM
ejpam-5662	92	16	distinct	distinct	ADJ
ejpam-5662	92	17	extremes	extreme	NOUN
ejpam-5662	93	1	[	[	X
ejpam-5662	93	2	27	27	NUM
ejpam-5662	93	3	]	]	PUNCT
ejpam-5662	93	4	.	.	PUNCT
ejpam-5662	94	1	there	there	PRON
ejpam-5662	94	2	is	be	VERB
ejpam-5662	94	3	substantial	substantial	ADJ
ejpam-5662	94	4	concordance	concordance	NOUN
ejpam-5662	94	5	when	when	SCONJ
ejpam-5662	94	6	comparing	compare	VERB
ejpam-5662	94	7	the	the	DET
ejpam-5662	94	8	approximate	approximate	ADJ
ejpam-5662	94	9	and	and	CCONJ
ejpam-5662	94	10	exact	exact	ADJ
ejpam-5662	94	11	frequencies	frequency	NOUN
ejpam-5662	94	12	across	across	ADP
ejpam-5662	94	13	various	various	ADJ
ejpam-5662	94	14	amplitudes	amplitude	NOUN
ejpam-5662	94	15	.	.	PUNCT
ejpam-5662	95	1	the	the	DET
ejpam-5662	95	2	hamiltonian	hamiltonian	ADJ
ejpam-5662	95	3	function	function	NOUN
ejpam-5662	95	4	derived	derive	VERB
ejpam-5662	95	5	from	from	ADP
ejpam-5662	95	6	the	the	DET
ejpam-5662	95	7	hff	hff	NOUN
ejpam-5662	95	8	has	have	AUX
ejpam-5662	95	9	garnered	garner	VERB
ejpam-5662	95	10	significant	significant	ADJ
ejpam-5662	95	11	attention	attention	NOUN
ejpam-5662	95	12	due	due	ADP
ejpam-5662	95	13	to	to	ADP
ejpam-5662	95	14	its	its	PRON
ejpam-5662	95	15	simplification	simplification	NOUN
ejpam-5662	95	16	of	of	ADP
ejpam-5662	95	17	the	the	DET
ejpam-5662	95	18	computational	computational	ADJ
ejpam-5662	95	19	analysis	analysis	NOUN
ejpam-5662	95	20	of	of	ADP
ejpam-5662	95	21	a	a	DET
ejpam-5662	95	22	complex	complex	ADJ
ejpam-5662	95	23	nonlinear	nonlinear	ADJ
ejpam-5662	95	24	vibration	vibration	NOUN
ejpam-5662	95	25	system	system	NOUN
ejpam-5662	95	26	.	.	PUNCT
ejpam-5662	96	1	the	the	DET
ejpam-5662	96	2	cubic	cubic	ADJ
ejpam-5662	96	3	-	-	PUNCT
ejpam-5662	96	4	quintic	quintic	ADJ
ejpam-5662	96	5	differential	differential	NOUN
ejpam-5662	96	6	operator	operator	NOUN
ejpam-5662	96	7	was	be	AUX
ejpam-5662	96	8	utilized	utilize	VERB
ejpam-5662	96	9	to	to	PART
ejpam-5662	96	10	illustrate	illustrate	VERB
ejpam-5662	96	11	the	the	DET
ejpam-5662	96	12	precision	precision	NOUN
ejpam-5662	96	13	and	and	CCONJ
ejpam-5662	96	14	simplicity	simplicity	NOUN
ejpam-5662	96	15	of	of	ADP
ejpam-5662	96	16	the	the	DET
ejpam-5662	96	17	calculation	calculation	NOUN
ejpam-5662	96	18	.	.	PUNCT
ejpam-5662	97	1	a	a	DET
ejpam-5662	97	2	direct	direct	ADJ
ejpam-5662	97	3	approach	approach	NOUN
ejpam-5662	97	4	for	for	ADP
ejpam-5662	97	5	resolving	resolve	VERB
ejpam-5662	97	6	the	the	DET
ejpam-5662	97	7	cubic	cubic	ADJ
ejpam-5662	97	8	-	-	PUNCT
ejpam-5662	97	9	quintic	quintic	ADJ
ejpam-5662	97	10	differential	differential	NOUN
ejpam-5662	97	11	operator	operator	NOUN
ejpam-5662	97	12	is	be	AUX
ejpam-5662	97	13	introduced	introduce	VERB
ejpam-5662	97	14	[	[	X
ejpam-5662	97	15	28	28	NUM
ejpam-5662	97	16	]	]	PUNCT
ejpam-5662	97	17	.	.	PUNCT
ejpam-5662	98	1	the	the	DET
ejpam-5662	98	2	method	method	NOUN
ejpam-5662	98	3	provided	provide	VERB
ejpam-5662	98	4	a	a	DET
ejpam-5662	98	5	highly	highly	ADV
ejpam-5662	98	6	effective	effective	ADJ
ejpam-5662	98	7	and	and	CCONJ
ejpam-5662	98	8	relatively	relatively	ADV
ejpam-5662	98	9	precise	precise	ADJ
ejpam-5662	98	10	means	mean	NOUN
ejpam-5662	98	11	to	to	PART
ejpam-5662	98	12	compute	compute	VERB
ejpam-5662	98	13	the	the	DET
ejpam-5662	98	14	frequency	frequency	NOUN
ejpam-5662	98	15	of	of	ADP
ejpam-5662	98	16	a	a	DET
ejpam-5662	98	17	nonlinear	nonlinear	ADJ
ejpam-5662	98	18	conservative	conservative	ADJ
ejpam-5662	98	19	oscillator	oscillator	NOUN
ejpam-5662	98	20	.	.	PUNCT
ejpam-5662	99	1	an	an	DET
ejpam-5662	99	2	exhibition	exhibition	NOUN
ejpam-5662	99	3	and	and	CCONJ
ejpam-5662	99	4	demonstration	demonstration	NOUN
ejpam-5662	99	5	of	of	ADP
ejpam-5662	99	6	the	the	DET
ejpam-5662	99	7	optimized	optimize	VERB
ejpam-5662	99	8	hff	hff	NOUN
ejpam-5662	99	9	for	for	ADP
ejpam-5662	99	10	nonlinear	nonlinear	ADJ
ejpam-5662	99	11	oscillators	oscillator	NOUN
ejpam-5662	99	12	are	be	AUX
ejpam-5662	99	13	provided	provide	VERB
ejpam-5662	99	14	[	[	X
ejpam-5662	99	15	29	29	NUM
ejpam-5662	99	16	]	]	PUNCT
ejpam-5662	99	17	.	.	PUNCT
ejpam-5662	100	1	a	a	DET
ejpam-5662	100	2	direct	direct	ADJ
ejpam-5662	100	3	frequency	frequency	NOUN
ejpam-5662	100	4	formula	formula	NOUN
ejpam-5662	100	5	in	in	ADP
ejpam-5662	100	6	fractal	fractal	ADJ
ejpam-5662	100	7	systems	system	NOUN
ejpam-5662	100	8	is	be	AUX
ejpam-5662	100	9	presented	present	VERB
ejpam-5662	100	10	and	and	CCONJ
ejpam-5662	100	11	derived	derive	VERB
ejpam-5662	100	12	from	from	ADP
ejpam-5662	100	13	the	the	DET
ejpam-5662	100	14	hff	hff	NOUN
ejpam-5662	101	1	[	[	X
ejpam-5662	101	2	30	30	NUM
ejpam-5662	101	3	]	]	PUNCT
ejpam-5662	101	4	.	.	PUNCT
ejpam-5662	102	1	the	the	DET
ejpam-5662	102	2	direct	direct	ADJ
ejpam-5662	102	3	calculation	calculation	NOUN
ejpam-5662	102	4	and	and	CCONJ
ejpam-5662	102	5	dependable	dependable	ADJ
ejpam-5662	102	6	results	result	NOUN
ejpam-5662	102	7	amalgamated	amalgamate	VERB
ejpam-5662	102	8	to	to	PART
ejpam-5662	102	9	produce	produce	VERB
ejpam-5662	102	10	a	a	DET
ejpam-5662	102	11	valuable	valuable	ADJ
ejpam-5662	102	12	instrument	instrument	NOUN
ejpam-5662	102	13	for	for	ADP
ejpam-5662	102	14	a	a	DET
ejpam-5662	102	15	comprehensive	comprehensive	ADJ
ejpam-5662	102	16	investigation	investigation	NOUN
ejpam-5662	102	17	of	of	ADP
ejpam-5662	102	18	fractal	fractal	ADJ
ejpam-5662	102	19	vibration	vibration	NOUN
ejpam-5662	102	20	phenomena	phenomenon	NOUN
ejpam-5662	102	21	.	.	PUNCT
ejpam-5662	103	1	the	the	DET
ejpam-5662	103	2	non	non	ADJ
ejpam-5662	103	3	-	-	ADJ
ejpam-5662	103	4	newtonian	newtonian	ADJ
ejpam-5662	103	5	fluids	fluid	NOUN
ejpam-5662	103	6	are	be	AUX
ejpam-5662	103	7	essential	essential	ADJ
ejpam-5662	103	8	in	in	ADP
ejpam-5662	103	9	various	various	ADJ
ejpam-5662	103	10	areas	area	NOUN
ejpam-5662	103	11	,	,	PUNCT
ejpam-5662	103	12	including	include	VERB
ejpam-5662	103	13	technology	technology	NOUN
ejpam-5662	103	14	and	and	CCONJ
ejpam-5662	103	15	industry	industry	NOUN
ejpam-5662	103	16	.	.	PUNCT
ejpam-5662	104	1	consequently	consequently	ADV
ejpam-5662	104	2	,	,	PUNCT
ejpam-5662	104	3	the	the	DET
ejpam-5662	104	4	study	study	NOUN
ejpam-5662	104	5	of	of	ADP
ejpam-5662	104	6	these	these	DET
ejpam-5662	104	7	fluids	fluid	NOUN
ejpam-5662	104	8	is	be	AUX
ejpam-5662	104	9	highly	highly	ADV
ejpam-5662	104	10	intriguing	intriguing	ADJ
ejpam-5662	104	11	.	.	PUNCT
ejpam-5662	105	1	the	the	DET
ejpam-5662	105	2	nonlinear	nonlinear	ADJ
ejpam-5662	105	3	stability	stability	NOUN
ejpam-5662	105	4	analysis	analysis	NOUN
ejpam-5662	105	5	concentrated	concentrate	VERB
ejpam-5662	105	6	on	on	ADP
ejpam-5662	105	7	several	several	ADJ
ejpam-5662	105	8	non	non	ADJ
ejpam-5662	105	9	-	-	ADJ
ejpam-5662	105	10	newtonian	newtonian	ADJ
ejpam-5662	105	11	fluids	fluid	NOUN
ejpam-5662	105	12	.	.	PUNCT
ejpam-5662	106	1	an	an	DET
ejpam-5662	106	2	illustration	illustration	NOUN
ejpam-5662	106	3	was	be	AUX
ejpam-5662	106	4	created	create	VERB
ejpam-5662	106	5	for	for	ADP
ejpam-5662	106	6	the	the	DET
ejpam-5662	106	7	creation	creation	NOUN
ejpam-5662	106	8	of	of	ADP
ejpam-5662	106	9	some	some	DET
ejpam-5662	106	10	dynamical	dynamical	ADJ
ejpam-5662	106	11	systems	system	NOUN
ejpam-5662	106	12	with	with	ADP
ejpam-5662	106	13	a	a	DET
ejpam-5662	106	14	flat	flat	ADJ
ejpam-5662	106	15	disturbed	disturbed	ADJ
ejpam-5662	106	16	interface	interface	NOUN
ejpam-5662	106	17	.	.	PUNCT
ejpam-5662	107	1	the	the	DET
ejpam-5662	107	2	main	main	ADJ
ejpam-5662	107	3	aim	aim	NOUN
ejpam-5662	107	4	of	of	ADP
ejpam-5662	107	5	this	this	DET
ejpam-5662	107	6	theoretical	theoretical	ADJ
ejpam-5662	107	7	analysis	analysis	NOUN
ejpam-5662	107	8	is	be	AUX
ejpam-5662	107	9	to	to	PART
ejpam-5662	107	10	utilize	utilize	VERB
ejpam-5662	107	11	the	the	DET
ejpam-5662	107	12	non	non	ADJ
ejpam-5662	107	13	-	-	ADJ
ejpam-5662	107	14	perturbative	perturbative	ADJ
ejpam-5662	107	15	approach	approach	NOUN
ejpam-5662	107	16	(	(	PUNCT
ejpam-5662	107	17	npa	npa	NOUN
ejpam-5662	107	18	)	)	PUNCT
ejpam-5662	107	19	to	to	PART
ejpam-5662	107	20	augment	augment	VERB
ejpam-5662	107	21	our	our	PRON
ejpam-5662	107	22	recent	recent	ADJ
ejpam-5662	107	23	findings	finding	NOUN
ejpam-5662	107	24	[	[	X
ejpam-5662	107	25	30	30	NUM
ejpam-5662	107	26	-	-	SYM
ejpam-5662	107	27	44	44	NUM
ejpam-5662	107	28	]	]	PUNCT
ejpam-5662	107	29	.	.	PUNCT
ejpam-5662	108	1	an	an	DET
ejpam-5662	108	2	overview	overview	NOUN
ejpam-5662	108	3	of	of	ADP
ejpam-5662	108	4	the	the	DET
ejpam-5662	108	5	actual	actual	ADJ
ejpam-5662	108	6	implementation	implementation	NOUN
ejpam-5662	108	7	and	and	CCONJ
ejpam-5662	108	8	physical	physical	ADJ
ejpam-5662	108	9	applications	application	NOUN
ejpam-5662	108	10	of	of	ADP
ejpam-5662	108	11	the	the	DET
ejpam-5662	108	12	mdo	mdo	PROPN
ejpam-5662	108	13	can	can	AUX
ejpam-5662	108	14	be	be	AUX
ejpam-5662	108	15	summarized	summarize	VERB
ejpam-5662	108	16	in	in	ADP
ejpam-5662	108	17	the	the	DET
ejpam-5662	108	18	following	follow	VERB
ejpam-5662	108	19	points	point	NOUN
ejpam-5662	108	20	:	:	PUNCT
ejpam-5662	108	21	a.	a.	NOUN
ejpam-5662	108	22	alanazy	alanazy	NOUN
ejpam-5662	108	23	,	,	PUNCT
ejpam-5662	108	24	g.	g.	PROPN
ejpam-5662	108	25	m.	m.	PROPN
ejpam-5662	108	26	moatimid	moatimid	PROPN
ejpam-5662	108	27	,	,	PUNCT
ejpam-5662	108	28	m.	m.	PROPN
ejpam-5662	108	29	a.	a.	PROPN
ejpam-5662	108	30	a.	a.	PROPN
ejpam-5662	108	31	mohamed	mohamed	PROPN
ejpam-5662	108	32	/	/	SYM
ejpam-5662	108	33	eur	eur	PROPN
ejpam-5662	108	34	.	.	PUNCT
ejpam-5662	109	1	j.	j.	PROPN
ejpam-5662	109	2	pure	pure	PROPN
ejpam-5662	109	3	appl	appl	PROPN
ejpam-5662	109	4	.	.	PROPN
ejpam-5662	109	5	math	math	PROPN
ejpam-5662	109	6	,	,	PUNCT
ejpam-5662	109	7	18	18	NUM
ejpam-5662	109	8	(	(	PUNCT
ejpam-5662	109	9	2	2	NUM
ejpam-5662	109	10	)	)	PUNCT
ejpam-5662	109	11	(	(	PUNCT
ejpam-5662	109	12	2025	2025	NUM
ejpam-5662	109	13	)	)	PUNCT
ejpam-5662	109	14	,	,	PUNCT
ejpam-5662	109	15	5662	5662	NUM
ejpam-5662	109	16	5	5	NUM
ejpam-5662	109	17	of	of	ADP
ejpam-5662	109	18	36	36	NUM
ejpam-5662	109	19	pragmatic	pragmatic	ADJ
ejpam-5662	109	20	execution	execution	NOUN
ejpam-5662	109	21	:	:	PUNCT
ejpam-5662	110	1	1	1	X
ejpam-5662	110	2	.	.	PUNCT
ejpam-5662	111	1	the	the	DET
ejpam-5662	111	2	mdo	mdo	PROPN
ejpam-5662	111	3	is	be	AUX
ejpam-5662	111	4	frequently	frequently	ADV
ejpam-5662	111	5	applied	apply	VERB
ejpam-5662	111	6	in	in	ADP
ejpam-5662	111	7	systems	system	NOUN
ejpam-5662	111	8	that	that	PRON
ejpam-5662	111	9	demonstrate	demonstrate	VERB
ejpam-5662	111	10	both	both	CCONJ
ejpam-5662	111	11	parametric	parametric	ADJ
ejpam-5662	111	12	and	and	CCONJ
ejpam-5662	111	13	nonlinear	nonlinear	ADJ
ejpam-5662	111	14	characteristics	characteristic	NOUN
ejpam-5662	111	15	.	.	PUNCT
ejpam-5662	112	1	this	this	PRON
ejpam-5662	112	2	necessitates	necessitate	VERB
ejpam-5662	112	3	the	the	DET
ejpam-5662	112	4	development	development	NOUN
ejpam-5662	112	5	of	of	ADP
ejpam-5662	112	6	an	an	DET
ejpam-5662	112	7	oscillator	oscillator	NOUN
ejpam-5662	112	8	that	that	PRON
ejpam-5662	112	9	is	be	AUX
ejpam-5662	112	10	:	:	PUNCT
ejpam-5662	112	11	i.	i.	NOUN
ejpam-5662	112	12	they	they	PRON
ejpam-5662	112	13	are	be	AUX
ejpam-5662	112	14	influenced	influence	VERB
ejpam-5662	112	15	by	by	ADP
ejpam-5662	112	16	periodic	periodic	ADJ
ejpam-5662	112	17	or	or	CCONJ
ejpam-5662	112	18	parametric	parametric	ADJ
ejpam-5662	112	19	forcing	forcing	NOUN
ejpam-5662	112	20	,	,	PUNCT
ejpam-5662	112	21	resulting	result	VERB
ejpam-5662	112	22	in	in	ADP
ejpam-5662	112	23	mathieu	mathieu	PROPN
ejpam-5662	112	24	-	-	PUNCT
ejpam-5662	112	25	like	like	ADJ
ejpam-5662	112	26	behavior	behavior	NOUN
ejpam-5662	112	27	.	.	PUNCT
ejpam-5662	113	1	ii	ii	PROPN
ejpam-5662	113	2	.	.	PUNCT
ejpam-5662	114	1	the	the	DET
ejpam-5662	114	2	restoring	restore	VERB
ejpam-5662	114	3	force	force	NOUN
ejpam-5662	114	4	incorporates	incorporate	VERB
ejpam-5662	114	5	nonlinear	nonlinear	ADJ
ejpam-5662	114	6	components	component	NOUN
ejpam-5662	114	7	,	,	PUNCT
ejpam-5662	114	8	reflecting	reflect	VERB
ejpam-5662	114	9	real	real	ADJ
ejpam-5662	114	10	-	-	PUNCT
ejpam-5662	114	11	world	world	NOUN
ejpam-5662	114	12	systems	system	NOUN
ejpam-5662	114	13	where	where	SCONJ
ejpam-5662	114	14	higher	high	ADJ
ejpam-5662	114	15	-	-	PUNCT
ejpam-5662	114	16	order	order	NOUN
ejpam-5662	114	17	effects	effect	NOUN
ejpam-5662	114	18	gain	gain	VERB
ejpam-5662	114	19	prominence	prominence	NOUN
ejpam-5662	114	20	.	.	PUNCT
ejpam-5662	115	1	2	2	X
ejpam-5662	115	2	.	.	X
ejpam-5662	115	3	the	the	DET
ejpam-5662	115	4	restoring	restore	VERB
ejpam-5662	115	5	force	force	NOUN
ejpam-5662	115	6	of	of	ADP
ejpam-5662	115	7	the	the	DET
ejpam-5662	115	8	oscillator	oscillator	NOUN
ejpam-5662	115	9	is	be	AUX
ejpam-5662	115	10	not	not	PART
ejpam-5662	115	11	proportional	proportional	ADJ
ejpam-5662	115	12	to	to	ADP
ejpam-5662	115	13	displacement	displacement	NOUN
ejpam-5662	115	14	and	and	CCONJ
ejpam-5662	115	15	includes	include	VERB
ejpam-5662	115	16	nonlinear	nonlinear	ADJ
ejpam-5662	115	17	components	component	NOUN
ejpam-5662	115	18	.	.	PUNCT
ejpam-5662	116	1	this	this	PRON
ejpam-5662	116	2	leads	lead	VERB
ejpam-5662	116	3	to	to	ADP
ejpam-5662	116	4	phenomena	phenomena	NOUN
ejpam-5662	116	5	such	such	ADJ
ejpam-5662	116	6	as	as	ADP
ejpam-5662	116	7	bi	bi	NOUN
ejpam-5662	116	8	-	-	NOUN
ejpam-5662	116	9	stability	stability	NOUN
ejpam-5662	116	10	or	or	CCONJ
ejpam-5662	116	11	multistability	multistability	NOUN
ejpam-5662	116	12	when	when	SCONJ
ejpam-5662	116	13	the	the	DET
ejpam-5662	116	14	system	system	NOUN
ejpam-5662	116	15	can	can	AUX
ejpam-5662	116	16	exhibit	exhibit	VERB
ejpam-5662	116	17	several	several	ADJ
ejpam-5662	116	18	stable	stable	ADJ
ejpam-5662	116	19	and	and	CCONJ
ejpam-5662	116	20	unstable	unstable	ADJ
ejpam-5662	116	21	states	state	NOUN
ejpam-5662	116	22	.	.	PUNCT
ejpam-5662	117	1	3	3	X
ejpam-5662	117	2	.	.	PUNCT
ejpam-5662	117	3	to	to	PART
ejpam-5662	117	4	emulate	emulate	VERB
ejpam-5662	117	5	the	the	DET
ejpam-5662	117	6	parametric	parametric	ADJ
ejpam-5662	117	7	characteristic	characteristic	NOUN
ejpam-5662	117	8	,	,	PUNCT
ejpam-5662	117	9	the	the	DET
ejpam-5662	117	10	system	system	NOUN
ejpam-5662	117	11	is	be	AUX
ejpam-5662	117	12	generally	generally	ADV
ejpam-5662	117	13	exposed	expose	VERB
ejpam-5662	117	14	to	to	ADP
ejpam-5662	117	15	periodic	periodic	ADJ
ejpam-5662	117	16	or	or	CCONJ
ejpam-5662	117	17	time	time	NOUN
ejpam-5662	117	18	-	-	PUNCT
ejpam-5662	117	19	dependent	dependent	ADJ
ejpam-5662	117	20	forcing	forcing	NOUN
ejpam-5662	117	21	,	,	PUNCT
ejpam-5662	117	22	frequently	frequently	ADV
ejpam-5662	117	23	in	in	ADP
ejpam-5662	117	24	contexts	context	NOUN
ejpam-5662	117	25	such	such	ADJ
ejpam-5662	117	26	as	as	ADP
ejpam-5662	117	27	mechanical	mechanical	ADJ
ejpam-5662	117	28	vibrations	vibration	NOUN
ejpam-5662	117	29	or	or	CCONJ
ejpam-5662	117	30	electrical	electrical	ADJ
ejpam-5662	117	31	circuits	circuit	NOUN
ejpam-5662	117	32	.	.	PUNCT
ejpam-5662	118	1	this	this	DET
ejpam-5662	118	2	forcing	forcing	NOUN
ejpam-5662	118	3	interacts	interact	VERB
ejpam-5662	118	4	with	with	ADP
ejpam-5662	118	5	the	the	DET
ejpam-5662	118	6	nonlinear	nonlinear	ADJ
ejpam-5662	118	7	terms	term	NOUN
ejpam-5662	118	8	to	to	PART
ejpam-5662	118	9	generate	generate	VERB
ejpam-5662	118	10	intricate	intricate	ADJ
ejpam-5662	118	11	dynamical	dynamical	ADJ
ejpam-5662	118	12	phenomena	phenomenon	NOUN
ejpam-5662	118	13	such	such	ADJ
ejpam-5662	118	14	as	as	ADP
ejpam-5662	118	15	chaotic	chaotic	ADJ
ejpam-5662	118	16	motion	motion	NOUN
ejpam-5662	118	17	,	,	PUNCT
ejpam-5662	118	18	bifurcations	bifurcation	NOUN
ejpam-5662	118	19	,	,	PUNCT
ejpam-5662	118	20	and	and	CCONJ
ejpam-5662	118	21	resonance	resonance	NOUN
ejpam-5662	118	22	.	.	PUNCT
ejpam-5662	119	1	4	4	NUM
ejpam-5662	119	2	.	.	X
ejpam-5662	119	3	due	due	ADP
ejpam-5662	119	4	to	to	ADP
ejpam-5662	119	5	the	the	DET
ejpam-5662	119	6	complexity	complexity	NOUN
ejpam-5662	119	7	of	of	ADP
ejpam-5662	119	8	the	the	DET
ejpam-5662	119	9	mdo	mdo	PROPN
ejpam-5662	119	10	,	,	PUNCT
ejpam-5662	119	11	numerical	numerical	ADJ
ejpam-5662	119	12	simulations	simulation	NOUN
ejpam-5662	119	13	are	be	AUX
ejpam-5662	119	14	frequently	frequently	ADV
ejpam-5662	119	15	necessary	necessary	ADJ
ejpam-5662	119	16	to	to	PART
ejpam-5662	119	17	evaluate	evaluate	VERB
ejpam-5662	119	18	its	its	PRON
ejpam-5662	119	19	behavior	behavior	NOUN
ejpam-5662	119	20	.	.	PUNCT
ejpam-5662	120	1	this	this	PRON
ejpam-5662	120	2	entails	entail	VERB
ejpam-5662	120	3	integrating	integrate	VERB
ejpam-5662	120	4	the	the	DET
ejpam-5662	120	5	equations	equation	NOUN
ejpam-5662	120	6	of	of	ADP
ejpam-5662	120	7	motion	motion	NOUN
ejpam-5662	120	8	,	,	PUNCT
ejpam-5662	120	9	frequently	frequently	ADV
ejpam-5662	120	10	employing	employ	VERB
ejpam-5662	120	11	techniques	technique	NOUN
ejpam-5662	120	12	such	such	ADJ
ejpam-5662	120	13	as	as	ADP
ejpam-5662	120	14	the	the	DET
ejpam-5662	120	15	runge	runge	NOUN
ejpam-5662	120	16	-	-	PUNCT
ejpam-5662	120	17	kutta	kutta	NOUN
ejpam-5662	120	18	method	method	NOUN
ejpam-5662	120	19	,	,	PUNCT
ejpam-5662	120	20	to	to	PART
ejpam-5662	120	21	analyze	analyze	VERB
ejpam-5662	120	22	the	the	DET
ejpam-5662	120	23	system	system	NOUN
ejpam-5662	120	24	’s	’s	PART
ejpam-5662	120	25	response	response	NOUN
ejpam-5662	120	26	to	to	ADP
ejpam-5662	120	27	various	various	ADJ
ejpam-5662	120	28	beginning	beginning	ADJ
ejpam-5662	120	29	circumstances	circumstance	NOUN
ejpam-5662	120	30	,	,	PUNCT
ejpam-5662	120	31	forcing	force	VERB
ejpam-5662	120	32	frequencies	frequency	NOUN
ejpam-5662	120	33	,	,	PUNCT
ejpam-5662	120	34	and	and	CCONJ
ejpam-5662	120	35	amplitudes	amplitude	NOUN
ejpam-5662	120	36	.	.	PUNCT
ejpam-5662	121	1	physical	physical	ADJ
ejpam-5662	121	2	applications	application	NOUN
ejpam-5662	121	3	:	:	PUNCT
ejpam-5662	122	1	1	1	X
ejpam-5662	122	2	.	.	X
ejpam-5662	123	1	this	this	DET
ejpam-5662	123	2	model	model	NOUN
ejpam-5662	123	3	describes	describe	VERB
ejpam-5662	123	4	the	the	DET
ejpam-5662	123	5	motion	motion	NOUN
ejpam-5662	123	6	of	of	ADP
ejpam-5662	123	7	beams	beam	NOUN
ejpam-5662	123	8	or	or	CCONJ
ejpam-5662	123	9	plates	plate	NOUN
ejpam-5662	123	10	subjected	subject	VERB
ejpam-5662	123	11	to	to	ADP
ejpam-5662	123	12	periodic	periodic	ADJ
ejpam-5662	123	13	external	external	ADJ
ejpam-5662	123	14	loads	load	NOUN
ejpam-5662	123	15	.	.	PUNCT
ejpam-5662	124	1	in	in	ADP
ejpam-5662	124	2	these	these	DET
ejpam-5662	124	3	instances	instance	NOUN
ejpam-5662	124	4	,	,	PUNCT
ejpam-5662	124	5	the	the	DET
ejpam-5662	124	6	system	system	NOUN
ejpam-5662	124	7	demonstrates	demonstrate	VERB
ejpam-5662	124	8	nonlinear	nonlinear	ADJ
ejpam-5662	124	9	vibrations	vibration	NOUN
ejpam-5662	124	10	resulting	result	VERB
ejpam-5662	124	11	from	from	ADP
ejpam-5662	124	12	both	both	CCONJ
ejpam-5662	124	13	parametric	parametric	ADJ
ejpam-5662	124	14	excitation	excitation	NOUN
ejpam-5662	124	15	and	and	CCONJ
ejpam-5662	124	16	inherent	inherent	ADJ
ejpam-5662	124	17	material	material	NOUN
ejpam-5662	124	18	nonlinearities	nonlinearitie	NOUN
ejpam-5662	124	19	.	.	PUNCT
ejpam-5662	125	1	2	2	X
ejpam-5662	125	2	.	.	X
ejpam-5662	125	3	the	the	DET
ejpam-5662	125	4	oscillator	oscillator	NOUN
ejpam-5662	125	5	is	be	AUX
ejpam-5662	125	6	applicable	applicable	ADJ
ejpam-5662	125	7	to	to	ADP
ejpam-5662	125	8	specific	specific	ADJ
ejpam-5662	125	9	electromechanical	electromechanical	ADJ
ejpam-5662	125	10	devices	device	NOUN
ejpam-5662	125	11	,	,	PUNCT
ejpam-5662	125	12	including	include	VERB
ejpam-5662	125	13	microelectromechanical	microelectromechanical	ADJ
ejpam-5662	125	14	systems	system	NOUN
ejpam-5662	125	15	and	and	CCONJ
ejpam-5662	125	16	nanomechanical	nanomechanical	ADJ
ejpam-5662	125	17	systems	system	NOUN
ejpam-5662	125	18	,	,	PUNCT
ejpam-5662	125	19	where	where	SCONJ
ejpam-5662	125	20	nonlinearities	nonlinearitie	NOUN
ejpam-5662	125	21	develop	develop	VERB
ejpam-5662	125	22	from	from	ADP
ejpam-5662	125	23	geometric	geometric	ADJ
ejpam-5662	125	24	limitations	limitation	NOUN
ejpam-5662	125	25	or	or	CCONJ
ejpam-5662	125	26	material	material	NOUN
ejpam-5662	125	27	characteristics	characteristic	NOUN
ejpam-5662	125	28	.	.	PUNCT
ejpam-5662	126	1	for	for	ADP
ejpam-5662	126	2	instance	instance	NOUN
ejpam-5662	126	3	,	,	PUNCT
ejpam-5662	126	4	it	it	PRON
ejpam-5662	126	5	can	can	AUX
ejpam-5662	126	6	delineate	delineate	VERB
ejpam-5662	126	7	the	the	DET
ejpam-5662	126	8	movement	movement	NOUN
ejpam-5662	126	9	of	of	ADP
ejpam-5662	126	10	a	a	DET
ejpam-5662	126	11	micro	micro	NOUN
ejpam-5662	126	12	-	-	ADJ
ejpam-5662	126	13	beam	beam	NOUN
ejpam-5662	126	14	subjected	subject	VERB
ejpam-5662	126	15	to	to	ADP
ejpam-5662	126	16	electrostatic	electrostatic	ADJ
ejpam-5662	126	17	actuation	actuation	NOUN
ejpam-5662	126	18	.	.	PUNCT
ejpam-5662	127	1	3	3	X
ejpam-5662	127	2	.	.	X
ejpam-5662	127	3	in	in	ADP
ejpam-5662	127	4	nonlinear	nonlinear	ADJ
ejpam-5662	127	5	optics	optic	NOUN
ejpam-5662	127	6	,	,	PUNCT
ejpam-5662	127	7	the	the	DET
ejpam-5662	127	8	mdo	mdo	PROPN
ejpam-5662	127	9	can	can	AUX
ejpam-5662	127	10	simulate	simulate	VERB
ejpam-5662	127	11	the	the	DET
ejpam-5662	127	12	dynamics	dynamic	NOUN
ejpam-5662	127	13	of	of	ADP
ejpam-5662	127	14	light	light	ADJ
ejpam-5662	127	15	propagation	propagation	NOUN
ejpam-5662	127	16	across	across	ADP
ejpam-5662	127	17	nonlinear	nonlinear	ADJ
ejpam-5662	127	18	media	medium	NOUN
ejpam-5662	127	19	,	,	PUNCT
ejpam-5662	127	20	whereas	whereas	SCONJ
ejpam-5662	127	21	the	the	DET
ejpam-5662	127	22	parametric	parametric	ADJ
ejpam-5662	127	23	driving	driving	NOUN
ejpam-5662	127	24	may	may	AUX
ejpam-5662	127	25	be	be	AUX
ejpam-5662	127	26	from	from	ADP
ejpam-5662	127	27	medium	medium	ADJ
ejpam-5662	127	28	modulations	modulation	NOUN
ejpam-5662	127	29	or	or	CCONJ
ejpam-5662	127	30	external	external	ADJ
ejpam-5662	127	31	influences	influence	NOUN
ejpam-5662	127	32	such	such	ADJ
ejpam-5662	127	33	as	as	ADP
ejpam-5662	127	34	fluctuating	fluctuate	VERB
ejpam-5662	127	35	laser	laser	NOUN
ejpam-5662	127	36	intensities	intensity	NOUN
ejpam-5662	127	37	.	.	PUNCT
ejpam-5662	128	1	4	4	X
ejpam-5662	128	2	.	.	X
ejpam-5662	128	3	in	in	ADP
ejpam-5662	128	4	structural	structural	ADJ
ejpam-5662	128	5	dynamics	dynamic	NOUN
ejpam-5662	128	6	,	,	PUNCT
ejpam-5662	128	7	it	it	PRON
ejpam-5662	128	8	can	can	AUX
ejpam-5662	128	9	describe	describe	VERB
ejpam-5662	128	10	structures	structure	NOUN
ejpam-5662	128	11	or	or	CCONJ
ejpam-5662	128	12	bridges	bridge	NOUN
ejpam-5662	128	13	subjected	subject	VERB
ejpam-5662	128	14	to	to	ADP
ejpam-5662	128	15	timevarying	timevarying	NOUN
ejpam-5662	128	16	stresses	stress	NOUN
ejpam-5662	128	17	,	,	PUNCT
ejpam-5662	128	18	such	such	ADJ
ejpam-5662	128	19	as	as	ADP
ejpam-5662	128	20	wind	wind	NOUN
ejpam-5662	128	21	or	or	CCONJ
ejpam-5662	128	22	earthquakes	earthquake	NOUN
ejpam-5662	128	23	,	,	PUNCT
ejpam-5662	128	24	when	when	SCONJ
ejpam-5662	128	25	nonlinear	nonlinear	ADJ
ejpam-5662	128	26	behavior	behavior	NOUN
ejpam-5662	128	27	significantly	significantly	ADV
ejpam-5662	128	28	influences	influence	VERB
ejpam-5662	128	29	the	the	DET
ejpam-5662	128	30	system	system	NOUN
ejpam-5662	128	31	’s	’s	PART
ejpam-5662	128	32	reaction	reaction	NOUN
ejpam-5662	128	33	to	to	ADP
ejpam-5662	128	34	external	external	ADJ
ejpam-5662	128	35	excitations	excitation	NOUN
ejpam-5662	128	36	.	.	PUNCT
ejpam-5662	129	1	5	5	X
ejpam-5662	129	2	.	.	X
ejpam-5662	129	3	certain	certain	ADJ
ejpam-5662	129	4	biological	biological	ADJ
ejpam-5662	129	5	systems	system	NOUN
ejpam-5662	129	6	,	,	PUNCT
ejpam-5662	129	7	such	such	ADJ
ejpam-5662	129	8	as	as	ADP
ejpam-5662	129	9	brain	brain	NOUN
ejpam-5662	129	10	oscillations	oscillation	NOUN
ejpam-5662	129	11	or	or	CCONJ
ejpam-5662	129	12	rhythmic	rhythmic	ADJ
ejpam-5662	129	13	physiological	physiological	ADJ
ejpam-5662	129	14	processes	process	NOUN
ejpam-5662	129	15	,	,	PUNCT
ejpam-5662	129	16	can	can	AUX
ejpam-5662	129	17	be	be	AUX
ejpam-5662	129	18	represented	represent	VERB
ejpam-5662	129	19	by	by	ADP
ejpam-5662	129	20	this	this	DET
ejpam-5662	129	21	type	type	NOUN
ejpam-5662	129	22	of	of	ADP
ejpam-5662	129	23	oscillator	oscillator	NOUN
ejpam-5662	129	24	when	when	SCONJ
ejpam-5662	129	25	they	they	PRON
ejpam-5662	129	26	display	display	VERB
ejpam-5662	129	27	nonlinear	nonlinear	ADJ
ejpam-5662	129	28	,	,	PUNCT
ejpam-5662	129	29	time	time	NOUN
ejpam-5662	129	30	-	-	PUNCT
ejpam-5662	129	31	dependent	dependent	ADJ
ejpam-5662	129	32	characteristics	characteristic	NOUN
ejpam-5662	129	33	.	.	PUNCT
ejpam-5662	130	1	a.	a.	PROPN
ejpam-5662	130	2	alanazy	alanazy	PROPN
ejpam-5662	130	3	,	,	PUNCT
ejpam-5662	130	4	g.	g.	PROPN
ejpam-5662	130	5	m.	m.	PROPN
ejpam-5662	130	6	moatimid	moatimid	PROPN
ejpam-5662	130	7	,	,	PUNCT
ejpam-5662	130	8	m.	m.	PROPN
ejpam-5662	130	9	a.	a.	PROPN
ejpam-5662	130	10	a.	a.	PROPN
ejpam-5662	130	11	mohamed	mohamed	PROPN
ejpam-5662	130	12	/	/	SYM
ejpam-5662	130	13	eur	eur	PROPN
ejpam-5662	130	14	.	.	PUNCT
ejpam-5662	131	1	j.	j.	PROPN
ejpam-5662	131	2	pure	pure	PROPN
ejpam-5662	131	3	appl	appl	PROPN
ejpam-5662	131	4	.	.	PROPN
ejpam-5662	131	5	math	math	PROPN
ejpam-5662	131	6	,	,	PUNCT
ejpam-5662	131	7	18	18	NUM
ejpam-5662	131	8	(	(	PUNCT
ejpam-5662	131	9	2	2	NUM
ejpam-5662	131	10	)	)	PUNCT
ejpam-5662	131	11	(	(	PUNCT
ejpam-5662	131	12	2025	2025	NUM
ejpam-5662	131	13	)	)	PUNCT
ejpam-5662	131	14	,	,	PUNCT
ejpam-5662	131	15	5662	5662	NUM
ejpam-5662	131	16	6	6	NUM
ejpam-5662	131	17	of	of	ADP
ejpam-5662	131	18	36	36	NUM
ejpam-5662	131	19	key	key	ADJ
ejpam-5662	131	20	phenomena	phenomenon	NOUN
ejpam-5662	131	21	:	:	PUNCT
ejpam-5662	132	1	1	1	X
ejpam-5662	132	2	.	.	PUNCT
ejpam-5662	133	1	the	the	DET
ejpam-5662	133	2	interplay	interplay	NOUN
ejpam-5662	133	3	of	of	ADP
ejpam-5662	133	4	parametric	parametric	ADJ
ejpam-5662	133	5	forcing	forcing	NOUN
ejpam-5662	133	6	and	and	CCONJ
ejpam-5662	133	7	nonlinearities	nonlinearitie	NOUN
ejpam-5662	133	8	can	can	AUX
ejpam-5662	133	9	lead	lead	VERB
ejpam-5662	133	10	the	the	DET
ejpam-5662	133	11	system	system	NOUN
ejpam-5662	133	12	to	to	PART
ejpam-5662	133	13	display	display	VERB
ejpam-5662	133	14	complex	complex	ADJ
ejpam-5662	133	15	dynamic	dynamic	ADJ
ejpam-5662	133	16	behavior	behavior	NOUN
ejpam-5662	133	17	,	,	PUNCT
ejpam-5662	133	18	including	include	VERB
ejpam-5662	133	19	bifurcations	bifurcation	NOUN
ejpam-5662	133	20	and	and	CCONJ
ejpam-5662	133	21	chaos	chaos	NOUN
ejpam-5662	133	22	.	.	PUNCT
ejpam-5662	134	1	2	2	X
ejpam-5662	134	2	.	.	X
ejpam-5662	134	3	the	the	DET
ejpam-5662	134	4	parametric	parametric	ADJ
ejpam-5662	134	5	driving	driving	NOUN
ejpam-5662	134	6	can	can	AUX
ejpam-5662	134	7	induce	induce	VERB
ejpam-5662	134	8	resonance	resonance	NOUN
ejpam-5662	134	9	at	at	ADP
ejpam-5662	134	10	particular	particular	ADJ
ejpam-5662	134	11	frequencies	frequency	NOUN
ejpam-5662	134	12	,	,	PUNCT
ejpam-5662	134	13	resulting	result	VERB
ejpam-5662	134	14	in	in	ADP
ejpam-5662	134	15	an	an	DET
ejpam-5662	134	16	amplified	amplify	VERB
ejpam-5662	134	17	system	system	NOUN
ejpam-5662	134	18	response	response	NOUN
ejpam-5662	134	19	,	,	PUNCT
ejpam-5662	134	20	as	as	ADV
ejpam-5662	134	21	well	well	ADV
ejpam-5662	134	22	as	as	ADP
ejpam-5662	134	23	sub	sub	ADJ
ejpam-5662	134	24	-	-	ADJ
ejpam-5662	134	25	harmonic	harmonic	ADJ
ejpam-5662	134	26	oscillations	oscillation	NOUN
ejpam-5662	134	27	,	,	PUNCT
ejpam-5662	134	28	when	when	SCONJ
ejpam-5662	134	29	the	the	DET
ejpam-5662	134	30	apparatus	apparatus	NOUN
ejpam-5662	134	31	fluctuates	fluctuate	VERB
ejpam-5662	134	32	at	at	ADP
ejpam-5662	134	33	a	a	DET
ejpam-5662	134	34	fraction	fraction	NOUN
ejpam-5662	134	35	of	of	ADP
ejpam-5662	134	36	the	the	DET
ejpam-5662	134	37	controlling	control	VERB
ejpam-5662	134	38	frequency	frequency	NOUN
ejpam-5662	134	39	.	.	PUNCT
ejpam-5662	135	1	recently	recently	ADV
ejpam-5662	135	2	,	,	PUNCT
ejpam-5662	135	3	barakat	barakat	PROPN
ejpam-5662	135	4	et	et	PROPN
ejpam-5662	135	5	al	al	PROPN
ejpam-5662	135	6	.	.	PUNCT
ejpam-5662	136	1	[	[	X
ejpam-5662	136	2	45	45	NUM
ejpam-5662	136	3	]	]	PUNCT
ejpam-5662	136	4	studied	study	VERB
ejpam-5662	136	5	a	a	DET
ejpam-5662	136	6	similar	similar	ADJ
ejpam-5662	136	7	problem	problem	NOUN
ejpam-5662	136	8	to	to	ADP
ejpam-5662	136	9	mdo	mdo	PROPN
ejpam-5662	136	10	in	in	ADP
ejpam-5662	136	11	the	the	DET
ejpam-5662	136	12	case	case	NOUN
ejpam-5662	136	13	of	of	ADP
ejpam-5662	136	14	cubic	cubic	ADJ
ejpam-5662	136	15	do	do	NOUN
ejpam-5662	136	16	.	.	PUNCT
ejpam-5662	137	1	in	in	ADP
ejpam-5662	137	2	their	their	PRON
ejpam-5662	137	3	work	work	NOUN
ejpam-5662	137	4	,	,	PUNCT
ejpam-5662	137	5	they	they	PRON
ejpam-5662	137	6	examined	examine	VERB
ejpam-5662	137	7	each	each	PRON
ejpam-5662	137	8	of	of	ADP
ejpam-5662	137	9	the	the	DET
ejpam-5662	137	10	stability	stability	NOUN
ejpam-5662	137	11	of	of	ADP
ejpam-5662	137	12	the	the	DET
ejpam-5662	137	13	trivial	trivial	ADJ
ejpam-5662	137	14	solution	solution	NOUN
ejpam-5662	137	15	-	-	PUNCT
ejpam-5662	137	16	perturbation	perturbation	NOUN
ejpam-5662	137	17	analysis	analysis	NOUN
ejpam-5662	137	18	of	of	ADP
ejpam-5662	137	19	the	the	DET
ejpam-5662	137	20	nonlinear	nonlinear	ADJ
ejpam-5662	137	21	system	system	NOUN
ejpam-5662	137	22	,	,	PUNCT
ejpam-5662	137	23	via	via	ADP
ejpam-5662	137	24	the	the	DET
ejpam-5662	137	25	multiple	multiple	ADJ
ejpam-5662	137	26	-	-	PUNCT
ejpam-5662	137	27	time	time	NOUN
ejpam-5662	137	28	scales	scale	NOUN
ejpam-5662	137	29	-	-	PUNCT
ejpam-5662	137	30	principle	principle	NOUN
ejpam-5662	137	31	parametric	parametric	ADJ
ejpam-5662	137	32	resonanceinternal	resonanceinternal	ADJ
ejpam-5662	137	33	resonance	resonance	NOUN
ejpam-5662	137	34	under	under	ADP
ejpam-5662	137	35	parametric	parametric	ADJ
ejpam-5662	137	36	excitation	excitation	NOUN
ejpam-5662	137	37	and	and	CCONJ
ejpam-5662	137	38	the	the	DET
ejpam-5662	137	39	stability	stability	NOUN
ejpam-5662	137	40	analysis	analysis	NOUN
ejpam-5662	137	41	-	-	PUNCT
ejpam-5662	137	42	combination	combination	NOUN
ejpam-5662	137	43	parametric	parametric	ADJ
ejpam-5662	137	44	resonances	resonance	NOUN
ejpam-5662	137	45	.	.	PUNCT
ejpam-5662	138	1	finally	finally	ADV
ejpam-5662	138	2	,	,	PUNCT
ejpam-5662	138	3	the	the	DET
ejpam-5662	138	4	non	non	ADJ
ejpam-5662	138	5	-	-	ADJ
ejpam-5662	138	6	resonant	resonant	ADJ
ejpam-5662	138	7	limit	limit	NOUN
ejpam-5662	138	8	cycles	cycle	NOUN
ejpam-5662	138	9	are	be	AUX
ejpam-5662	138	10	discussed	discuss	VERB
ejpam-5662	138	11	.	.	PUNCT
ejpam-5662	139	1	the	the	DET
ejpam-5662	139	2	npa	npa	NOUN
ejpam-5662	139	3	of	of	ADP
ejpam-5662	139	4	a	a	DET
ejpam-5662	139	5	coupled	couple	VERB
ejpam-5662	139	6	nonlinear	nonlinear	ADJ
ejpam-5662	139	7	oscillator	oscillator	NOUN
ejpam-5662	139	8	like	like	ADP
ejpam-5662	139	9	the	the	DET
ejpam-5662	139	10	mathieu	mathieu	PROPN
ejpam-5662	139	11	oscillator	oscillator	NOUN
ejpam-5662	139	12	is	be	AUX
ejpam-5662	139	13	included	include	VERB
ejpam-5662	139	14	in	in	ADP
ejpam-5662	139	15	this	this	DET
ejpam-5662	139	16	paper	paper	NOUN
ejpam-5662	139	17	,	,	PUNCT
ejpam-5662	139	18	which	which	PRON
ejpam-5662	139	19	builds	build	VERB
ejpam-5662	139	20	on	on	ADP
ejpam-5662	139	21	our	our	PRON
ejpam-5662	139	22	earlier	early	ADJ
ejpam-5662	139	23	work	work	NOUN
ejpam-5662	139	24	[	[	X
ejpam-5662	139	25	46	46	NUM
ejpam-5662	139	26	]	]	PUNCT
ejpam-5662	139	27	and	and	CCONJ
ejpam-5662	139	28	is	be	AUX
ejpam-5662	139	29	considered	consider	VERB
ejpam-5662	139	30	as	as	ADP
ejpam-5662	139	31	a	a	DET
ejpam-5662	139	32	new	new	ADJ
ejpam-5662	139	33	direction	direction	NOUN
ejpam-5662	139	34	in	in	ADP
ejpam-5662	139	35	the	the	DET
ejpam-5662	139	36	procedure	procedure	NOUN
ejpam-5662	139	37	of	of	ADP
ejpam-5662	139	38	the	the	DET
ejpam-5662	139	39	npa	npa	NOUN
ejpam-5662	139	40	.	.	PUNCT
ejpam-5662	140	1	therefore	therefore	ADV
ejpam-5662	140	2	,	,	PUNCT
ejpam-5662	140	3	two	two	NUM
ejpam-5662	140	4	coupled	couple	VERB
ejpam-5662	140	5	linear	linear	NOUN
ejpam-5662	140	6	odes	ode	NOUN
ejpam-5662	140	7	are	be	AUX
ejpam-5662	140	8	obtained	obtain	VERB
ejpam-5662	140	9	as	as	ADP
ejpam-5662	140	10	compared	compare	VERB
ejpam-5662	140	11	with	with	ADP
ejpam-5662	140	12	the	the	DET
ejpam-5662	140	13	nonlinear	nonlinear	ADJ
ejpam-5662	140	14	ones	one	NOUN
ejpam-5662	140	15	.	.	PUNCT
ejpam-5662	141	1	to	to	PART
ejpam-5662	141	2	crystalize	crystalize	VERB
ejpam-5662	141	3	the	the	DET
ejpam-5662	141	4	presentation	presentation	NOUN
ejpam-5662	141	5	of	of	ADP
ejpam-5662	141	6	the	the	DET
ejpam-5662	141	7	article	article	NOUN
ejpam-5662	141	8	,	,	PUNCT
ejpam-5662	141	9	the	the	DET
ejpam-5662	141	10	rest	rest	NOUN
ejpam-5662	141	11	of	of	ADP
ejpam-5662	141	12	the	the	DET
ejpam-5662	141	13	paper	paper	NOUN
ejpam-5662	141	14	is	be	AUX
ejpam-5662	141	15	organized	organize	VERB
ejpam-5662	141	16	as	as	SCONJ
ejpam-5662	141	17	follows	follow	VERB
ejpam-5662	141	18	:	:	PUNCT
ejpam-5662	141	19	a	a	DET
ejpam-5662	141	20	brief	brief	ADJ
ejpam-5662	141	21	description	description	NOUN
ejpam-5662	141	22	of	of	ADP
ejpam-5662	141	23	the	the	DET
ejpam-5662	141	24	npa	npa	NOUN
ejpam-5662	141	25	of	of	ADP
ejpam-5662	141	26	the	the	DET
ejpam-5662	141	27	coupled	couple	VERB
ejpam-5662	141	28	system	system	NOUN
ejpam-5662	141	29	is	be	AUX
ejpam-5662	141	30	presented	present	VERB
ejpam-5662	141	31	in	in	ADP
ejpam-5662	141	32	§	§	PROPN
ejpam-5662	141	33	2	2	NUM
ejpam-5662	141	34	.	.	PUNCT
ejpam-5662	142	1	the	the	DET
ejpam-5662	142	2	npa	npa	NOUN
ejpam-5662	142	3	of	of	ADP
ejpam-5662	142	4	the	the	DET
ejpam-5662	142	5	coupled	couple	VERB
ejpam-5662	142	6	system	system	NOUN
ejpam-5662	142	7	is	be	AUX
ejpam-5662	142	8	obtainable	obtainable	ADJ
ejpam-5662	142	9	in	in	ADP
ejpam-5662	142	10	§	§	PROPN
ejpam-5662	142	11	3	3	NUM
ejpam-5662	142	12	.	.	PUNCT
ejpam-5662	143	1	in	in	ADP
ejpam-5662	143	2	this	this	DET
ejpam-5662	143	3	section	section	NOUN
ejpam-5662	143	4	,	,	PUNCT
ejpam-5662	143	5	an	an	DET
ejpam-5662	143	6	excellent	excellent	NOUN
ejpam-5662	143	7	between	between	ADP
ejpam-5662	143	8	the	the	DET
ejpam-5662	143	9	nonlinear	nonlinear	NOUN
ejpam-5662	143	10	in	in	ADP
ejpam-5662	143	11	addition	addition	NOUN
ejpam-5662	143	12	to	to	ADP
ejpam-5662	143	13	the	the	DET
ejpam-5662	143	14	linear	linear	ADJ
ejpam-5662	143	15	odes	ode	NOUN
ejpam-5662	143	16	is	be	AUX
ejpam-5662	143	17	announced	announce	VERB
ejpam-5662	143	18	.	.	PUNCT
ejpam-5662	144	1	the	the	DET
ejpam-5662	144	2	damped	damped	ADJ
ejpam-5662	144	3	tdof	tdof	NOUN
ejpam-5662	144	4	of	of	ADP
ejpam-5662	144	5	the	the	DET
ejpam-5662	144	6	mdo	mdo	PROPN
ejpam-5662	144	7	configuration	configuration	NOUN
ejpam-5662	144	8	is	be	AUX
ejpam-5662	144	9	accessible	accessible	ADJ
ejpam-5662	144	10	in	in	ADP
ejpam-5662	144	11	§	§	PROPN
ejpam-5662	144	12	4	4	NUM
ejpam-5662	144	13	.	.	PUNCT
ejpam-5662	145	1	the	the	DET
ejpam-5662	145	2	un	un	PROPN
ejpam-5662	145	3	-	-	ADJ
ejpam-5662	145	4	damped	damped	ADJ
ejpam-5662	145	5	tdof	tdof	NOUN
ejpam-5662	145	6	of	of	ADP
ejpam-5662	145	7	the	the	DET
ejpam-5662	145	8	mdo	mdo	PROPN
ejpam-5662	145	9	configuration	configuration	NOUN
ejpam-5662	145	10	is	be	AUX
ejpam-5662	145	11	offered	offer	VERB
ejpam-5662	145	12	in	in	ADP
ejpam-5662	145	13	§	§	PROPN
ejpam-5662	145	14	5	5	NUM
ejpam-5662	145	15	.	.	PUNCT
ejpam-5662	146	1	the	the	DET
ejpam-5662	146	2	concluding	concluding	NOUN
ejpam-5662	146	3	remarks	remark	NOUN
ejpam-5662	146	4	are	be	AUX
ejpam-5662	146	5	summarized	summarize	VERB
ejpam-5662	146	6	in	in	ADP
ejpam-5662	146	7	§	§	PROPN
ejpam-5662	146	8	6	6	NUM
ejpam-5662	146	9	.	.	NOUN
ejpam-5662	146	10	2	2	NUM
ejpam-5662	146	11	.	.	X
ejpam-5662	146	12	a	a	DET
ejpam-5662	146	13	brief	brief	ADJ
ejpam-5662	146	14	description	description	NOUN
ejpam-5662	146	15	of	of	ADP
ejpam-5662	146	16	npa	npa	PROPN
ejpam-5662	146	17	in	in	ADP
ejpam-5662	146	18	the	the	DET
ejpam-5662	146	19	coupled	couple	VERB
ejpam-5662	146	20	system	system	NOUN
ejpam-5662	146	21	this	this	DET
ejpam-5662	146	22	section	section	NOUN
ejpam-5662	146	23	is	be	AUX
ejpam-5662	146	24	devoted	devote	VERB
ejpam-5662	146	25	to	to	ADP
ejpam-5662	146	26	developing	develop	VERB
ejpam-5662	146	27	the	the	DET
ejpam-5662	146	28	previous	previous	ADJ
ejpam-5662	146	29	procedure	procedure	NOUN
ejpam-5662	146	30	of	of	ADP
ejpam-5662	146	31	the	the	DET
ejpam-5662	146	32	npa	npa	NOUN
ejpam-5662	146	33	for	for	ADP
ejpam-5662	146	34	a	a	DET
ejpam-5662	146	35	single	single	ADJ
ejpam-5662	146	36	nonlinear	nonlinear	ADJ
ejpam-5662	146	37	ode	ode	NOUN
ejpam-5662	146	38	as	as	SCONJ
ejpam-5662	146	39	previously	previously	ADV
ejpam-5662	146	40	given	give	VERB
ejpam-5662	146	41	[	[	PUNCT
ejpam-5662	146	42	30	30	NUM
ejpam-5662	146	43	-	-	SYM
ejpam-5662	146	44	44	44	NUM
ejpam-5662	146	45	and	and	CCONJ
ejpam-5662	146	46	46	46	NUM
ejpam-5662	146	47	]	]	PUNCT
ejpam-5662	146	48	considering	consider	VERB
ejpam-5662	146	49	the	the	DET
ejpam-5662	146	50	coupled	couple	VERB
ejpam-5662	146	51	nonlinear	nonlinear	NOUN
ejpam-5662	146	52	odes	ode	NOUN
ejpam-5662	146	53	.	.	PUNCT
ejpam-5662	147	1	simply	simply	ADV
ejpam-5662	147	2	,	,	PUNCT
ejpam-5662	147	3	this	this	DET
ejpam-5662	147	4	coupled	couple	VERB
ejpam-5662	147	5	system	system	NOUN
ejpam-5662	147	6	may	may	AUX
ejpam-5662	147	7	be	be	AUX
ejpam-5662	147	8	written	write	VERB
ejpam-5662	147	9	as	as	SCONJ
ejpam-5662	147	10	follows	follow	VERB
ejpam-5662	147	11	:	:	PUNCT
ejpam-5662	147	12	ẍ+	ẍ+	PROPN
ejpam-5662	147	13	f1(x	f1(x	PROPN
ejpam-5662	147	14	,	,	PUNCT
ejpam-5662	147	15	ẋ	ẋ	PROPN
ejpam-5662	147	16	,	,	PUNCT
ejpam-5662	147	17	ẍ	ẍ	PROPN
ejpam-5662	147	18	,	,	PUNCT
ejpam-5662	147	19	y	y	PROPN
ejpam-5662	147	20	,	,	PUNCT
ejpam-5662	147	21	ẏ	ẏ	PROPN
ejpam-5662	147	22	,	,	PUNCT
ejpam-5662	147	23	ÿ	ÿ	PROPN
ejpam-5662	147	24	)	)	PUNCT
ejpam-5662	147	25	+	+	SYM
ejpam-5662	148	1	f2(x	f2(x	PROPN
ejpam-5662	148	2	,	,	PUNCT
ejpam-5662	148	3	ẋ	ẋ	PROPN
ejpam-5662	148	4	,	,	PUNCT
ejpam-5662	148	5	ẍ	ẍ	PROPN
ejpam-5662	148	6	,	,	PUNCT
ejpam-5662	148	7	y	y	PROPN
ejpam-5662	148	8	,	,	PUNCT
ejpam-5662	148	9	ẏ	ẏ	PROPN
ejpam-5662	148	10	,	,	PUNCT
ejpam-5662	148	11	ÿ	ÿ	ADJ
ejpam-5662	148	12	)	)	PUNCT
ejpam-5662	148	13	=	=	SYM
ejpam-5662	148	14	f3(x	f3(x	PROPN
ejpam-5662	148	15	,	,	PUNCT
ejpam-5662	148	16	ẋ	ẋ	PROPN
ejpam-5662	148	17	,	,	PUNCT
ejpam-5662	148	18	ẍ	ẍ	PROPN
ejpam-5662	148	19	,	,	PUNCT
ejpam-5662	148	20	y	y	PROPN
ejpam-5662	148	21	,	,	PUNCT
ejpam-5662	148	22	ẏ	ẏ	PROPN
ejpam-5662	148	23	,	,	PUNCT
ejpam-5662	148	24	ÿ	ÿ	PROPN
ejpam-5662	148	25	)	)	PUNCT
ejpam-5662	148	26	,	,	PUNCT
ejpam-5662	148	27	(	(	PUNCT
ejpam-5662	148	28	1	1	X
ejpam-5662	148	29	)	)	PUNCT
ejpam-5662	148	30	and	and	CCONJ
ejpam-5662	148	31	ÿ	ÿ	PROPN
ejpam-5662	148	32	+	+	PROPN
ejpam-5662	148	33	h1(y	h1(y	PROPN
ejpam-5662	148	34	,	,	PUNCT
ejpam-5662	148	35	ẏ	ẏ	PROPN
ejpam-5662	148	36	,	,	PUNCT
ejpam-5662	148	37	ÿ	ÿ	PROPN
ejpam-5662	148	38	,	,	PUNCT
ejpam-5662	148	39	x	x	X
ejpam-5662	148	40	,	,	PUNCT
ejpam-5662	148	41	ẋ	ẋ	PROPN
ejpam-5662	148	42	,	,	PUNCT
ejpam-5662	148	43	ẍ	ẍ	X
ejpam-5662	148	44	)	)	PUNCT
ejpam-5662	149	1	+	+	CCONJ
ejpam-5662	150	1	h2(y	h2(y	PROPN
ejpam-5662	150	2	,	,	PUNCT
ejpam-5662	150	3	ẏ	ẏ	NOUN
ejpam-5662	150	4	,	,	PUNCT
ejpam-5662	150	5	ÿ	ÿ	PROPN
ejpam-5662	150	6	,	,	PUNCT
ejpam-5662	150	7	x	x	X
ejpam-5662	150	8	,	,	PUNCT
ejpam-5662	150	9	ẋ	ẋ	PROPN
ejpam-5662	150	10	,	,	PUNCT
ejpam-5662	150	11	ẍ	ẍ	X
ejpam-5662	150	12	)	)	PUNCT
ejpam-5662	150	13	=	=	SYM
ejpam-5662	151	1	h3(y	h3(y	PROPN
ejpam-5662	151	2	,	,	PUNCT
ejpam-5662	151	3	ẏ	ẏ	NOUN
ejpam-5662	151	4	,	,	PUNCT
ejpam-5662	151	5	ÿ	ÿ	PROPN
ejpam-5662	151	6	,	,	PUNCT
ejpam-5662	151	7	x	x	X
ejpam-5662	151	8	,	,	PUNCT
ejpam-5662	151	9	ẋ	ẋ	PROPN
ejpam-5662	151	10	,	,	PUNCT
ejpam-5662	151	11	ẍ	ẍ	PROPN
ejpam-5662	151	12	)	)	PUNCT
ejpam-5662	151	13	,	,	PUNCT
ejpam-5662	151	14	(	(	PUNCT
ejpam-5662	151	15	2	2	X
ejpam-5662	151	16	)	)	PUNCT
ejpam-5662	151	17	where	where	SCONJ
ejpam-5662	151	18	f1	f1	NOUN
ejpam-5662	151	19	as	as	ADV
ejpam-5662	151	20	well	well	ADV
ejpam-5662	151	21	as	as	ADP
ejpam-5662	151	22	h1represent	h1represent	ADJ
ejpam-5662	151	23	odd	odd	ADJ
ejpam-5662	151	24	functions	function	NOUN
ejpam-5662	151	25	that	that	PRON
ejpam-5662	151	26	relate	relate	VERB
ejpam-5662	151	27	to	to	ADP
ejpam-5662	151	28	the	the	DET
ejpam-5662	151	29	damping	damp	VERB
ejpam-5662	151	30	forces	force	NOUN
ejpam-5662	151	31	,	,	PUNCT
ejpam-5662	151	32	f2	f2	PROPN
ejpam-5662	151	33	and	and	CCONJ
ejpam-5662	151	34	h2	h2	NOUN
ejpam-5662	151	35	refer	refer	VERB
ejpam-5662	151	36	to	to	ADP
ejpam-5662	151	37	some	some	DET
ejpam-5662	151	38	other	other	ADJ
ejpam-5662	151	39	odd	odd	ADJ
ejpam-5662	151	40	functions	function	NOUN
ejpam-5662	151	41	.	.	PUNCT
ejpam-5662	152	1	away	away	ADV
ejpam-5662	152	2	from	from	ADP
ejpam-5662	152	3	the	the	DET
ejpam-5662	152	4	damping	damp	VERB
ejpam-5662	152	5	forces	force	NOUN
ejpam-5662	152	6	and	and	CCONJ
ejpam-5662	152	7	the	the	DET
ejpam-5662	152	8	restoring	restore	VERB
ejpam-5662	152	9	forces	force	NOUN
ejpam-5662	152	10	,	,	PUNCT
ejpam-5662	152	11	the	the	DET
ejpam-5662	152	12	functions	function	NOUN
ejpam-5662	152	13	f3	f3	VERB
ejpam-5662	152	14	and	and	CCONJ
ejpam-5662	152	15	h3	h3	NOUN
ejpam-5662	152	16	signify	signify	VERB
ejpam-5662	152	17	even	even	ADV
ejpam-5662	152	18	functions	function	NOUN
ejpam-5662	152	19	.	.	PUNCT
ejpam-5662	153	1	as	as	ADV
ejpam-5662	153	2	well	well	ADV
ejpam-5662	153	3	from	from	ADP
ejpam-5662	153	4	the	the	DET
ejpam-5662	153	5	perturbation	perturbation	NOUN
ejpam-5662	153	6	approaches	approach	NOUN
ejpam-5662	153	7	[	[	X
ejpam-5662	153	8	7	7	NUM
ejpam-5662	153	9	,	,	PUNCT
ejpam-5662	153	10	12	12	NUM
ejpam-5662	153	11	]	]	PUNCT
ejpam-5662	153	12	;	;	PUNCT
ejpam-5662	153	13	the	the	DET
ejpam-5662	153	14	odd	odd	ADJ
ejpam-5662	153	15	functions	function	NOUN
ejpam-5662	153	16	produce	produce	VERB
ejpam-5662	153	17	secular	secular	ADJ
ejpam-5662	153	18	terms	term	NOUN
ejpam-5662	153	19	.	.	PUNCT
ejpam-5662	154	1	in	in	ADP
ejpam-5662	154	2	contrast	contrast	NOUN
ejpam-5662	154	3	,	,	PUNCT
ejpam-5662	154	4	the	the	DET
ejpam-5662	154	5	even	even	ADJ
ejpam-5662	154	6	functions	function	NOUN
ejpam-5662	154	7	do	do	AUX
ejpam-5662	154	8	not	not	PART
ejpam-5662	154	9	yield	yield	VERB
ejpam-5662	154	10	any	any	DET
ejpam-5662	154	11	secular	secular	ADJ
ejpam-5662	154	12	terms	term	NOUN
ejpam-5662	154	13	.	.	PUNCT
ejpam-5662	155	1	for	for	ADP
ejpam-5662	155	2	straightforwardness	straightforwardness	NOUN
ejpam-5662	155	3	,	,	PUNCT
ejpam-5662	155	4	the	the	DET
ejpam-5662	155	5	given	give	VERB
ejpam-5662	155	6	procedure	procedure	NOUN
ejpam-5662	155	7	is	be	AUX
ejpam-5662	155	8	not	not	PART
ejpam-5662	155	9	greatly	greatly	ADV
ejpam-5662	155	10	different	different	ADJ
ejpam-5662	155	11	from	from	ADP
ejpam-5662	155	12	the	the	DET
ejpam-5662	155	13	case	case	NOUN
ejpam-5662	155	14	of	of	ADP
ejpam-5662	155	15	single	single	ADJ
ejpam-5662	155	16	linear	linear	ADJ
ejpam-5662	155	17	ode	ode	PROPN
ejpam-5662	155	18	.	.	PUNCT
ejpam-5662	156	1	as	as	SCONJ
ejpam-5662	156	2	previously	previously	ADV
ejpam-5662	156	3	revealed	reveal	VERB
ejpam-5662	156	4	,	,	PUNCT
ejpam-5662	156	5	the	the	DET
ejpam-5662	156	6	aim	aim	NOUN
ejpam-5662	156	7	is	be	AUX
ejpam-5662	156	8	to	to	PART
ejpam-5662	156	9	transform	transform	VERB
ejpam-5662	156	10	the	the	DET
ejpam-5662	156	11	coupled	couple	VERB
ejpam-5662	156	12	nonlinear	nonlinear	PROPN
ejpam-5662	156	13	eqs	eqs	PROPN
ejpam-5662	156	14	.	.	PUNCT
ejpam-5662	157	1	(	(	PUNCT
ejpam-5662	157	2	1	1	X
ejpam-5662	157	3	)	)	PUNCT
ejpam-5662	157	4	and	and	CCONJ
ejpam-5662	157	5	(	(	PUNCT
ejpam-5662	157	6	2	2	X
ejpam-5662	157	7	)	)	PUNCT
ejpam-5662	157	8	to	to	ADP
ejpam-5662	157	9	another	another	DET
ejpam-5662	157	10	equivalent	equivalent	ADJ
ejpam-5662	157	11	linear	linear	ADJ
ejpam-5662	157	12	equation	equation	NOUN
ejpam-5662	157	13	in	in	ADP
ejpam-5662	157	14	the	the	DET
ejpam-5662	157	15	form	form	NOUN
ejpam-5662	157	16	of	of	ADP
ejpam-5662	157	17	the	the	DET
ejpam-5662	157	18	simple	simple	ADJ
ejpam-5662	157	19	harmonic	harmonic	ADJ
ejpam-5662	157	20	motion	motion	NOUN
ejpam-5662	157	21	.	.	PUNCT
ejpam-5662	158	1	for	for	ADP
ejpam-5662	158	2	this	this	DET
ejpam-5662	158	3	purpose	purpose	NOUN
ejpam-5662	158	4	,	,	PUNCT
ejpam-5662	158	5	consider	consider	VERB
ejpam-5662	158	6	two	two	NUM
ejpam-5662	158	7	guessing	guess	VERB
ejpam-5662	158	8	(	(	PUNCT
ejpam-5662	158	9	trial	trial	NOUN
ejpam-5662	158	10	)	)	PUNCT
ejpam-5662	158	11	solutions	solution	NOUN
ejpam-5662	158	12	of	of	ADP
ejpam-5662	158	13	the	the	DET
ejpam-5662	158	14	given	give	VERB
ejpam-5662	158	15	nonlinear	nonlinear	ADJ
ejpam-5662	158	16	odes	ode	NOUN
ejpam-5662	158	17	that	that	PRON
ejpam-5662	158	18	are	be	AUX
ejpam-5662	158	19	given	give	VERB
ejpam-5662	158	20	in	in	ADP
ejpam-5662	158	21	eqs	eqs	PROPN
ejpam-5662	158	22	.	.	PUNCT
ejpam-5662	159	1	(	(	PUNCT
ejpam-5662	159	2	1	1	X
ejpam-5662	159	3	)	)	PUNCT
ejpam-5662	159	4	and	and	CCONJ
ejpam-5662	159	5	(	(	PUNCT
ejpam-5662	159	6	2	2	X
ejpam-5662	159	7	)	)	PUNCT
ejpam-5662	159	8	as	as	SCONJ
ejpam-5662	159	9	follows	follow	VERB
ejpam-5662	159	10	:	:	PUNCT
ejpam-5662	159	11	a.	a.	NOUN
ejpam-5662	159	12	alanazy	alanazy	NOUN
ejpam-5662	159	13	,	,	PUNCT
ejpam-5662	159	14	g.	g.	PROPN
ejpam-5662	159	15	m.	m.	PROPN
ejpam-5662	159	16	moatimid	moatimid	PROPN
ejpam-5662	159	17	,	,	PUNCT
ejpam-5662	159	18	m.	m.	PROPN
ejpam-5662	159	19	a.	a.	PROPN
ejpam-5662	159	20	a.	a.	PROPN
ejpam-5662	159	21	mohamed	mohamed	PROPN
ejpam-5662	159	22	/	/	SYM
ejpam-5662	159	23	eur	eur	PROPN
ejpam-5662	159	24	.	.	PUNCT
ejpam-5662	160	1	j.	j.	PROPN
ejpam-5662	160	2	pure	pure	PROPN
ejpam-5662	160	3	appl	appl	PROPN
ejpam-5662	160	4	.	.	PROPN
ejpam-5662	160	5	math	math	PROPN
ejpam-5662	160	6	,	,	PUNCT
ejpam-5662	160	7	18	18	NUM
ejpam-5662	160	8	(	(	PUNCT
ejpam-5662	160	9	2	2	NUM
ejpam-5662	160	10	)	)	PUNCT
ejpam-5662	160	11	(	(	PUNCT
ejpam-5662	160	12	2025	2025	NUM
ejpam-5662	160	13	)	)	PUNCT
ejpam-5662	160	14	,	,	PUNCT
ejpam-5662	160	15	5662	5662	NUM
ejpam-5662	160	16	7	7	NUM
ejpam-5662	160	17	of	of	ADP
ejpam-5662	160	18	36	36	NUM
ejpam-5662	160	19	ũ(t	ũ(t	NOUN
ejpam-5662	160	20	)	)	PUNCT
ejpam-5662	160	21	=	=	SYM
ejpam-5662	160	22	a	a	DET
ejpam-5662	160	23	cosω1	cosω1	PROPN
ejpam-5662	160	24	t	t	PROPN
ejpam-5662	160	25	,	,	PUNCT
ejpam-5662	160	26	and	and	CCONJ
ejpam-5662	160	27	ṽ(t	ṽ(t	PROPN
ejpam-5662	160	28	)	)	PUNCT
ejpam-5662	161	1	=	=	SYM
ejpam-5662	162	1	b	b	X
ejpam-5662	162	2	cosω2	cosω2	PROPN
ejpam-5662	162	3	t	t	PROPN
ejpam-5662	162	4	,	,	PUNCT
ejpam-5662	162	5	(	(	PUNCT
ejpam-5662	162	6	3	3	X
ejpam-5662	162	7	)	)	PUNCT
ejpam-5662	162	8	where	where	SCONJ
ejpam-5662	162	9	ω1	ω1	PROPN
ejpam-5662	162	10	and	and	CCONJ
ejpam-5662	162	11	ω2	ω2	ADJ
ejpam-5662	162	12	characterize	characterize	VERB
ejpam-5662	162	13	the	the	DET
ejpam-5662	162	14	total	total	ADJ
ejpam-5662	162	15	frequencies	frequency	NOUN
ejpam-5662	162	16	that	that	PRON
ejpam-5662	162	17	are	be	AUX
ejpam-5662	162	18	determined	determine	VERB
ejpam-5662	162	19	later	later	ADV
ejpam-5662	162	20	.	.	PUNCT
ejpam-5662	163	1	the	the	DET
ejpam-5662	163	2	solutions	solution	NOUN
ejpam-5662	163	3	given	give	VERB
ejpam-5662	163	4	in	in	ADP
ejpam-5662	163	5	eq	eq	ADP
ejpam-5662	163	6	.	.	PUNCT
ejpam-5662	163	7	(	(	PUNCT
ejpam-5662	163	8	3	3	X
ejpam-5662	163	9	)	)	PUNCT
ejpam-5662	163	10	obey	obey	VERB
ejpam-5662	163	11	the	the	DET
ejpam-5662	163	12	following	following	ADJ
ejpam-5662	163	13	standard	standard	ADJ
ejpam-5662	163	14	initial	initial	ADJ
ejpam-5662	163	15	conditions	condition	NOUN
ejpam-5662	163	16	(	(	PUNCT
ejpam-5662	163	17	ics	ics	NOUN
ejpam-5662	163	18	):	):	PUNCT
ejpam-5662	163	19	ũ(0	ũ(0	NUM
ejpam-5662	163	20	)	)	PUNCT
ejpam-5662	163	21	=	=	SYM
ejpam-5662	163	22	a	a	PRON
ejpam-5662	163	23	,	,	PUNCT
ejpam-5662	163	24	˙̃u(0	˙̃u(0	ADJ
ejpam-5662	163	25	)	)	PUNCT
ejpam-5662	164	1	=	=	SYM
ejpam-5662	164	2	0	0	NUM
ejpam-5662	164	3	,	,	PUNCT
ejpam-5662	164	4	ṽ(0	ṽ(0	NOUN
ejpam-5662	164	5	)	)	PUNCT
ejpam-5662	164	6	=	=	SYM
ejpam-5662	164	7	b	b	NOUN
ejpam-5662	164	8	,	,	PUNCT
ejpam-5662	164	9	and	and	CCONJ
ejpam-5662	164	10	˙̃v(0	˙̃v(0	NOUN
ejpam-5662	164	11	)	)	PUNCT
ejpam-5662	165	1	=	=	SYM
ejpam-5662	165	2	0	0	X
ejpam-5662	165	3	.	.	PUNCT
ejpam-5662	166	1	(	(	PUNCT
ejpam-5662	166	2	4	4	X
ejpam-5662	166	3	)	)	PUNCT
ejpam-5662	166	4	now	now	ADV
ejpam-5662	166	5	,	,	PUNCT
ejpam-5662	166	6	the	the	DET
ejpam-5662	166	7	goal	goal	NOUN
ejpam-5662	166	8	here	here	ADV
ejpam-5662	166	9	is	be	AUX
ejpam-5662	166	10	to	to	PART
ejpam-5662	166	11	obtain	obtain	VERB
ejpam-5662	166	12	the	the	DET
ejpam-5662	166	13	corresponding	corresponding	ADJ
ejpam-5662	166	14	linear	linear	NOUN
ejpam-5662	166	15	odes	ode	NOUN
ejpam-5662	166	16	.	.	PUNCT
ejpam-5662	167	1	for	for	ADP
ejpam-5662	167	2	this	this	DET
ejpam-5662	167	3	aim	aim	NOUN
ejpam-5662	167	4	,	,	PUNCT
ejpam-5662	167	5	following	follow	VERB
ejpam-5662	167	6	the	the	DET
ejpam-5662	167	7	aforementioned	aforementioned	ADJ
ejpam-5662	167	8	works	work	NOUN
ejpam-5662	167	9	[	[	PUNCT
ejpam-5662	167	10	30	30	NUM
ejpam-5662	167	11	-	-	SYM
ejpam-5662	167	12	44	44	NUM
ejpam-5662	167	13	]	]	PUNCT
ejpam-5662	167	14	for	for	ADP
ejpam-5662	167	15	the	the	DET
ejpam-5662	167	16	single	single	ADJ
ejpam-5662	167	17	nonlinear	nonlinear	ADJ
ejpam-5662	167	18	ode	ode	PROPN
ejpam-5662	167	19	.	.	PUNCT
ejpam-5662	168	1	the	the	DET
ejpam-5662	168	2	equivalent	equivalent	ADJ
ejpam-5662	168	3	damping	damp	VERB
ejpam-5662	168	4	term	term	NOUN
ejpam-5662	168	5	is	be	AUX
ejpam-5662	168	6	given	give	VERB
ejpam-5662	168	7	as	as	SCONJ
ejpam-5662	168	8	follows	follow	VERB
ejpam-5662	168	9	:	:	PUNCT
ejpam-5662	168	10	σeqv1	σeqv1	X
ejpam-5662	169	1	=	=	SYM
ejpam-5662	169	2	∫	∫	PROPN
ejpam-5662	169	3	2π	2π	NOUN
ejpam-5662	169	4	/	/	SYM
ejpam-5662	169	5	ω1	ω1	PROPN
ejpam-5662	169	6	0	0	PUNCT
ejpam-5662	169	7	˙̃u	˙̃u	PROPN
ejpam-5662	169	8	f1(ũ	f1(ũ	PROPN
ejpam-5662	169	9	,	,	PUNCT
ejpam-5662	169	10	˙̃u	˙̃u	PROPN
ejpam-5662	169	11	,	,	PUNCT
ejpam-5662	169	12	¨̃u	¨̃u	PROPN
ejpam-5662	169	13	,	,	PUNCT
ejpam-5662	169	14	ṽ	ṽ	PROPN
ejpam-5662	169	15	,	,	PUNCT
ejpam-5662	169	16	˙̃v	˙̃v	PROPN
ejpam-5662	169	17	,	,	PUNCT
ejpam-5662	169	18	¨̃v)dt/	¨̃v)dt/	VERB
ejpam-5662	169	19	∫	∫	PROPN
ejpam-5662	169	20	2π	2π	NOUN
ejpam-5662	169	21	/	/	SYM
ejpam-5662	169	22	ω1	ω1	PROPN
ejpam-5662	169	23	0	0	PUNCT
ejpam-5662	169	24	˙̃u2dt	˙̃u2dt	PUNCT
ejpam-5662	169	25	=	=	SYM
ejpam-5662	169	26	g1(ω1	g1(ω1	NOUN
ejpam-5662	169	27	,	,	PUNCT
ejpam-5662	169	28	ω2	ω2	NUM
ejpam-5662	169	29	)	)	PUNCT
ejpam-5662	169	30	.	.	PUNCT
ejpam-5662	170	1	(	(	PUNCT
ejpam-5662	170	2	5	5	X
ejpam-5662	170	3	)	)	PUNCT
ejpam-5662	170	4	it	it	PRON
ejpam-5662	170	5	would	would	AUX
ejpam-5662	170	6	be	be	AUX
ejpam-5662	170	7	mentioned	mention	VERB
ejpam-5662	170	8	that	that	SCONJ
ejpam-5662	170	9	the	the	DET
ejpam-5662	170	10	function	function	NOUN
ejpam-5662	170	11	g1	g1	PROPN
ejpam-5662	170	12	includes	include	VERB
ejpam-5662	170	13	all	all	DET
ejpam-5662	170	14	the	the	DET
ejpam-5662	170	15	constants	constant	NOUN
ejpam-5662	170	16	that	that	PRON
ejpam-5662	170	17	appear	appear	VERB
ejpam-5662	170	18	in	in	ADP
ejpam-5662	170	19	the	the	DET
ejpam-5662	170	20	function	function	NOUN
ejpam-5662	170	21	f1	f1	NOUN
ejpam-5662	170	22	in	in	ADP
ejpam-5662	170	23	addition	addition	NOUN
ejpam-5662	170	24	to	to	ADP
ejpam-5662	170	25	the	the	DET
ejpam-5662	170	26	unknown	unknown	ADJ
ejpam-5662	170	27	frequencies	frequency	NOUN
ejpam-5662	170	28	.	.	PUNCT
ejpam-5662	171	1	on	on	ADP
ejpam-5662	171	2	the	the	DET
ejpam-5662	171	3	other	other	ADJ
ejpam-5662	171	4	hand	hand	NOUN
ejpam-5662	171	5	,	,	PUNCT
ejpam-5662	171	6	the	the	DET
ejpam-5662	171	7	equivalent	equivalent	ADJ
ejpam-5662	171	8	frequency	frequency	NOUN
ejpam-5662	171	9	may	may	AUX
ejpam-5662	171	10	be	be	AUX
ejpam-5662	171	11	evaluated	evaluate	VERB
ejpam-5662	171	12	as	as	SCONJ
ejpam-5662	171	13	follows	follow	VERB
ejpam-5662	171	14	:	:	PUNCT
ejpam-5662	171	15	ϖ2	ϖ2	NOUN
ejpam-5662	171	16	eqv1	eqv1	PROPN
ejpam-5662	171	17	=	=	SYM
ejpam-5662	172	1	∫	∫	PROPN
ejpam-5662	172	2	2π	2π	NOUN
ejpam-5662	172	3	/	/	SYM
ejpam-5662	172	4	ω1	ω1	PROPN
ejpam-5662	172	5	0	0	NUM
ejpam-5662	172	6	ũ	ũ	PROPN
ejpam-5662	172	7	f2(ũ	f2(ũ	PROPN
ejpam-5662	172	8	,	,	PUNCT
ejpam-5662	172	9	˙̃u	˙̃u	PROPN
ejpam-5662	172	10	,	,	PUNCT
ejpam-5662	172	11	¨̃u	¨̃u	PROPN
ejpam-5662	172	12	,	,	PUNCT
ejpam-5662	172	13	ṽ	ṽ	PROPN
ejpam-5662	172	14	,	,	PUNCT
ejpam-5662	172	15	˙̃v	˙̃v	PROPN
ejpam-5662	172	16	,	,	PUNCT
ejpam-5662	172	17	¨̃v)dt/	¨̃v)dt/	VERB
ejpam-5662	172	18	∫	∫	PROPN
ejpam-5662	172	19	2π	2π	NOUN
ejpam-5662	172	20	/	/	SYM
ejpam-5662	172	21	ω1	ω1	PROPN
ejpam-5662	172	22	0	0	NUM
ejpam-5662	172	23	ũ2dt	ũ2dt	NOUN
ejpam-5662	172	24	=	=	NOUN
ejpam-5662	172	25	g2(ω1	g2(ω1	NOUN
ejpam-5662	172	26	,	,	PUNCT
ejpam-5662	172	27	ω2	ω2	NUM
ejpam-5662	172	28	)	)	PUNCT
ejpam-5662	172	29	.	.	PUNCT
ejpam-5662	173	1	(	(	PUNCT
ejpam-5662	173	2	6	6	X
ejpam-5662	173	3	)	)	PUNCT
ejpam-5662	173	4	the	the	DET
ejpam-5662	173	5	function	function	NOUN
ejpam-5662	173	6	g2	g2	PROPN
ejpam-5662	173	7	incorporates	incorporate	VERB
ejpam-5662	173	8	all	all	DET
ejpam-5662	173	9	the	the	DET
ejpam-5662	173	10	parameters	parameter	NOUN
ejpam-5662	173	11	that	that	PRON
ejpam-5662	173	12	perform	perform	VERB
ejpam-5662	173	13	the	the	DET
ejpam-5662	173	14	function	function	NOUN
ejpam-5662	173	15	f2	f2	ADJ
ejpam-5662	173	16	and	and	CCONJ
ejpam-5662	173	17	unidentified	unidentified	ADJ
ejpam-5662	173	18	frequencies	frequency	NOUN
ejpam-5662	173	19	that	that	PRON
ejpam-5662	173	20	exist	exist	VERB
ejpam-5662	173	21	within	within	ADP
ejpam-5662	173	22	it	it	PRON
ejpam-5662	173	23	.	.	PUNCT
ejpam-5662	174	1	concerning	concern	VERB
ejpam-5662	174	2	the	the	DET
ejpam-5662	174	3	quadratic	quadratic	ADJ
ejpam-5662	174	4	function	function	NOUN
ejpam-5662	174	5	f3	f3	NOUN
ejpam-5662	174	6	,	,	PUNCT
ejpam-5662	174	7	actually	actually	ADV
ejpam-5662	174	8	,	,	PUNCT
ejpam-5662	174	9	the	the	DET
ejpam-5662	174	10	corresponding	corresponding	ADJ
ejpam-5662	174	11	term	term	NOUN
ejpam-5662	174	12	represents	represent	VERB
ejpam-5662	174	13	a	a	DET
ejpam-5662	174	14	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5662	174	15	part	part	NOUN
ejpam-5662	174	16	.	.	PUNCT
ejpam-5662	175	1	as	as	SCONJ
ejpam-5662	175	2	previously	previously	ADV
ejpam-5662	175	3	shown	show	VERB
ejpam-5662	175	4	[	[	PUNCT
ejpam-5662	175	5	30	30	NUM
ejpam-5662	175	6	-	-	SYM
ejpam-5662	175	7	44	44	NUM
ejpam-5662	175	8	and	and	CCONJ
ejpam-5662	175	9	46	46	NUM
ejpam-5662	175	10	]	]	PUNCT
ejpam-5662	175	11	,	,	PUNCT
ejpam-5662	175	12	this	this	DET
ejpam-5662	175	13	non	non	ADJ
ejpam-5662	175	14	-	-	ADJ
ejpam-5662	175	15	homogeneous	homogeneous	ADJ
ejpam-5662	175	16	part	part	NOUN
ejpam-5662	175	17	can	can	AUX
ejpam-5662	175	18	be	be	AUX
ejpam-5662	175	19	determined	determine	VERB
ejpam-5662	175	20	by	by	ADP
ejpam-5662	175	21	the	the	DET
ejpam-5662	175	22	following	follow	VERB
ejpam-5662	175	23	direct	direct	ADJ
ejpam-5662	175	24	substitutions	substitution	NOUN
ejpam-5662	175	25	:	:	PUNCT
ejpam-5662	175	26	replace	replace	VERB
ejpam-5662	175	27	:	:	PUNCT
ejpam-5662	175	28	u	u	NOUN
ejpam-5662	175	29	→	→	PUNCT
ejpam-5662	175	30	a	a	DET
ejpam-5662	175	31	2	2	NUM
ejpam-5662	175	32	√	√	NUM
ejpam-5662	175	33	2	2	NUM
ejpam-5662	175	34	,	,	PUNCT
ejpam-5662	175	35	u̇	u̇	PROPN
ejpam-5662	175	36	→	→	PUNCT
ejpam-5662	175	37	aω1	aω1	ADV
ejpam-5662	175	38	2	2	NUM
ejpam-5662	175	39	√	√	NUM
ejpam-5662	175	40	2	2	NUM
ejpam-5662	175	41	,	,	PUNCT
ejpam-5662	175	42	ü	ü	VERB
ejpam-5662	176	1	→	→	SYM
ejpam-5662	176	2	aω2	aω2	PROPN
ejpam-5662	176	3	1	1	NUM
ejpam-5662	176	4	2	2	NUM
ejpam-5662	176	5	√	√	NUM
ejpam-5662	176	6	2	2	NUM
ejpam-5662	176	7	,	,	PUNCT
ejpam-5662	176	8	v	v	INTJ
ejpam-5662	176	9	→	→	SYM
ejpam-5662	176	10	b	b	PROPN
ejpam-5662	176	11	2	2	NUM
ejpam-5662	176	12	√	√	NUM
ejpam-5662	176	13	2	2	NUM
ejpam-5662	176	14	,	,	PUNCT
ejpam-5662	176	15	v̇	v̇	NOUN
ejpam-5662	176	16	→	→	SYM
ejpam-5662	176	17	bω2	bω2	NOUN
ejpam-5662	176	18	2	2	NUM
ejpam-5662	176	19	√	√	NUM
ejpam-5662	176	20	2	2	NUM
ejpam-5662	176	21	,	,	PUNCT
ejpam-5662	176	22	and	and	CCONJ
ejpam-5662	176	23	v̈	v̈	PRON
ejpam-5662	176	24	→	→	PUNCT
ejpam-5662	176	25	bω2	bω2	NOUN
ejpam-5662	176	26	2	2	NUM
ejpam-5662	176	27	2	2	NUM
ejpam-5662	176	28	√	√	NUM
ejpam-5662	176	29	2	2	NUM
ejpam-5662	176	30	.	.	PUNCT
ejpam-5662	177	1	the	the	DET
ejpam-5662	177	2	non	non	ADJ
ejpam-5662	177	3	-	-	ADJ
ejpam-5662	177	4	homogeneous	homogeneous	ADJ
ejpam-5662	177	5	part	part	NOUN
ejpam-5662	177	6	of	of	ADP
ejpam-5662	177	7	the	the	DET
ejpam-5662	177	8	corresponding	corresponding	ADJ
ejpam-5662	177	9	linear	linear	PROPN
ejpam-5662	177	10	ode	ode	NOUN
ejpam-5662	177	11	may	may	AUX
ejpam-5662	177	12	be	be	AUX
ejpam-5662	177	13	estimated	estimate	VERB
ejpam-5662	177	14	as	as	SCONJ
ejpam-5662	177	15	follows	follow	VERB
ejpam-5662	177	16	:	:	PUNCT
ejpam-5662	178	1	λ1	λ1	ADJ
ejpam-5662	178	2	=	=	SYM
ejpam-5662	178	3	f3	f3	PROPN
ejpam-5662	178	4	(	(	PUNCT
ejpam-5662	178	5	a	a	DET
ejpam-5662	178	6	2	2	NUM
ejpam-5662	178	7	√	√	NUM
ejpam-5662	178	8	2	2	NUM
ejpam-5662	178	9	,	,	PUNCT
ejpam-5662	178	10	aω1	aω1	ADV
ejpam-5662	178	11	2	2	NUM
ejpam-5662	178	12	√	√	NUM
ejpam-5662	178	13	2	2	NUM
ejpam-5662	178	14	,	,	PUNCT
ejpam-5662	178	15	aω2	aω2	PROPN
ejpam-5662	178	16	1	1	NUM
ejpam-5662	178	17	2	2	NUM
ejpam-5662	178	18	√	√	NUM
ejpam-5662	178	19	2	2	NUM
ejpam-5662	178	20	,	,	PUNCT
ejpam-5662	178	21	b	b	PROPN
ejpam-5662	178	22	2	2	NUM
ejpam-5662	178	23	√	√	NUM
ejpam-5662	178	24	2	2	NUM
ejpam-5662	178	25	,	,	PUNCT
ejpam-5662	178	26	bω2	bω2	NOUN
ejpam-5662	178	27	2	2	NUM
ejpam-5662	178	28	√	√	NUM
ejpam-5662	178	29	2	2	NUM
ejpam-5662	178	30	,	,	PUNCT
ejpam-5662	178	31	bω2	bω2	NOUN
ejpam-5662	178	32	2	2	NUM
ejpam-5662	178	33	2	2	NUM
ejpam-5662	178	34	√	√	NUM
ejpam-5662	178	35	2	2	NUM
ejpam-5662	178	36	)	)	PUNCT
ejpam-5662	178	37	.	.	PUNCT
ejpam-5662	179	1	(	(	PUNCT
ejpam-5662	179	2	7	7	X
ejpam-5662	179	3	)	)	PUNCT
ejpam-5662	179	4	finally	finally	ADV
ejpam-5662	179	5	,	,	PUNCT
ejpam-5662	179	6	the	the	DET
ejpam-5662	179	7	corresponding	corresponding	ADJ
ejpam-5662	179	8	linear	linear	ADJ
ejpam-5662	179	9	ode	ode	NOUN
ejpam-5662	179	10	that	that	PRON
ejpam-5662	179	11	corresponds	correspond	VERB
ejpam-5662	179	12	to	to	ADP
ejpam-5662	179	13	eq	eq	NOUN
ejpam-5662	179	14	.	.	PUNCT
ejpam-5662	180	1	(	(	PUNCT
ejpam-5662	180	2	1	1	X
ejpam-5662	180	3	)	)	PUNCT
ejpam-5662	180	4	may	may	AUX
ejpam-5662	180	5	be	be	AUX
ejpam-5662	180	6	formulated	formulate	VERB
ejpam-5662	180	7	as	as	SCONJ
ejpam-5662	180	8	follows	follow	VERB
ejpam-5662	180	9	:	:	PUNCT
ejpam-5662	180	10	ü+	ü+	NUM
ejpam-5662	180	11	σeqv1u̇+ϖ2	σeqv1u̇+ϖ2	NOUN
ejpam-5662	180	12	eqv1u	eqv1u	NOUN
ejpam-5662	180	13	=	=	SYM
ejpam-5662	180	14	λ1	λ1	PROPN
ejpam-5662	180	15	.	.	PUNCT
ejpam-5662	181	1	(	(	PUNCT
ejpam-5662	181	2	8)	8)	NUM
ejpam-5662	181	3	in	in	ADP
ejpam-5662	181	4	accordance	accordance	NOUN
ejpam-5662	181	5	with	with	ADP
ejpam-5662	181	6	the	the	DET
ejpam-5662	181	7	standard	standard	ADJ
ejpam-5662	181	8	normal	normal	ADJ
ejpam-5662	181	9	form	form	NOUN
ejpam-5662	181	10	,	,	PUNCT
ejpam-5662	181	11	the	the	DET
ejpam-5662	181	12	middle	middle	ADJ
ejpam-5662	181	13	term	term	NOUN
ejpam-5662	181	14	in	in	ADP
ejpam-5662	181	15	eq	eq	ADP
ejpam-5662	181	16	.	.	PUNCT
ejpam-5662	182	1	(	(	PUNCT
ejpam-5662	182	2	8)	8)	NUM
ejpam-5662	182	3	may	may	AUX
ejpam-5662	182	4	be	be	AUX
ejpam-5662	182	5	removed	remove	VERB
ejpam-5662	182	6	via	via	ADP
ejpam-5662	182	7	the	the	DET
ejpam-5662	182	8	transformation	transformation	NOUN
ejpam-5662	182	9	:	:	PUNCT
ejpam-5662	182	10	u(t	u(t	NOUN
ejpam-5662	182	11	)	)	PUNCT
ejpam-5662	182	12	=	=	SYM
ejpam-5662	182	13	ũ(t)exp(−σeqv1t/2	ũ(t)exp(−σeqv1t/2	PROPN
ejpam-5662	182	14	)	)	PUNCT
ejpam-5662	182	15	,	,	PUNCT
ejpam-5662	182	16	(	(	PUNCT
ejpam-5662	182	17	9	9	X
ejpam-5662	182	18	)	)	PUNCT
ejpam-5662	182	19	where	where	SCONJ
ejpam-5662	182	20	f1(t	f1(t	VERB
ejpam-5662	182	21	)	)	PUNCT
ejpam-5662	182	22	is	be	AUX
ejpam-5662	182	23	an	an	DET
ejpam-5662	182	24	arbitrary	arbitrary	ADJ
ejpam-5662	182	25	function	function	NOUN
ejpam-5662	182	26	.	.	PUNCT
ejpam-5662	183	1	the	the	DET
ejpam-5662	183	2	new	new	ADJ
ejpam-5662	183	3	function	function	NOUN
ejpam-5662	183	4	f1(t	f1(t	PROPN
ejpam-5662	183	5	)	)	PUNCT
ejpam-5662	183	6	will	will	AUX
ejpam-5662	183	7	be	be	AUX
ejpam-5662	183	8	determined	determine	VERB
ejpam-5662	183	9	via	via	ADP
ejpam-5662	183	10	the	the	DET
ejpam-5662	183	11	linear	linear	ADJ
ejpam-5662	183	12	ode	ode	NOUN
ejpam-5662	183	13	as	as	SCONJ
ejpam-5662	183	14	given	give	VERB
ejpam-5662	183	15	in	in	ADP
ejpam-5662	183	16	eq	eq	ADP
ejpam-5662	183	17	.	.	PUNCT
ejpam-5662	184	1	(	(	PUNCT
ejpam-5662	184	2	8)	8)	NUM
ejpam-5662	184	3	:	:	PUNCT
ejpam-5662	184	4	¨̃u+ω2	¨̃u+ω2	NUM
ejpam-5662	184	5	1ũ	1ũ	NUM
ejpam-5662	184	6	=	=	SYM
ejpam-5662	184	7	λ1exp(σeqv1/2	λ1exp(σeqv1/2	NOUN
ejpam-5662	184	8	)	)	PUNCT
ejpam-5662	184	9	,	,	PUNCT
ejpam-5662	184	10	(	(	PUNCT
ejpam-5662	184	11	10	10	NUM
ejpam-5662	184	12	)	)	PUNCT
ejpam-5662	184	13	where	where	SCONJ
ejpam-5662	184	14	ω2	ω2	ADJ
ejpam-5662	184	15	1	1	NUM
ejpam-5662	184	16	=	=	NOUN
ejpam-5662	184	17	ϖ2	ϖ2	NOUN
ejpam-5662	184	18	eqv1	eqv1	NOUN
ejpam-5662	184	19	−	−	NOUN
ejpam-5662	184	20	1	1	NUM
ejpam-5662	184	21	4	4	NUM
ejpam-5662	184	22	σ2	σ2	PROPN
ejpam-5662	184	23	eqv1	eqv1	PROPN
ejpam-5662	184	24	,	,	PUNCT
ejpam-5662	184	25	(	(	PUNCT
ejpam-5662	184	26	11	11	NUM
ejpam-5662	184	27	)	)	PUNCT
ejpam-5662	184	28	a.	a.	NOUN
ejpam-5662	184	29	alanazy	alanazy	NOUN
ejpam-5662	184	30	,	,	PUNCT
ejpam-5662	184	31	g.	g.	PROPN
ejpam-5662	184	32	m.	m.	PROPN
ejpam-5662	184	33	moatimid	moatimid	PROPN
ejpam-5662	184	34	,	,	PUNCT
ejpam-5662	184	35	m.	m.	PROPN
ejpam-5662	184	36	a.	a.	PROPN
ejpam-5662	184	37	a.	a.	PROPN
ejpam-5662	184	38	mohamed	mohamed	PROPN
ejpam-5662	184	39	/	/	SYM
ejpam-5662	184	40	eur	eur	PROPN
ejpam-5662	184	41	.	.	PUNCT
ejpam-5662	185	1	j.	j.	PROPN
ejpam-5662	185	2	pure	pure	PROPN
ejpam-5662	185	3	appl	appl	PROPN
ejpam-5662	185	4	.	.	PROPN
ejpam-5662	185	5	math	math	PROPN
ejpam-5662	185	6	,	,	PUNCT
ejpam-5662	185	7	18	18	NUM
ejpam-5662	185	8	(	(	PUNCT
ejpam-5662	185	9	2	2	NUM
ejpam-5662	185	10	)	)	PUNCT
ejpam-5662	185	11	(	(	PUNCT
ejpam-5662	185	12	2025	2025	NUM
ejpam-5662	185	13	)	)	PUNCT
ejpam-5662	185	14	,	,	PUNCT
ejpam-5662	185	15	5662	5662	NUM
ejpam-5662	185	16	8	8	NUM
ejpam-5662	185	17	of	of	ADP
ejpam-5662	185	18	36	36	NUM
ejpam-5662	185	19	which	which	PRON
ejpam-5662	185	20	signifies	signify	VERB
ejpam-5662	185	21	the	the	DET
ejpam-5662	185	22	square	square	NOUN
ejpam-5662	185	23	of	of	ADP
ejpam-5662	185	24	the	the	DET
ejpam-5662	185	25	total	total	ADJ
ejpam-5662	185	26	frequency	frequency	NOUN
ejpam-5662	185	27	of	of	ADP
ejpam-5662	185	28	the	the	DET
ejpam-5662	185	29	first	first	ADJ
ejpam-5662	185	30	linear	linear	PROPN
ejpam-5662	185	31	ode	ode	PROPN
ejpam-5662	185	32	.	.	PUNCT
ejpam-5662	186	1	additionally	additionally	ADV
ejpam-5662	186	2	,	,	PUNCT
ejpam-5662	186	3	the	the	DET
ejpam-5662	186	4	stability	stability	NOUN
ejpam-5662	186	5	criteria	criterion	NOUN
ejpam-5662	186	6	are	be	AUX
ejpam-5662	186	7	evaluated	evaluate	VERB
ejpam-5662	186	8	through	through	ADP
ejpam-5662	186	9	the	the	DET
ejpam-5662	186	10	following	following	NOUN
ejpam-5662	186	11	:	:	PUNCT
ejpam-5662	186	12	ω2	ω2	ADJ
ejpam-5662	186	13	1	1	NUM
ejpam-5662	186	14	>	>	SYM
ejpam-5662	186	15	0	0	NUM
ejpam-5662	186	16	,	,	PUNCT
ejpam-5662	186	17	and	and	CCONJ
ejpam-5662	186	18	σeqv1	σeqv1	PROPN
ejpam-5662	186	19	>	>	X
ejpam-5662	186	20	0	0	X
ejpam-5662	186	21	.	.	PUNCT
ejpam-5662	187	1	(	(	PUNCT
ejpam-5662	187	2	12	12	NUM
ejpam-5662	187	3	)	)	PUNCT
ejpam-5662	187	4	using	use	VERB
ejpam-5662	187	5	similar	similar	ADJ
ejpam-5662	187	6	arguments	argument	NOUN
ejpam-5662	187	7	that	that	PRON
ejpam-5662	187	8	are	be	AUX
ejpam-5662	187	9	previously	previously	ADV
ejpam-5662	187	10	given	give	VERB
ejpam-5662	187	11	,	,	PUNCT
ejpam-5662	187	12	the	the	DET
ejpam-5662	187	13	second	second	ADJ
ejpam-5662	187	14	comparable	comparable	ADJ
ejpam-5662	187	15	linear	linear	ADJ
ejpam-5662	187	16	ode	ode	NOUN
ejpam-5662	187	17	is	be	AUX
ejpam-5662	187	18	given	give	VERB
ejpam-5662	187	19	as	as	ADP
ejpam-5662	187	20	:	:	PUNCT
ejpam-5662	187	21	v̈	v̈	PROPN
ejpam-5662	187	22	+	+	CCONJ
ejpam-5662	187	23	σeqv2v̇	σeqv2v̇	NUM
ejpam-5662	188	1	+	+	ADJ
ejpam-5662	188	2	ϖ2	ϖ2	NOUN
ejpam-5662	188	3	eqv2v	eqv2v	NOUN
ejpam-5662	188	4	=	=	SYM
ejpam-5662	188	5	λ2	λ2	PROPN
ejpam-5662	188	6	.	.	PUNCT
ejpam-5662	188	7	(	(	PUNCT
ejpam-5662	188	8	13	13	NUM
ejpam-5662	188	9	)	)	PUNCT
ejpam-5662	188	10	as	as	SCONJ
ejpam-5662	188	11	previously	previously	ADV
ejpam-5662	188	12	shown	show	VERB
ejpam-5662	188	13	the	the	DET
ejpam-5662	188	14	parameters	parameter	NOUN
ejpam-5662	188	15	σeqv2	σeqv2	ADJ
ejpam-5662	188	16	and	and	CCONJ
ejpam-5662	188	17	ϖ2	ϖ2	NOUN
ejpam-5662	188	18	eqv2	eqv2	PROPN
ejpam-5662	188	19	are	be	AUX
ejpam-5662	188	20	determined	determine	VERB
ejpam-5662	188	21	as	as	SCONJ
ejpam-5662	188	22	shown	show	VERB
ejpam-5662	188	23	in	in	ADP
ejpam-5662	188	24	eqs	eqs	PROPN
ejpam-5662	188	25	.	.	PUNCT
ejpam-5662	189	1	(	(	PUNCT
ejpam-5662	189	2	5	5	NUM
ejpam-5662	189	3	)	)	PUNCT
ejpam-5662	189	4	and	and	CCONJ
ejpam-5662	189	5	(	(	PUNCT
ejpam-5662	189	6	6	6	NUM
ejpam-5662	189	7	)	)	PUNCT
ejpam-5662	189	8	.	.	PUNCT
ejpam-5662	190	1	remember	remember	VERB
ejpam-5662	190	2	that	that	SCONJ
ejpam-5662	190	3	the	the	DET
ejpam-5662	190	4	integration	integration	NOUN
ejpam-5662	190	5	is	be	AUX
ejpam-5662	190	6	evaluated	evaluate	VERB
ejpam-5662	190	7	over	over	ADP
ejpam-5662	190	8	the	the	DET
ejpam-5662	190	9	interval	interval	NOUN
ejpam-5662	190	10	0	0	PUNCT
ejpam-5662	190	11	→	→	SYM
ejpam-5662	190	12	2π	2π	NOUN
ejpam-5662	190	13	/	/	SYM
ejpam-5662	190	14	ω2	ω2	ADJ
ejpam-5662	190	15	.	.	PUNCT
ejpam-5662	191	1	once	once	ADV
ejpam-5662	191	2	more	more	ADV
ejpam-5662	191	3	,	,	PUNCT
ejpam-5662	191	4	the	the	DET
ejpam-5662	191	5	middle	middle	ADJ
ejpam-5662	191	6	term	term	NOUN
ejpam-5662	191	7	in	in	ADP
ejpam-5662	191	8	eq	eq	ADP
ejpam-5662	191	9	.	.	PUNCT
ejpam-5662	192	1	(	(	PUNCT
ejpam-5662	192	2	13	13	NUM
ejpam-5662	192	3	)	)	PUNCT
ejpam-5662	192	4	could	could	AUX
ejpam-5662	192	5	be	be	AUX
ejpam-5662	192	6	ignored	ignore	VERB
ejpam-5662	192	7	via	via	ADP
ejpam-5662	192	8	the	the	DET
ejpam-5662	192	9	following	follow	VERB
ejpam-5662	192	10	normal	normal	ADJ
ejpam-5662	192	11	form	form	NOUN
ejpam-5662	192	12	:	:	PUNCT
ejpam-5662	192	13	v(t	v(t	NUM
ejpam-5662	192	14	)	)	PUNCT
ejpam-5662	192	15	=	=	PUNCT
ejpam-5662	193	1	ṽ(t)exp(−σeqv2t/2	ṽ(t)exp(−σeqv2t/2	X
ejpam-5662	193	2	)	)	PUNCT
ejpam-5662	193	3	,	,	PUNCT
ejpam-5662	193	4	(	(	PUNCT
ejpam-5662	193	5	14	14	NUM
ejpam-5662	193	6	)	)	PUNCT
ejpam-5662	193	7	the	the	DET
ejpam-5662	193	8	unknown	unknown	ADJ
ejpam-5662	193	9	function	function	NOUN
ejpam-5662	193	10	f2(t	f2(t	PROPN
ejpam-5662	193	11	)	)	PUNCT
ejpam-5662	193	12	is	be	AUX
ejpam-5662	193	13	determined	determine	VERB
ejpam-5662	193	14	as	as	ADP
ejpam-5662	193	15	:	:	PUNCT
ejpam-5662	193	16	¨̃v	¨̃v	PROPN
ejpam-5662	193	17	+	+	PROPN
ejpam-5662	193	18	ω2	ω2	ADJ
ejpam-5662	193	19	2ṽ	2ṽ	NUM
ejpam-5662	193	20	=	=	SYM
ejpam-5662	193	21	λ2exp(σeqv2t/2	λ2exp(σeqv2t/2	NOUN
ejpam-5662	193	22	)	)	PUNCT
ejpam-5662	193	23	,	,	PUNCT
ejpam-5662	193	24	(	(	PUNCT
ejpam-5662	193	25	15	15	NUM
ejpam-5662	193	26	)	)	PUNCT
ejpam-5662	193	27	where	where	SCONJ
ejpam-5662	193	28	ω2	ω2	ADJ
ejpam-5662	193	29	2	2	NUM
ejpam-5662	193	30	=	=	NOUN
ejpam-5662	193	31	ϖ2	ϖ2	NOUN
ejpam-5662	193	32	eqv2	eqv2	NOUN
ejpam-5662	193	33	−	−	NOUN
ejpam-5662	193	34	1	1	NUM
ejpam-5662	193	35	4	4	NUM
ejpam-5662	193	36	σ2	σ2	NOUN
ejpam-5662	193	37	eqv2	eqv2	PROPN
ejpam-5662	193	38	,	,	PUNCT
ejpam-5662	193	39	(	(	PUNCT
ejpam-5662	193	40	16	16	NUM
ejpam-5662	193	41	)	)	PUNCT
ejpam-5662	193	42	which	which	PRON
ejpam-5662	193	43	denotes	denote	VERB
ejpam-5662	193	44	the	the	DET
ejpam-5662	193	45	square	square	NOUN
ejpam-5662	193	46	of	of	ADP
ejpam-5662	193	47	the	the	DET
ejpam-5662	193	48	total	total	ADJ
ejpam-5662	193	49	frequency	frequency	NOUN
ejpam-5662	193	50	of	of	ADP
ejpam-5662	193	51	the	the	DET
ejpam-5662	193	52	second	second	ADJ
ejpam-5662	193	53	linear	linear	ADJ
ejpam-5662	193	54	ode	ode	PROPN
ejpam-5662	193	55	.	.	PUNCT
ejpam-5662	194	1	furthermore	furthermore	ADV
ejpam-5662	194	2	,	,	PUNCT
ejpam-5662	194	3	the	the	DET
ejpam-5662	194	4	stability	stability	NOUN
ejpam-5662	194	5	requirements	requirement	NOUN
ejpam-5662	194	6	are	be	AUX
ejpam-5662	194	7	assessed	assess	VERB
ejpam-5662	194	8	using	use	VERB
ejpam-5662	194	9	the	the	DET
ejpam-5662	194	10	following	following	NOUN
ejpam-5662	194	11	:	:	PUNCT
ejpam-5662	194	12	ω2	ω2	PROPN
ejpam-5662	194	13	2	2	NUM
ejpam-5662	194	14	>	>	SYM
ejpam-5662	194	15	0	0	NUM
ejpam-5662	194	16	,	,	PUNCT
ejpam-5662	194	17	and	and	CCONJ
ejpam-5662	194	18	σeqv2	σeqv2	ADJ
ejpam-5662	194	19	>	>	X
ejpam-5662	194	20	0	0	X
ejpam-5662	194	21	.	.	PUNCT
ejpam-5662	195	1	(	(	PUNCT
ejpam-5662	195	2	17	17	NUM
ejpam-5662	195	3	)	)	PUNCT
ejpam-5662	195	4	to	to	ADP
ejpam-5662	195	5	this	this	DET
ejpam-5662	195	6	end	end	NOUN
ejpam-5662	195	7	,	,	PUNCT
ejpam-5662	195	8	it	it	PRON
ejpam-5662	195	9	should	should	AUX
ejpam-5662	195	10	be	be	AUX
ejpam-5662	195	11	mentioned	mention	VERB
ejpam-5662	195	12	that	that	SCONJ
ejpam-5662	195	13	the	the	DET
ejpam-5662	195	14	total	total	ADJ
ejpam-5662	195	15	frequencies	frequency	NOUN
ejpam-5662	195	16	ω1	ω1	PROPN
ejpam-5662	195	17	and	and	CCONJ
ejpam-5662	195	18	ω2are	ω2are	NOUN
ejpam-5662	195	19	evaluated	evaluate	VERB
ejpam-5662	195	20	via	via	ADP
ejpam-5662	195	21	the	the	DET
ejpam-5662	195	22	mathematica	mathematica	PROPN
ejpam-5662	195	23	software	software	PROPN
ejpam-5662	195	24	(	(	PUNCT
ejpam-5662	195	25	ms	ms	NOUN
ejpam-5662	195	26	)	)	PUNCT
ejpam-5662	195	27	during	during	ADP
ejpam-5662	195	28	the	the	DET
ejpam-5662	195	29	command	command	NOUN
ejpam-5662	195	30	findroot	findroot	NOUN
ejpam-5662	195	31	for	for	ADP
ejpam-5662	195	32	the	the	DET
ejpam-5662	195	33	coupled	couple	VERB
ejpam-5662	195	34	equations	equation	NOUN
ejpam-5662	195	35	(	(	PUNCT
ejpam-5662	195	36	11	11	NUM
ejpam-5662	195	37	)	)	PUNCT
ejpam-5662	195	38	and	and	CCONJ
ejpam-5662	195	39	(	(	PUNCT
ejpam-5662	195	40	16	16	NUM
ejpam-5662	195	41	)	)	PUNCT
ejpam-5662	195	42	.	.	PUNCT
ejpam-5662	196	1	3	3	X
ejpam-5662	196	2	.	.	NOUN
ejpam-5662	196	3	significance	significance	NOUN
ejpam-5662	196	4	of	of	ADP
ejpam-5662	196	5	the	the	DET
ejpam-5662	196	6	problem	problem	NOUN
ejpam-5662	196	7	the	the	DET
ejpam-5662	196	8	tdof	tdof	NOUN
ejpam-5662	196	9	of	of	ADP
ejpam-5662	196	10	mdo	mdo	PROPN
ejpam-5662	196	11	is	be	AUX
ejpam-5662	196	12	an	an	DET
ejpam-5662	196	13	extension	extension	NOUN
ejpam-5662	196	14	of	of	ADP
ejpam-5662	196	15	the	the	DET
ejpam-5662	196	16	classical	classical	ADJ
ejpam-5662	196	17	do	do	AUX
ejpam-5662	196	18	model	model	NOUN
ejpam-5662	196	19	that	that	PRON
ejpam-5662	196	20	describes	describe	VERB
ejpam-5662	196	21	a	a	DET
ejpam-5662	196	22	more	more	ADV
ejpam-5662	196	23	complex	complex	ADJ
ejpam-5662	196	24	and	and	CCONJ
ejpam-5662	196	25	nonlinear	nonlinear	ADJ
ejpam-5662	196	26	dynamical	dynamical	ADJ
ejpam-5662	196	27	system	system	NOUN
ejpam-5662	196	28	of	of	ADP
ejpam-5662	196	29	tdof	tdof	NOUN
ejpam-5662	196	30	.	.	PUNCT
ejpam-5662	197	1	this	this	DET
ejpam-5662	197	2	oscillator	oscillator	NOUN
ejpam-5662	197	3	typically	typically	ADV
ejpam-5662	197	4	arises	arise	VERB
ejpam-5662	197	5	in	in	ADP
ejpam-5662	197	6	the	the	DET
ejpam-5662	197	7	study	study	NOUN
ejpam-5662	197	8	of	of	ADP
ejpam-5662	197	9	nonlinear	nonlinear	ADJ
ejpam-5662	197	10	vibrations	vibration	NOUN
ejpam-5662	197	11	,	,	PUNCT
ejpam-5662	197	12	resonance	resonance	NOUN
ejpam-5662	197	13	phenomena	phenomenon	NOUN
ejpam-5662	197	14	,	,	PUNCT
ejpam-5662	197	15	and	and	CCONJ
ejpam-5662	197	16	stability	stability	NOUN
ejpam-5662	197	17	analysis	analysis	NOUN
ejpam-5662	197	18	in	in	ADP
ejpam-5662	197	19	various	various	ADJ
ejpam-5662	197	20	engineering	engineering	NOUN
ejpam-5662	197	21	and	and	CCONJ
ejpam-5662	197	22	physical	physical	ADJ
ejpam-5662	197	23	systems	system	NOUN
ejpam-5662	197	24	.	.	PUNCT
ejpam-5662	198	1	in	in	ADP
ejpam-5662	198	2	what	what	PRON
ejpam-5662	198	3	follows	follow	VERB
ejpam-5662	198	4	,	,	PUNCT
ejpam-5662	198	5	some	some	DET
ejpam-5662	198	6	features	feature	NOUN
ejpam-5662	198	7	of	of	ADP
ejpam-5662	198	8	the	the	DET
ejpam-5662	198	9	given	give	VERB
ejpam-5662	198	10	problem	problem	NOUN
ejpam-5662	198	11	will	will	AUX
ejpam-5662	198	12	be	be	AUX
ejpam-5662	198	13	raised	raise	VERB
ejpam-5662	198	14	.	.	PUNCT
ejpam-5662	199	1	1	1	X
ejpam-5662	199	2	.	.	X
ejpam-5662	199	3	mathieu	mathieu	PROPN
ejpam-5662	199	4	term	term	PROPN
ejpam-5662	199	5	supplements	supplement	NOUN
ejpam-5662	199	6	parametric	parametric	ADJ
ejpam-5662	199	7	excitation	excitation	NOUN
ejpam-5662	199	8	to	to	ADP
ejpam-5662	199	9	the	the	DET
ejpam-5662	199	10	ode	ode	PROPN
ejpam-5662	199	11	,	,	PUNCT
ejpam-5662	199	12	which	which	PRON
ejpam-5662	199	13	leads	lead	VERB
ejpam-5662	199	14	a	a	DET
ejpam-5662	199	15	system	system	NOUN
ejpam-5662	199	16	to	to	PART
ejpam-5662	199	17	be	be	AUX
ejpam-5662	199	18	non	non	ADJ
ejpam-5662	199	19	-	-	ADJ
ejpam-5662	199	20	autonomous	autonomous	ADJ
ejpam-5662	199	21	.	.	PUNCT
ejpam-5662	200	1	parametric	parametric	ADJ
ejpam-5662	200	2	excitation	excitation	NOUN
ejpam-5662	200	3	indicates	indicate	VERB
ejpam-5662	200	4	that	that	SCONJ
ejpam-5662	200	5	some	some	DET
ejpam-5662	200	6	system	system	NOUN
ejpam-5662	200	7	parameters	parameter	NOUN
ejpam-5662	200	8	differ	differ	VERB
ejpam-5662	200	9	with	with	ADP
ejpam-5662	200	10	time	time	NOUN
ejpam-5662	200	11	,	,	PUNCT
ejpam-5662	200	12	frequently	frequently	ADV
ejpam-5662	200	13	in	in	ADP
ejpam-5662	200	14	sinusoidal	sinusoidal	ADJ
ejpam-5662	200	15	waves	wave	NOUN
ejpam-5662	200	16	,	,	PUNCT
ejpam-5662	200	17	giving	give	VERB
ejpam-5662	200	18	a	a	DET
ejpam-5662	200	19	more	more	ADV
ejpam-5662	200	20	complex	complex	ADJ
ejpam-5662	200	21	dynamic	dynamic	ADJ
ejpam-5662	200	22	performance	performance	NOUN
ejpam-5662	200	23	.	.	PUNCT
ejpam-5662	201	1	this	this	DET
ejpam-5662	201	2	term	term	NOUN
ejpam-5662	201	3	is	be	AUX
ejpam-5662	201	4	a	a	DET
ejpam-5662	201	5	reason	reason	NOUN
ejpam-5662	201	6	for	for	ADP
ejpam-5662	201	7	phenomena	phenomenon	NOUN
ejpam-5662	201	8	such	such	ADJ
ejpam-5662	201	9	as	as	ADP
ejpam-5662	201	10	parametric	parametric	ADJ
ejpam-5662	201	11	resonance	resonance	NOUN
ejpam-5662	201	12	.	.	PUNCT
ejpam-5662	202	1	2	2	X
ejpam-5662	202	2	.	.	X
ejpam-5662	202	3	the	the	DET
ejpam-5662	202	4	cubic	cubic	NOUN
ejpam-5662	202	5	-	-	PUNCT
ejpam-5662	202	6	do	do	NOUN
ejpam-5662	202	7	,	,	PUNCT
ejpam-5662	202	8	which	which	PRON
ejpam-5662	202	9	presents	present	VERB
ejpam-5662	202	10	a	a	DET
ejpam-5662	202	11	restoring	restore	VERB
ejpam-5662	202	12	force	force	NOUN
ejpam-5662	202	13	that	that	PRON
ejpam-5662	202	14	is	be	AUX
ejpam-5662	202	15	proportional	proportional	ADJ
ejpam-5662	202	16	to	to	ADP
ejpam-5662	202	17	the	the	DET
ejpam-5662	202	18	cube	cube	NOUN
ejpam-5662	202	19	of	of	ADP
ejpam-5662	202	20	the	the	DET
ejpam-5662	202	21	displacement	displacement	NOUN
ejpam-5662	202	22	,	,	PUNCT
ejpam-5662	202	23	makes	make	VERB
ejpam-5662	202	24	the	the	DET
ejpam-5662	202	25	system	system	NOUN
ejpam-5662	202	26	’s	’s	PART
ejpam-5662	202	27	behavior	behavior	NOUN
ejpam-5662	202	28	depend	depend	VERB
ejpam-5662	202	29	strongly	strongly	ADV
ejpam-5662	202	30	on	on	ADP
ejpam-5662	202	31	amplitude	amplitude	NOUN
ejpam-5662	202	32	.	.	PUNCT
ejpam-5662	203	1	the	the	DET
ejpam-5662	203	2	duffing	duffing	NOUN
ejpam-5662	203	3	term	term	NOUN
ejpam-5662	203	4	can	can	AUX
ejpam-5662	203	5	result	result	VERB
ejpam-5662	203	6	in	in	ADP
ejpam-5662	203	7	hardening	harden	VERB
ejpam-5662	203	8	or	or	CCONJ
ejpam-5662	203	9	softening	soften	VERB
ejpam-5662	203	10	stiffness	stiffness	NOUN
ejpam-5662	203	11	features	feature	NOUN
ejpam-5662	203	12	.	.	PUNCT
ejpam-5662	204	1	a.	a.	PROPN
ejpam-5662	204	2	alanazy	alanazy	PROPN
ejpam-5662	204	3	,	,	PUNCT
ejpam-5662	204	4	g.	g.	PROPN
ejpam-5662	204	5	m.	m.	PROPN
ejpam-5662	204	6	moatimid	moatimid	PROPN
ejpam-5662	204	7	,	,	PUNCT
ejpam-5662	204	8	m.	m.	PROPN
ejpam-5662	204	9	a.	a.	PROPN
ejpam-5662	204	10	a.	a.	PROPN
ejpam-5662	204	11	mohamed	mohamed	PROPN
ejpam-5662	204	12	/	/	SYM
ejpam-5662	204	13	eur	eur	PROPN
ejpam-5662	204	14	.	.	PUNCT
ejpam-5662	205	1	j.	j.	PROPN
ejpam-5662	205	2	pure	pure	PROPN
ejpam-5662	205	3	appl	appl	PROPN
ejpam-5662	205	4	.	.	PROPN
ejpam-5662	205	5	math	math	PROPN
ejpam-5662	205	6	,	,	PUNCT
ejpam-5662	205	7	18	18	NUM
ejpam-5662	205	8	(	(	PUNCT
ejpam-5662	205	9	2	2	NUM
ejpam-5662	205	10	)	)	PUNCT
ejpam-5662	205	11	(	(	PUNCT
ejpam-5662	205	12	2025	2025	NUM
ejpam-5662	205	13	)	)	PUNCT
ejpam-5662	205	14	,	,	PUNCT
ejpam-5662	205	15	5662	5662	NUM
ejpam-5662	205	16	9	9	NUM
ejpam-5662	205	17	of	of	ADP
ejpam-5662	205	18	36	36	NUM
ejpam-5662	205	19	3	3	NUM
ejpam-5662	205	20	.	.	PUNCT
ejpam-5662	206	1	the	the	DET
ejpam-5662	206	2	quantic	quantic	NOUN
ejpam-5662	206	3	-	-	PUNCT
ejpam-5662	206	4	do	do	NOUN
ejpam-5662	206	5	signifies	signify	VERB
ejpam-5662	206	6	a	a	DET
ejpam-5662	206	7	higher	high	ADJ
ejpam-5662	206	8	-	-	PUNCT
ejpam-5662	206	9	order	order	NOUN
ejpam-5662	206	10	restoring	restore	VERB
ejpam-5662	206	11	force	force	NOUN
ejpam-5662	206	12	.	.	PUNCT
ejpam-5662	207	1	this	this	PRON
ejpam-5662	207	2	enhances	enhance	VERB
ejpam-5662	207	3	additional	additional	ADJ
ejpam-5662	207	4	complexity	complexity	NOUN
ejpam-5662	207	5	,	,	PUNCT
ejpam-5662	207	6	permitting	permit	VERB
ejpam-5662	207	7	more	more	ADV
ejpam-5662	207	8	applicable	applicable	ADJ
ejpam-5662	207	9	dynamical	dynamical	ADJ
ejpam-5662	207	10	behavior	behavior	NOUN
ejpam-5662	207	11	,	,	PUNCT
ejpam-5662	207	12	such	such	ADJ
ejpam-5662	207	13	as	as	ADP
ejpam-5662	207	14	bifurcations	bifurcation	NOUN
ejpam-5662	207	15	,	,	PUNCT
ejpam-5662	207	16	multiple	multiple	ADJ
ejpam-5662	207	17	stable	stable	ADJ
ejpam-5662	207	18	equilibria	equilibrium	NOUN
ejpam-5662	207	19	,	,	PUNCT
ejpam-5662	207	20	and	and	CCONJ
ejpam-5662	207	21	chaotic	chaotic	ADJ
ejpam-5662	207	22	motion	motion	NOUN
ejpam-5662	207	23	under	under	ADP
ejpam-5662	207	24	definite	definite	ADJ
ejpam-5662	207	25	conditions	condition	NOUN
ejpam-5662	207	26	.	.	PUNCT
ejpam-5662	208	1	4	4	X
ejpam-5662	208	2	.	.	X
ejpam-5662	208	3	mathieu	mathieu	PROPN
ejpam-5662	208	4	’s	’s	PART
ejpam-5662	208	5	term	term	NOUN
ejpam-5662	208	6	presents	present	VERB
ejpam-5662	208	7	the	the	DET
ejpam-5662	208	8	probability	probability	NOUN
ejpam-5662	208	9	of	of	ADP
ejpam-5662	208	10	parametric	parametric	ADJ
ejpam-5662	208	11	resonance	resonance	NOUN
ejpam-5662	208	12	,	,	PUNCT
ejpam-5662	208	13	where	where	SCONJ
ejpam-5662	208	14	definite	definite	ADJ
ejpam-5662	208	15	motivating	motivating	NOUN
ejpam-5662	208	16	frequencies	frequency	NOUN
ejpam-5662	208	17	lead	lead	VERB
ejpam-5662	208	18	to	to	ADP
ejpam-5662	208	19	enormous	enormous	ADJ
ejpam-5662	208	20	amplitude	amplitude	NOUN
ejpam-5662	208	21	oscillations	oscillation	NOUN
ejpam-5662	208	22	.	.	PUNCT
ejpam-5662	209	1	5	5	X
ejpam-5662	209	2	.	.	X
ejpam-5662	209	3	the	the	DET
ejpam-5662	209	4	mixture	mixture	NOUN
ejpam-5662	209	5	of	of	ADP
ejpam-5662	209	6	cubic	cubic	ADJ
ejpam-5662	209	7	and	and	CCONJ
ejpam-5662	209	8	quintic	quintic	ADJ
ejpam-5662	209	9	nonlinearities	nonlinearitie	NOUN
ejpam-5662	209	10	leads	lead	VERB
ejpam-5662	209	11	to	to	ADP
ejpam-5662	209	12	enhancement	enhancement	VERB
ejpam-5662	209	13	dynamic	dynamic	ADJ
ejpam-5662	209	14	behaviors	behavior	NOUN
ejpam-5662	209	15	,	,	PUNCT
ejpam-5662	209	16	such	such	ADJ
ejpam-5662	209	17	as	as	ADP
ejpam-5662	209	18	bifurcations	bifurcation	NOUN
ejpam-5662	209	19	,	,	PUNCT
ejpam-5662	209	20	chaotic	chaotic	ADJ
ejpam-5662	209	21	motion	motion	NOUN
ejpam-5662	209	22	,	,	PUNCT
ejpam-5662	209	23	and	and	CCONJ
ejpam-5662	209	24	limit	limit	VERB
ejpam-5662	209	25	cycles	cycle	NOUN
ejpam-5662	209	26	.	.	PUNCT
ejpam-5662	210	1	6	6	X
ejpam-5662	210	2	.	.	X
ejpam-5662	210	3	the	the	DET
ejpam-5662	210	4	tdof	tdof	ADJ
ejpam-5662	210	5	systems	system	NOUN
ejpam-5662	210	6	may	may	AUX
ejpam-5662	210	7	be	be	AUX
ejpam-5662	210	8	combined	combine	VERB
ejpam-5662	210	9	in	in	ADP
ejpam-5662	210	10	several	several	ADJ
ejpam-5662	210	11	ways	way	NOUN
ejpam-5662	210	12	,	,	PUNCT
ejpam-5662	210	13	which	which	PRON
ejpam-5662	210	14	increases	increase	VERB
ejpam-5662	210	15	the	the	DET
ejpam-5662	210	16	complexity	complexity	NOUN
ejpam-5662	210	17	of	of	ADP
ejpam-5662	210	18	the	the	DET
ejpam-5662	210	19	system	system	NOUN
ejpam-5662	210	20	’s	’s	PART
ejpam-5662	210	21	structure	structure	NOUN
ejpam-5662	210	22	.	.	PUNCT
ejpam-5662	211	1	some	some	DET
ejpam-5662	211	2	application	application	NOUN
ejpam-5662	211	3	1	1	NUM
ejpam-5662	211	4	.	.	PUNCT
ejpam-5662	211	5	mechanical	mechanical	ADJ
ejpam-5662	211	6	systems	system	NOUN
ejpam-5662	211	7	(	(	PUNCT
ejpam-5662	211	8	suspension	suspension	NOUN
ejpam-5662	211	9	systems	system	NOUN
ejpam-5662	211	10	,	,	PUNCT
ejpam-5662	211	11	pendulums	pendulum	NOUN
ejpam-5662	211	12	with	with	ADP
ejpam-5662	211	13	elastic	elastic	ADJ
ejpam-5662	211	14	supports	support	NOUN
ejpam-5662	211	15	)	)	PUNCT
ejpam-5662	211	16	.	.	PUNCT
ejpam-5662	212	1	2	2	X
ejpam-5662	212	2	.	.	X
ejpam-5662	212	3	structural	structural	ADJ
ejpam-5662	212	4	engineering	engineering	NOUN
ejpam-5662	212	5	(	(	PUNCT
ejpam-5662	212	6	vibration	vibration	NOUN
ejpam-5662	212	7	of	of	ADP
ejpam-5662	212	8	beams	beam	NOUN
ejpam-5662	212	9	,	,	PUNCT
ejpam-5662	212	10	plates	plate	NOUN
ejpam-5662	212	11	,	,	PUNCT
ejpam-5662	212	12	and	and	CCONJ
ejpam-5662	212	13	shells	shell	NOUN
ejpam-5662	212	14	)	)	PUNCT
ejpam-5662	212	15	.	.	PUNCT
ejpam-5662	213	1	3	3	X
ejpam-5662	213	2	.	.	X
ejpam-5662	213	3	control	control	NOUN
ejpam-5662	213	4	systems	system	NOUN
ejpam-5662	213	5	and	and	CCONJ
ejpam-5662	213	6	robotics	robotic	NOUN
ejpam-5662	213	7	.	.	PUNCT
ejpam-5662	214	1	4	4	X
ejpam-5662	214	2	.	.	X
ejpam-5662	214	3	nonlinear	nonlinear	ADJ
ejpam-5662	214	4	optics	optic	NOUN
ejpam-5662	214	5	(	(	PUNCT
ejpam-5662	214	6	wave	wave	NOUN
ejpam-5662	214	7	propagation	propagation	NOUN
ejpam-5662	214	8	in	in	ADP
ejpam-5662	214	9	nonlinear	nonlinear	ADJ
ejpam-5662	214	10	media	medium	NOUN
ejpam-5662	214	11	)	)	PUNCT
ejpam-5662	214	12	.	.	PUNCT
ejpam-5662	215	1	4	4	X
ejpam-5662	215	2	.	.	X
ejpam-5662	215	3	damped	damp	VERB
ejpam-5662	215	4	tdof	tdof	NOUN
ejpam-5662	215	5	of	of	ADP
ejpam-5662	215	6	mdo	mdo	PROPN
ejpam-5662	215	7	configuration	configuration	NOUN
ejpam-5662	215	8	the	the	DET
ejpam-5662	215	9	current	current	ADJ
ejpam-5662	215	10	study	study	NOUN
ejpam-5662	215	11	investigates	investigate	VERB
ejpam-5662	215	12	a	a	DET
ejpam-5662	215	13	general	general	ADJ
ejpam-5662	215	14	version	version	NOUN
ejpam-5662	215	15	of	of	ADP
ejpam-5662	215	16	the	the	DET
ejpam-5662	215	17	damping	damp	VERB
ejpam-5662	215	18	tdof	tdof	NOUN
ejpam-5662	215	19	of	of	ADP
ejpam-5662	215	20	mdo	mdo	PROPN
ejpam-5662	215	21	,	,	PUNCT
ejpam-5662	215	22	which	which	PRON
ejpam-5662	215	23	deliberates	deliberate	VERB
ejpam-5662	215	24	the	the	DET
ejpam-5662	215	25	synchronous	synchronous	ADJ
ejpam-5662	215	26	parametric	parametric	ADJ
ejpam-5662	215	27	excitation	excitation	NOUN
ejpam-5662	215	28	in	in	ADP
ejpam-5662	215	29	a	a	DET
ejpam-5662	215	30	tdof	tdof	ADJ
ejpam-5662	215	31	nonlinear	nonlinear	ADJ
ejpam-5662	215	32	system	system	NOUN
ejpam-5662	215	33	with	with	ADP
ejpam-5662	215	34	a	a	DET
ejpam-5662	215	35	filled	fill	VERB
ejpam-5662	215	36	excitation	excitation	NOUN
ejpam-5662	215	37	matrix	matrix	NOUN
ejpam-5662	215	38	.	.	PUNCT
ejpam-5662	216	1	the	the	DET
ejpam-5662	216	2	synchronous	synchronous	ADJ
ejpam-5662	216	3	parametric	parametric	ADJ
ejpam-5662	216	4	excitation	excitation	NOUN
ejpam-5662	216	5	denotes	denote	VERB
ejpam-5662	216	6	the	the	DET
ejpam-5662	216	7	state	state	NOUN
ejpam-5662	216	8	where	where	SCONJ
ejpam-5662	216	9	each	each	DET
ejpam-5662	216	10	degree	degree	NOUN
ejpam-5662	216	11	of	of	ADP
ejpam-5662	216	12	freedom	freedom	NOUN
ejpam-5662	216	13	includes	include	VERB
ejpam-5662	216	14	the	the	DET
ejpam-5662	216	15	same	same	ADJ
ejpam-5662	216	16	or	or	CCONJ
ejpam-5662	216	17	harmonically	harmonically	ADV
ejpam-5662	216	18	related	relate	VERB
ejpam-5662	216	19	frequencies	frequency	NOUN
ejpam-5662	216	20	that	that	PRON
ejpam-5662	216	21	excite	excite	VERB
ejpam-5662	216	22	all	all	DET
ejpam-5662	216	23	degrees	degree	NOUN
ejpam-5662	216	24	of	of	ADP
ejpam-5662	216	25	freedom	freedom	NOUN
ejpam-5662	216	26	simultaneously	simultaneously	ADV
ejpam-5662	216	27	.	.	PUNCT
ejpam-5662	217	1	this	this	PRON
ejpam-5662	217	2	indicates	indicate	VERB
ejpam-5662	217	3	that	that	SCONJ
ejpam-5662	217	4	the	the	DET
ejpam-5662	217	5	parametric	parametric	ADJ
ejpam-5662	217	6	excitation	excitation	NOUN
ejpam-5662	217	7	terms	term	NOUN
ejpam-5662	217	8	influencing	influence	VERB
ejpam-5662	217	9	both	both	DET
ejpam-5662	217	10	degrees	degree	NOUN
ejpam-5662	217	11	of	of	ADP
ejpam-5662	217	12	freedom	freedom	NOUN
ejpam-5662	217	13	in	in	ADP
ejpam-5662	217	14	a	a	DET
ejpam-5662	217	15	tdof	tdof	NOUN
ejpam-5662	217	16	of	of	ADP
ejpam-5662	217	17	mdo	mdo	PROPN
ejpam-5662	217	18	are	be	AUX
ejpam-5662	217	19	driven	drive	VERB
ejpam-5662	217	20	by	by	ADP
ejpam-5662	217	21	the	the	DET
ejpam-5662	217	22	same	same	ADJ
ejpam-5662	217	23	or	or	CCONJ
ejpam-5662	217	24	synchronized	synchronize	VERB
ejpam-5662	217	25	periodic	periodic	ADJ
ejpam-5662	217	26	function	function	NOUN
ejpam-5662	217	27	,	,	PUNCT
ejpam-5662	217	28	usually	usually	ADV
ejpam-5662	217	29	a	a	DET
ejpam-5662	217	30	sinusoidal	sinusoidal	ADJ
ejpam-5662	217	31	function	function	NOUN
ejpam-5662	217	32	of	of	ADP
ejpam-5662	217	33	time	time	NOUN
ejpam-5662	217	34	.	.	PUNCT
ejpam-5662	218	1	this	this	PRON
ejpam-5662	218	2	opposes	oppose	VERB
ejpam-5662	218	3	the	the	DET
ejpam-5662	218	4	asynchronous	asynchronous	ADJ
ejpam-5662	218	5	parametric	parametric	ADJ
ejpam-5662	218	6	excitation	excitation	NOUN
ejpam-5662	218	7	which	which	PRON
ejpam-5662	218	8	indicates	indicate	VERB
ejpam-5662	218	9	that	that	SCONJ
ejpam-5662	218	10	the	the	DET
ejpam-5662	218	11	excitation	excitation	NOUN
ejpam-5662	218	12	acting	act	VERB
ejpam-5662	218	13	on	on	ADP
ejpam-5662	218	14	the	the	DET
ejpam-5662	218	15	two	two	NUM
ejpam-5662	218	16	degrees	degree	NOUN
ejpam-5662	218	17	of	of	ADP
ejpam-5662	218	18	freedom	freedom	NOUN
ejpam-5662	218	19	occurs	occur	VERB
ejpam-5662	218	20	at	at	ADP
ejpam-5662	218	21	different	different	ADJ
ejpam-5662	218	22	frequencies	frequency	NOUN
ejpam-5662	218	23	or	or	CCONJ
ejpam-5662	218	24	phases	phase	NOUN
ejpam-5662	218	25	as	as	SCONJ
ejpam-5662	218	26	discussed	discuss	VERB
ejpam-5662	218	27	by	by	ADP
ejpam-5662	218	28	[	[	X
ejpam-5662	218	29	38	38	NUM
ejpam-5662	218	30	]	]	PUNCT
ejpam-5662	218	31	.	.	PUNCT
ejpam-5662	219	1	what	what	PRON
ejpam-5662	219	2	follows	follow	VERB
ejpam-5662	219	3	,	,	PUNCT
ejpam-5662	219	4	are	be	AUX
ejpam-5662	219	5	some	some	DET
ejpam-5662	219	6	applications	application	NOUN
ejpam-5662	219	7	of	of	ADP
ejpam-5662	219	8	parametric	parametric	ADJ
ejpam-5662	219	9	excitation	excitation	NOUN
ejpam-5662	219	10	:	:	PUNCT
ejpam-5662	219	11	1	1	NUM
ejpam-5662	219	12	.	.	X
ejpam-5662	219	13	light	light	ADJ
ejpam-5662	219	14	transmission	transmission	NOUN
ejpam-5662	219	15	in	in	ADP
ejpam-5662	219	16	nonlinear	nonlinear	ADJ
ejpam-5662	219	17	media	medium	NOUN
ejpam-5662	219	18	can	can	AUX
ejpam-5662	219	19	be	be	AUX
ejpam-5662	219	20	affected	affect	VERB
ejpam-5662	219	21	by	by	ADP
ejpam-5662	219	22	synchronous	synchronous	ADJ
ejpam-5662	219	23	parametric	parametric	ADJ
ejpam-5662	219	24	stimulation	stimulation	NOUN
ejpam-5662	219	25	in	in	ADP
ejpam-5662	219	26	optical	optical	ADJ
ejpam-5662	219	27	systems	system	NOUN
ejpam-5662	219	28	.	.	PUNCT
ejpam-5662	220	1	2	2	X
ejpam-5662	220	2	.	.	X
ejpam-5662	220	3	synchronous	synchronous	ADJ
ejpam-5662	220	4	parametric	parametric	ADJ
ejpam-5662	220	5	excitation	excitation	NOUN
ejpam-5662	220	6	can	can	AUX
ejpam-5662	220	7	be	be	AUX
ejpam-5662	220	8	utilized	utilize	VERB
ejpam-5662	220	9	in	in	ADP
ejpam-5662	220	10	structural	structural	ADJ
ejpam-5662	220	11	engineering	engineering	NOUN
ejpam-5662	220	12	vibration	vibration	NOUN
ejpam-5662	220	13	control	control	NOUN
ejpam-5662	220	14	systems	system	NOUN
ejpam-5662	220	15	.	.	PUNCT
ejpam-5662	221	1	3	3	X
ejpam-5662	221	2	.	.	X
ejpam-5662	221	3	systems	system	NOUN
ejpam-5662	221	4	that	that	PRON
ejpam-5662	221	5	maximize	maximize	VERB
ejpam-5662	221	6	energy	energy	NOUN
ejpam-5662	221	7	reduction	reduction	NOUN
ejpam-5662	221	8	by	by	ADP
ejpam-5662	221	9	using	use	VERB
ejpam-5662	221	10	parametric	parametric	ADJ
ejpam-5662	221	11	resonance	resonance	NOUN
ejpam-5662	221	12	,	,	PUNCT
ejpam-5662	221	13	in	in	ADP
ejpam-5662	221	14	which	which	PRON
ejpam-5662	221	15	the	the	DET
ejpam-5662	221	16	excitation	excitation	NOUN
ejpam-5662	221	17	indicates	indicate	VERB
ejpam-5662	221	18	enormous	enormous	ADJ
ejpam-5662	221	19	oscillations	oscillation	NOUN
ejpam-5662	221	20	.	.	PUNCT
ejpam-5662	222	1	a.	a.	PROPN
ejpam-5662	222	2	alanazy	alanazy	PROPN
ejpam-5662	222	3	,	,	PUNCT
ejpam-5662	222	4	g.	g.	PROPN
ejpam-5662	222	5	m.	m.	PROPN
ejpam-5662	222	6	moatimid	moatimid	PROPN
ejpam-5662	222	7	,	,	PUNCT
ejpam-5662	222	8	m.	m.	PROPN
ejpam-5662	222	9	a.	a.	PROPN
ejpam-5662	222	10	a.	a.	PROPN
ejpam-5662	222	11	mohamed	mohamed	PROPN
ejpam-5662	222	12	/	/	SYM
ejpam-5662	222	13	eur	eur	PROPN
ejpam-5662	222	14	.	.	PUNCT
ejpam-5662	223	1	j.	j.	PROPN
ejpam-5662	223	2	pure	pure	PROPN
ejpam-5662	223	3	appl	appl	PROPN
ejpam-5662	223	4	.	.	PROPN
ejpam-5662	223	5	math	math	PROPN
ejpam-5662	223	6	,	,	PUNCT
ejpam-5662	223	7	18	18	NUM
ejpam-5662	223	8	(	(	PUNCT
ejpam-5662	223	9	2	2	NUM
ejpam-5662	223	10	)	)	PUNCT
ejpam-5662	223	11	(	(	PUNCT
ejpam-5662	223	12	2025	2025	NUM
ejpam-5662	223	13	)	)	PUNCT
ejpam-5662	223	14	,	,	PUNCT
ejpam-5662	223	15	5662	5662	NUM
ejpam-5662	223	16	10	10	NUM
ejpam-5662	223	17	of	of	ADP
ejpam-5662	223	18	36	36	NUM
ejpam-5662	223	19	in	in	ADP
ejpam-5662	223	20	order	order	NOUN
ejpam-5662	223	21	to	to	PART
ejpam-5662	223	22	accomplish	accomplish	VERB
ejpam-5662	223	23	that	that	PRON
ejpam-5662	223	24	,	,	PUNCT
ejpam-5662	223	25	the	the	DET
ejpam-5662	223	26	nonlinear	nonlinear	ADJ
ejpam-5662	223	27	tdof	tdof	NOUN
ejpam-5662	223	28	of	of	ADP
ejpam-5662	223	29	the	the	DET
ejpam-5662	223	30	mdo	mdo	PROPN
ejpam-5662	223	31	system	system	NOUN
ejpam-5662	223	32	is	be	AUX
ejpam-5662	223	33	suggested	suggest	VERB
ejpam-5662	223	34	as	as	SCONJ
ejpam-5662	223	35	follows	follow	VERB
ejpam-5662	223	36	[	[	X
ejpam-5662	223	37	45	45	NUM
ejpam-5662	223	38	]	]	PUNCT
ejpam-5662	223	39	:	:	PUNCT
ejpam-5662	223	40	ẍ+	ẍ+	PROPN
ejpam-5662	223	41	ω2	ω2	ADJ
ejpam-5662	223	42	1x+	1x+	NUM
ejpam-5662	223	43	µ1ẋ+	µ1ẋ+	NUM
ejpam-5662	223	44	γ1x	γ1x	X
ejpam-5662	223	45	3	3	NUM
ejpam-5662	223	46	+	+	CCONJ
ejpam-5662	223	47	λ1x	λ1x	PUNCT
ejpam-5662	223	48	5	5	NUM
ejpam-5662	223	49	+	+	SYM
ejpam-5662	223	50	α1ẋ	α1ẋ	PROPN
ejpam-5662	223	51	3	3	NUM
ejpam-5662	223	52	+	+	NUM
ejpam-5662	223	53	η11x	η11x	NOUN
ejpam-5662	223	54	cosωpt+	cosωpt+	X
ejpam-5662	223	55	η12y	η12y	PROPN
ejpam-5662	223	56	cosωpt	cosωpt	NOUN
ejpam-5662	223	57	=	=	NOUN
ejpam-5662	223	58	0	0	PROPN
ejpam-5662	223	59	,	,	PUNCT
ejpam-5662	223	60	(	(	PUNCT
ejpam-5662	223	61	18	18	NUM
ejpam-5662	223	62	)	)	PUNCT
ejpam-5662	223	63	and	and	CCONJ
ejpam-5662	223	64	ÿ	ÿ	PROPN
ejpam-5662	223	65	+	+	CCONJ
ejpam-5662	223	66	ω2	ω2	ADJ
ejpam-5662	223	67	2y	2y	PROPN
ejpam-5662	223	68	+	+	CCONJ
ejpam-5662	223	69	µ2ẏ	µ2ẏ	VERB
ejpam-5662	223	70	+	+	CCONJ
ejpam-5662	223	71	γ2y	γ2y	PROPN
ejpam-5662	223	72	3	3	NUM
ejpam-5662	223	73	+	+	CCONJ
ejpam-5662	223	74	λ2y	λ2y	PROPN
ejpam-5662	223	75	5	5	NUM
ejpam-5662	223	76	+	+	CCONJ
ejpam-5662	223	77	α2ẏ	α2ẏ	PROPN
ejpam-5662	223	78	3	3	NUM
ejpam-5662	224	1	+	+	CCONJ
ejpam-5662	224	2	η21x	η21x	PROPN
ejpam-5662	224	3	cosωpt+	cosωpt+	INTJ
ejpam-5662	224	4	η22y	η22y	ADV
ejpam-5662	224	5	cosωpt	cosωpt	NOUN
ejpam-5662	224	6	=	=	SYM
ejpam-5662	224	7	0	0	NUM
ejpam-5662	224	8	,	,	PUNCT
ejpam-5662	224	9	(	(	PUNCT
ejpam-5662	224	10	19	19	NUM
ejpam-5662	224	11	)	)	PUNCT
ejpam-5662	224	12	where	where	SCONJ
ejpam-5662	224	13	ω1	ω1	PROPN
ejpam-5662	224	14	,	,	PUNCT
ejpam-5662	224	15	and	and	CCONJ
ejpam-5662	224	16	ω2	ω2	NOUN
ejpam-5662	224	17	are	be	AUX
ejpam-5662	224	18	the	the	DET
ejpam-5662	224	19	natural	natural	ADJ
ejpam-5662	224	20	frequencies	frequency	NOUN
ejpam-5662	224	21	of	of	ADP
ejpam-5662	224	22	the	the	DET
ejpam-5662	224	23	two	two	NUM
ejpam-5662	224	24	oscillators	oscillator	NOUN
ejpam-5662	224	25	,	,	PUNCT
ejpam-5662	224	26	µ1	µ1	PROPN
ejpam-5662	224	27	,	,	PUNCT
ejpam-5662	224	28	and	and	CCONJ
ejpam-5662	224	29	µ2	µ2	PROPN
ejpam-5662	224	30	are	be	AUX
ejpam-5662	224	31	the	the	DET
ejpam-5662	224	32	linear	linear	ADJ
ejpam-5662	224	33	damping	damp	VERB
ejpam-5662	224	34	coefficients	coefficient	NOUN
ejpam-5662	224	35	,	,	PUNCT
ejpam-5662	224	36	γ1	γ1	NOUN
ejpam-5662	224	37	,	,	PUNCT
ejpam-5662	224	38	and	and	CCONJ
ejpam-5662	224	39	γ2	γ2	PROPN
ejpam-5662	224	40	are	be	AUX
ejpam-5662	224	41	the	the	DET
ejpam-5662	224	42	nonlinear	nonlinear	ADJ
ejpam-5662	224	43	cubic	cubic	ADJ
ejpam-5662	224	44	coefficients	coefficient	NOUN
ejpam-5662	224	45	,	,	PUNCT
ejpam-5662	224	46	λ1	λ1	ADJ
ejpam-5662	224	47	,	,	PUNCT
ejpam-5662	224	48	and	and	CCONJ
ejpam-5662	224	49	λ2	λ2	NOUN
ejpam-5662	224	50	are	be	AUX
ejpam-5662	224	51	the	the	DET
ejpam-5662	224	52	nonlinear	nonlinear	ADJ
ejpam-5662	224	53	quintic	quintic	ADJ
ejpam-5662	224	54	coefficients	coefficient	NOUN
ejpam-5662	224	55	,	,	PUNCT
ejpam-5662	224	56	α1	α1	NOUN
ejpam-5662	224	57	,	,	PUNCT
ejpam-5662	224	58	and	and	CCONJ
ejpam-5662	224	59	α2	α2	PROPN
ejpam-5662	224	60	are	be	AUX
ejpam-5662	224	61	the	the	DET
ejpam-5662	224	62	nonlinear	nonlinear	ADJ
ejpam-5662	224	63	damping	damp	VERB
ejpam-5662	224	64	coefficients	coefficient	NOUN
ejpam-5662	224	65	,	,	PUNCT
ejpam-5662	224	66	η11	η11	NOUN
ejpam-5662	224	67	,	,	PUNCT
ejpam-5662	224	68	η21	η21	PROPN
ejpam-5662	224	69	,	,	PUNCT
ejpam-5662	224	70	η12	η12	NOUN
ejpam-5662	224	71	,	,	PUNCT
ejpam-5662	224	72	and	and	CCONJ
ejpam-5662	224	73	η22	η22	PROPN
ejpam-5662	224	74	are	be	AUX
ejpam-5662	224	75	the	the	DET
ejpam-5662	224	76	joint	joint	ADJ
ejpam-5662	224	77	excited	excited	ADJ
ejpam-5662	224	78	amplitudes	amplitude	NOUN
ejpam-5662	224	79	of	of	ADP
ejpam-5662	224	80	the	the	DET
ejpam-5662	224	81	two	two	NUM
ejpam-5662	224	82	oscillators	oscillator	NOUN
ejpam-5662	224	83	,	,	PUNCT
ejpam-5662	224	84	and	and	CCONJ
ejpam-5662	224	85	ωp	ωp	ADV
ejpam-5662	224	86	is	be	AUX
ejpam-5662	224	87	the	the	DET
ejpam-5662	224	88	excited	excited	ADJ
ejpam-5662	224	89	frequency	frequency	NOUN
ejpam-5662	224	90	.	.	PUNCT
ejpam-5662	225	1	the	the	DET
ejpam-5662	225	2	suggested	suggest	VERB
ejpam-5662	225	3	ics	ic	NOUN
ejpam-5662	225	4	of	of	ADP
ejpam-5662	225	5	eq	eq	PROPN
ejpam-5662	225	6	.	.	PUNCT
ejpam-5662	226	1	(	(	PUNCT
ejpam-5662	226	2	18	18	NUM
ejpam-5662	226	3	)	)	PUNCT
ejpam-5662	226	4	and	and	CCONJ
ejpam-5662	226	5	(	(	PUNCT
ejpam-5662	226	6	19	19	NUM
ejpam-5662	226	7	)	)	PUNCT
ejpam-5662	226	8	are	be	AUX
ejpam-5662	226	9	regularly	regularly	ADV
ejpam-5662	226	10	assumed	assume	VERB
ejpam-5662	226	11	as	as	ADP
ejpam-5662	226	12	[	[	X
ejpam-5662	226	13	30	30	NUM
ejpam-5662	226	14	-	-	SYM
ejpam-5662	226	15	44	44	NUM
ejpam-5662	226	16	and	and	CCONJ
ejpam-5662	226	17	46	46	NUM
ejpam-5662	226	18	]	]	X
ejpam-5662	226	19	:	:	PUNCT
ejpam-5662	226	20	x(0	x(0	PROPN
ejpam-5662	226	21	)	)	PUNCT
ejpam-5662	227	1	=	=	SYM
ejpam-5662	228	1	a	a	DET
ejpam-5662	228	2	,	,	PUNCT
ejpam-5662	228	3	y(0	y(0	PROPN
ejpam-5662	228	4	)	)	PUNCT
ejpam-5662	228	5	=	=	SYM
ejpam-5662	228	6	b	b	PROPN
ejpam-5662	228	7	,	,	PUNCT
ejpam-5662	228	8	ẋ(0	ẋ(0	X
ejpam-5662	228	9	)	)	PUNCT
ejpam-5662	228	10	=	=	SYM
ejpam-5662	228	11	0	0	NUM
ejpam-5662	228	12	,	,	PUNCT
ejpam-5662	228	13	and	and	CCONJ
ejpam-5662	228	14	ẏ(0	ẏ(0	NOUN
ejpam-5662	228	15	)	)	PUNCT
ejpam-5662	228	16	=	=	SYM
ejpam-5662	229	1	0	0	X
ejpam-5662	229	2	.	.	PUNCT
ejpam-5662	229	3	(	(	PUNCT
ejpam-5662	229	4	20	20	NUM
ejpam-5662	229	5	)	)	PUNCT
ejpam-5662	229	6	eqs	eqs	PROPN
ejpam-5662	229	7	.	.	PUNCT
ejpam-5662	230	1	(	(	PUNCT
ejpam-5662	230	2	18	18	NUM
ejpam-5662	230	3	)	)	PUNCT
ejpam-5662	230	4	and	and	CCONJ
ejpam-5662	230	5	(	(	PUNCT
ejpam-5662	230	6	19	19	NUM
ejpam-5662	230	7	)	)	PUNCT
ejpam-5662	230	8	could	could	AUX
ejpam-5662	230	9	be	be	AUX
ejpam-5662	230	10	re	re	VERB
ejpam-5662	230	11	-	-	VERB
ejpam-5662	230	12	written	write	VERB
ejpam-5662	230	13	as	as	ADP
ejpam-5662	230	14	:	:	PUNCT
ejpam-5662	230	15	ẍ+	ẍ+	PROPN
ejpam-5662	230	16	f1(x	f1(x	PROPN
ejpam-5662	230	17	,	,	PUNCT
ejpam-5662	230	18	ẋ	ẋ	PROPN
ejpam-5662	230	19	,	,	PUNCT
ejpam-5662	230	20	ẍ	ẍ	PROPN
ejpam-5662	230	21	,	,	PUNCT
ejpam-5662	230	22	y	y	PROPN
ejpam-5662	230	23	,	,	PUNCT
ejpam-5662	230	24	ẏ	ẏ	PROPN
ejpam-5662	230	25	,	,	PUNCT
ejpam-5662	230	26	ÿ	ÿ	PROPN
ejpam-5662	230	27	)	)	PUNCT
ejpam-5662	230	28	+	+	SYM
ejpam-5662	231	1	f2(x	f2(x	PROPN
ejpam-5662	231	2	,	,	PUNCT
ejpam-5662	231	3	ẋ	ẋ	PROPN
ejpam-5662	231	4	,	,	PUNCT
ejpam-5662	231	5	ẍ	ẍ	PROPN
ejpam-5662	231	6	,	,	PUNCT
ejpam-5662	231	7	y	y	PROPN
ejpam-5662	231	8	,	,	PUNCT
ejpam-5662	231	9	ẏ	ẏ	PROPN
ejpam-5662	231	10	,	,	PUNCT
ejpam-5662	231	11	ÿ	ÿ	ADJ
ejpam-5662	231	12	)	)	PUNCT
ejpam-5662	231	13	=	=	SYM
ejpam-5662	231	14	0	0	NUM
ejpam-5662	231	15	,	,	PUNCT
ejpam-5662	231	16	(	(	PUNCT
ejpam-5662	231	17	21	21	NUM
ejpam-5662	231	18	)	)	PUNCT
ejpam-5662	231	19	and	and	CCONJ
ejpam-5662	231	20	ÿ	ÿ	PROPN
ejpam-5662	231	21	+	+	PROPN
ejpam-5662	231	22	h1(y	h1(y	PROPN
ejpam-5662	231	23	,	,	PUNCT
ejpam-5662	231	24	ẏ	ẏ	PROPN
ejpam-5662	231	25	,	,	PUNCT
ejpam-5662	231	26	ÿ	ÿ	PROPN
ejpam-5662	231	27	,	,	PUNCT
ejpam-5662	231	28	x	x	X
ejpam-5662	231	29	,	,	PUNCT
ejpam-5662	231	30	ẋ	ẋ	PROPN
ejpam-5662	231	31	,	,	PUNCT
ejpam-5662	231	32	ẍ	ẍ	X
ejpam-5662	231	33	)	)	PUNCT
ejpam-5662	232	1	+	+	PUNCT
ejpam-5662	232	2	h2(y	h2(y	PROPN
ejpam-5662	232	3	,	,	PUNCT
ejpam-5662	232	4	ẏ	ẏ	PROPN
ejpam-5662	232	5	,	,	PUNCT
ejpam-5662	232	6	ÿ	ÿ	PROPN
ejpam-5662	232	7	,	,	PUNCT
ejpam-5662	232	8	x	x	X
ejpam-5662	232	9	,	,	PUNCT
ejpam-5662	232	10	ẋ	ẋ	PROPN
ejpam-5662	232	11	,	,	PUNCT
ejpam-5662	232	12	ẍ	ẍ	X
ejpam-5662	232	13	)	)	PUNCT
ejpam-5662	232	14	=	=	SYM
ejpam-5662	232	15	0	0	NUM
ejpam-5662	232	16	,	,	PUNCT
ejpam-5662	232	17	(	(	PUNCT
ejpam-5662	232	18	22	22	NUM
ejpam-5662	232	19	)	)	PUNCT
ejpam-5662	232	20	where	where	SCONJ
ejpam-5662	232	21	f1(x	f1(x	VERB
ejpam-5662	232	22	,	,	PUNCT
ejpam-5662	232	23	ẋ	ẋ	PROPN
ejpam-5662	232	24	,	,	PUNCT
ejpam-5662	232	25	ẍ	ẍ	PROPN
ejpam-5662	232	26	,	,	PUNCT
ejpam-5662	232	27	y	y	PROPN
ejpam-5662	232	28	,	,	PUNCT
ejpam-5662	232	29	ẏ	ẏ	PROPN
ejpam-5662	232	30	,	,	PUNCT
ejpam-5662	232	31	ÿ)and	ÿ)and	PROPN
ejpam-5662	232	32	h1(x	h1(x	NOUN
ejpam-5662	232	33	,	,	PUNCT
ejpam-5662	232	34	ẋ	ẋ	PROPN
ejpam-5662	232	35	,	,	PUNCT
ejpam-5662	232	36	ẍ	ẍ	PROPN
ejpam-5662	232	37	,	,	PUNCT
ejpam-5662	232	38	y	y	PROPN
ejpam-5662	232	39	,	,	PUNCT
ejpam-5662	232	40	ẏ	ẏ	PROPN
ejpam-5662	232	41	,	,	PUNCT
ejpam-5662	232	42	ÿ	ÿ	ADJ
ejpam-5662	232	43	)	)	PUNCT
ejpam-5662	232	44	are	be	AUX
ejpam-5662	232	45	the	the	DET
ejpam-5662	232	46	odd	odd	ADJ
ejpam-5662	232	47	secular	secular	ADJ
ejpam-5662	232	48	terms	term	NOUN
ejpam-5662	232	49	in	in	ADP
ejpam-5662	232	50	the	the	DET
ejpam-5662	232	51	two	two	NUM
ejpam-5662	232	52	oscillators	oscillator	NOUN
ejpam-5662	232	53	,	,	PUNCT
ejpam-5662	232	54	while	while	SCONJ
ejpam-5662	232	55	f2(x	f2(x	PROPN
ejpam-5662	232	56	,	,	PUNCT
ejpam-5662	232	57	ẋ	ẋ	PROPN
ejpam-5662	232	58	,	,	PUNCT
ejpam-5662	232	59	ẍ	ẍ	PROPN
ejpam-5662	232	60	,	,	PUNCT
ejpam-5662	232	61	y	y	PROPN
ejpam-5662	232	62	,	,	PUNCT
ejpam-5662	232	63	ẏ	ẏ	PROPN
ejpam-5662	232	64	,	,	PUNCT
ejpam-5662	232	65	ÿ	ÿ	PROPN
ejpam-5662	232	66	)	)	PUNCT
ejpam-5662	232	67	andh2(x	andh2(x	NOUN
ejpam-5662	232	68	,	,	PUNCT
ejpam-5662	232	69	ẋ	ẋ	PROPN
ejpam-5662	232	70	,	,	PUNCT
ejpam-5662	232	71	ẍ	ẍ	PROPN
ejpam-5662	232	72	,	,	PUNCT
ejpam-5662	232	73	y	y	PROPN
ejpam-5662	232	74	,	,	PUNCT
ejpam-5662	232	75	ẏ	ẏ	PROPN
ejpam-5662	232	76	,	,	PUNCT
ejpam-5662	232	77	ÿ	ÿ	ADJ
ejpam-5662	232	78	)	)	PUNCT
ejpam-5662	232	79	are	be	AUX
ejpam-5662	232	80	the	the	DET
ejpam-5662	232	81	damping	damp	VERB
ejpam-5662	232	82	secular	secular	ADJ
ejpam-5662	232	83	terms	term	NOUN
ejpam-5662	232	84	in	in	ADP
ejpam-5662	232	85	them	they	PRON
ejpam-5662	232	86	.	.	PUNCT
ejpam-5662	233	1	these	these	DET
ejpam-5662	233	2	terms	term	NOUN
ejpam-5662	233	3	are	be	AUX
ejpam-5662	233	4	defined	define	VERB
ejpam-5662	233	5	as	as	ADP
ejpam-5662	233	6	:	:	PUNCT
ejpam-5662	233	7	f1(x	f1(x	NUM
ejpam-5662	233	8	,	,	PUNCT
ejpam-5662	233	9	ẋ	ẋ	PROPN
ejpam-5662	233	10	,	,	PUNCT
ejpam-5662	233	11	ẍ	ẍ	PROPN
ejpam-5662	233	12	,	,	PUNCT
ejpam-5662	233	13	y	y	PROPN
ejpam-5662	233	14	,	,	PUNCT
ejpam-5662	233	15	ẏ	ẏ	PROPN
ejpam-5662	233	16	,	,	PUNCT
ejpam-5662	233	17	ÿ	ÿ	ADJ
ejpam-5662	233	18	)	)	PUNCT
ejpam-5662	233	19	=	=	SYM
ejpam-5662	234	1	ω2	ω2	ADJ
ejpam-5662	234	2	1x+	1x+	NUM
ejpam-5662	234	3	γ1x	γ1x	NOUN
ejpam-5662	234	4	3	3	NUM
ejpam-5662	234	5	+	+	CCONJ
ejpam-5662	234	6	λ1x	λ1x	PUNCT
ejpam-5662	234	7	5	5	NUM
ejpam-5662	234	8	+	+	NUM
ejpam-5662	234	9	η11x	η11x	NOUN
ejpam-5662	234	10	cosωpt+	cosωpt+	NOUN
ejpam-5662	234	11	η12y	η12y	PROPN
ejpam-5662	234	12	cosωpt	cosωpt	NOUN
ejpam-5662	234	13	,	,	PUNCT
ejpam-5662	234	14	(	(	PUNCT
ejpam-5662	234	15	23	23	NUM
ejpam-5662	234	16	)	)	PUNCT
ejpam-5662	234	17	f2(x	f2(x	PROPN
ejpam-5662	234	18	,	,	PUNCT
ejpam-5662	234	19	ẋ	ẋ	PROPN
ejpam-5662	234	20	,	,	PUNCT
ejpam-5662	234	21	ẍ	ẍ	PROPN
ejpam-5662	234	22	,	,	PUNCT
ejpam-5662	234	23	y	y	PROPN
ejpam-5662	234	24	,	,	PUNCT
ejpam-5662	234	25	ẏ	ẏ	PROPN
ejpam-5662	234	26	,	,	PUNCT
ejpam-5662	234	27	ÿ	ÿ	ADJ
ejpam-5662	234	28	)	)	PUNCT
ejpam-5662	234	29	=	=	PUNCT
ejpam-5662	234	30	µ1ẋ+	µ1ẋ+	NUM
ejpam-5662	234	31	α1ẋ	α1ẋ	PROPN
ejpam-5662	234	32	3	3	NUM
ejpam-5662	234	33	,	,	PUNCT
ejpam-5662	234	34	(	(	PUNCT
ejpam-5662	234	35	24	24	NUM
ejpam-5662	234	36	)	)	PUNCT
ejpam-5662	234	37	h1(x	h1(x	PROPN
ejpam-5662	234	38	,	,	PUNCT
ejpam-5662	234	39	ẋ	ẋ	PROPN
ejpam-5662	234	40	,	,	PUNCT
ejpam-5662	234	41	ẍ	ẍ	PROPN
ejpam-5662	234	42	,	,	PUNCT
ejpam-5662	234	43	y	y	PROPN
ejpam-5662	234	44	,	,	PUNCT
ejpam-5662	234	45	ẏ	ẏ	PROPN
ejpam-5662	234	46	,	,	PUNCT
ejpam-5662	234	47	ÿ	ÿ	ADJ
ejpam-5662	234	48	)	)	PUNCT
ejpam-5662	234	49	=	=	SYM
ejpam-5662	234	50	ω2	ω2	ADJ
ejpam-5662	234	51	2y	2y	PROPN
ejpam-5662	234	52	+	+	CCONJ
ejpam-5662	234	53	γ2y	γ2y	X
ejpam-5662	234	54	3	3	NUM
ejpam-5662	234	55	+	+	CCONJ
ejpam-5662	234	56	λ2y	λ2y	PROPN
ejpam-5662	234	57	5	5	NUM
ejpam-5662	234	58	+	+	NUM
ejpam-5662	234	59	η21x	η21x	PROPN
ejpam-5662	234	60	cosωpt+	cosωpt+	PROPN
ejpam-5662	234	61	η22y	η22y	ADV
ejpam-5662	234	62	cosωpt	cosωpt	PROPN
ejpam-5662	234	63	,	,	PUNCT
ejpam-5662	234	64	(	(	PUNCT
ejpam-5662	234	65	25	25	NUM
ejpam-5662	234	66	)	)	PUNCT
ejpam-5662	234	67	and	and	CCONJ
ejpam-5662	234	68	h2(x	h2(x	PROPN
ejpam-5662	234	69	,	,	PUNCT
ejpam-5662	234	70	ẋ	ẋ	PROPN
ejpam-5662	234	71	,	,	PUNCT
ejpam-5662	234	72	ẍ	ẍ	PROPN
ejpam-5662	234	73	,	,	PUNCT
ejpam-5662	234	74	y	y	PROPN
ejpam-5662	234	75	,	,	PUNCT
ejpam-5662	234	76	ẏ	ẏ	PROPN
ejpam-5662	234	77	,	,	PUNCT
ejpam-5662	234	78	ÿ	ÿ	ADJ
ejpam-5662	234	79	)	)	PUNCT
ejpam-5662	234	80	=	=	VERB
ejpam-5662	234	81	µ2ẏ	µ2ẏ	VERB
ejpam-5662	234	82	+	+	CCONJ
ejpam-5662	234	83	α2ẏ	α2ẏ	ADJ
ejpam-5662	234	84	3	3	NUM
ejpam-5662	234	85	.	.	PUNCT
ejpam-5662	235	1	(	(	PUNCT
ejpam-5662	235	2	26	26	NUM
ejpam-5662	235	3	)	)	PUNCT
ejpam-5662	235	4	the	the	DET
ejpam-5662	235	5	trial	trial	NOUN
ejpam-5662	235	6	solutions	solution	NOUN
ejpam-5662	235	7	of	of	ADP
ejpam-5662	235	8	the	the	DET
ejpam-5662	235	9	system	system	NOUN
ejpam-5662	235	10	as	as	SCONJ
ejpam-5662	235	11	given	give	VERB
ejpam-5662	235	12	in	in	ADP
ejpam-5662	235	13	eqs	eqs	PROPN
ejpam-5662	235	14	.	.	PUNCT
ejpam-5662	236	1	(	(	PUNCT
ejpam-5662	236	2	21	21	NUM
ejpam-5662	236	3	)	)	PUNCT
ejpam-5662	236	4	and	and	CCONJ
ejpam-5662	236	5	(	(	PUNCT
ejpam-5662	236	6	22	22	NUM
ejpam-5662	236	7	)	)	PUNCT
ejpam-5662	236	8	are	be	AUX
ejpam-5662	236	9	assumed	assume	VERB
ejpam-5662	236	10	,	,	PUNCT
ejpam-5662	236	11	as	as	ADP
ejpam-5662	236	12	per	per	ADP
ejpam-5662	236	13	the	the	DET
ejpam-5662	236	14	npa	npa	NOUN
ejpam-5662	236	15	method	method	NOUN
ejpam-5662	236	16	,	,	PUNCT
ejpam-5662	236	17	as	as	ADP
ejpam-5662	236	18	:	:	PUNCT
ejpam-5662	236	19	ũ	ũ	PROPN
ejpam-5662	236	20	=	=	PROPN
ejpam-5662	236	21	a	a	DET
ejpam-5662	236	22	cosω1	cosω1	PROPN
ejpam-5662	236	23	t	t	PROPN
ejpam-5662	236	24	,	,	PUNCT
ejpam-5662	236	25	ṽ	ṽ	PROPN
ejpam-5662	236	26	=	=	SYM
ejpam-5662	236	27	b	b	PROPN
ejpam-5662	236	28	cosω2	cosω2	PROPN
ejpam-5662	236	29	t	t	PROPN
ejpam-5662	236	30	,	,	PUNCT
ejpam-5662	236	31	(	(	PUNCT
ejpam-5662	236	32	27	27	NUM
ejpam-5662	236	33	)	)	PUNCT
ejpam-5662	236	34	where	where	SCONJ
ejpam-5662	236	35	a	a	PRON
ejpam-5662	236	36	and	and	CCONJ
ejpam-5662	236	37	b	b	NOUN
ejpam-5662	236	38	denote	denote	VERB
ejpam-5662	236	39	the	the	DET
ejpam-5662	236	40	amplitudes	amplitude	NOUN
ejpam-5662	236	41	of	of	ADP
ejpam-5662	236	42	the	the	DET
ejpam-5662	236	43	equivalent	equivalent	ADJ
ejpam-5662	236	44	solutions	solution	NOUN
ejpam-5662	236	45	,	,	PUNCT
ejpam-5662	236	46	whereas	whereas	SCONJ
ejpam-5662	236	47	ω1	ω1	PROPN
ejpam-5662	236	48	and	and	CCONJ
ejpam-5662	236	49	ω2	ω2	ADJ
ejpam-5662	236	50	are	be	AUX
ejpam-5662	236	51	the	the	DET
ejpam-5662	236	52	total	total	ADJ
ejpam-5662	236	53	frequencies	frequency	NOUN
ejpam-5662	236	54	to	to	PART
ejpam-5662	236	55	be	be	AUX
ejpam-5662	236	56	estimated	estimate	VERB
ejpam-5662	236	57	later	later	ADV
ejpam-5662	236	58	.	.	PUNCT
ejpam-5662	237	1	the	the	DET
ejpam-5662	237	2	functions	function	NOUN
ejpam-5662	237	3	u	u	NOUN
ejpam-5662	237	4	and	and	CCONJ
ejpam-5662	237	5	v	v	NOUN
ejpam-5662	237	6	satisfy	satisfy	VERB
ejpam-5662	237	7	the	the	DET
ejpam-5662	237	8	equivalent	equivalent	ADJ
ejpam-5662	237	9	system	system	NOUN
ejpam-5662	237	10	:	:	PUNCT
ejpam-5662	237	11	{	{	PUNCT
ejpam-5662	237	12	ü+	ü+	INTJ
ejpam-5662	237	13	ξ1u̇+ϖ2	ξ1u̇+ϖ2	NOUN
ejpam-5662	237	14	1u	1u	NUM
ejpam-5662	237	15	=	=	SYM
ejpam-5662	237	16	0	0	NUM
ejpam-5662	237	17	v̈	v̈	NOUN
ejpam-5662	237	18	+	+	CCONJ
ejpam-5662	237	19	ξ2v̇	ξ2v̇	VERB
ejpam-5662	237	20	+	+	ADV
ejpam-5662	237	21	ϖ2	ϖ2	NOUN
ejpam-5662	237	22	2v	2v	NOUN
ejpam-5662	237	23	=	=	SYM
ejpam-5662	237	24	0	0	PROPN
ejpam-5662	237	25	.	.	PUNCT
ejpam-5662	238	1	(	(	PUNCT
ejpam-5662	238	2	28	28	NUM
ejpam-5662	238	3	)	)	PUNCT
ejpam-5662	238	4	through	through	ADP
ejpam-5662	238	5	the	the	DET
ejpam-5662	238	6	inspection	inspection	NOUN
ejpam-5662	238	7	of	of	ADP
ejpam-5662	238	8	this	this	DET
ejpam-5662	238	9	system	system	NOUN
ejpam-5662	238	10	,	,	PUNCT
ejpam-5662	238	11	one	one	PRON
ejpam-5662	238	12	can	can	AUX
ejpam-5662	238	13	expect	expect	VERB
ejpam-5662	238	14	that	that	SCONJ
ejpam-5662	238	15	the	the	DET
ejpam-5662	238	16	solutions	solution	NOUN
ejpam-5662	238	17	’	'	PUNCT
ejpam-5662	238	18	behavior	behavior	NOUN
ejpam-5662	238	19	for	for	ADP
ejpam-5662	238	20	their	their	PRON
ejpam-5662	238	21	equations	equation	NOUN
ejpam-5662	238	22	has	have	AUX
ejpam-5662	238	23	damping	damp	VERB
ejpam-5662	238	24	manners	manner	NOUN
ejpam-5662	238	25	throughout	throughout	ADP
ejpam-5662	238	26	the	the	DET
ejpam-5662	238	27	explored	explore	VERB
ejpam-5662	238	28	time	time	NOUN
ejpam-5662	238	29	interval	interval	NOUN
ejpam-5662	238	30	.	.	PUNCT
ejpam-5662	239	1	the	the	DET
ejpam-5662	239	2	factors	factor	NOUN
ejpam-5662	239	3	a.	a.	PROPN
ejpam-5662	239	4	alanazy	alanazy	PROPN
ejpam-5662	239	5	,	,	PUNCT
ejpam-5662	239	6	g.	g.	PROPN
ejpam-5662	239	7	m.	m.	PROPN
ejpam-5662	239	8	moatimid	moatimid	PROPN
ejpam-5662	239	9	,	,	PUNCT
ejpam-5662	239	10	m.	m.	PROPN
ejpam-5662	239	11	a.	a.	PROPN
ejpam-5662	239	12	a.	a.	PROPN
ejpam-5662	239	13	mohamed	mohamed	PROPN
ejpam-5662	239	14	/	/	SYM
ejpam-5662	239	15	eur	eur	PROPN
ejpam-5662	239	16	.	.	PUNCT
ejpam-5662	240	1	j.	j.	PROPN
ejpam-5662	240	2	pure	pure	PROPN
ejpam-5662	240	3	appl	appl	PROPN
ejpam-5662	240	4	.	.	PROPN
ejpam-5662	240	5	math	math	PROPN
ejpam-5662	240	6	,	,	PUNCT
ejpam-5662	240	7	18	18	NUM
ejpam-5662	240	8	(	(	PUNCT
ejpam-5662	240	9	2	2	NUM
ejpam-5662	240	10	)	)	PUNCT
ejpam-5662	240	11	(	(	PUNCT
ejpam-5662	240	12	2025	2025	NUM
ejpam-5662	240	13	)	)	PUNCT
ejpam-5662	240	14	,	,	PUNCT
ejpam-5662	240	15	5662	5662	NUM
ejpam-5662	240	16	11	11	NUM
ejpam-5662	240	17	of	of	ADP
ejpam-5662	240	18	36	36	NUM
ejpam-5662	240	19	ω1	ω1	PROPN
ejpam-5662	240	20	,	,	PUNCT
ejpam-5662	240	21	and	and	CCONJ
ejpam-5662	240	22	ω2	ω2	ADJ
ejpam-5662	240	23	and	and	CCONJ
ejpam-5662	240	24	ξ1	ξ1	NOUN
ejpam-5662	240	25	,	,	PUNCT
ejpam-5662	240	26	and	and	CCONJ
ejpam-5662	240	27	ξ2	ξ2	NOUN
ejpam-5662	240	28	are	be	AUX
ejpam-5662	240	29	known	know	VERB
ejpam-5662	240	30	by	by	ADP
ejpam-5662	240	31	equivalent	equivalent	ADJ
ejpam-5662	240	32	frequencies	frequency	NOUN
ejpam-5662	240	33	and	and	CCONJ
ejpam-5662	240	34	equivalent	equivalent	ADJ
ejpam-5662	240	35	damping	damp	VERB
ejpam-5662	240	36	coefficients	coefficient	NOUN
ejpam-5662	240	37	,	,	PUNCT
ejpam-5662	240	38	which	which	PRON
ejpam-5662	240	39	are	be	AUX
ejpam-5662	240	40	defined	define	VERB
ejpam-5662	240	41	as	as	SCONJ
ejpam-5662	240	42	follows	follow	VERB
ejpam-5662	240	43	:	:	PUNCT
ejpam-5662	240	44	(	(	PUNCT
ejpam-5662	240	45	i	i	NOUN
ejpam-5662	240	46	)	)	PUNCT
ejpam-5662	240	47	the	the	DET
ejpam-5662	240	48	equivalent	equivalent	ADJ
ejpam-5662	240	49	frequencies	frequency	NOUN
ejpam-5662	240	50	to	to	PART
ejpam-5662	240	51	determine	determine	VERB
ejpam-5662	240	52	the	the	DET
ejpam-5662	240	53	equivalent	equivalent	ADJ
ejpam-5662	240	54	frequency	frequency	NOUN
ejpam-5662	240	55	,	,	PUNCT
ejpam-5662	240	56	the	the	DET
ejpam-5662	240	57	hff	hff	NOUN
ejpam-5662	240	58	technique	technique	NOUN
ejpam-5662	240	59	can	can	AUX
ejpam-5662	240	60	be	be	AUX
ejpam-5662	240	61	utilized	utilize	VERB
ejpam-5662	240	62	with	with	ADP
ejpam-5662	240	63	the	the	DET
ejpam-5662	240	64	odd	odd	ADJ
ejpam-5662	240	65	terms	term	NOUN
ejpam-5662	240	66	f1(x	f1(x	PROPN
ejpam-5662	240	67	,	,	PUNCT
ejpam-5662	240	68	ẋ	ẋ	PROPN
ejpam-5662	240	69	,	,	PUNCT
ejpam-5662	240	70	ẍ	ẍ	PROPN
ejpam-5662	240	71	,	,	PUNCT
ejpam-5662	240	72	y	y	PROPN
ejpam-5662	240	73	,	,	PUNCT
ejpam-5662	240	74	ẏ	ẏ	PROPN
ejpam-5662	240	75	,	,	PUNCT
ejpam-5662	240	76	ÿ	ÿ	PROPN
ejpam-5662	240	77	)	)	PUNCT
ejpam-5662	240	78	and	and	CCONJ
ejpam-5662	240	79	h1(x	h1(x	NOUN
ejpam-5662	240	80	,	,	PUNCT
ejpam-5662	240	81	ẋ	ẋ	PROPN
ejpam-5662	240	82	,	,	PUNCT
ejpam-5662	240	83	ẍ	ẍ	PROPN
ejpam-5662	240	84	,	,	PUNCT
ejpam-5662	240	85	y	y	PROPN
ejpam-5662	240	86	,	,	PUNCT
ejpam-5662	240	87	ẏ	ẏ	PROPN
ejpam-5662	240	88	,	,	PUNCT
ejpam-5662	240	89	ÿ	ÿ	PROPN
ejpam-5662	240	90	)	)	PUNCT
ejpam-5662	240	91	as	as	ADP
ejpam-5662	240	92	:	:	PUNCT
ejpam-5662	240	93	ϖ2	ϖ2	NOUN
ejpam-5662	240	94	1	1	NUM
ejpam-5662	240	95	=	=	SYM
ejpam-5662	240	96	∫	∫	PROPN
ejpam-5662	240	97	2π	2π	NOUN
ejpam-5662	240	98	/	/	SYM
ejpam-5662	240	99	ω1	ω1	PROPN
ejpam-5662	240	100	0	0	NUM
ejpam-5662	240	101	ũf1(ũ	ũf1(ũ	PROPN
ejpam-5662	240	102	,	,	PUNCT
ejpam-5662	240	103	˙̃u	˙̃u	PROPN
ejpam-5662	240	104	,	,	PUNCT
ejpam-5662	240	105	¨̃u	¨̃u	PROPN
ejpam-5662	240	106	,	,	PUNCT
ejpam-5662	240	107	ṽ	ṽ	PROPN
ejpam-5662	240	108	,	,	PUNCT
ejpam-5662	240	109	˙̃v	˙̃v	PROPN
ejpam-5662	240	110	,	,	PUNCT
ejpam-5662	240	111	¨̃v	¨̃v	PROPN
ejpam-5662	240	112	)	)	PUNCT
ejpam-5662	240	113	dt/	dt/	VERB
ejpam-5662	240	114	∫	∫	PROPN
ejpam-5662	240	115	2π	2π	NOUN
ejpam-5662	240	116	/	/	SYM
ejpam-5662	240	117	ω1	ω1	PROPN
ejpam-5662	240	118	0	0	NUM
ejpam-5662	240	119	ũ2dt	ũ2dt	NOUN
ejpam-5662	240	120	=	=	NOUN
ejpam-5662	240	121	a1	a1	NOUN
ejpam-5662	240	122	+	+	CCONJ
ejpam-5662	240	123	ω2	ω2	ADJ
ejpam-5662	240	124	1	1	NUM
ejpam-5662	240	125	+	+	NUM
ejpam-5662	240	126	a2	a2	PROPN
ejpam-5662	240	127	sin	sin	NOUN
ejpam-5662	240	128	(	(	PUNCT
ejpam-5662	240	129	2πωp	2πωp	NUM
ejpam-5662	240	130	ω1	ω1	NOUN
ejpam-5662	240	131	)	)	PUNCT
ejpam-5662	241	1	+	+	NUM
ejpam-5662	241	2	a3	a3	NOUN
ejpam-5662	241	3	sin	sin	NOUN
ejpam-5662	241	4	(	(	PUNCT
ejpam-5662	241	5	2π(ω2	2π(ω2	NUM
ejpam-5662	241	6	−	−	NOUN
ejpam-5662	241	7	ωp	ωp	NOUN
ejpam-5662	241	8	)	)	PUNCT
ejpam-5662	241	9	ω1	ω1	PROPN
ejpam-5662	241	10	)	)	PUNCT
ejpam-5662	241	11	+	+	NUM
ejpam-5662	241	12	a4	a4	NOUN
ejpam-5662	241	13	sin	sin	NOUN
ejpam-5662	241	14	(	(	PUNCT
ejpam-5662	241	15	2π(ω2	2π(ω2	NUM
ejpam-5662	241	16	−	−	NOUN
ejpam-5662	241	17	ωp	ωp	NOUN
ejpam-5662	241	18	)	)	PUNCT
ejpam-5662	241	19	ω1	ω1	PROPN
ejpam-5662	241	20	)	)	PUNCT
ejpam-5662	241	21	,	,	PUNCT
ejpam-5662	241	22	(	(	PUNCT
ejpam-5662	241	23	29	29	NUM
ejpam-5662	241	24	)	)	PUNCT
ejpam-5662	241	25	ϖ2	ϖ2	NOUN
ejpam-5662	241	26	2	2	NUM
ejpam-5662	241	27	=	=	SYM
ejpam-5662	241	28	∫	∫	PROPN
ejpam-5662	241	29	2π	2π	NOUN
ejpam-5662	241	30	/	/	SYM
ejpam-5662	241	31	ω1	ω1	PROPN
ejpam-5662	241	32	0	0	NUM
ejpam-5662	241	33	ũh1(ũ	ũh1(ũ	PROPN
ejpam-5662	241	34	,	,	PUNCT
ejpam-5662	241	35	˙̃u	˙̃u	PROPN
ejpam-5662	241	36	,	,	PUNCT
ejpam-5662	241	37	¨̃u	¨̃u	PROPN
ejpam-5662	241	38	,	,	PUNCT
ejpam-5662	241	39	ṽ	ṽ	PROPN
ejpam-5662	241	40	,	,	PUNCT
ejpam-5662	241	41	˙̃v	˙̃v	PROPN
ejpam-5662	241	42	,	,	PUNCT
ejpam-5662	241	43	¨̃v	¨̃v	PROPN
ejpam-5662	241	44	)	)	PUNCT
ejpam-5662	241	45	dt/	dt/	VERB
ejpam-5662	241	46	∫	∫	PROPN
ejpam-5662	241	47	2π	2π	NOUN
ejpam-5662	241	48	/	/	SYM
ejpam-5662	241	49	ω1	ω1	PROPN
ejpam-5662	241	50	0	0	NUM
ejpam-5662	241	51	ũ2dt	ũ2dt	NOUN
ejpam-5662	241	52	=	=	PUNCT
ejpam-5662	241	53	a5	a5	PROPN
ejpam-5662	241	54	+	+	CCONJ
ejpam-5662	241	55	ω2	ω2	ADJ
ejpam-5662	241	56	2	2	NUM
ejpam-5662	241	57	+	+	CCONJ
ejpam-5662	241	58	a6	a6	NOUN
ejpam-5662	241	59	sin	sin	NOUN
ejpam-5662	241	60	(	(	PUNCT
ejpam-5662	241	61	2πωp	2πωp	NUM
ejpam-5662	241	62	ω2	ω2	NOUN
ejpam-5662	241	63	)	)	PUNCT
ejpam-5662	242	1	+	+	CCONJ
ejpam-5662	242	2	a7	a7	ADJ
ejpam-5662	242	3	sin	sin	NOUN
ejpam-5662	242	4	(	(	PUNCT
ejpam-5662	242	5	2π(ω1	2π(ω1	NUM
ejpam-5662	242	6	−	−	NOUN
ejpam-5662	242	7	ωp	ωp	NOUN
ejpam-5662	242	8	)	)	PUNCT
ejpam-5662	242	9	ω2	ω2	CCONJ
ejpam-5662	242	10	)	)	PUNCT
ejpam-5662	243	1	+	+	CCONJ
ejpam-5662	243	2	a8	a8	PROPN
ejpam-5662	243	3	sin	sin	NOUN
ejpam-5662	243	4	(	(	PUNCT
ejpam-5662	243	5	2π(ω1	2π(ω1	NUM
ejpam-5662	243	6	−	−	NOUN
ejpam-5662	243	7	ωp	ωp	NOUN
ejpam-5662	243	8	)	)	PUNCT
ejpam-5662	243	9	ω2	ω2	CCONJ
ejpam-5662	243	10	)	)	PUNCT
ejpam-5662	243	11	,	,	PUNCT
ejpam-5662	243	12	(	(	PUNCT
ejpam-5662	243	13	30	30	NUM
ejpam-5662	243	14	)	)	PUNCT
ejpam-5662	243	15	where	where	SCONJ
ejpam-5662	243	16	the	the	DET
ejpam-5662	243	17	coefficients	coefficient	NOUN
ejpam-5662	243	18	a1	a1	NOUN
ejpam-5662	243	19	→	→	SYM
ejpam-5662	243	20	a8	a8	PROPN
ejpam-5662	243	21	are	be	AUX
ejpam-5662	243	22	defined	define	VERB
ejpam-5662	243	23	through	through	ADP
ejpam-5662	243	24	the	the	DET
ejpam-5662	243	25	appendix	appendix	NOUN
ejpam-5662	243	26	.	.	PUNCT
ejpam-5662	244	1	(	(	PUNCT
ejpam-5662	244	2	ii	ii	NOUN
ejpam-5662	244	3	)	)	PUNCT
ejpam-5662	244	4	the	the	DET
ejpam-5662	244	5	equivalent	equivalent	ADJ
ejpam-5662	244	6	damping	damping	NOUN
ejpam-5662	244	7	:	:	PUNCT
ejpam-5662	244	8	the	the	DET
ejpam-5662	244	9	calculation	calculation	NOUN
ejpam-5662	244	10	of	of	ADP
ejpam-5662	244	11	the	the	DET
ejpam-5662	244	12	equivalent	equivalent	ADJ
ejpam-5662	244	13	damping	damp	VERB
ejpam-5662	244	14	coefficients	coefficient	NOUN
ejpam-5662	244	15	utilizing	utilize	VERB
ejpam-5662	244	16	the	the	DET
ejpam-5662	244	17	hff	hff	NOUN
ejpam-5662	244	18	and	and	CCONJ
ejpam-5662	244	19	by	by	ADP
ejpam-5662	244	20	employing	employ	VERB
ejpam-5662	244	21	the	the	DET
ejpam-5662	244	22	odd	odd	ADJ
ejpam-5662	244	23	terms	term	NOUN
ejpam-5662	244	24	f2(x	f2(x	PROPN
ejpam-5662	244	25	,	,	PUNCT
ejpam-5662	244	26	ẋ	ẋ	PROPN
ejpam-5662	244	27	,	,	PUNCT
ejpam-5662	244	28	ẍ	ẍ	PROPN
ejpam-5662	244	29	,	,	PUNCT
ejpam-5662	244	30	y	y	PROPN
ejpam-5662	244	31	,	,	PUNCT
ejpam-5662	244	32	ẏ	ẏ	PROPN
ejpam-5662	244	33	,	,	PUNCT
ejpam-5662	244	34	ÿ	ÿ	PROPN
ejpam-5662	244	35	)	)	PUNCT
ejpam-5662	244	36	and	and	CCONJ
ejpam-5662	244	37	h2(x	h2(x	PROPN
ejpam-5662	244	38	,	,	PUNCT
ejpam-5662	244	39	ẋ	ẋ	PROPN
ejpam-5662	244	40	,	,	PUNCT
ejpam-5662	244	41	ẍ	ẍ	PROPN
ejpam-5662	244	42	,	,	PUNCT
ejpam-5662	244	43	y	y	PROPN
ejpam-5662	244	44	,	,	PUNCT
ejpam-5662	244	45	ẏ	ẏ	PROPN
ejpam-5662	244	46	,	,	PUNCT
ejpam-5662	244	47	ÿ	ÿ	PROPN
ejpam-5662	244	48	)	)	PUNCT
ejpam-5662	244	49	through	through	ADP
ejpam-5662	244	50	the	the	DET
ejpam-5662	244	51	integrations	integration	NOUN
ejpam-5662	244	52	:	:	PUNCT
ejpam-5662	244	53	ξ1	ξ1	NOUN
ejpam-5662	244	54	=	=	SYM
ejpam-5662	244	55	∫	∫	PROPN
ejpam-5662	244	56	2π	2π	NOUN
ejpam-5662	244	57	/	/	SYM
ejpam-5662	244	58	ω1	ω1	PROPN
ejpam-5662	244	59	0	0	NUM
ejpam-5662	244	60	ũf2(ũ	ũf2(ũ	PROPN
ejpam-5662	244	61	,	,	PUNCT
ejpam-5662	244	62	˙̃u	˙̃u	PROPN
ejpam-5662	244	63	,	,	PUNCT
ejpam-5662	244	64	¨̃u	¨̃u	PROPN
ejpam-5662	244	65	,	,	PUNCT
ejpam-5662	244	66	ṽ	ṽ	PROPN
ejpam-5662	244	67	,	,	PUNCT
ejpam-5662	244	68	˙̃v	˙̃v	PROPN
ejpam-5662	244	69	,	,	PUNCT
ejpam-5662	244	70	¨̃v	¨̃v	PROPN
ejpam-5662	244	71	)	)	PUNCT
ejpam-5662	244	72	dt/	dt/	VERB
ejpam-5662	244	73	∫	∫	PROPN
ejpam-5662	244	74	2π	2π	NOUN
ejpam-5662	244	75	/	/	SYM
ejpam-5662	244	76	ω1	ω1	PROPN
ejpam-5662	244	77	0	0	NUM
ejpam-5662	244	78	˙̃u2dt	˙̃u2dt	PUNCT
ejpam-5662	245	1	=	=	SYM
ejpam-5662	245	2	µ1	µ1	PROPN
ejpam-5662	245	3	+	+	NOUN
ejpam-5662	245	4	3	3	NUM
ejpam-5662	245	5	4	4	NUM
ejpam-5662	245	6	a2α1ω	a2α1ω	SYM
ejpam-5662	245	7	2	2	NUM
ejpam-5662	245	8	1	1	NUM
ejpam-5662	245	9	,	,	PUNCT
ejpam-5662	245	10	(	(	PUNCT
ejpam-5662	245	11	31	31	NUM
ejpam-5662	245	12	)	)	PUNCT
ejpam-5662	245	13	ξ2	ξ2	NOUN
ejpam-5662	245	14	=	=	SYM
ejpam-5662	245	15	∫	∫	PROPN
ejpam-5662	246	1	2π	2π	NOUN
ejpam-5662	246	2	/	/	SYM
ejpam-5662	246	3	ω1	ω1	PROPN
ejpam-5662	246	4	0	0	NUM
ejpam-5662	246	5	ṽh2(ũ	ṽh2(ũ	PROPN
ejpam-5662	246	6	,	,	PUNCT
ejpam-5662	246	7	˙̃u	˙̃u	PROPN
ejpam-5662	246	8	,	,	PUNCT
ejpam-5662	246	9	¨̃u	¨̃u	PROPN
ejpam-5662	246	10	,	,	PUNCT
ejpam-5662	246	11	ṽ	ṽ	PROPN
ejpam-5662	246	12	,	,	PUNCT
ejpam-5662	246	13	˙̃v	˙̃v	PROPN
ejpam-5662	246	14	,	,	PUNCT
ejpam-5662	246	15	¨̃v	¨̃v	PROPN
ejpam-5662	246	16	)	)	PUNCT
ejpam-5662	246	17	dt/	dt/	VERB
ejpam-5662	246	18	∫	∫	PROPN
ejpam-5662	246	19	2π	2π	NOUN
ejpam-5662	246	20	/	/	SYM
ejpam-5662	246	21	ω1	ω1	PROPN
ejpam-5662	246	22	0	0	PUNCT
ejpam-5662	246	23	˙̃v2dt	˙̃v2dt	PROPN
ejpam-5662	246	24	=	=	VERB
ejpam-5662	247	1	µ2	µ2	NOUN
ejpam-5662	247	2	+	+	CCONJ
ejpam-5662	247	3	3	3	NUM
ejpam-5662	247	4	4	4	NUM
ejpam-5662	247	5	b2α2ω	b2α2ω	SYM
ejpam-5662	247	6	2	2	NUM
ejpam-5662	247	7	2	2	NUM
ejpam-5662	247	8	.	.	PUNCT
ejpam-5662	248	1	(	(	PUNCT
ejpam-5662	248	2	32	32	NUM
ejpam-5662	248	3	)	)	PUNCT
ejpam-5662	248	4	in	in	ADP
ejpam-5662	248	5	light	light	NOUN
ejpam-5662	248	6	of	of	ADP
ejpam-5662	248	7	this	this	PRON
ejpam-5662	248	8	,	,	PUNCT
ejpam-5662	248	9	it	it	PRON
ejpam-5662	248	10	should	should	AUX
ejpam-5662	248	11	be	be	AUX
ejpam-5662	248	12	noted	note	VERB
ejpam-5662	248	13	that	that	SCONJ
ejpam-5662	248	14	the	the	DET
ejpam-5662	248	15	corresponding	correspond	VERB
ejpam-5662	248	16	frequencies	frequency	NOUN
ejpam-5662	248	17	ϖ1	ϖ1	VERB
ejpam-5662	248	18	,	,	PUNCT
ejpam-5662	248	19	and	and	CCONJ
ejpam-5662	248	20	ϖ2	ϖ2	NOUN
ejpam-5662	248	21	and	and	CCONJ
ejpam-5662	248	22	the	the	DET
ejpam-5662	248	23	damping	damp	VERB
ejpam-5662	248	24	coefficients	coefficient	NOUN
ejpam-5662	248	25	ξ1	ξ1	NOUN
ejpam-5662	248	26	,	,	PUNCT
ejpam-5662	248	27	and	and	CCONJ
ejpam-5662	248	28	ξ2	ξ2	NOUN
ejpam-5662	248	29	are	be	AUX
ejpam-5662	248	30	calculated	calculate	VERB
ejpam-5662	248	31	as	as	ADP
ejpam-5662	248	32	functions	function	NOUN
ejpam-5662	248	33	of	of	ADP
ejpam-5662	248	34	the	the	DET
ejpam-5662	248	35	total	total	ADJ
ejpam-5662	248	36	frequencies	frequency	NOUN
ejpam-5662	248	37	ω1	ω1	PROPN
ejpam-5662	248	38	,	,	PUNCT
ejpam-5662	248	39	and	and	CCONJ
ejpam-5662	248	40	ω2	ω2	ADV
ejpam-5662	248	41	using	use	VERB
ejpam-5662	248	42	the	the	DET
ejpam-5662	248	43	ms	ms	NOUN
ejpam-5662	248	44	;	;	PUNCT
ejpam-5662	248	45	hence	hence	ADV
ejpam-5662	248	46	,	,	PUNCT
ejpam-5662	248	47	these	these	DET
ejpam-5662	248	48	forms	form	NOUN
ejpam-5662	248	49	are	be	AUX
ejpam-5662	248	50	relegated	relegate	VERB
ejpam-5662	248	51	to	to	ADP
ejpam-5662	248	52	the	the	DET
ejpam-5662	248	53	appendix	appendix	NOUN
ejpam-5662	248	54	because	because	SCONJ
ejpam-5662	248	55	of	of	ADP
ejpam-5662	248	56	their	their	PRON
ejpam-5662	248	57	complex	complex	ADJ
ejpam-5662	248	58	formulas	formula	NOUN
ejpam-5662	248	59	.	.	PUNCT
ejpam-5662	249	1	assume	assume	VERB
ejpam-5662	249	2	the	the	DET
ejpam-5662	249	3	following	follow	VERB
ejpam-5662	249	4	standard	standard	ADJ
ejpam-5662	249	5	normal	normal	ADJ
ejpam-5662	249	6	forms	form	NOUN
ejpam-5662	249	7	:	:	PUNCT
ejpam-5662	249	8	u(t	u(t	NOUN
ejpam-5662	249	9	)	)	PUNCT
ejpam-5662	249	10	=	=	SYM
ejpam-5662	249	11	ũ(t)exp(−ξ1	ũ(t)exp(−ξ1	PROPN
ejpam-5662	249	12	t/2	t/2	NUM
ejpam-5662	249	13	)	)	PUNCT
ejpam-5662	249	14	.	.	PUNCT
ejpam-5662	250	1	(	(	PUNCT
ejpam-5662	250	2	33	33	NUM
ejpam-5662	250	3	)	)	PUNCT
ejpam-5662	250	4	v(t	v(t	NOUN
ejpam-5662	250	5	)	)	PUNCT
ejpam-5662	250	6	=	=	SYM
ejpam-5662	251	1	ṽ(t)exp(−ξ2	ṽ(t)exp(−ξ2	PROPN
ejpam-5662	251	2	t/2	t/2	NUM
ejpam-5662	251	3	)	)	PUNCT
ejpam-5662	251	4	.	.	PUNCT
ejpam-5662	252	1	(	(	PUNCT
ejpam-5662	252	2	34	34	NUM
ejpam-5662	252	3	)	)	PUNCT
ejpam-5662	252	4	therefore	therefore	ADV
ejpam-5662	252	5	,	,	PUNCT
ejpam-5662	252	6	substituting	substitute	VERB
ejpam-5662	252	7	by	by	ADP
ejpam-5662	252	8	eqs	eqs	PROPN
ejpam-5662	252	9	.	.	PUNCT
ejpam-5662	253	1	(	(	PUNCT
ejpam-5662	253	2	33	33	NUM
ejpam-5662	253	3	)	)	PUNCT
ejpam-5662	253	4	and	and	CCONJ
ejpam-5662	253	5	(	(	PUNCT
ejpam-5662	253	6	34	34	NUM
ejpam-5662	253	7	)	)	PUNCT
ejpam-5662	253	8	into	into	ADP
ejpam-5662	253	9	eqs	eqs	PROPN
ejpam-5662	253	10	.	.	PUNCT
ejpam-5662	254	1	(	(	PUNCT
ejpam-5662	254	2	28	28	NUM
ejpam-5662	254	3	)	)	PUNCT
ejpam-5662	254	4	,	,	PUNCT
ejpam-5662	254	5	one	one	PRON
ejpam-5662	254	6	gets	get	VERB
ejpam-5662	254	7	:	:	PUNCT
ejpam-5662	254	8	¨̃u(t	¨̃u(t	NUM
ejpam-5662	254	9	)	)	PUNCT
ejpam-5662	254	10	+	+	NUM
ejpam-5662	254	11	ω2	ω2	ADJ
ejpam-5662	254	12	1ũ(t	1ũ(t	NUM
ejpam-5662	254	13	)	)	PUNCT
ejpam-5662	254	14	=	=	SYM
ejpam-5662	255	1	0	0	NUM
ejpam-5662	255	2	,	,	PUNCT
ejpam-5662	255	3	(	(	PUNCT
ejpam-5662	255	4	35	35	NUM
ejpam-5662	255	5	)	)	PUNCT
ejpam-5662	255	6	and	and	CCONJ
ejpam-5662	255	7	¨̃v(t	¨̃v(t	NOUN
ejpam-5662	255	8	)	)	PUNCT
ejpam-5662	255	9	+	+	NUM
ejpam-5662	255	10	ω2	ω2	ADJ
ejpam-5662	255	11	2ṽ(t	2ṽ(t	NUM
ejpam-5662	255	12	)	)	PUNCT
ejpam-5662	255	13	=	=	SYM
ejpam-5662	255	14	0	0	NUM
ejpam-5662	255	15	,	,	PUNCT
ejpam-5662	255	16	(	(	PUNCT
ejpam-5662	255	17	36	36	NUM
ejpam-5662	255	18	)	)	PUNCT
ejpam-5662	255	19	a.	a.	NOUN
ejpam-5662	255	20	alanazy	alanazy	NOUN
ejpam-5662	255	21	,	,	PUNCT
ejpam-5662	255	22	g.	g.	PROPN
ejpam-5662	255	23	m.	m.	PROPN
ejpam-5662	255	24	moatimid	moatimid	PROPN
ejpam-5662	255	25	,	,	PUNCT
ejpam-5662	255	26	m.	m.	PROPN
ejpam-5662	255	27	a.	a.	PROPN
ejpam-5662	255	28	a.	a.	PROPN
ejpam-5662	255	29	mohamed	mohamed	PROPN
ejpam-5662	255	30	/	/	SYM
ejpam-5662	255	31	eur	eur	PROPN
ejpam-5662	255	32	.	.	PUNCT
ejpam-5662	256	1	j.	j.	PROPN
ejpam-5662	256	2	pure	pure	PROPN
ejpam-5662	256	3	appl	appl	PROPN
ejpam-5662	256	4	.	.	PROPN
ejpam-5662	256	5	math	math	PROPN
ejpam-5662	256	6	,	,	PUNCT
ejpam-5662	256	7	18	18	NUM
ejpam-5662	256	8	(	(	PUNCT
ejpam-5662	256	9	2	2	NUM
ejpam-5662	256	10	)	)	PUNCT
ejpam-5662	256	11	(	(	PUNCT
ejpam-5662	256	12	2025	2025	NUM
ejpam-5662	256	13	)	)	PUNCT
ejpam-5662	256	14	,	,	PUNCT
ejpam-5662	256	15	5662	5662	NUM
ejpam-5662	256	16	12	12	NUM
ejpam-5662	256	17	of	of	ADP
ejpam-5662	256	18	36	36	NUM
ejpam-5662	256	19	where	where	SCONJ
ejpam-5662	256	20	ω2	ω2	ADJ
ejpam-5662	256	21	1	1	NUM
ejpam-5662	256	22	=	=	SYM
ejpam-5662	256	23	ϖ2	ϖ2	NOUN
ejpam-5662	256	24	1	1	NUM
ejpam-5662	256	25	−	−	PROPN
ejpam-5662	256	26	ξ21/4	ξ21/4	INTJ
ejpam-5662	256	27	,	,	PUNCT
ejpam-5662	256	28	(	(	PUNCT
ejpam-5662	256	29	37	37	NUM
ejpam-5662	256	30	)	)	PUNCT
ejpam-5662	256	31	ω2	ω2	NOUN
ejpam-5662	256	32	2	2	X
ejpam-5662	256	33	=	=	SYM
ejpam-5662	256	34	ϖ2	ϖ2	NOUN
ejpam-5662	256	35	2	2	NUM
ejpam-5662	256	36	−	−	NOUN
ejpam-5662	256	37	ξ22/4	ξ22/4	PROPN
ejpam-5662	256	38	.	.	PUNCT
ejpam-5662	257	1	(	(	PUNCT
ejpam-5662	257	2	38	38	NUM
ejpam-5662	257	3	)	)	PUNCT
ejpam-5662	257	4	the	the	DET
ejpam-5662	257	5	goal	goal	NOUN
ejpam-5662	257	6	of	of	ADP
ejpam-5662	257	7	the	the	DET
ejpam-5662	257	8	current	current	ADJ
ejpam-5662	257	9	method	method	NOUN
ejpam-5662	257	10	is	be	AUX
ejpam-5662	257	11	to	to	PART
ejpam-5662	257	12	comprehend	comprehend	VERB
ejpam-5662	257	13	an	an	DET
ejpam-5662	257	14	auxiliary	auxiliary	ADJ
ejpam-5662	257	15	type	type	NOUN
ejpam-5662	257	16	of	of	ADP
ejpam-5662	257	17	the	the	DET
ejpam-5662	257	18	inferred	infer	VERB
ejpam-5662	257	19	nonlinear	nonlinear	NOUN
ejpam-5662	257	20	odes	ode	NOUN
ejpam-5662	257	21	.	.	PUNCT
ejpam-5662	258	1	the	the	DET
ejpam-5662	258	2	following	follow	VERB
ejpam-5662	258	3	figs	fig	NOUN
ejpam-5662	258	4	and	and	CCONJ
ejpam-5662	258	5	tables	table	NOUN
ejpam-5662	258	6	demonstrate	demonstrate	VERB
ejpam-5662	258	7	high	high	ADJ
ejpam-5662	258	8	convergence	convergence	NOUN
ejpam-5662	258	9	between	between	ADP
ejpam-5662	258	10	these	these	DET
ejpam-5662	258	11	two	two	NUM
ejpam-5662	258	12	responses	response	NOUN
ejpam-5662	258	13	,	,	PUNCT
ejpam-5662	258	14	confirming	confirm	VERB
ejpam-5662	258	15	the	the	DET
ejpam-5662	258	16	methodology	methodology	NOUN
ejpam-5662	258	17	’s	’s	PART
ejpam-5662	258	18	accuracy	accuracy	NOUN
ejpam-5662	258	19	and	and	CCONJ
ejpam-5662	258	20	insight	insight	NOUN
ejpam-5662	258	21	.	.	PUNCT
ejpam-5662	259	1	it	it	PRON
ejpam-5662	259	2	is	be	AUX
ejpam-5662	259	3	important	important	ADJ
ejpam-5662	259	4	to	to	PART
ejpam-5662	259	5	note	note	VERB
ejpam-5662	259	6	that	that	SCONJ
ejpam-5662	259	7	the	the	DET
ejpam-5662	259	8	nonlinear	nonlinear	ADJ
ejpam-5662	259	9	odes	ode	VERB
ejpam-5662	259	10	as	as	SCONJ
ejpam-5662	259	11	given	give	VERB
ejpam-5662	259	12	in	in	ADP
ejpam-5662	259	13	eqs	eqs	PROPN
ejpam-5662	259	14	.	.	PUNCT
ejpam-5662	260	1	(	(	PUNCT
ejpam-5662	260	2	18	18	NUM
ejpam-5662	260	3	)	)	PUNCT
ejpam-5662	260	4	and	and	CCONJ
ejpam-5662	260	5	(	(	PUNCT
ejpam-5662	260	6	19	19	NUM
ejpam-5662	260	7	)	)	PUNCT
ejpam-5662	260	8	are	be	AUX
ejpam-5662	260	9	replaced	replace	VERB
ejpam-5662	260	10	by	by	ADP
ejpam-5662	260	11	alternating	alternate	VERB
ejpam-5662	260	12	linear	linear	ADJ
ejpam-5662	260	13	odes	ode	NOUN
ejpam-5662	260	14	.	.	PUNCT
ejpam-5662	261	1	as	as	SCONJ
ejpam-5662	261	2	given	give	VERB
ejpam-5662	261	3	in	in	ADP
ejpam-5662	261	4	eq	eq	ADP
ejpam-5662	261	5	.	.	PUNCT
ejpam-5662	262	1	(	(	PUNCT
ejpam-5662	262	2	28	28	NUM
ejpam-5662	262	3	)	)	PUNCT
ejpam-5662	262	4	utilizing	utilize	VERB
ejpam-5662	262	5	the	the	DET
ejpam-5662	262	6	npa	npa	NOUN
ejpam-5662	262	7	.	.	PUNCT
ejpam-5662	263	1	the	the	DET
ejpam-5662	263	2	(	(	PUNCT
ejpam-5662	263	3	ndsolve	ndsolve	NOUN
ejpam-5662	263	4	)	)	PUNCT
ejpam-5662	263	5	command	command	NOUN
ejpam-5662	263	6	is	be	AUX
ejpam-5662	263	7	used	use	VERB
ejpam-5662	263	8	in	in	ADP
ejpam-5662	263	9	conjunction	conjunction	NOUN
ejpam-5662	263	10	with	with	ADP
ejpam-5662	263	11	the	the	DET
ejpam-5662	263	12	ms	ms	NOUN
ejpam-5662	263	13	to	to	PART
ejpam-5662	263	14	compare	compare	VERB
ejpam-5662	263	15	the	the	DET
ejpam-5662	263	16	numerical	numerical	ADJ
ejpam-5662	263	17	solutions	solution	NOUN
ejpam-5662	263	18	(	(	PUNCT
ejpam-5662	263	19	nss	nss	NOUN
ejpam-5662	263	20	)	)	PUNCT
ejpam-5662	263	21	of	of	ADP
ejpam-5662	263	22	these	these	DET
ejpam-5662	263	23	two	two	NUM
ejpam-5662	263	24	systems	system	NOUN
ejpam-5662	263	25	in	in	ADP
ejpam-5662	263	26	view	view	NOUN
ejpam-5662	263	27	of	of	ADP
ejpam-5662	263	28	the	the	DET
ejpam-5662	263	29	above	above	ADJ
ejpam-5662	263	30	values	value	NOUN
ejpam-5662	263	31	of	of	ADP
ejpam-5662	263	32	the	the	DET
ejpam-5662	263	33	system	system	NOUN
ejpam-5662	263	34	coefficients	coefficient	NOUN
ejpam-5662	263	35	.	.	PUNCT
ejpam-5662	264	1	the	the	DET
ejpam-5662	264	2	nss	nss	NOUN
ejpam-5662	264	3	of	of	ADP
ejpam-5662	264	4	the	the	DET
ejpam-5662	264	5	coupled	couple	VERB
ejpam-5662	264	6	system	system	NOUN
ejpam-5662	264	7	,	,	PUNCT
ejpam-5662	264	8	as	as	SCONJ
ejpam-5662	264	9	provided	provide	VERB
ejpam-5662	264	10	in	in	ADP
ejpam-5662	264	11	eqs	eqs	PROPN
ejpam-5662	264	12	.	.	PUNCT
ejpam-5662	265	1	(	(	PUNCT
ejpam-5662	265	2	18	18	NUM
ejpam-5662	265	3	)	)	PUNCT
ejpam-5662	265	4	,	,	PUNCT
ejpam-5662	265	5	(	(	PUNCT
ejpam-5662	265	6	19	19	NUM
ejpam-5662	265	7	)	)	PUNCT
ejpam-5662	265	8	,	,	PUNCT
ejpam-5662	265	9	and	and	CCONJ
ejpam-5662	265	10	the	the	DET
ejpam-5662	265	11	npa	npa	NOUN
ejpam-5662	265	12	solution	solution	NOUN
ejpam-5662	265	13	,	,	PUNCT
ejpam-5662	265	14	as	as	SCONJ
ejpam-5662	265	15	provided	provide	VERB
ejpam-5662	265	16	by	by	ADP
ejpam-5662	265	17	eqs	eqs	PROPN
ejpam-5662	265	18	.	.	PUNCT
ejpam-5662	266	1	(	(	PUNCT
ejpam-5662	266	2	28	28	NUM
ejpam-5662	266	3	)	)	PUNCT
ejpam-5662	266	4	are	be	AUX
ejpam-5662	266	5	compared	compare	VERB
ejpam-5662	266	6	for	for	ADP
ejpam-5662	266	7	convenience	convenience	NOUN
ejpam-5662	266	8	in	in	ADP
ejpam-5662	266	9	figs	fig	NOUN
ejpam-5662	266	10	.	.	PUNCT
ejpam-5662	267	1	1	1	NUM
ejpam-5662	267	2	and	and	CCONJ
ejpam-5662	267	3	2	2	NUM
ejpam-5662	267	4	and	and	CCONJ
ejpam-5662	267	5	tables	table	NOUN
ejpam-5662	267	6	1	1	NUM
ejpam-5662	267	7	and	and	CCONJ
ejpam-5662	267	8	2	2	NUM
ejpam-5662	267	9	.	.	X
ejpam-5662	268	1	the	the	DET
ejpam-5662	268	2	nonlinear	nonlinear	ADJ
ejpam-5662	268	3	stability	stability	NOUN
ejpam-5662	268	4	analysis	analysis	NOUN
ejpam-5662	268	5	was	be	AUX
ejpam-5662	268	6	the	the	DET
ejpam-5662	268	7	focus	focus	NOUN
ejpam-5662	268	8	of	of	ADP
ejpam-5662	268	9	the	the	DET
ejpam-5662	268	10	first	first	ADJ
ejpam-5662	268	11	model	model	NOUN
ejpam-5662	268	12	.	.	PUNCT
ejpam-5662	269	1	this	this	DET
ejpam-5662	269	2	new	new	ADJ
ejpam-5662	269	3	method	method	NOUN
ejpam-5662	269	4	is	be	AUX
ejpam-5662	269	5	thought	think	VERB
ejpam-5662	269	6	to	to	PART
ejpam-5662	269	7	be	be	AUX
ejpam-5662	269	8	comprehensive	comprehensive	ADJ
ejpam-5662	269	9	,	,	PUNCT
ejpam-5662	269	10	striking	striking	ADJ
ejpam-5662	269	11	,	,	PUNCT
ejpam-5662	269	12	consistent	consistent	ADJ
ejpam-5662	269	13	,	,	PUNCT
ejpam-5662	269	14	easy	easy	ADJ
ejpam-5662	269	15	to	to	PART
ejpam-5662	269	16	use	use	VERB
ejpam-5662	269	17	,	,	PUNCT
ejpam-5662	269	18	and	and	CCONJ
ejpam-5662	269	19	effective	effective	ADJ
ejpam-5662	269	20	in	in	ADP
ejpam-5662	269	21	setting	set	VERB
ejpam-5662	269	22	itself	itself	PRON
ejpam-5662	269	23	apart	apart	ADV
ejpam-5662	269	24	from	from	ADP
ejpam-5662	269	25	the	the	DET
ejpam-5662	269	26	more	more	ADV
ejpam-5662	269	27	recent	recent	ADJ
ejpam-5662	269	28	methods	method	NOUN
ejpam-5662	269	29	.	.	PUNCT
ejpam-5662	270	1	it	it	PRON
ejpam-5662	270	2	may	may	AUX
ejpam-5662	270	3	be	be	AUX
ejpam-5662	270	4	used	use	VERB
ejpam-5662	270	5	to	to	PART
ejpam-5662	270	6	examine	examine	VERB
ejpam-5662	270	7	a	a	DET
ejpam-5662	270	8	number	number	NOUN
ejpam-5662	270	9	of	of	ADP
ejpam-5662	270	10	dynamical	dynamical	ADJ
ejpam-5662	270	11	system	system	NOUN
ejpam-5662	270	12	categories	category	NOUN
ejpam-5662	270	13	,	,	PUNCT
ejpam-5662	270	14	such	such	ADJ
ejpam-5662	270	15	as	as	ADP
ejpam-5662	270	16	hydrodynamic	hydrodynamic	ADJ
ejpam-5662	270	17	stability	stability	NOUN
ejpam-5662	270	18	.	.	PUNCT
ejpam-5662	271	1	as	as	SCONJ
ejpam-5662	271	2	can	can	AUX
ejpam-5662	271	3	be	be	AUX
ejpam-5662	271	4	seen	see	VERB
ejpam-5662	271	5	,	,	PUNCT
ejpam-5662	271	6	there	there	PRON
ejpam-5662	271	7	is	be	VERB
ejpam-5662	271	8	a	a	DET
ejpam-5662	271	9	significant	significant	ADJ
ejpam-5662	271	10	convergence	convergence	NOUN
ejpam-5662	271	11	between	between	ADP
ejpam-5662	271	12	the	the	DET
ejpam-5662	271	13	two	two	NUM
ejpam-5662	271	14	results	result	NOUN
ejpam-5662	271	15	in	in	ADP
ejpam-5662	271	16	these	these	DET
ejpam-5662	271	17	figures	figure	NOUN
ejpam-5662	271	18	and	and	CCONJ
ejpam-5662	271	19	tables	table	NOUN
ejpam-5662	271	20	.	.	PUNCT
ejpam-5662	272	1	as	as	SCONJ
ejpam-5662	272	2	estimated	estimate	VERB
ejpam-5662	272	3	by	by	ADP
ejpam-5662	272	4	the	the	DET
ejpam-5662	272	5	ms	ms	PROPN
ejpam-5662	272	6	,	,	PUNCT
ejpam-5662	272	7	the	the	DET
ejpam-5662	272	8	assessed	assessed	ADJ
ejpam-5662	272	9	absolute	absolute	ADJ
ejpam-5662	272	10	error	error	NOUN
ejpam-5662	272	11	equals	equal	VERB
ejpam-5662	272	12	0.0064	0.0064	NUM
ejpam-5662	272	13	for	for	ADP
ejpam-5662	272	14	x	x	NOUN
ejpam-5662	272	15	distribution	distribution	NOUN
ejpam-5662	272	16	and	and	CCONJ
ejpam-5662	272	17	0.0021	0.0021	NUM
ejpam-5662	272	18	for	for	ADP
ejpam-5662	272	19	y	y	NOUN
ejpam-5662	272	20	distribution	distribution	NOUN
ejpam-5662	272	21	in	in	ADP
ejpam-5662	272	22	view	view	NOUN
ejpam-5662	272	23	of	of	ADP
ejpam-5662	272	24	the	the	DET
ejpam-5662	272	25	following	follow	VERB
ejpam-5662	272	26	data	datum	NOUN
ejpam-5662	272	27	:	:	PUNCT
ejpam-5662	272	28	µ1	µ1	PROPN
ejpam-5662	272	29	=	=	SYM
ejpam-5662	272	30	0.2	0.2	NUM
ejpam-5662	272	31	,	,	PUNCT
ejpam-5662	272	32	µ2	µ2	PROPN
ejpam-5662	272	33	=	=	PROPN
ejpam-5662	272	34	0.5	0.5	NUM
ejpam-5662	272	35	,	,	PUNCT
ejpam-5662	272	36	α1	α1	PROPN
ejpam-5662	272	37	=	=	SYM
ejpam-5662	272	38	0.1	0.1	NUM
ejpam-5662	272	39	,	,	PUNCT
ejpam-5662	272	40	α2	α2	NOUN
ejpam-5662	272	41	=	=	SYM
ejpam-5662	272	42	0.3	0.3	NUM
ejpam-5662	272	43	,	,	PUNCT
ejpam-5662	272	44	ω1	ω1	PROPN
ejpam-5662	272	45	=	=	SYM
ejpam-5662	272	46	2	2	NUM
ejpam-5662	272	47	,	,	PUNCT
ejpam-5662	272	48	ω2	ω2	NOUN
ejpam-5662	272	49	=	=	SYM
ejpam-5662	272	50	1.5	1.5	NUM
ejpam-5662	272	51	,	,	PUNCT
ejpam-5662	272	52	γ1	γ1	NOUN
ejpam-5662	272	53	=	=	NOUN
ejpam-5662	272	54	0.3	0.3	NUM
ejpam-5662	272	55	,	,	PUNCT
ejpam-5662	272	56	γ2	γ2	PROPN
ejpam-5662	272	57	=	=	NUM
ejpam-5662	272	58	0.3	0.3	NUM
ejpam-5662	272	59	,	,	PUNCT
ejpam-5662	272	60	η11	η11	NOUN
ejpam-5662	272	61	=	=	SYM
ejpam-5662	272	62	0.1	0.1	NUM
ejpam-5662	272	63	,	,	PUNCT
ejpam-5662	272	64	η12	η12	VERB
ejpam-5662	272	65	=	=	NOUN
ejpam-5662	272	66	0.2	0.2	NUM
ejpam-5662	272	67	,	,	PUNCT
ejpam-5662	272	68	η21	η21	NOUN
ejpam-5662	272	69	=	=	SYM
ejpam-5662	272	70	0.1	0.1	NUM
ejpam-5662	272	71	,	,	PUNCT
ejpam-5662	272	72	η22	η22	NOUN
ejpam-5662	272	73	=	=	NUM
ejpam-5662	272	74	0.2	0.2	NUM
ejpam-5662	272	75	,	,	PUNCT
ejpam-5662	272	76	ωp	ωp	NOUN
ejpam-5662	272	77	=	=	NOUN
ejpam-5662	272	78	0.5	0.5	NUM
ejpam-5662	272	79	,	,	PUNCT
ejpam-5662	272	80	λ1	λ1	PROPN
ejpam-5662	272	81	=	=	SYM
ejpam-5662	272	82	0.2	0.2	NUM
ejpam-5662	272	83	,	,	PUNCT
ejpam-5662	272	84	λ12	λ12	ADJ
ejpam-5662	272	85	=	=	NUM
ejpam-5662	272	86	0.3	0.3	NUM
ejpam-5662	272	87	,	,	PUNCT
ejpam-5662	272	88	a	a	DET
ejpam-5662	272	89	=	=	NOUN
ejpam-5662	272	90	0.05	0.05	NUM
ejpam-5662	272	91	and	and	CCONJ
ejpam-5662	272	92	b	b	NOUN
ejpam-5662	272	93	=	=	SYM
ejpam-5662	272	94	0.05	0.05	NUM
ejpam-5662	272	95	.	.	PUNCT
ejpam-5662	273	1	figure	figure	NOUN
ejpam-5662	273	2	1	1	NUM
ejpam-5662	273	3	:	:	PUNCT
ejpam-5662	273	4	demonstrates	demonstrate	VERB
ejpam-5662	273	5	the	the	DET
ejpam-5662	273	6	matching	matching	NOUN
ejpam-5662	273	7	between	between	ADP
ejpam-5662	273	8	the	the	DET
ejpam-5662	273	9	solutions	solution	NOUN
ejpam-5662	273	10	of	of	ADP
ejpam-5662	273	11	the	the	DET
ejpam-5662	273	12	nonlinear	nonlinear	ADJ
ejpam-5662	273	13	dynamical	dynamical	ADJ
ejpam-5662	273	14	system	system	NOUN
ejpam-5662	273	15	(	(	PUNCT
ejpam-5662	273	16	18	18	NUM
ejpam-5662	273	17	)	)	PUNCT
ejpam-5662	273	18	and	and	CCONJ
ejpam-5662	273	19	(	(	PUNCT
ejpam-5662	273	20	19	19	NUM
ejpam-5662	273	21	)	)	PUNCT
ejpam-5662	273	22	and	and	CCONJ
ejpam-5662	273	23	those	those	PRON
ejpam-5662	273	24	of	of	ADP
ejpam-5662	273	25	the	the	DET
ejpam-5662	273	26	npa	npa	NOUN
ejpam-5662	273	27	system	system	NOUN
ejpam-5662	273	28	(	(	PUNCT
ejpam-5662	273	29	28	28	NUM
ejpam-5662	273	30	)	)	PUNCT
ejpam-5662	273	31	for	for	ADP
ejpam-5662	273	32	the	the	DET
ejpam-5662	273	33	oscillator	oscillator	NOUN
ejpam-5662	273	34	.	.	PUNCT
ejpam-5662	274	1	a.	a.	PROPN
ejpam-5662	274	2	alanazy	alanazy	PROPN
ejpam-5662	274	3	,	,	PUNCT
ejpam-5662	274	4	g.	g.	PROPN
ejpam-5662	274	5	m.	m.	PROPN
ejpam-5662	274	6	moatimid	moatimid	PROPN
ejpam-5662	274	7	,	,	PUNCT
ejpam-5662	274	8	m.	m.	PROPN
ejpam-5662	274	9	a.	a.	PROPN
ejpam-5662	274	10	a.	a.	PROPN
ejpam-5662	274	11	mohamed	mohamed	PROPN
ejpam-5662	274	12	/	/	SYM
ejpam-5662	274	13	eur	eur	PROPN
ejpam-5662	274	14	.	.	PUNCT
ejpam-5662	275	1	j.	j.	PROPN
ejpam-5662	275	2	pure	pure	PROPN
ejpam-5662	275	3	appl	appl	PROPN
ejpam-5662	275	4	.	.	PROPN
ejpam-5662	275	5	math	math	PROPN
ejpam-5662	275	6	,	,	PUNCT
ejpam-5662	275	7	18	18	NUM
ejpam-5662	275	8	(	(	PUNCT
ejpam-5662	275	9	2	2	NUM
ejpam-5662	275	10	)	)	PUNCT
ejpam-5662	275	11	(	(	PUNCT
ejpam-5662	275	12	2025	2025	NUM
ejpam-5662	275	13	)	)	PUNCT
ejpam-5662	275	14	,	,	PUNCT
ejpam-5662	275	15	5662	5662	NUM
ejpam-5662	275	16	13	13	NUM
ejpam-5662	275	17	of	of	ADP
ejpam-5662	275	18	36	36	NUM
ejpam-5662	275	19	table	table	NOUN
ejpam-5662	275	20	1	1	NUM
ejpam-5662	275	21	:	:	PUNCT
ejpam-5662	275	22	validates	validate	VERB
ejpam-5662	275	23	the	the	DET
ejpam-5662	275	24	convergence	convergence	NOUN
ejpam-5662	275	25	of	of	ADP
ejpam-5662	275	26	the	the	DET
ejpam-5662	275	27	original	original	ADJ
ejpam-5662	275	28	and	and	CCONJ
ejpam-5662	275	29	npa	npa	NOUN
ejpam-5662	275	30	solutions	solution	NOUN
ejpam-5662	275	31	for	for	ADP
ejpam-5662	275	32	the	the	DET
ejpam-5662	275	33	x	x	NOUN
ejpam-5662	275	34	oscillator	oscillator	NOUN
ejpam-5662	275	35	.	.	PUNCT
ejpam-5662	276	1	t	t	PROPN
ejpam-5662	276	2	real	real	ADJ
ejpam-5662	276	3	oscillator	oscillator	NOUN
ejpam-5662	276	4	x	x	NOUN
ejpam-5662	276	5	approximate	approximate	ADJ
ejpam-5662	276	6	oscillator	oscillator	NOUN
ejpam-5662	276	7	absolute	absolute	ADJ
ejpam-5662	276	8	error	error	NOUN
ejpam-5662	276	9	0	0	NUM
ejpam-5662	276	10	0.05	0.05	NUM
ejpam-5662	276	11	0.05	0.05	NUM
ejpam-5662	276	12	0	0	NUM
ejpam-5662	276	13	.	.	PROPN
ejpam-5662	276	14	5	5	NUM
ejpam-5662	276	15	-0.025963	-0.025963	NOUN
ejpam-5662	276	16	-0.0228042	-0.0228042	NOUN
ejpam-5662	277	1	0.00315881	0.00315881	NUM
ejpam-5662	277	2	10	10	NUM
ejpam-5662	277	3	0.00792326	0.00792326	NUM
ejpam-5662	277	4	0.00153441	0.00153441	NUM
ejpam-5662	277	5	0.00638885	0.00638885	NUM
ejpam-5662	277	6	15	15	NUM
ejpam-5662	277	7	0.00310068	0.00310068	NUM
ejpam-5662	277	8	0.00702038	0.00702038	NUM
ejpam-5662	277	9	0.00391969	0.00391969	NUM
ejpam-5662	277	10	20	20	NUM
ejpam-5662	277	11	-0.00489663	-0.00489663	NOUN
ejpam-5662	277	12	-0.00667517	-0.00667517	VERB
ejpam-5662	277	13	0.00177854	0.00177854	NUM
ejpam-5662	277	14	25	25	NUM
ejpam-5662	278	1	0.00412394	0.00412394	NUM
ejpam-5662	278	2	0.00323986	0.00323986	NUM
ejpam-5662	278	3	0.000884078	0.000884078	NUM
ejpam-5662	278	4	30	30	NUM
ejpam-5662	278	5	-0.00238374	-0.00238374	NOUN
ejpam-5662	278	6	-0.000375066	-0.000375066	NOUN
ejpam-5662	279	1	0.00200867	0.00200867	NUM
ejpam-5662	279	2	35	35	NUM
ejpam-5662	279	3	0.00098347	0.00098347	NUM
ejpam-5662	279	4	-0.000860581	-0.000860581	NOUN
ejpam-5662	279	5	0.00184405	0.00184405	NUM
ejpam-5662	279	6	40	40	NUM
ejpam-5662	279	7	-0.0000360658	-0.0000360658	NOUN
ejpam-5662	279	8	0.000886748	0.000886748	NUM
ejpam-5662	279	9	0.000922813	0.000922813	NUM
ejpam-5662	279	10	45	45	NUM
ejpam-5662	279	11	-0.000237634	-0.000237634	PROPN
ejpam-5662	279	12	-0.000456704	-0.000456704	PROPN
ejpam-5662	280	1	0.00021907	0.00021907	NUM
ejpam-5662	280	2	50	50	NUM
ejpam-5662	280	3	0.000278283	0.000278283	NUM
ejpam-5662	280	4	0.0000727985	0.0000727985	NUM
ejpam-5662	280	5	0.000205485	0.000205485	NUM
ejpam-5662	280	6	figure	figure	NOUN
ejpam-5662	280	7	2	2	NUM
ejpam-5662	280	8	:	:	PUNCT
ejpam-5662	280	9	demonstrates	demonstrate	VERB
ejpam-5662	280	10	the	the	DET
ejpam-5662	280	11	matching	matching	NOUN
ejpam-5662	280	12	between	between	ADP
ejpam-5662	280	13	the	the	DET
ejpam-5662	280	14	solutions	solution	NOUN
ejpam-5662	280	15	of	of	ADP
ejpam-5662	280	16	the	the	DET
ejpam-5662	280	17	nonlinear	nonlinear	ADJ
ejpam-5662	280	18	dynamical	dynamical	ADJ
ejpam-5662	280	19	system	system	NOUN
ejpam-5662	280	20	(	(	PUNCT
ejpam-5662	280	21	18	18	NUM
ejpam-5662	280	22	)	)	PUNCT
ejpam-5662	280	23	and	and	CCONJ
ejpam-5662	280	24	(	(	PUNCT
ejpam-5662	280	25	19	19	NUM
ejpam-5662	280	26	)	)	PUNCT
ejpam-5662	280	27	and	and	CCONJ
ejpam-5662	280	28	those	those	PRON
ejpam-5662	280	29	of	of	ADP
ejpam-5662	280	30	the	the	DET
ejpam-5662	280	31	npa	npa	NOUN
ejpam-5662	280	32	system	system	NOUN
ejpam-5662	280	33	(	(	PUNCT
ejpam-5662	280	34	28	28	NUM
ejpam-5662	280	35	)	)	PUNCT
ejpam-5662	280	36	for	for	ADP
ejpam-5662	280	37	the	the	DET
ejpam-5662	280	38	oscillator	oscillator	NOUN
ejpam-5662	280	39	.	.	PUNCT
ejpam-5662	281	1	a.	a.	PROPN
ejpam-5662	281	2	alanazy	alanazy	PROPN
ejpam-5662	281	3	,	,	PUNCT
ejpam-5662	281	4	g.	g.	PROPN
ejpam-5662	281	5	m.	m.	PROPN
ejpam-5662	281	6	moatimid	moatimid	PROPN
ejpam-5662	281	7	,	,	PUNCT
ejpam-5662	281	8	m.	m.	PROPN
ejpam-5662	281	9	a.	a.	PROPN
ejpam-5662	281	10	a.	a.	PROPN
ejpam-5662	281	11	mohamed	mohamed	PROPN
ejpam-5662	281	12	/	/	SYM
ejpam-5662	281	13	eur	eur	PROPN
ejpam-5662	281	14	.	.	PUNCT
ejpam-5662	282	1	j.	j.	PROPN
ejpam-5662	282	2	pure	pure	PROPN
ejpam-5662	282	3	appl	appl	PROPN
ejpam-5662	282	4	.	.	PROPN
ejpam-5662	282	5	math	math	PROPN
ejpam-5662	282	6	,	,	PUNCT
ejpam-5662	282	7	18	18	NUM
ejpam-5662	282	8	(	(	PUNCT
ejpam-5662	282	9	2	2	NUM
ejpam-5662	282	10	)	)	PUNCT
ejpam-5662	282	11	(	(	PUNCT
ejpam-5662	282	12	2025	2025	NUM
ejpam-5662	282	13	)	)	PUNCT
ejpam-5662	282	14	,	,	PUNCT
ejpam-5662	282	15	5662	5662	NUM
ejpam-5662	282	16	14	14	NUM
ejpam-5662	282	17	of	of	ADP
ejpam-5662	282	18	36	36	NUM
ejpam-5662	282	19	table	table	NOUN
ejpam-5662	282	20	2	2	NUM
ejpam-5662	282	21	:	:	PUNCT
ejpam-5662	282	22	validates	validate	VERB
ejpam-5662	282	23	the	the	DET
ejpam-5662	282	24	convergence	convergence	NOUN
ejpam-5662	282	25	of	of	ADP
ejpam-5662	282	26	the	the	DET
ejpam-5662	282	27	original	original	ADJ
ejpam-5662	282	28	and	and	CCONJ
ejpam-5662	282	29	npa	npa	NOUN
ejpam-5662	282	30	solutions	solution	NOUN
ejpam-5662	282	31	for	for	ADP
ejpam-5662	282	32	the	the	DET
ejpam-5662	282	33	y	y	PROPN
ejpam-5662	282	34	oscillator	oscillator	NOUN
ejpam-5662	282	35	.	.	PUNCT
ejpam-5662	283	1	t	t	PROPN
ejpam-5662	283	2	real	real	ADJ
ejpam-5662	283	3	oscillator	oscillator	NOUN
ejpam-5662	283	4	y	y	PROPN
ejpam-5662	283	5	approximate	approximate	PROPN
ejpam-5662	283	6	oscillator	oscillator	PROPN
ejpam-5662	283	7	absolute	absolute	ADJ
ejpam-5662	283	8	error	error	NOUN
ejpam-5662	283	9	0	0	NUM
ejpam-5662	283	10	0.05	0.05	NUM
ejpam-5662	283	11	0.05	0.05	NUM
ejpam-5662	283	12	0	0	NUM
ejpam-5662	283	13	.	.	PUNCT
ejpam-5662	284	1	5	5	NUM
ejpam-5662	284	2	0.00631459	0.00631459	NUM
ejpam-5662	284	3	0.0058608	0.0058608	NUM
ejpam-5662	284	4	0.000453797	0.000453797	NUM
ejpam-5662	284	5	10	10	NUM
ejpam-5662	284	6	-0.00238827	-0.00238827	NOUN
ejpam-5662	284	7	-0.00323727	-0.00323727	VERB
ejpam-5662	285	1	0.000849002	0.000849002	NUM
ejpam-5662	285	2	15	15	NUM
ejpam-5662	285	3	-0.000359652	-0.000359652	NOUN
ejpam-5662	285	4	-0.000941673	-0.000941673	PROPN
ejpam-5662	285	5	0.000582021	0.000582021	NUM
ejpam-5662	286	1	20	20	NUM
ejpam-5662	286	2	0.000675203	0.000675203	NUM
ejpam-5662	286	3	0.000129051	0.000129051	NUM
ejpam-5662	286	4	0.000546152	0.000546152	NUM
ejpam-5662	286	5	25	25	NUM
ejpam-5662	286	6	0.000208416	0.000208416	NUM
ejpam-5662	286	7	0.0000952715	0.0000952715	NUM
ejpam-5662	286	8	0.000113144	0.000113144	NUM
ejpam-5662	286	9	30	30	NUM
ejpam-5662	286	10	-0.00019148	-0.00019148	NOUN
ejpam-5662	286	11	3.12676	3.12676	NUM
ejpam-5662	286	12	∗	∗	NOUN
ejpam-5662	286	13	10−6	10−6	NUM
ejpam-5662	286	14	0.000194607	0.000194607	NUM
ejpam-5662	286	15	35	35	NUM
ejpam-5662	286	16	-0.000129185	-0.000129185	NOUN
ejpam-5662	286	17	−7.32034	−7.32034	X
ejpam-5662	286	18	∗	∗	NOUN
ejpam-5662	286	19	10−6	10−6	NUM
ejpam-5662	286	20	0.000121864	0.000121864	NUM
ejpam-5662	286	21	40	40	NUM
ejpam-5662	286	22	0.0000458095	0.0000458095	NUM
ejpam-5662	286	23	−1.30373	−1.30373	NOUN
ejpam-5662	286	24	∗	∗	NOUN
ejpam-5662	286	25	10−6	10−6	NUM
ejpam-5662	286	26	0.0000471132	0.0000471132	NUM
ejpam-5662	286	27	45	45	NUM
ejpam-5662	286	28	0.0000670557	0.0000670557	NUM
ejpam-5662	286	29	4.10079	4.10079	NUM
ejpam-5662	286	30	∗	∗	NOUN
ejpam-5662	286	31	10−7	10−7	NUM
ejpam-5662	286	32	0.0000666456	0.0000666456	NUM
ejpam-5662	286	33	50	50	NUM
ejpam-5662	286	34	0.0000201414	0.0000201414	NUM
ejpam-5662	286	35	1.65056	1.65056	NUM
ejpam-5662	286	36	∗	∗	NOUN
ejpam-5662	286	37	10−7	10−7	NUM
ejpam-5662	286	38	0.0000199764	0.0000199764	NUM
ejpam-5662	286	39	the	the	DET
ejpam-5662	286	40	solutions	solution	NOUN
ejpam-5662	286	41	of	of	ADP
ejpam-5662	286	42	the	the	DET
ejpam-5662	286	43	system	system	NOUN
ejpam-5662	286	44	of	of	ADP
ejpam-5662	286	45	eqs	eqs	PROPN
ejpam-5662	286	46	.	.	PUNCT
ejpam-5662	287	1	(	(	PUNCT
ejpam-5662	287	2	35	35	NUM
ejpam-5662	287	3	)	)	PUNCT
ejpam-5662	287	4	and	and	CCONJ
ejpam-5662	287	5	(	(	PUNCT
ejpam-5662	287	6	36	36	NUM
ejpam-5662	287	7	)	)	PUNCT
ejpam-5662	287	8	using	use	VERB
ejpam-5662	287	9	the	the	DET
ejpam-5662	287	10	npa	npa	NOUN
ejpam-5662	287	11	are	be	AUX
ejpam-5662	287	12	graphically	graphically	ADV
ejpam-5662	287	13	represented	represent	VERB
ejpam-5662	287	14	in	in	ADP
ejpam-5662	287	15	figs	fig	NOUN
ejpam-5662	287	16	.	.	PUNCT
ejpam-5662	288	1	3	3	NUM
ejpam-5662	288	2	-	-	SYM
ejpam-5662	288	3	16	16	NUM
ejpam-5662	288	4	,	,	PUNCT
ejpam-5662	288	5	when	when	SCONJ
ejpam-5662	288	6	the	the	DET
ejpam-5662	288	7	above	above	ADV
ejpam-5662	288	8	-	-	PUNCT
ejpam-5662	288	9	considered	consider	VERB
ejpam-5662	288	10	values	value	NOUN
ejpam-5662	288	11	of	of	ADP
ejpam-5662	288	12	the	the	DET
ejpam-5662	288	13	parameters	parameter	NOUN
ejpam-5662	288	14	are	be	AUX
ejpam-5662	288	15	used	use	VERB
ejpam-5662	288	16	.	.	PUNCT
ejpam-5662	289	1	firstly	firstly	ADV
ejpam-5662	289	2	,	,	PUNCT
ejpam-5662	289	3	figs	fig	NOUN
ejpam-5662	289	4	.	.	PUNCT
ejpam-5662	290	1	3	3	NUM
ejpam-5662	290	2	-	-	SYM
ejpam-5662	290	3	8	8	NUM
ejpam-5662	290	4	are	be	AUX
ejpam-5662	290	5	plotted	plot	VERB
ejpam-5662	290	6	to	to	PART
ejpam-5662	290	7	examine	examine	VERB
ejpam-5662	290	8	the	the	DET
ejpam-5662	290	9	influences	influence	NOUN
ejpam-5662	290	10	of	of	ADP
ejpam-5662	290	11	the	the	DET
ejpam-5662	290	12	relevant	relevant	ADJ
ejpam-5662	290	13	factors	factor	NOUN
ejpam-5662	290	14	ω1	ω1	PROPN
ejpam-5662	290	15	,	,	PUNCT
ejpam-5662	290	16	ω2	ω2	ADJ
ejpam-5662	290	17	,	,	PUNCT
ejpam-5662	290	18	γ1	γ1	NOUN
ejpam-5662	290	19	,	,	PUNCT
ejpam-5662	290	20	γ2	γ2	PROPN
ejpam-5662	290	21	,	,	PUNCT
ejpam-5662	290	22	η11	η11	NOUN
ejpam-5662	290	23	,	,	PUNCT
ejpam-5662	290	24	η21	η21	PROPN
ejpam-5662	290	25	,	,	PUNCT
ejpam-5662	290	26	η12	η12	NOUN
ejpam-5662	290	27	,	,	PUNCT
ejpam-5662	290	28	η22	η22	PROPN
ejpam-5662	290	29	,	,	PUNCT
ejpam-5662	290	30	λ1	λ1	ADJ
ejpam-5662	290	31	,	,	PUNCT
ejpam-5662	290	32	λ2	λ2	NOUN
ejpam-5662	290	33	,	,	PUNCT
ejpam-5662	290	34	and	and	CCONJ
ejpam-5662	290	35	ωp	ωp	PRON
ejpam-5662	290	36	on	on	ADP
ejpam-5662	290	37	the	the	DET
ejpam-5662	290	38	time	time	NOUN
ejpam-5662	290	39	-	-	PUNCT
ejpam-5662	290	40	dependent	dependent	ADJ
ejpam-5662	290	41	variation	variation	NOUN
ejpam-5662	290	42	and	and	CCONJ
ejpam-5662	290	43	the	the	DET
ejpam-5662	290	44	polar	polar	ADJ
ejpam-5662	290	45	plots	plot	NOUN
ejpam-5662	290	46	of	of	ADP
ejpam-5662	290	47	u(t	u(t	NOUN
ejpam-5662	290	48	)	)	PUNCT
ejpam-5662	290	49	and	and	CCONJ
ejpam-5662	290	50	v(t	v(t	NOUN
ejpam-5662	290	51	)	)	PUNCT
ejpam-5662	290	52	.	.	PUNCT
ejpam-5662	291	1	these	these	DET
ejpam-5662	291	2	parameters	parameter	NOUN
ejpam-5662	291	3	take	take	VERB
ejpam-5662	291	4	the	the	DET
ejpam-5662	291	5	abovementioned	abovementione	VERB
ejpam-5662	291	6	values	value	NOUN
ejpam-5662	291	7	that	that	PRON
ejpam-5662	291	8	vary	vary	VERB
ejpam-5662	291	9	from	from	ADP
ejpam-5662	291	10	one	one	NUM
ejpam-5662	291	11	figure	figure	NOUN
ejpam-5662	291	12	to	to	ADP
ejpam-5662	291	13	another	another	PRON
ejpam-5662	291	14	with	with	ADP
ejpam-5662	291	15	the	the	DET
ejpam-5662	291	16	variation	variation	NOUN
ejpam-5662	291	17	of	of	ADP
ejpam-5662	291	18	each	each	DET
ejpam-5662	291	19	studied	study	VERB
ejpam-5662	291	20	parameter	parameter	NOUN
ejpam-5662	291	21	.	.	PUNCT
ejpam-5662	292	1	examining	examine	VERB
ejpam-5662	292	2	the	the	DET
ejpam-5662	292	3	waves	wave	NOUN
ejpam-5662	292	4	of	of	ADP
ejpam-5662	292	5	time	time	NOUN
ejpam-5662	292	6	history	history	NOUN
ejpam-5662	292	7	,	,	PUNCT
ejpam-5662	292	8	it	it	PRON
ejpam-5662	292	9	is	be	AUX
ejpam-5662	292	10	apparent	apparent	ADJ
ejpam-5662	292	11	that	that	SCONJ
ejpam-5662	292	12	these	these	DET
ejpam-5662	292	13	waves	wave	NOUN
ejpam-5662	292	14	exhibit	exhibit	VERB
ejpam-5662	292	15	damping	damp	VERB
ejpam-5662	292	16	periodic	periodic	ADJ
ejpam-5662	292	17	shapes	shape	NOUN
ejpam-5662	292	18	across	across	ADP
ejpam-5662	292	19	the	the	DET
ejpam-5662	292	20	whole	whole	ADJ
ejpam-5662	292	21	duration	duration	NOUN
ejpam-5662	292	22	.	.	PUNCT
ejpam-5662	293	1	the	the	DET
ejpam-5662	293	2	oscillation	oscillation	NOUN
ejpam-5662	293	3	numbers	number	NOUN
ejpam-5662	293	4	for	for	ADP
ejpam-5662	293	5	both	both	DET
ejpam-5662	293	6	solutions	solution	NOUN
ejpam-5662	293	7	vary	vary	VERB
ejpam-5662	293	8	based	base	VERB
ejpam-5662	293	9	on	on	ADP
ejpam-5662	293	10	the	the	DET
ejpam-5662	293	11	factors	factor	NOUN
ejpam-5662	293	12	that	that	PRON
ejpam-5662	293	13	are	be	AUX
ejpam-5662	293	14	in	in	ADP
ejpam-5662	293	15	effect	effect	NOUN
ejpam-5662	293	16	,	,	PUNCT
ejpam-5662	293	17	as	as	SCONJ
ejpam-5662	293	18	seen	see	VERB
ejpam-5662	293	19	by	by	ADP
ejpam-5662	293	20	the	the	DET
ejpam-5662	293	21	graphs	graph	NOUN
ejpam-5662	293	22	.	.	PUNCT
ejpam-5662	294	1	the	the	DET
ejpam-5662	294	2	effects	effect	NOUN
ejpam-5662	294	3	of	of	ADP
ejpam-5662	294	4	the	the	DET
ejpam-5662	294	5	natural	natural	ADJ
ejpam-5662	294	6	frequencies	frequency	NOUN
ejpam-5662	294	7	ω1	ω1	PROPN
ejpam-5662	294	8	and	and	CCONJ
ejpam-5662	294	9	ω2	ω2	NOUN
ejpam-5662	294	10	are	be	AUX
ejpam-5662	294	11	shown	show	VERB
ejpam-5662	294	12	through	through	ADP
ejpam-5662	294	13	figs	fig	NOUN
ejpam-5662	294	14	.	.	PUNCT
ejpam-5662	295	1	3	3	X
ejpam-5662	295	2	.	.	X
ejpam-5662	295	3	it	it	PRON
ejpam-5662	295	4	is	be	AUX
ejpam-5662	295	5	seen	see	VERB
ejpam-5662	295	6	from	from	ADP
ejpam-5662	295	7	this	this	DET
ejpam-5662	295	8	figure	figure	NOUN
ejpam-5662	295	9	that	that	SCONJ
ejpam-5662	295	10	the	the	DET
ejpam-5662	295	11	amplitudes	amplitude	NOUN
ejpam-5662	295	12	of	of	ADP
ejpam-5662	295	13	the	the	DET
ejpam-5662	295	14	waves	wave	NOUN
ejpam-5662	295	15	for	for	ADP
ejpam-5662	295	16	the	the	DET
ejpam-5662	295	17	two	two	NUM
ejpam-5662	295	18	solutions	solution	NOUN
ejpam-5662	295	19	continue	continue	VERB
ejpam-5662	295	20	damping	damp	VERB
ejpam-5662	295	21	,	,	PUNCT
ejpam-5662	295	22	while	while	SCONJ
ejpam-5662	295	23	the	the	DET
ejpam-5662	295	24	number	number	NOUN
ejpam-5662	295	25	of	of	ADP
ejpam-5662	295	26	vibrations	vibration	NOUN
ejpam-5662	295	27	increases	increase	NOUN
ejpam-5662	295	28	significantly	significantly	ADV
ejpam-5662	295	29	with	with	ADP
ejpam-5662	295	30	the	the	DET
ejpam-5662	295	31	growth	growth	NOUN
ejpam-5662	295	32	of	of	ADP
ejpam-5662	295	33	ω1	ω1	PROPN
ejpam-5662	295	34	and	and	CCONJ
ejpam-5662	295	35	ω2	ω2	ADJ
ejpam-5662	295	36	.	.	PUNCT
ejpam-5662	296	1	furthermore	furthermore	ADV
ejpam-5662	296	2	,	,	PUNCT
ejpam-5662	296	3	the	the	DET
ejpam-5662	296	4	wavelengths	wavelength	NOUN
ejpam-5662	296	5	are	be	AUX
ejpam-5662	296	6	shrinking	shrink	VERB
ejpam-5662	296	7	with	with	ADP
ejpam-5662	296	8	the	the	DET
ejpam-5662	296	9	rise	rise	NOUN
ejpam-5662	296	10	of	of	ADP
ejpam-5662	296	11	these	these	DET
ejpam-5662	296	12	two	two	NUM
ejpam-5662	296	13	frequencies	frequency	NOUN
ejpam-5662	296	14	.	.	PUNCT
ejpam-5662	297	1	an	an	DET
ejpam-5662	297	2	acceleration	acceleration	NOUN
ejpam-5662	297	3	in	in	ADP
ejpam-5662	297	4	the	the	DET
ejpam-5662	297	5	waves	wave	NOUN
ejpam-5662	297	6	is	be	AUX
ejpam-5662	297	7	observed	observe	VERB
ejpam-5662	297	8	also	also	ADV
ejpam-5662	297	9	due	due	ADP
ejpam-5662	297	10	to	to	ADP
ejpam-5662	297	11	their	their	PRON
ejpam-5662	297	12	growth	growth	NOUN
ejpam-5662	297	13	,	,	PUNCT
ejpam-5662	297	14	this	this	DET
ejpam-5662	297	15	acceleration	acceleration	NOUN
ejpam-5662	297	16	is	be	AUX
ejpam-5662	297	17	greater	great	ADJ
ejpam-5662	297	18	for	for	ADP
ejpam-5662	297	19	u(t	u(t	NOUN
ejpam-5662	297	20	)	)	PUNCT
ejpam-5662	297	21	than	than	ADP
ejpam-5662	297	22	v(t	v(t	NOUN
ejpam-5662	297	23	)	)	PUNCT
ejpam-5662	297	24	which	which	PRON
ejpam-5662	297	25	is	be	AUX
ejpam-5662	297	26	due	due	ADJ
ejpam-5662	297	27	to	to	ADP
ejpam-5662	297	28	the	the	DET
ejpam-5662	297	29	bigger	big	ADJ
ejpam-5662	297	30	of	of	ADP
ejpam-5662	297	31	ω1	ω1	PROPN
ejpam-5662	297	32	than	than	ADP
ejpam-5662	297	33	ω2	ω2	ADJ
ejpam-5662	297	34	.	.	PUNCT
ejpam-5662	298	1	the	the	DET
ejpam-5662	298	2	presence	presence	NOUN
ejpam-5662	298	3	of	of	ADP
ejpam-5662	298	4	quintic	quintic	ADJ
ejpam-5662	298	5	and	and	CCONJ
ejpam-5662	298	6	cubic	cubic	ADJ
ejpam-5662	298	7	nonlinearities	nonlinearitie	NOUN
ejpam-5662	298	8	in	in	ADP
ejpam-5662	298	9	the	the	DET
ejpam-5662	298	10	mathieu	mathieu	PROPN
ejpam-5662	298	11	system	system	NOUN
ejpam-5662	298	12	,	,	PUNCT
ejpam-5662	298	13	especially	especially	ADV
ejpam-5662	298	14	at	at	ADP
ejpam-5662	298	15	large	large	ADJ
ejpam-5662	298	16	oscillation	oscillation	NOUN
ejpam-5662	298	17	amplitudes	amplitude	NOUN
ejpam-5662	298	18	,	,	PUNCT
ejpam-5662	298	19	alters	alter	VERB
ejpam-5662	298	20	naturally	naturally	ADV
ejpam-5662	298	21	the	the	DET
ejpam-5662	298	22	actual	actual	ADJ
ejpam-5662	298	23	frequencies	frequency	NOUN
ejpam-5662	298	24	.	.	PUNCT
ejpam-5662	299	1	this	this	PRON
ejpam-5662	299	2	is	be	AUX
ejpam-5662	299	3	referred	refer	VERB
ejpam-5662	299	4	to	to	ADP
ejpam-5662	299	5	as	as	ADP
ejpam-5662	299	6	amplitude	amplitude	NOUN
ejpam-5662	299	7	-	-	PUNCT
ejpam-5662	299	8	dependent	dependent	ADJ
ejpam-5662	299	9	frequency	frequency	NOUN
ejpam-5662	299	10	or	or	CCONJ
ejpam-5662	299	11	nonlinear	nonlinear	ADJ
ejpam-5662	299	12	frequency	frequency	NOUN
ejpam-5662	299	13	shift	shift	NOUN
ejpam-5662	299	14	.	.	PUNCT
ejpam-5662	300	1	the	the	DET
ejpam-5662	300	2	npa	npa	NOUN
ejpam-5662	300	3	is	be	AUX
ejpam-5662	300	4	used	use	VERB
ejpam-5662	300	5	in	in	ADP
ejpam-5662	300	6	the	the	DET
ejpam-5662	300	7	current	current	ADJ
ejpam-5662	300	8	study	study	NOUN
ejpam-5662	300	9	to	to	PART
ejpam-5662	300	10	realize	realize	VERB
ejpam-5662	300	11	these	these	DET
ejpam-5662	300	12	new	new	ADJ
ejpam-5662	300	13	frequencies	frequency	NOUN
ejpam-5662	300	14	,	,	PUNCT
ejpam-5662	300	15	as	as	SCONJ
ejpam-5662	300	16	seen	see	VERB
ejpam-5662	300	17	above	above	ADV
ejpam-5662	300	18	.	.	PUNCT
ejpam-5662	301	1	in	in	ADP
ejpam-5662	301	2	a	a	DET
ejpam-5662	301	3	fully	fully	ADV
ejpam-5662	301	4	linear	linear	ADJ
ejpam-5662	301	5	system	system	NOUN
ejpam-5662	301	6	,	,	PUNCT
ejpam-5662	301	7	the	the	DET
ejpam-5662	301	8	natural	natural	ADJ
ejpam-5662	301	9	frequency	frequency	NOUN
ejpam-5662	301	10	remains	remain	VERB
ejpam-5662	301	11	constant	constant	ADJ
ejpam-5662	301	12	;	;	PUNCT
ejpam-5662	301	13	however	however	ADV
ejpam-5662	301	14	,	,	PUNCT
ejpam-5662	301	15	in	in	ADP
ejpam-5662	301	16	a	a	DET
ejpam-5662	301	17	nonlinear	nonlinear	ADJ
ejpam-5662	301	18	system	system	NOUN
ejpam-5662	301	19	,	,	PUNCT
ejpam-5662	301	20	such	such	ADJ
ejpam-5662	301	21	as	as	ADP
ejpam-5662	301	22	the	the	DET
ejpam-5662	301	23	do	do	NOUN
ejpam-5662	301	24	,	,	PUNCT
ejpam-5662	301	25	the	the	DET
ejpam-5662	301	26	nonlinear	nonlinear	ADJ
ejpam-5662	301	27	restoring	restore	VERB
ejpam-5662	301	28	forces	force	NOUN
ejpam-5662	301	29	cause	cause	VERB
ejpam-5662	301	30	the	the	DET
ejpam-5662	301	31	effective	effective	ADJ
ejpam-5662	301	32	natural	natural	ADJ
ejpam-5662	301	33	frequency	frequency	NOUN
ejpam-5662	301	34	to	to	PART
ejpam-5662	301	35	vary	vary	VERB
ejpam-5662	301	36	with	with	ADP
ejpam-5662	301	37	the	the	DET
ejpam-5662	301	38	oscillation	oscillation	NOUN
ejpam-5662	301	39	amplitude	amplitude	NOUN
ejpam-5662	301	40	.	.	PUNCT
ejpam-5662	302	1	additionally	additionally	ADV
ejpam-5662	302	2	,	,	PUNCT
ejpam-5662	302	3	it	it	PRON
ejpam-5662	302	4	is	be	AUX
ejpam-5662	302	5	seen	see	VERB
ejpam-5662	302	6	from	from	ADP
ejpam-5662	302	7	figs	fig	NOUN
ejpam-5662	302	8	.	.	PUNCT
ejpam-5662	303	1	4	4	NUM
ejpam-5662	303	2	that	that	PRON
ejpam-5662	303	3	the	the	DET
ejpam-5662	303	4	amplitudes	amplitude	NOUN
ejpam-5662	303	5	of	of	ADP
ejpam-5662	303	6	the	the	DET
ejpam-5662	303	7	waves	wave	NOUN
ejpam-5662	303	8	for	for	ADP
ejpam-5662	303	9	the	the	DET
ejpam-5662	303	10	two	two	NUM
ejpam-5662	303	11	solutions	solution	NOUN
ejpam-5662	303	12	are	be	AUX
ejpam-5662	303	13	damped	damp	VERB
ejpam-5662	303	14	,	,	PUNCT
ejpam-5662	303	15	whereas	whereas	SCONJ
ejpam-5662	303	16	the	the	DET
ejpam-5662	303	17	number	number	NOUN
ejpam-5662	303	18	of	of	ADP
ejpam-5662	303	19	vibrations	vibration	NOUN
ejpam-5662	303	20	is	be	AUX
ejpam-5662	303	21	approximately	approximately	ADV
ejpam-5662	303	22	constant	constant	ADJ
ejpam-5662	303	23	with	with	ADP
ejpam-5662	303	24	the	the	DET
ejpam-5662	303	25	growth	growth	NOUN
ejpam-5662	303	26	of	of	ADP
ejpam-5662	303	27	the	the	DET
ejpam-5662	303	28	cubic	cubic	ADJ
ejpam-5662	303	29	factors	factor	NOUN
ejpam-5662	303	30	γ1	γ1	NOUN
ejpam-5662	303	31	and	and	CCONJ
ejpam-5662	303	32	γ2	γ2	PROPN
ejpam-5662	303	33	.	.	PUNCT
ejpam-5662	304	1	the	the	DET
ejpam-5662	304	2	wavelengths	wavelength	NOUN
ejpam-5662	304	3	are	be	AUX
ejpam-5662	304	4	found	find	VERB
ejpam-5662	304	5	unvarying	unvarye	VERB
ejpam-5662	304	6	with	with	ADP
ejpam-5662	304	7	the	the	DET
ejpam-5662	304	8	impact	impact	NOUN
ejpam-5662	304	9	of	of	ADP
ejpam-5662	304	10	γ1	γ1	NOUN
ejpam-5662	304	11	and	and	CCONJ
ejpam-5662	304	12	γ2	γ2	NOUN
ejpam-5662	304	13	,	,	PUNCT
ejpam-5662	304	14	meanwhile	meanwhile	ADV
ejpam-5662	304	15	,	,	PUNCT
ejpam-5662	304	16	a	a	DET
ejpam-5662	304	17	notable	notable	ADJ
ejpam-5662	304	18	delay	delay	NOUN
ejpam-5662	304	19	in	in	ADP
ejpam-5662	304	20	the	the	DET
ejpam-5662	304	21	waves	wave	NOUN
ejpam-5662	304	22	is	be	AUX
ejpam-5662	304	23	obtained	obtain	VERB
ejpam-5662	304	24	in	in	ADP
ejpam-5662	304	25	figs	fig	NOUN
ejpam-5662	304	26	.	.	PUNCT
ejpam-5662	305	1	4	4	NUM
ejpam-5662	305	2	with	with	ADP
ejpam-5662	305	3	the	the	DET
ejpam-5662	305	4	rise	rise	NOUN
ejpam-5662	305	5	of	of	ADP
ejpam-5662	305	6	these	these	DET
ejpam-5662	305	7	cubic	cubic	ADJ
ejpam-5662	305	8	coefficients	coefficient	NOUN
ejpam-5662	305	9	.	.	PUNCT
ejpam-5662	306	1	systems	system	NOUN
ejpam-5662	306	2	with	with	ADP
ejpam-5662	306	3	cubic	cubic	ADJ
ejpam-5662	306	4	nonlinearities	nonlinearitie	NOUN
ejpam-5662	306	5	do	do	AUX
ejpam-5662	306	6	not	not	PART
ejpam-5662	306	7	have	have	VERB
ejpam-5662	306	8	a	a	DET
ejpam-5662	306	9	set	set	VERB
ejpam-5662	306	10	natural	natural	ADJ
ejpam-5662	306	11	frequency	frequency	NOUN
ejpam-5662	306	12	of	of	ADP
ejpam-5662	306	13	oscillation	oscillation	NOUN
ejpam-5662	306	14	,	,	PUNCT
ejpam-5662	306	15	in	in	ADP
ejpam-5662	306	16	contrast	contrast	NOUN
ejpam-5662	306	17	to	to	ADP
ejpam-5662	306	18	linear	linear	PROPN
ejpam-5662	306	19	systems	system	NOUN
ejpam-5662	306	20	.	.	PUNCT
ejpam-5662	307	1	instead	instead	ADV
ejpam-5662	307	2	,	,	PUNCT
ejpam-5662	307	3	the	the	DET
ejpam-5662	307	4	amplitude	amplitude	NOUN
ejpam-5662	307	5	starts	start	VERB
ejpam-5662	307	6	to	to	PART
ejpam-5662	307	7	depend	depend	VERB
ejpam-5662	307	8	on	on	ADP
ejpam-5662	307	9	the	the	DET
ejpam-5662	307	10	inherent	inherent	ADJ
ejpam-5662	307	11	frequency	frequency	NOUN
ejpam-5662	307	12	.	.	PUNCT
ejpam-5662	308	1	intricate	intricate	ADJ
ejpam-5662	308	2	behaviors	behavior	NOUN
ejpam-5662	308	3	and	and	CCONJ
ejpam-5662	308	4	improved	improved	ADJ
ejpam-5662	308	5	system	system	NOUN
ejpam-5662	308	6	dynamics	dynamic	NOUN
ejpam-5662	308	7	are	be	AUX
ejpam-5662	308	8	a.	a.	NOUN
ejpam-5662	308	9	alanazy	alanazy	NOUN
ejpam-5662	308	10	,	,	PUNCT
ejpam-5662	308	11	g.	g.	PROPN
ejpam-5662	308	12	m.	m.	PROPN
ejpam-5662	308	13	moatimid	moatimid	PROPN
ejpam-5662	308	14	,	,	PUNCT
ejpam-5662	308	15	m.	m.	PROPN
ejpam-5662	308	16	a.	a.	PROPN
ejpam-5662	308	17	a.	a.	PROPN
ejpam-5662	308	18	mohamed	mohamed	PROPN
ejpam-5662	308	19	/	/	SYM
ejpam-5662	308	20	eur	eur	PROPN
ejpam-5662	308	21	.	.	PUNCT
ejpam-5662	309	1	j.	j.	PROPN
ejpam-5662	309	2	pure	pure	PROPN
ejpam-5662	309	3	appl	appl	PROPN
ejpam-5662	309	4	.	.	PROPN
ejpam-5662	309	5	math	math	PROPN
ejpam-5662	309	6	,	,	PUNCT
ejpam-5662	309	7	18	18	NUM
ejpam-5662	309	8	(	(	PUNCT
ejpam-5662	309	9	2	2	NUM
ejpam-5662	309	10	)	)	PUNCT
ejpam-5662	309	11	(	(	PUNCT
ejpam-5662	309	12	2025	2025	NUM
ejpam-5662	309	13	)	)	PUNCT
ejpam-5662	309	14	,	,	PUNCT
ejpam-5662	309	15	5662	5662	NUM
ejpam-5662	309	16	15	15	NUM
ejpam-5662	309	17	of	of	ADP
ejpam-5662	309	18	36	36	NUM
ejpam-5662	309	19	provided	provide	VERB
ejpam-5662	309	20	by	by	ADP
ejpam-5662	309	21	cubic	cubic	ADJ
ejpam-5662	309	22	nonlinearities	nonlinearitie	NOUN
ejpam-5662	309	23	,	,	PUNCT
ejpam-5662	309	24	which	which	PRON
ejpam-5662	309	25	are	be	AUX
ejpam-5662	309	26	not	not	PART
ejpam-5662	309	27	possible	possible	ADJ
ejpam-5662	309	28	in	in	ADP
ejpam-5662	309	29	simply	simply	ADV
ejpam-5662	309	30	linear	linear	PROPN
ejpam-5662	309	31	systems	system	NOUN
ejpam-5662	309	32	.	.	PUNCT
ejpam-5662	310	1	figs	fig	NOUN
ejpam-5662	310	2	.	.	PUNCT
ejpam-5662	311	1	5	5	NUM
ejpam-5662	311	2	are	be	AUX
ejpam-5662	311	3	plotted	plot	VERB
ejpam-5662	311	4	to	to	PART
ejpam-5662	311	5	examine	examine	VERB
ejpam-5662	311	6	the	the	DET
ejpam-5662	311	7	influence	influence	NOUN
ejpam-5662	311	8	of	of	ADP
ejpam-5662	311	9	the	the	DET
ejpam-5662	311	10	coefficients	coefficient	NOUN
ejpam-5662	311	11	of	of	ADP
ejpam-5662	311	12	the	the	DET
ejpam-5662	311	13	periodic	periodic	ADJ
ejpam-5662	311	14	terms	term	NOUN
ejpam-5662	311	15	of	of	ADP
ejpam-5662	311	16	x	x	PRON
ejpam-5662	311	17	in	in	ADP
ejpam-5662	311	18	the	the	DET
ejpam-5662	311	19	nonlinear	nonlinear	ADJ
ejpam-5662	311	20	system	system	NOUN
ejpam-5662	311	21	of	of	ADP
ejpam-5662	311	22	mathieu	mathieu	PROPN
ejpam-5662	311	23	eqs	eqs	PROPN
ejpam-5662	311	24	.	.	PUNCT
ejpam-5662	312	1	(	(	PUNCT
ejpam-5662	312	2	18	18	NUM
ejpam-5662	312	3	)	)	PUNCT
ejpam-5662	312	4	and	and	CCONJ
ejpam-5662	312	5	(	(	PUNCT
ejpam-5662	312	6	19	19	NUM
ejpam-5662	312	7	)	)	PUNCT
ejpam-5662	312	8	,	,	PUNCT
ejpam-5662	312	9	η11	η11	NOUN
ejpam-5662	312	10	and	and	CCONJ
ejpam-5662	312	11	η21	η21	PROPN
ejpam-5662	312	12	,	,	PUNCT
ejpam-5662	312	13	on	on	ADP
ejpam-5662	312	14	both	both	DET
ejpam-5662	312	15	u(t	u(t	NOUN
ejpam-5662	312	16	)	)	PUNCT
ejpam-5662	312	17	and	and	CCONJ
ejpam-5662	312	18	v(t	v(t	NOUN
ejpam-5662	312	19	)	)	PUNCT
ejpam-5662	312	20	,	,	PUNCT
ejpam-5662	312	21	respectively	respectively	ADV
ejpam-5662	312	22	.	.	PUNCT
ejpam-5662	313	1	from	from	ADP
ejpam-5662	313	2	these	these	DET
ejpam-5662	313	3	figures	figure	NOUN
ejpam-5662	313	4	,	,	PUNCT
ejpam-5662	313	5	one	one	PRON
ejpam-5662	313	6	sees	see	VERB
ejpam-5662	313	7	that	that	SCONJ
ejpam-5662	313	8	the	the	DET
ejpam-5662	313	9	amplitudes	amplitude	NOUN
ejpam-5662	313	10	of	of	ADP
ejpam-5662	313	11	the	the	DET
ejpam-5662	313	12	waves	wave	NOUN
ejpam-5662	313	13	are	be	AUX
ejpam-5662	313	14	decreasing	decrease	VERB
ejpam-5662	313	15	,	,	PUNCT
ejpam-5662	313	16	meanwhile	meanwhile	ADV
ejpam-5662	313	17	the	the	DET
ejpam-5662	313	18	wavelengths	wavelength	NOUN
ejpam-5662	313	19	remain	remain	VERB
ejpam-5662	313	20	slightly	slightly	ADV
ejpam-5662	313	21	stable	stable	ADJ
ejpam-5662	313	22	for	for	ADP
ejpam-5662	313	23	u(t	u(t	NOUN
ejpam-5662	313	24	)	)	PUNCT
ejpam-5662	313	25	and	and	CCONJ
ejpam-5662	313	26	v(t	v(t	NOUN
ejpam-5662	313	27	)	)	PUNCT
ejpam-5662	313	28	with	with	ADP
ejpam-5662	313	29	the	the	DET
ejpam-5662	313	30	rise	rise	NOUN
ejpam-5662	313	31	of	of	ADP
ejpam-5662	313	32	η11	η11	NOUN
ejpam-5662	313	33	and	and	CCONJ
ejpam-5662	313	34	η21	η21	NOUN
ejpam-5662	313	35	.	.	PUNCT
ejpam-5662	314	1	moreover	moreover	ADV
ejpam-5662	314	2	,	,	PUNCT
ejpam-5662	314	3	figs	fig	NOUN
ejpam-5662	314	4	.	.	X
ejpam-5662	315	1	6	6	NUM
ejpam-5662	315	2	are	be	AUX
ejpam-5662	315	3	schemed	scheme	VERB
ejpam-5662	315	4	to	to	PART
ejpam-5662	315	5	illustrate	illustrate	VERB
ejpam-5662	315	6	the	the	DET
ejpam-5662	315	7	effects	effect	NOUN
ejpam-5662	315	8	of	of	ADP
ejpam-5662	315	9	the	the	DET
ejpam-5662	315	10	coefficients	coefficient	NOUN
ejpam-5662	315	11	of	of	ADP
ejpam-5662	315	12	the	the	DET
ejpam-5662	315	13	periodic	periodic	ADJ
ejpam-5662	315	14	terms	term	NOUN
ejpam-5662	315	15	of	of	ADP
ejpam-5662	315	16	y	y	PROPN
ejpam-5662	315	17	in	in	ADP
ejpam-5662	315	18	the	the	DET
ejpam-5662	315	19	nonlinear	nonlinear	ADJ
ejpam-5662	315	20	system	system	NOUN
ejpam-5662	315	21	of	of	ADP
ejpam-5662	315	22	mathieu	mathieu	PROPN
ejpam-5662	315	23	eqs	eqs	PROPN
ejpam-5662	315	24	.	.	PUNCT
ejpam-5662	316	1	(	(	PUNCT
ejpam-5662	316	2	18	18	NUM
ejpam-5662	316	3	)	)	PUNCT
ejpam-5662	316	4	and	and	CCONJ
ejpam-5662	316	5	(	(	PUNCT
ejpam-5662	316	6	19	19	NUM
ejpam-5662	316	7	)	)	PUNCT
ejpam-5662	316	8	,	,	PUNCT
ejpam-5662	316	9	η12and	η12and	PROPN
ejpam-5662	316	10	η22	η22	PROPN
ejpam-5662	316	11	,	,	PUNCT
ejpam-5662	316	12	on	on	ADP
ejpam-5662	316	13	both	both	DET
ejpam-5662	316	14	u(t	u(t	NOUN
ejpam-5662	316	15	)	)	PUNCT
ejpam-5662	316	16	and	and	CCONJ
ejpam-5662	316	17	v(t	v(t	NOUN
ejpam-5662	316	18	)	)	PUNCT
ejpam-5662	316	19	,	,	PUNCT
ejpam-5662	316	20	individually	individually	ADV
ejpam-5662	316	21	.	.	PUNCT
ejpam-5662	317	1	these	these	DET
ejpam-5662	317	2	figures	figure	NOUN
ejpam-5662	317	3	indicate	indicate	VERB
ejpam-5662	317	4	similar	similar	ADJ
ejpam-5662	317	5	impacts	impact	NOUN
ejpam-5662	317	6	as	as	ADP
ejpam-5662	317	7	figs	fig	NOUN
ejpam-5662	317	8	.	.	PUNCT
ejpam-5662	318	1	4	4	X
ejpam-5662	318	2	.	.	X
ejpam-5662	318	3	physically	physically	ADV
ejpam-5662	318	4	,	,	PUNCT
ejpam-5662	318	5	parametric	parametric	ADJ
ejpam-5662	318	6	resonance	resonance	NOUN
ejpam-5662	318	7	is	be	AUX
ejpam-5662	318	8	made	make	VERB
ejpam-5662	318	9	possible	possible	ADJ
ejpam-5662	318	10	by	by	ADP
ejpam-5662	318	11	the	the	DET
ejpam-5662	318	12	rise	rise	NOUN
ejpam-5662	318	13	of	of	ADP
ejpam-5662	318	14	the	the	DET
ejpam-5662	318	15	excited	excited	ADJ
ejpam-5662	318	16	amplitudes	amplitude	NOUN
ejpam-5662	318	17	.	.	PUNCT
ejpam-5662	319	1	this	this	PRON
ejpam-5662	319	2	can	can	AUX
ejpam-5662	319	3	lead	lead	VERB
ejpam-5662	319	4	to	to	ADP
ejpam-5662	319	5	nonlinear	nonlinear	ADJ
ejpam-5662	319	6	phenomena	phenomenon	NOUN
ejpam-5662	319	7	such	such	ADJ
ejpam-5662	319	8	as	as	ADP
ejpam-5662	319	9	high	high	ADJ
ejpam-5662	319	10	amplitude	amplitude	NOUN
ejpam-5662	319	11	oscillations	oscillation	NOUN
ejpam-5662	319	12	,	,	PUNCT
ejpam-5662	319	13	amplitudedependent	amplitudedependent	ADJ
ejpam-5662	319	14	resonance	resonance	NOUN
ejpam-5662	319	15	,	,	PUNCT
ejpam-5662	319	16	and	and	CCONJ
ejpam-5662	319	17	perhaps	perhaps	ADV
ejpam-5662	319	18	instability	instability	NOUN
ejpam-5662	319	19	.	.	PUNCT
ejpam-5662	320	1	higher	high	ADJ
ejpam-5662	320	2	stimulation	stimulation	NOUN
ejpam-5662	320	3	amplitudes	amplitude	NOUN
ejpam-5662	320	4	extend	extend	VERB
ejpam-5662	320	5	the	the	DET
ejpam-5662	320	6	instability	instability	NOUN
ejpam-5662	320	7	zones	zone	NOUN
ejpam-5662	320	8	and	and	CCONJ
ejpam-5662	320	9	increase	increase	VERB
ejpam-5662	320	10	the	the	DET
ejpam-5662	320	11	system	system	NOUN
ejpam-5662	320	12	’s	’s	PART
ejpam-5662	320	13	susceptibility	susceptibility	NOUN
ejpam-5662	320	14	to	to	PART
ejpam-5662	320	15	parametric	parametric	ADJ
ejpam-5662	320	16	resonance	resonance	NOUN
ejpam-5662	320	17	and	and	CCONJ
ejpam-5662	320	18	enormous	enormous	ADJ
ejpam-5662	320	19	oscillations	oscillation	NOUN
ejpam-5662	320	20	.	.	PUNCT
ejpam-5662	321	1	figs	fig	NOUN
ejpam-5662	321	2	.	.	PUNCT
ejpam-5662	322	1	7	7	NUM
ejpam-5662	322	2	are	be	AUX
ejpam-5662	322	3	plotted	plot	VERB
ejpam-5662	322	4	to	to	PART
ejpam-5662	322	5	inspect	inspect	VERB
ejpam-5662	322	6	the	the	DET
ejpam-5662	322	7	influence	influence	NOUN
ejpam-5662	322	8	of	of	ADP
ejpam-5662	322	9	the	the	DET
ejpam-5662	322	10	quinitic	quinitic	ADJ
ejpam-5662	322	11	coefficients	coefficient	NOUN
ejpam-5662	322	12	λ1	λ1	ADJ
ejpam-5662	322	13	and	and	CCONJ
ejpam-5662	322	14	λ2	λ2	NOUN
ejpam-5662	322	15	in	in	ADP
ejpam-5662	322	16	the	the	DET
ejpam-5662	322	17	coupled	couple	VERB
ejpam-5662	322	18	system	system	NOUN
ejpam-5662	322	19	(	(	PUNCT
ejpam-5662	322	20	18	18	NUM
ejpam-5662	322	21	)	)	PUNCT
ejpam-5662	322	22	and	and	CCONJ
ejpam-5662	322	23	(	(	PUNCT
ejpam-5662	322	24	19	19	NUM
ejpam-5662	322	25	)	)	PUNCT
ejpam-5662	322	26	.	.	PUNCT
ejpam-5662	323	1	the	the	DET
ejpam-5662	323	2	amplitudes	amplitude	NOUN
ejpam-5662	323	3	of	of	ADP
ejpam-5662	323	4	the	the	DET
ejpam-5662	323	5	waves	wave	NOUN
ejpam-5662	323	6	as	as	ADV
ejpam-5662	323	7	well	well	ADV
ejpam-5662	323	8	as	as	ADP
ejpam-5662	323	9	the	the	DET
ejpam-5662	323	10	number	number	NOUN
ejpam-5662	323	11	of	of	ADP
ejpam-5662	323	12	vibrations	vibration	NOUN
ejpam-5662	323	13	for	for	ADP
ejpam-5662	323	14	the	the	DET
ejpam-5662	323	15	two	two	NUM
ejpam-5662	323	16	solutions	solution	NOUN
ejpam-5662	323	17	declined	decline	VERB
ejpam-5662	323	18	with	with	ADP
ejpam-5662	323	19	the	the	DET
ejpam-5662	323	20	growth	growth	NOUN
ejpam-5662	323	21	of	of	ADP
ejpam-5662	323	22	the	the	DET
ejpam-5662	323	23	quinitic	quinitic	ADJ
ejpam-5662	323	24	factors	factor	NOUN
ejpam-5662	323	25	λ1	λ1	ADJ
ejpam-5662	323	26	and	and	CCONJ
ejpam-5662	323	27	λ2	λ2	NOUN
ejpam-5662	323	28	.	.	PUNCT
ejpam-5662	324	1	the	the	DET
ejpam-5662	324	2	wavelengths	wavelength	NOUN
ejpam-5662	324	3	are	be	AUX
ejpam-5662	324	4	found	find	VERB
ejpam-5662	324	5	unvarying	unvarye	VERB
ejpam-5662	324	6	with	with	ADP
ejpam-5662	324	7	the	the	DET
ejpam-5662	324	8	impact	impact	NOUN
ejpam-5662	324	9	of	of	ADP
ejpam-5662	324	10	λ1and	λ1and	PRON
ejpam-5662	324	11	λ2	λ2	NOUN
ejpam-5662	324	12	,	,	PUNCT
ejpam-5662	324	13	meanwhile	meanwhile	ADV
ejpam-5662	324	14	,	,	PUNCT
ejpam-5662	324	15	an	an	DET
ejpam-5662	324	16	insignificant	insignificant	ADJ
ejpam-5662	324	17	delay	delay	NOUN
ejpam-5662	324	18	in	in	ADP
ejpam-5662	324	19	the	the	DET
ejpam-5662	324	20	waves	wave	NOUN
ejpam-5662	324	21	is	be	AUX
ejpam-5662	324	22	obtained	obtain	VERB
ejpam-5662	324	23	in	in	ADP
ejpam-5662	324	24	figs	fig	NOUN
ejpam-5662	324	25	.	.	PUNCT
ejpam-5662	325	1	7	7	NUM
ejpam-5662	325	2	with	with	ADP
ejpam-5662	325	3	the	the	DET
ejpam-5662	325	4	rise	rise	NOUN
ejpam-5662	325	5	of	of	ADP
ejpam-5662	325	6	these	these	DET
ejpam-5662	325	7	quintic	quintic	ADJ
ejpam-5662	325	8	coefficients	coefficient	NOUN
ejpam-5662	325	9	.	.	PUNCT
ejpam-5662	326	1	the	the	DET
ejpam-5662	326	2	dynamic	dynamic	ADJ
ejpam-5662	326	3	behavior	behavior	NOUN
ejpam-5662	326	4	of	of	ADP
ejpam-5662	326	5	a	a	DET
ejpam-5662	326	6	tdof	tdof	NOUN
ejpam-5662	326	7	of	of	ADP
ejpam-5662	326	8	mdo	mdo	PROPN
ejpam-5662	326	9	is	be	AUX
ejpam-5662	326	10	further	far	ADV
ejpam-5662	326	11	complicated	complicate	VERB
ejpam-5662	326	12	by	by	ADP
ejpam-5662	326	13	quintic	quintic	ADJ
ejpam-5662	326	14	nonlinearities	nonlinearitie	NOUN
ejpam-5662	326	15	,	,	PUNCT
ejpam-5662	326	16	particularly	particularly	ADV
ejpam-5662	326	17	when	when	SCONJ
ejpam-5662	326	18	paired	pair	VERB
ejpam-5662	326	19	with	with	ADP
ejpam-5662	326	20	parametric	parametric	ADJ
ejpam-5662	326	21	excitation	excitation	NOUN
ejpam-5662	326	22	and	and	CCONJ
ejpam-5662	326	23	other	other	ADJ
ejpam-5662	326	24	nonlinear	nonlinear	ADJ
ejpam-5662	326	25	effects	effect	NOUN
ejpam-5662	326	26	like	like	ADP
ejpam-5662	326	27	cubic	cubic	ADJ
ejpam-5662	326	28	terms	term	NOUN
ejpam-5662	326	29	.	.	PUNCT
ejpam-5662	327	1	higher	high	ADJ
ejpam-5662	327	2	-	-	PUNCT
ejpam-5662	327	3	order	order	NOUN
ejpam-5662	327	4	stiffness	stiffness	NOUN
ejpam-5662	327	5	effects	effect	NOUN
ejpam-5662	327	6	brought	bring	VERB
ejpam-5662	327	7	forth	forth	ADP
ejpam-5662	327	8	by	by	ADP
ejpam-5662	327	9	the	the	DET
ejpam-5662	327	10	quintic	quintic	ADJ
ejpam-5662	327	11	term	term	NOUN
ejpam-5662	327	12	affect	affect	VERB
ejpam-5662	327	13	the	the	DET
ejpam-5662	327	14	stability	stability	NOUN
ejpam-5662	327	15	,	,	PUNCT
ejpam-5662	327	16	bifurcation	bifurcation	NOUN
ejpam-5662	327	17	structures	structure	NOUN
ejpam-5662	327	18	,	,	PUNCT
ejpam-5662	327	19	and	and	CCONJ
ejpam-5662	327	20	oscillations	oscillation	NOUN
ejpam-5662	327	21	of	of	ADP
ejpam-5662	327	22	the	the	DET
ejpam-5662	327	23	system	system	NOUN
ejpam-5662	327	24	.	.	PUNCT
ejpam-5662	328	1	at	at	ADP
ejpam-5662	328	2	higher	high	ADJ
ejpam-5662	328	3	oscillation	oscillation	NOUN
ejpam-5662	328	4	amplitudes	amplitude	NOUN
ejpam-5662	328	5	,	,	PUNCT
ejpam-5662	328	6	the	the	DET
ejpam-5662	328	7	quintic	quintic	ADJ
ejpam-5662	328	8	term	term	NOUN
ejpam-5662	328	9	changes	change	VERB
ejpam-5662	328	10	the	the	DET
ejpam-5662	328	11	behavior	behavior	NOUN
ejpam-5662	328	12	of	of	ADP
ejpam-5662	328	13	the	the	DET
ejpam-5662	328	14	system	system	NOUN
ejpam-5662	328	15	and	and	CCONJ
ejpam-5662	328	16	may	may	AUX
ejpam-5662	328	17	be	be	AUX
ejpam-5662	328	18	combined	combine	VERB
ejpam-5662	328	19	with	with	ADP
ejpam-5662	328	20	cubic	cubic	ADJ
ejpam-5662	328	21	nonlinearities	nonlinearitie	NOUN
ejpam-5662	328	22	and	and	CCONJ
ejpam-5662	328	23	parametric	parametric	ADJ
ejpam-5662	328	24	stimulation	stimulation	NOUN
ejpam-5662	328	25	to	to	PART
ejpam-5662	328	26	produce	produce	VERB
ejpam-5662	328	27	complex	complex	ADJ
ejpam-5662	328	28	dynamics	dynamic	NOUN
ejpam-5662	328	29	.	.	PUNCT
ejpam-5662	329	1	similar	similar	ADJ
ejpam-5662	329	2	to	to	ADP
ejpam-5662	329	3	cubic	cubic	ADJ
ejpam-5662	329	4	nonlinearities	nonlinearitie	NOUN
ejpam-5662	329	5	,	,	PUNCT
ejpam-5662	329	6	quintic	quintic	ADJ
ejpam-5662	329	7	nonlinearities	nonlinearitie	NOUN
ejpam-5662	329	8	cause	cause	VERB
ejpam-5662	329	9	the	the	DET
ejpam-5662	329	10	system	system	NOUN
ejpam-5662	329	11	’s	’s	PART
ejpam-5662	329	12	natural	natural	ADJ
ejpam-5662	329	13	frequencies	frequency	NOUN
ejpam-5662	329	14	to	to	PART
ejpam-5662	329	15	change	change	VERB
ejpam-5662	329	16	as	as	SCONJ
ejpam-5662	329	17	the	the	DET
ejpam-5662	329	18	amplitude	amplitude	NOUN
ejpam-5662	329	19	grows	grow	VERB
ejpam-5662	329	20	.	.	PUNCT
ejpam-5662	330	1	at	at	ADP
ejpam-5662	330	2	larger	large	ADJ
ejpam-5662	330	3	amplitudes	amplitude	NOUN
ejpam-5662	330	4	,	,	PUNCT
ejpam-5662	330	5	the	the	DET
ejpam-5662	330	6	frequency	frequency	NOUN
ejpam-5662	330	7	-	-	PUNCT
ejpam-5662	330	8	amplitude	amplitude	NOUN
ejpam-5662	330	9	dependency	dependency	NOUN
ejpam-5662	330	10	becomes	become	VERB
ejpam-5662	330	11	more	more	ADV
ejpam-5662	330	12	pronounced	pronounced	ADJ
ejpam-5662	330	13	due	due	ADP
ejpam-5662	330	14	to	to	ADP
ejpam-5662	330	15	the	the	DET
ejpam-5662	330	16	higher	high	ADJ
ejpam-5662	330	17	-	-	PUNCT
ejpam-5662	330	18	order	order	NOUN
ejpam-5662	330	19	frequency	frequency	NOUN
ejpam-5662	330	20	shift	shift	NOUN
ejpam-5662	330	21	introduced	introduce	VERB
ejpam-5662	330	22	by	by	ADP
ejpam-5662	330	23	the	the	DET
ejpam-5662	330	24	quintic	quintic	ADJ
ejpam-5662	330	25	term	term	NOUN
ejpam-5662	330	26	.	.	PUNCT
ejpam-5662	331	1	at	at	ADP
ejpam-5662	331	2	this	this	DET
ejpam-5662	331	3	end	end	NOUN
ejpam-5662	331	4	,	,	PUNCT
ejpam-5662	331	5	figs	fig	NOUN
ejpam-5662	331	6	.	.	PUNCT
ejpam-5662	331	7	8	8	NUM
ejpam-5662	331	8	show	show	VERB
ejpam-5662	331	9	the	the	DET
ejpam-5662	331	10	impact	impact	NOUN
ejpam-5662	331	11	of	of	ADP
ejpam-5662	331	12	the	the	DET
ejpam-5662	331	13	excited	excited	ADJ
ejpam-5662	331	14	frequency	frequency	NOUN
ejpam-5662	331	15	ωp	ωp	NOUN
ejpam-5662	331	16	,	,	PUNCT
ejpam-5662	331	17	of	of	ADP
ejpam-5662	331	18	the	the	DET
ejpam-5662	331	19	two	two	NUM
ejpam-5662	331	20	waves	wave	NOUN
ejpam-5662	331	21	x	x	PUNCT
ejpam-5662	331	22	and	and	CCONJ
ejpam-5662	331	23	y	y	PROPN
ejpam-5662	331	24	which	which	PRON
ejpam-5662	331	25	characterizes	characterize	VERB
ejpam-5662	331	26	the	the	DET
ejpam-5662	331	27	two	two	NUM
ejpam-5662	331	28	coupled	couple	VERB
ejpam-5662	331	29	oscillators	oscillator	NOUN
ejpam-5662	331	30	on	on	ADP
ejpam-5662	331	31	the	the	DET
ejpam-5662	331	32	distributions	distribution	NOUN
ejpam-5662	331	33	u(t	u(t	NOUN
ejpam-5662	331	34	)	)	PUNCT
ejpam-5662	331	35	and	and	CCONJ
ejpam-5662	331	36	v(t	v(t	NOUN
ejpam-5662	331	37	)	)	PUNCT
ejpam-5662	331	38	.	.	PUNCT
ejpam-5662	332	1	it	it	PRON
ejpam-5662	332	2	is	be	AUX
ejpam-5662	332	3	seen	see	VERB
ejpam-5662	332	4	also	also	ADV
ejpam-5662	332	5	from	from	ADP
ejpam-5662	332	6	these	these	DET
ejpam-5662	332	7	figures	figure	NOUN
ejpam-5662	332	8	that	that	SCONJ
ejpam-5662	332	9	wavelengths	wavelength	NOUN
ejpam-5662	332	10	and	and	CCONJ
ejpam-5662	332	11	the	the	DET
ejpam-5662	332	12	number	number	NOUN
ejpam-5662	332	13	of	of	ADP
ejpam-5662	332	14	waves	wave	NOUN
ejpam-5662	332	15	remain	remain	VERB
ejpam-5662	332	16	unvarying	unvarying	ADJ
ejpam-5662	332	17	,	,	PUNCT
ejpam-5662	332	18	while	while	SCONJ
ejpam-5662	332	19	significant	significant	ADJ
ejpam-5662	332	20	progress	progress	NOUN
ejpam-5662	332	21	in	in	ADP
ejpam-5662	332	22	the	the	DET
ejpam-5662	332	23	waves	wave	NOUN
ejpam-5662	332	24	is	be	AUX
ejpam-5662	332	25	obtained	obtain	VERB
ejpam-5662	332	26	in	in	ADP
ejpam-5662	332	27	figs	fig	NOUN
ejpam-5662	332	28	.	.	PUNCT
ejpam-5662	333	1	8	8	NUM
ejpam-5662	333	2	with	with	ADP
ejpam-5662	333	3	the	the	DET
ejpam-5662	333	4	rise	rise	NOUN
ejpam-5662	333	5	of	of	ADP
ejpam-5662	333	6	ωp	ωp	PROPN
ejpam-5662	333	7	.	.	PUNCT
ejpam-5662	334	1	the	the	DET
ejpam-5662	334	2	excited	excited	ADJ
ejpam-5662	334	3	frequency	frequency	NOUN
ejpam-5662	334	4	in	in	ADP
ejpam-5662	334	5	a	a	DET
ejpam-5662	334	6	tdof	tdof	NOUN
ejpam-5662	334	7	of	of	ADP
ejpam-5662	334	8	mdo	mdo	PROPN
ejpam-5662	334	9	is	be	AUX
ejpam-5662	334	10	crucial	crucial	ADJ
ejpam-5662	334	11	in	in	ADP
ejpam-5662	334	12	determining	determine	VERB
ejpam-5662	334	13	how	how	SCONJ
ejpam-5662	334	14	the	the	DET
ejpam-5662	334	15	system	system	NOUN
ejpam-5662	334	16	reacts	react	VERB
ejpam-5662	334	17	to	to	PART
ejpam-5662	334	18	parametric	parametric	ADJ
ejpam-5662	334	19	stimulation	stimulation	NOUN
ejpam-5662	334	20	.	.	PUNCT
ejpam-5662	335	1	bifurcations	bifurcation	NOUN
ejpam-5662	335	2	,	,	PUNCT
ejpam-5662	335	3	stability	stability	NOUN
ejpam-5662	335	4	,	,	PUNCT
ejpam-5662	335	5	oscillation	oscillation	NOUN
ejpam-5662	335	6	amplitude	amplitude	NOUN
ejpam-5662	335	7	,	,	PUNCT
ejpam-5662	335	8	the	the	DET
ejpam-5662	335	9	beginning	beginning	NOUN
ejpam-5662	335	10	of	of	ADP
ejpam-5662	335	11	parametric	parametric	ADJ
ejpam-5662	335	12	resonance	resonance	NOUN
ejpam-5662	335	13	,	,	PUNCT
ejpam-5662	335	14	and	and	CCONJ
ejpam-5662	335	15	the	the	DET
ejpam-5662	335	16	shift	shift	NOUN
ejpam-5662	335	17	to	to	ADP
ejpam-5662	335	18	complex	complex	ADJ
ejpam-5662	335	19	and	and	CCONJ
ejpam-5662	335	20	chaotic	chaotic	ADJ
ejpam-5662	335	21	dynamics	dynamic	NOUN
ejpam-5662	335	22	are	be	AUX
ejpam-5662	335	23	all	all	PRON
ejpam-5662	335	24	influenced	influence	VERB
ejpam-5662	335	25	by	by	ADP
ejpam-5662	335	26	the	the	DET
ejpam-5662	335	27	excited	excited	ADJ
ejpam-5662	335	28	frequency	frequency	NOUN
ejpam-5662	335	29	.	.	PUNCT
ejpam-5662	336	1	the	the	DET
ejpam-5662	336	2	excited	excited	ADJ
ejpam-5662	336	3	frequency	frequency	NOUN
ejpam-5662	336	4	ωp	ωp	ADV
ejpam-5662	336	5	has	have	VERB
ejpam-5662	336	6	a	a	DET
ejpam-5662	336	7	significant	significant	ADJ
ejpam-5662	336	8	impact	impact	NOUN
ejpam-5662	336	9	on	on	ADP
ejpam-5662	336	10	the	the	DET
ejpam-5662	336	11	system	system	NOUN
ejpam-5662	336	12	’s	’s	PART
ejpam-5662	336	13	response	response	NOUN
ejpam-5662	336	14	amplitude	amplitude	NOUN
ejpam-5662	336	15	.	.	PUNCT
ejpam-5662	337	1	the	the	DET
ejpam-5662	337	2	large	large	ADJ
ejpam-5662	337	3	oscillations	oscillation	NOUN
ejpam-5662	337	4	can	can	AUX
ejpam-5662	337	5	result	result	VERB
ejpam-5662	337	6	from	from	ADP
ejpam-5662	337	7	even	even	ADV
ejpam-5662	337	8	tiny	tiny	ADJ
ejpam-5662	337	9	parametric	parametric	ADJ
ejpam-5662	337	10	stimulation	stimulation	NOUN
ejpam-5662	337	11	around	around	ADP
ejpam-5662	337	12	resonant	resonant	ADJ
ejpam-5662	337	13	frequencies	frequency	NOUN
ejpam-5662	337	14	.	.	PUNCT
ejpam-5662	338	1	the	the	DET
ejpam-5662	338	2	magnitude	magnitude	NOUN
ejpam-5662	338	3	of	of	ADP
ejpam-5662	338	4	the	the	DET
ejpam-5662	338	5	oscillatory	oscillatory	ADJ
ejpam-5662	338	6	response	response	NOUN
ejpam-5662	338	7	of	of	ADP
ejpam-5662	338	8	the	the	DET
ejpam-5662	338	9	system	system	NOUN
ejpam-5662	338	10	is	be	AUX
ejpam-5662	338	11	determined	determine	VERB
ejpam-5662	338	12	by	by	ADP
ejpam-5662	338	13	the	the	DET
ejpam-5662	338	14	connection	connection	NOUN
ejpam-5662	338	15	between	between	ADP
ejpam-5662	338	16	ωp	ωp	PRON
ejpam-5662	338	17	and	and	CCONJ
ejpam-5662	338	18	its	its	PRON
ejpam-5662	338	19	inherent	inherent	ADJ
ejpam-5662	338	20	frequencies	frequency	NOUN
ejpam-5662	338	21	.	.	PUNCT
ejpam-5662	339	1	based	base	VERB
ejpam-5662	339	2	on	on	ADP
ejpam-5662	339	3	the	the	DET
ejpam-5662	339	4	aforementioned	aforementioned	ADJ
ejpam-5662	339	5	findings	finding	NOUN
ejpam-5662	339	6	,	,	PUNCT
ejpam-5662	339	7	one	one	PRON
ejpam-5662	339	8	might	might	AUX
ejpam-5662	339	9	conclude	conclude	VERB
ejpam-5662	339	10	that	that	SCONJ
ejpam-5662	339	11	these	these	DET
ejpam-5662	339	12	outcomes	outcome	NOUN
ejpam-5662	339	13	can	can	AUX
ejpam-5662	339	14	aid	aid	VERB
ejpam-5662	339	15	in	in	ADP
ejpam-5662	339	16	the	the	DET
ejpam-5662	339	17	development	development	NOUN
ejpam-5662	339	18	and	and	CCONJ
ejpam-5662	339	19	regulation	regulation	NOUN
ejpam-5662	339	20	of	of	ADP
ejpam-5662	339	21	systems	system	NOUN
ejpam-5662	339	22	that	that	PRON
ejpam-5662	339	23	rely	rely	VERB
ejpam-5662	339	24	on	on	ADP
ejpam-5662	339	25	periodic	periodic	ADJ
ejpam-5662	339	26	solutions	solution	NOUN
ejpam-5662	339	27	.	.	PUNCT
ejpam-5662	340	1	for	for	ADP
ejpam-5662	340	2	example	example	NOUN
ejpam-5662	340	3	,	,	PUNCT
ejpam-5662	340	4	engineers	engineer	NOUN
ejpam-5662	340	5	may	may	AUX
ejpam-5662	340	6	utilize	utilize	VERB
ejpam-5662	340	7	periodic	periodic	ADJ
ejpam-5662	340	8	behavior	behavior	NOUN
ejpam-5662	340	9	in	in	ADP
ejpam-5662	340	10	mechanical	mechanical	ADJ
ejpam-5662	340	11	systems	system	NOUN
ejpam-5662	340	12	to	to	PART
ejpam-5662	340	13	improve	improve	VERB
ejpam-5662	340	14	system	system	NOUN
ejpam-5662	340	15	performance	performance	NOUN
ejpam-5662	340	16	or	or	CCONJ
ejpam-5662	340	17	design	design	NOUN
ejpam-5662	340	18	systems	system	NOUN
ejpam-5662	340	19	that	that	PRON
ejpam-5662	340	20	operate	operate	VERB
ejpam-5662	340	21	effectively	effectively	ADV
ejpam-5662	340	22	at	at	ADP
ejpam-5662	340	23	particular	particular	ADJ
ejpam-5662	340	24	frequencies	frequency	NOUN
ejpam-5662	340	25	.	.	PUNCT
ejpam-5662	341	1	the	the	DET
ejpam-5662	341	2	interaction	interaction	NOUN
ejpam-5662	341	3	between	between	ADP
ejpam-5662	341	4	parametric	parametric	ADJ
ejpam-5662	341	5	excitation	excitation	NOUN
ejpam-5662	341	6	,	,	PUNCT
ejpam-5662	341	7	excitation	excitation	NOUN
ejpam-5662	341	8	frequency	frequency	NOUN
ejpam-5662	341	9	,	,	PUNCT
ejpam-5662	341	10	and	and	CCONJ
ejpam-5662	341	11	nonlinearities	nonlinearitie	NOUN
ejpam-5662	341	12	results	result	VERB
ejpam-5662	341	13	in	in	ADP
ejpam-5662	341	14	complia	complia	PROPN
ejpam-5662	341	15	.	.	PUNCT
ejpam-5662	342	1	alanazy	alanazy	PROPN
ejpam-5662	342	2	,	,	PUNCT
ejpam-5662	342	3	g.	g.	PROPN
ejpam-5662	342	4	m.	m.	PROPN
ejpam-5662	342	5	moatimid	moatimid	PROPN
ejpam-5662	342	6	,	,	PUNCT
ejpam-5662	342	7	m.	m.	PROPN
ejpam-5662	342	8	a.	a.	PROPN
ejpam-5662	342	9	a.	a.	PROPN
ejpam-5662	342	10	mohamed	mohamed	PROPN
ejpam-5662	342	11	/	/	SYM
ejpam-5662	342	12	eur	eur	PROPN
ejpam-5662	342	13	.	.	PUNCT
ejpam-5662	343	1	j.	j.	PROPN
ejpam-5662	343	2	pure	pure	PROPN
ejpam-5662	343	3	appl	appl	PROPN
ejpam-5662	343	4	.	.	PROPN
ejpam-5662	343	5	math	math	PROPN
ejpam-5662	343	6	,	,	PUNCT
ejpam-5662	343	7	18	18	NUM
ejpam-5662	343	8	(	(	PUNCT
ejpam-5662	343	9	2	2	NUM
ejpam-5662	343	10	)	)	PUNCT
ejpam-5662	343	11	(	(	PUNCT
ejpam-5662	343	12	2025	2025	NUM
ejpam-5662	343	13	)	)	PUNCT
ejpam-5662	343	14	,	,	PUNCT
ejpam-5662	343	15	5662	5662	NUM
ejpam-5662	343	16	16	16	NUM
ejpam-5662	343	17	of	of	ADP
ejpam-5662	343	18	36	36	NUM
ejpam-5662	343	19	cated	cat	VERB
ejpam-5662	343	20	behavior	behavior	NOUN
ejpam-5662	343	21	of	of	ADP
ejpam-5662	343	22	the	the	DET
ejpam-5662	343	23	system	system	NOUN
ejpam-5662	343	24	.	.	PUNCT
ejpam-5662	344	1	the	the	DET
ejpam-5662	344	2	system	system	NOUN
ejpam-5662	344	3	may	may	AUX
ejpam-5662	344	4	exhibit	exhibit	VERB
ejpam-5662	344	5	bifurcations	bifurcation	NOUN
ejpam-5662	344	6	,	,	PUNCT
ejpam-5662	344	7	nonlinear	nonlinear	ADJ
ejpam-5662	344	8	frequency	frequency	NOUN
ejpam-5662	344	9	changes	change	NOUN
ejpam-5662	344	10	,	,	PUNCT
ejpam-5662	344	11	enhanced	enhance	VERB
ejpam-5662	344	12	oscillations	oscillation	NOUN
ejpam-5662	344	13	,	,	PUNCT
ejpam-5662	344	14	or	or	CCONJ
ejpam-5662	344	15	even	even	ADV
ejpam-5662	344	16	chaotic	chaotic	ADJ
ejpam-5662	344	17	motion	motion	NOUN
ejpam-5662	344	18	close	close	ADJ
ejpam-5662	344	19	to	to	ADP
ejpam-5662	344	20	resonances	resonance	NOUN
ejpam-5662	344	21	.	.	PUNCT
ejpam-5662	345	1	especially	especially	ADV
ejpam-5662	345	2	with	with	ADP
ejpam-5662	345	3	large	large	ADJ
ejpam-5662	345	4	oscillations	oscillation	NOUN
ejpam-5662	345	5	,	,	PUNCT
ejpam-5662	345	6	quintic	quintic	ADJ
ejpam-5662	345	7	terms	term	NOUN
ejpam-5662	345	8	improve	improve	VERB
ejpam-5662	345	9	the	the	DET
ejpam-5662	345	10	amplitude	amplitude	NOUN
ejpam-5662	345	11	dependency	dependency	NOUN
ejpam-5662	345	12	of	of	ADP
ejpam-5662	345	13	these	these	DET
ejpam-5662	345	14	effects	effect	NOUN
ejpam-5662	345	15	.	.	PUNCT
ejpam-5662	346	1	figure	figure	VERB
ejpam-5662	346	2	3	3	NUM
ejpam-5662	346	3	:	:	PUNCT
ejpam-5662	346	4	the	the	DET
ejpam-5662	346	5	effect	effect	NOUN
ejpam-5662	346	6	of	of	ADP
ejpam-5662	346	7	the	the	DET
ejpam-5662	346	8	natural	natural	ADJ
ejpam-5662	346	9	frequencies	frequency	NOUN
ejpam-5662	346	10	ω1	ω1	ADJ
ejpam-5662	346	11	and	and	CCONJ
ejpam-5662	346	12	ω2	ω2	ADJ
ejpam-5662	346	13	on	on	ADP
ejpam-5662	346	14	the	the	DET
ejpam-5662	346	15	time	time	NOUN
ejpam-5662	346	16	-	-	PUNCT
ejpam-5662	346	17	dependent	dependent	ADJ
ejpam-5662	346	18	variation	variation	NOUN
ejpam-5662	346	19	of	of	ADP
ejpam-5662	346	20	u(t	u(t	NOUN
ejpam-5662	346	21	)	)	PUNCT
ejpam-5662	346	22	and	and	CCONJ
ejpam-5662	346	23	v(t	v(t	NOUN
ejpam-5662	346	24	)	)	PUNCT
ejpam-5662	346	25	.	.	PUNCT
ejpam-5662	347	1	figure	figure	VERB
ejpam-5662	347	2	4	4	NUM
ejpam-5662	347	3	:	:	PUNCT
ejpam-5662	347	4	the	the	DET
ejpam-5662	347	5	effect	effect	NOUN
ejpam-5662	347	6	of	of	ADP
ejpam-5662	347	7	the	the	DET
ejpam-5662	347	8	cubic	cubic	ADJ
ejpam-5662	347	9	coefficients	coefficient	NOUN
ejpam-5662	347	10	γ1	γ1	NOUN
ejpam-5662	347	11	and	and	CCONJ
ejpam-5662	347	12	γ2	γ2	NOUN
ejpam-5662	347	13	on	on	ADP
ejpam-5662	347	14	the	the	DET
ejpam-5662	347	15	time	time	NOUN
ejpam-5662	347	16	-	-	PUNCT
ejpam-5662	347	17	dependent	dependent	ADJ
ejpam-5662	347	18	variation	variation	NOUN
ejpam-5662	347	19	of	of	ADP
ejpam-5662	347	20	u(t	u(t	NOUN
ejpam-5662	347	21	)	)	PUNCT
ejpam-5662	347	22	and	and	CCONJ
ejpam-5662	347	23	v(t	v(t	NOUN
ejpam-5662	347	24	)	)	PUNCT
ejpam-5662	347	25	.	.	PUNCT
ejpam-5662	348	1	figure	figure	VERB
ejpam-5662	348	2	5	5	NUM
ejpam-5662	348	3	:	:	PUNCT
ejpam-5662	348	4	the	the	DET
ejpam-5662	348	5	effect	effect	NOUN
ejpam-5662	348	6	of	of	ADP
ejpam-5662	348	7	the	the	DET
ejpam-5662	348	8	excited	excited	ADJ
ejpam-5662	348	9	amplitudes	amplitude	NOUN
ejpam-5662	348	10	η11	η11	NOUN
ejpam-5662	348	11	and	and	CCONJ
ejpam-5662	348	12	η21	η21	NOUN
ejpam-5662	348	13	on	on	ADP
ejpam-5662	348	14	the	the	DET
ejpam-5662	348	15	time	time	NOUN
ejpam-5662	348	16	-	-	PUNCT
ejpam-5662	348	17	dependent	dependent	ADJ
ejpam-5662	348	18	deviation	deviation	NOUN
ejpam-5662	348	19	of	of	ADP
ejpam-5662	348	20	u(t	u(t	NOUN
ejpam-5662	348	21	)	)	PUNCT
ejpam-5662	348	22	and	and	CCONJ
ejpam-5662	348	23	v(t	v(t	NOUN
ejpam-5662	348	24	)	)	PUNCT
ejpam-5662	348	25	.	.	PUNCT
ejpam-5662	349	1	a.	a.	PROPN
ejpam-5662	349	2	alanazy	alanazy	PROPN
ejpam-5662	349	3	,	,	PUNCT
ejpam-5662	349	4	g.	g.	PROPN
ejpam-5662	349	5	m.	m.	PROPN
ejpam-5662	349	6	moatimid	moatimid	PROPN
ejpam-5662	349	7	,	,	PUNCT
ejpam-5662	349	8	m.	m.	PROPN
ejpam-5662	349	9	a.	a.	PROPN
ejpam-5662	349	10	a.	a.	PROPN
ejpam-5662	349	11	mohamed	mohamed	PROPN
ejpam-5662	349	12	/	/	SYM
ejpam-5662	349	13	eur	eur	PROPN
ejpam-5662	349	14	.	.	PUNCT
ejpam-5662	350	1	j.	j.	PROPN
ejpam-5662	350	2	pure	pure	PROPN
ejpam-5662	350	3	appl	appl	PROPN
ejpam-5662	350	4	.	.	PROPN
ejpam-5662	350	5	math	math	PROPN
ejpam-5662	350	6	,	,	PUNCT
ejpam-5662	350	7	18	18	NUM
ejpam-5662	350	8	(	(	PUNCT
ejpam-5662	350	9	2	2	NUM
ejpam-5662	350	10	)	)	PUNCT
ejpam-5662	350	11	(	(	PUNCT
ejpam-5662	350	12	2025	2025	NUM
ejpam-5662	350	13	)	)	PUNCT
ejpam-5662	350	14	,	,	PUNCT
ejpam-5662	350	15	5662	5662	NUM
ejpam-5662	350	16	17	17	NUM
ejpam-5662	350	17	of	of	ADP
ejpam-5662	350	18	36	36	NUM
ejpam-5662	350	19	figure	figure	NOUN
ejpam-5662	350	20	6	6	NUM
ejpam-5662	350	21	:	:	PUNCT
ejpam-5662	350	22	the	the	DET
ejpam-5662	350	23	effect	effect	NOUN
ejpam-5662	350	24	of	of	ADP
ejpam-5662	350	25	the	the	DET
ejpam-5662	350	26	excited	excited	ADJ
ejpam-5662	350	27	amplitudes	amplitude	NOUN
ejpam-5662	350	28	η12	η12	VERB
ejpam-5662	350	29	and	and	CCONJ
ejpam-5662	350	30	η22	η22	NOUN
ejpam-5662	350	31	on	on	ADP
ejpam-5662	350	32	the	the	DET
ejpam-5662	350	33	time	time	NOUN
ejpam-5662	350	34	-	-	PUNCT
ejpam-5662	350	35	dependent	dependent	ADJ
ejpam-5662	350	36	deviation	deviation	NOUN
ejpam-5662	350	37	of	of	ADP
ejpam-5662	350	38	u(t	u(t	NOUN
ejpam-5662	350	39	)	)	PUNCT
ejpam-5662	350	40	and	and	CCONJ
ejpam-5662	350	41	v(t	v(t	NOUN
ejpam-5662	350	42	)	)	PUNCT
ejpam-5662	350	43	.	.	PUNCT
ejpam-5662	351	1	figure	figure	VERB
ejpam-5662	351	2	7	7	NUM
ejpam-5662	351	3	:	:	PUNCT
ejpam-5662	351	4	the	the	DET
ejpam-5662	351	5	effect	effect	NOUN
ejpam-5662	351	6	of	of	ADP
ejpam-5662	351	7	the	the	DET
ejpam-5662	351	8	quinitic	quinitic	ADJ
ejpam-5662	351	9	coefficients	coefficient	NOUN
ejpam-5662	351	10	λ1	λ1	ADJ
ejpam-5662	351	11	and	and	CCONJ
ejpam-5662	351	12	λ2	λ2	NOUN
ejpam-5662	351	13	on	on	ADP
ejpam-5662	351	14	the	the	DET
ejpam-5662	351	15	time	time	NOUN
ejpam-5662	351	16	-	-	PUNCT
ejpam-5662	351	17	dependent	dependent	ADJ
ejpam-5662	351	18	distribution	distribution	NOUN
ejpam-5662	351	19	of	of	ADP
ejpam-5662	351	20	u(t	u(t	NOUN
ejpam-5662	351	21	)	)	PUNCT
ejpam-5662	351	22	and	and	CCONJ
ejpam-5662	351	23	v(t	v(t	NOUN
ejpam-5662	351	24	)	)	PUNCT
ejpam-5662	351	25	.	.	PUNCT
ejpam-5662	351	26	.	.	PUNCT
ejpam-5662	352	1	figure	figure	VERB
ejpam-5662	352	2	8	8	NUM
ejpam-5662	352	3	:	:	PUNCT
ejpam-5662	352	4	the	the	DET
ejpam-5662	352	5	effect	effect	NOUN
ejpam-5662	352	6	of	of	ADP
ejpam-5662	352	7	the	the	DET
ejpam-5662	352	8	excited	excited	ADJ
ejpam-5662	352	9	frequency	frequency	NOUN
ejpam-5662	352	10	ωp	ωp	PRON
ejpam-5662	352	11	on	on	ADP
ejpam-5662	352	12	the	the	DET
ejpam-5662	352	13	time	time	NOUN
ejpam-5662	352	14	-	-	PUNCT
ejpam-5662	352	15	dependent	dependent	ADJ
ejpam-5662	352	16	distribution	distribution	NOUN
ejpam-5662	352	17	of	of	ADP
ejpam-5662	352	18	u(t)andv(t	u(t)andv(t	NOUN
ejpam-5662	352	19	)	)	PUNCT
ejpam-5662	352	20	.	.	PUNCT
ejpam-5662	353	1	a.	a.	PROPN
ejpam-5662	353	2	alanazy	alanazy	PROPN
ejpam-5662	353	3	,	,	PUNCT
ejpam-5662	353	4	g.	g.	PROPN
ejpam-5662	353	5	m.	m.	PROPN
ejpam-5662	353	6	moatimid	moatimid	PROPN
ejpam-5662	353	7	,	,	PUNCT
ejpam-5662	353	8	m.	m.	PROPN
ejpam-5662	353	9	a.	a.	PROPN
ejpam-5662	353	10	a.	a.	PROPN
ejpam-5662	353	11	mohamed	mohamed	PROPN
ejpam-5662	353	12	/	/	SYM
ejpam-5662	353	13	eur	eur	PROPN
ejpam-5662	353	14	.	.	PUNCT
ejpam-5662	354	1	j.	j.	PROPN
ejpam-5662	354	2	pure	pure	PROPN
ejpam-5662	354	3	appl	appl	PROPN
ejpam-5662	354	4	.	.	PROPN
ejpam-5662	354	5	math	math	PROPN
ejpam-5662	354	6	,	,	PUNCT
ejpam-5662	354	7	18	18	NUM
ejpam-5662	354	8	(	(	PUNCT
ejpam-5662	354	9	2	2	NUM
ejpam-5662	354	10	)	)	PUNCT
ejpam-5662	354	11	(	(	PUNCT
ejpam-5662	354	12	2025	2025	NUM
ejpam-5662	354	13	)	)	PUNCT
ejpam-5662	354	14	,	,	PUNCT
ejpam-5662	354	15	5662	5662	NUM
ejpam-5662	354	16	18	18	NUM
ejpam-5662	354	17	of	of	ADP
ejpam-5662	354	18	36	36	NUM
ejpam-5662	354	19	figs	fig	NOUN
ejpam-5662	354	20	.	.	PUNCT
ejpam-5662	355	1	9	9	NUM
ejpam-5662	355	2	-	-	SYM
ejpam-5662	355	3	14	14	NUM
ejpam-5662	355	4	indicate	indicate	VERB
ejpam-5662	355	5	the	the	DET
ejpam-5662	355	6	polarplots	polarplot	NOUN
ejpam-5662	355	7	of	of	ADP
ejpam-5662	355	8	the	the	DET
ejpam-5662	355	9	suggested	suggest	VERB
ejpam-5662	355	10	solutions	solution	NOUN
ejpam-5662	355	11	as	as	SCONJ
ejpam-5662	355	12	given	give	VERB
ejpam-5662	355	13	in	in	ADP
ejpam-5662	355	14	eq	eq	ADP
ejpam-5662	355	15	.	.	PUNCT
ejpam-5662	356	1	(	(	PUNCT
ejpam-5662	356	2	27	27	NUM
ejpam-5662	356	3	)	)	PUNCT
ejpam-5662	356	4	through	through	ADP
ejpam-5662	356	5	the	the	DET
ejpam-5662	356	6	time	time	NOUN
ejpam-5662	356	7	interval	interval	NOUN
ejpam-5662	356	8	[	[	X
ejpam-5662	356	9	0	0	NUM
ejpam-5662	356	10	,	,	PUNCT
ejpam-5662	356	11	50π	50π	NUM
ejpam-5662	356	12	]	]	PUNCT
ejpam-5662	356	13	with	with	ADP
ejpam-5662	356	14	the	the	DET
ejpam-5662	356	15	distinction	distinction	NOUN
ejpam-5662	356	16	of	of	ADP
ejpam-5662	356	17	the	the	DET
ejpam-5662	356	18	parameters	parameter	NOUN
ejpam-5662	356	19	ω1	ω1	PROPN
ejpam-5662	356	20	,	,	PUNCT
ejpam-5662	356	21	ω2	ω2	ADJ
ejpam-5662	356	22	,	,	PUNCT
ejpam-5662	356	23	µ1	µ1	PROPN
ejpam-5662	356	24	,	,	PUNCT
ejpam-5662	356	25	µ2	µ2	NOUN
ejpam-5662	356	26	,	,	PUNCT
ejpam-5662	356	27	α1	α1	PROPN
ejpam-5662	356	28	,	,	PUNCT
ejpam-5662	356	29	α2	α2	ADJ
ejpam-5662	356	30	,	,	PUNCT
ejpam-5662	356	31	λ1	λ1	ADJ
ejpam-5662	356	32	,	,	PUNCT
ejpam-5662	356	33	and	and	CCONJ
ejpam-5662	356	34	λ2	λ2	NOUN
ejpam-5662	356	35	to	to	PART
ejpam-5662	356	36	illustrate	illustrate	VERB
ejpam-5662	356	37	the	the	DET
ejpam-5662	356	38	polarized	polarize	VERB
ejpam-5662	356	39	behavior	behavior	NOUN
ejpam-5662	356	40	of	of	ADP
ejpam-5662	356	41	the	the	DET
ejpam-5662	356	42	functions	function	NOUN
ejpam-5662	356	43	u(t	u(t	NOUN
ejpam-5662	356	44	)	)	PUNCT
ejpam-5662	356	45	and	and	CCONJ
ejpam-5662	356	46	v(t	v(t	NOUN
ejpam-5662	356	47	)	)	PUNCT
ejpam-5662	356	48	as	as	SCONJ
ejpam-5662	356	49	defined	define	VERB
ejpam-5662	356	50	in	in	ADP
ejpam-5662	356	51	eq	eq	ADP
ejpam-5662	356	52	.	.	PUNCT
ejpam-5662	357	1	(	(	PUNCT
ejpam-5662	357	2	27	27	NUM
ejpam-5662	357	3	)	)	PUNCT
ejpam-5662	357	4	in	in	ADP
ejpam-5662	357	5	terms	term	NOUN
ejpam-5662	357	6	of	of	ADP
ejpam-5662	357	7	the	the	DET
ejpam-5662	357	8	total	total	ADJ
ejpam-5662	357	9	frequencies	frequency	NOUN
ejpam-5662	357	10	ω1	ω1	PROPN
ejpam-5662	357	11	and	and	CCONJ
ejpam-5662	357	12	ω2	ω2	ADJ
ejpam-5662	357	13	,	,	PUNCT
ejpam-5662	357	14	respectively	respectively	ADV
ejpam-5662	357	15	.	.	PUNCT
ejpam-5662	358	1	according	accord	VERB
ejpam-5662	358	2	to	to	ADP
ejpam-5662	358	3	the	the	DET
ejpam-5662	358	4	same	same	ADJ
ejpam-5662	358	5	above	above	ADP
ejpam-5662	358	6	data	datum	NOUN
ejpam-5662	358	7	except	except	SCONJ
ejpam-5662	358	8	that	that	SCONJ
ejpam-5662	358	9	a	a	DET
ejpam-5662	358	10	=	=	SYM
ejpam-5662	358	11	b	b	NOUN
ejpam-5662	358	12	=	=	SYM
ejpam-5662	358	13	0.5	0.5	NUM
ejpam-5662	358	14	,	,	PUNCT
ejpam-5662	358	15	such	such	ADJ
ejpam-5662	358	16	data	datum	NOUN
ejpam-5662	358	17	vary	vary	VERB
ejpam-5662	358	18	from	from	ADP
ejpam-5662	358	19	one	one	NUM
ejpam-5662	358	20	figure	figure	NOUN
ejpam-5662	358	21	to	to	ADP
ejpam-5662	358	22	another	another	PRON
ejpam-5662	358	23	according	accord	VERB
ejpam-5662	358	24	to	to	ADP
ejpam-5662	358	25	the	the	DET
ejpam-5662	358	26	studied	studied	ADJ
ejpam-5662	358	27	parameter	parameter	NOUN
ejpam-5662	358	28	.	.	PUNCT
ejpam-5662	359	1	figs	fig	NOUN
ejpam-5662	359	2	.	.	PUNCT
ejpam-5662	360	1	9	9	NUM
ejpam-5662	360	2	and	and	CCONJ
ejpam-5662	360	3	10	10	NUM
ejpam-5662	360	4	are	be	AUX
ejpam-5662	360	5	plotted	plot	VERB
ejpam-5662	360	6	due	due	ADP
ejpam-5662	360	7	to	to	ADP
ejpam-5662	360	8	the	the	DET
ejpam-5662	360	9	changed	change	VERB
ejpam-5662	360	10	values	value	NOUN
ejpam-5662	360	11	of	of	ADP
ejpam-5662	360	12	the	the	DET
ejpam-5662	360	13	natural	natural	ADJ
ejpam-5662	360	14	frequencies	frequency	NOUN
ejpam-5662	360	15	ω1	ω1	PROPN
ejpam-5662	360	16	and	and	CCONJ
ejpam-5662	360	17	ω2	ω2	ADJ
ejpam-5662	360	18	.	.	PUNCT
ejpam-5662	361	1	it	it	PRON
ejpam-5662	361	2	is	be	AUX
ejpam-5662	361	3	exposed	expose	VERB
ejpam-5662	361	4	from	from	ADP
ejpam-5662	361	5	these	these	DET
ejpam-5662	361	6	figures	figure	NOUN
ejpam-5662	361	7	that	that	SCONJ
ejpam-5662	361	8	,	,	PUNCT
ejpam-5662	361	9	with	with	ADP
ejpam-5662	361	10	the	the	DET
ejpam-5662	361	11	rising	rising	NOUN
ejpam-5662	361	12	of	of	ADP
ejpam-5662	361	13	ω1	ω1	PROPN
ejpam-5662	361	14	and	and	CCONJ
ejpam-5662	361	15	ω2	ω2	ADJ
ejpam-5662	361	16	,	,	PUNCT
ejpam-5662	361	17	the	the	DET
ejpam-5662	361	18	curvilinear	curvilinear	PROPN
ejpam-5662	361	19	circles	circle	NOUN
ejpam-5662	361	20	regulate	regulate	VERB
ejpam-5662	361	21	and	and	CCONJ
ejpam-5662	361	22	collect	collect	VERB
ejpam-5662	361	23	in	in	ADP
ejpam-5662	361	24	a	a	DET
ejpam-5662	361	25	more	more	ADV
ejpam-5662	361	26	uniform	uniform	ADJ
ejpam-5662	361	27	style	style	NOUN
ejpam-5662	361	28	about	about	ADP
ejpam-5662	361	29	the	the	DET
ejpam-5662	361	30	core	core	NOUN
ejpam-5662	361	31	.	.	PUNCT
ejpam-5662	362	1	these	these	DET
ejpam-5662	362	2	outcomes	outcome	NOUN
ejpam-5662	362	3	are	be	AUX
ejpam-5662	362	4	approved	approve	VERB
ejpam-5662	362	5	by	by	ADP
ejpam-5662	362	6	the	the	DET
ejpam-5662	362	7	stimulating	stimulating	ADJ
ejpam-5662	362	8	effects	effect	NOUN
ejpam-5662	362	9	of	of	ADP
ejpam-5662	362	10	the	the	DET
ejpam-5662	362	11	parameters	parameter	NOUN
ejpam-5662	362	12	ω1	ω1	PROPN
ejpam-5662	362	13	and	and	CCONJ
ejpam-5662	362	14	ω2	ω2	ADJ
ejpam-5662	362	15	that	that	PRON
ejpam-5662	362	16	appear	appear	VERB
ejpam-5662	362	17	in	in	ADP
ejpam-5662	362	18	the	the	DET
ejpam-5662	362	19	figs	fig	NOUN
ejpam-5662	362	20	.	.	PUNCT
ejpam-5662	363	1	3	3	X
ejpam-5662	363	2	.	.	X
ejpam-5662	363	3	moreover	moreover	ADV
ejpam-5662	363	4	,	,	PUNCT
ejpam-5662	363	5	a	a	DET
ejpam-5662	363	6	symmetric	symmetric	ADJ
ejpam-5662	363	7	distribution	distribution	NOUN
ejpam-5662	363	8	encircles	encircle	VERB
ejpam-5662	363	9	the	the	DET
ejpam-5662	363	10	centers	center	NOUN
ejpam-5662	363	11	of	of	ADP
ejpam-5662	363	12	the	the	DET
ejpam-5662	363	13	rounded	rounded	ADJ
ejpam-5662	363	14	,	,	PUNCT
ejpam-5662	363	15	connected	connected	ADJ
ejpam-5662	363	16	curves	curve	NOUN
ejpam-5662	363	17	.	.	PUNCT
ejpam-5662	364	1	this	this	DET
ejpam-5662	364	2	dispersion	dispersion	NOUN
ejpam-5662	364	3	may	may	AUX
ejpam-5662	364	4	be	be	AUX
ejpam-5662	364	5	used	use	VERB
ejpam-5662	364	6	to	to	PART
ejpam-5662	364	7	determine	determine	VERB
ejpam-5662	364	8	the	the	DET
ejpam-5662	364	9	stable	stable	ADJ
ejpam-5662	364	10	form	form	NOUN
ejpam-5662	364	11	in	in	ADP
ejpam-5662	364	12	which	which	PRON
ejpam-5662	364	13	these	these	DET
ejpam-5662	364	14	curves	curve	NOUN
ejpam-5662	364	15	operate	operate	VERB
ejpam-5662	364	16	.	.	PUNCT
ejpam-5662	365	1	the	the	DET
ejpam-5662	365	2	impact	impact	NOUN
ejpam-5662	365	3	of	of	ADP
ejpam-5662	365	4	the	the	DET
ejpam-5662	365	5	modifying	modify	VERB
ejpam-5662	365	6	elements	element	NOUN
ejpam-5662	365	7	determines	determine	VERB
ejpam-5662	365	8	how	how	SCONJ
ejpam-5662	365	9	much	much	ADJ
ejpam-5662	365	10	the	the	DET
ejpam-5662	365	11	intersecting	intersecting	ADJ
ejpam-5662	365	12	plots	plot	NOUN
ejpam-5662	365	13	circulate	circulate	VERB
ejpam-5662	365	14	.	.	PUNCT
ejpam-5662	366	1	figs	fig	NOUN
ejpam-5662	366	2	.	.	PUNCT
ejpam-5662	367	1	11	11	NUM
ejpam-5662	367	2	and	and	CCONJ
ejpam-5662	367	3	12	12	NUM
ejpam-5662	367	4	are	be	AUX
ejpam-5662	367	5	plotted	plot	VERB
ejpam-5662	367	6	discussing	discuss	VERB
ejpam-5662	367	7	the	the	DET
ejpam-5662	367	8	variations	variation	NOUN
ejpam-5662	367	9	of	of	ADP
ejpam-5662	367	10	the	the	DET
ejpam-5662	367	11	damping	damp	VERB
ejpam-5662	367	12	coefficients	coefficient	NOUN
ejpam-5662	367	13	µ1	µ1	PROPN
ejpam-5662	367	14	andµ2	andµ2	NOUN
ejpam-5662	367	15	,	,	PUNCT
ejpam-5662	367	16	to	to	PART
ejpam-5662	367	17	illustrate	illustrate	VERB
ejpam-5662	367	18	the	the	DET
ejpam-5662	367	19	polarplot	polarplot	NOUN
ejpam-5662	367	20	of	of	ADP
ejpam-5662	367	21	the	the	DET
ejpam-5662	367	22	functions	function	NOUN
ejpam-5662	367	23	u(t	u(t	NOUN
ejpam-5662	367	24	)	)	PUNCT
ejpam-5662	367	25	and	and	CCONJ
ejpam-5662	367	26	v(t	v(t	NOUN
ejpam-5662	367	27	)	)	PUNCT
ejpam-5662	367	28	as	as	SCONJ
ejpam-5662	367	29	signified	signify	VERB
ejpam-5662	367	30	in	in	ADP
ejpam-5662	367	31	eq	eq	ADP
ejpam-5662	367	32	.	.	PUNCT
ejpam-5662	368	1	(	(	PUNCT
ejpam-5662	368	2	27	27	NUM
ejpam-5662	368	3	)	)	PUNCT
ejpam-5662	368	4	utilizing	utilize	VERB
ejpam-5662	368	5	the	the	DET
ejpam-5662	368	6	different	different	ADJ
ejpam-5662	368	7	parameters	parameter	NOUN
ejpam-5662	368	8	and	and	CCONJ
ejpam-5662	368	9	the	the	DET
ejpam-5662	368	10	total	total	ADJ
ejpam-5662	368	11	frequencies	frequency	NOUN
ejpam-5662	368	12	ω1and	ω1and	PUNCT
ejpam-5662	368	13	ω2	ω2	ADJ
ejpam-5662	368	14	.	.	PUNCT
ejpam-5662	369	1	it	it	PRON
ejpam-5662	369	2	is	be	AUX
ejpam-5662	369	3	detected	detect	VERB
ejpam-5662	369	4	that	that	SCONJ
ejpam-5662	369	5	the	the	DET
ejpam-5662	369	6	impacts	impact	NOUN
ejpam-5662	369	7	of	of	ADP
ejpam-5662	369	8	µ1	µ1	NOUN
ejpam-5662	369	9	and	and	CCONJ
ejpam-5662	369	10	µ2	µ2	PROPN
ejpam-5662	369	11	oppose	oppose	VERB
ejpam-5662	369	12	the	the	DET
ejpam-5662	369	13	influence	influence	NOUN
ejpam-5662	369	14	of	of	ADP
ejpam-5662	369	15	ω1	ω1	PROPN
ejpam-5662	369	16	and	and	CCONJ
ejpam-5662	369	17	ω2	ω2	ADJ
ejpam-5662	369	18	,	,	PUNCT
ejpam-5662	369	19	where	where	SCONJ
ejpam-5662	369	20	the	the	DET
ejpam-5662	369	21	loops	loop	NOUN
ejpam-5662	369	22	are	be	AUX
ejpam-5662	369	23	dispersed	disperse	VERB
ejpam-5662	369	24	more	more	ADJ
ejpam-5662	369	25	about	about	ADP
ejpam-5662	369	26	the	the	DET
ejpam-5662	369	27	center	center	NOUN
ejpam-5662	369	28	,	,	PUNCT
ejpam-5662	369	29	but	but	CCONJ
ejpam-5662	369	30	the	the	DET
ejpam-5662	369	31	behavior	behavior	NOUN
ejpam-5662	369	32	is	be	AUX
ejpam-5662	369	33	still	still	ADV
ejpam-5662	369	34	uniformly	uniformly	ADV
ejpam-5662	369	35	stable	stable	ADJ
ejpam-5662	369	36	.	.	PUNCT
ejpam-5662	370	1	this	this	DET
ejpam-5662	370	2	model	model	NOUN
ejpam-5662	370	3	has	have	VERB
ejpam-5662	370	4	a	a	DET
ejpam-5662	370	5	symmetric	symmetric	ADJ
ejpam-5662	370	6	distribution	distribution	NOUN
ejpam-5662	370	7	around	around	ADP
ejpam-5662	370	8	the	the	DET
ejpam-5662	370	9	centers	center	NOUN
ejpam-5662	370	10	of	of	ADP
ejpam-5662	370	11	the	the	DET
ejpam-5662	370	12	circular	circular	ADJ
ejpam-5662	370	13	,	,	PUNCT
ejpam-5662	370	14	linked	link	VERB
ejpam-5662	370	15	curves	curve	NOUN
ejpam-5662	370	16	.	.	PUNCT
ejpam-5662	371	1	these	these	DET
ejpam-5662	371	2	curves	curve	NOUN
ejpam-5662	371	3	could	could	AUX
ejpam-5662	371	4	function	function	VERB
ejpam-5662	371	5	in	in	ADP
ejpam-5662	371	6	a	a	DET
ejpam-5662	371	7	steady	steady	ADJ
ejpam-5662	371	8	state	state	NOUN
ejpam-5662	371	9	,	,	PUNCT
ejpam-5662	371	10	as	as	SCONJ
ejpam-5662	371	11	indicated	indicate	VERB
ejpam-5662	371	12	by	by	ADP
ejpam-5662	371	13	this	this	DET
ejpam-5662	371	14	distribution	distribution	NOUN
ejpam-5662	371	15	.	.	PUNCT
ejpam-5662	372	1	the	the	DET
ejpam-5662	372	2	influence	influence	NOUN
ejpam-5662	372	3	of	of	ADP
ejpam-5662	372	4	the	the	DET
ejpam-5662	372	5	influencing	influence	VERB
ejpam-5662	372	6	factors	factor	NOUN
ejpam-5662	372	7	causes	cause	VERB
ejpam-5662	372	8	the	the	DET
ejpam-5662	372	9	circulation	circulation	NOUN
ejpam-5662	372	10	of	of	ADP
ejpam-5662	372	11	the	the	DET
ejpam-5662	372	12	connected	connected	ADJ
ejpam-5662	372	13	plots	plot	NOUN
ejpam-5662	372	14	to	to	PART
ejpam-5662	372	15	diminish	diminish	VERB
ejpam-5662	372	16	.	.	PUNCT
ejpam-5662	373	1	furthermore	furthermore	ADV
ejpam-5662	373	2	,	,	PUNCT
ejpam-5662	373	3	the	the	DET
ejpam-5662	373	4	polarplots	polarplot	NOUN
ejpam-5662	373	5	of	of	ADP
ejpam-5662	373	6	the	the	DET
ejpam-5662	373	7	recommended	recommend	VERB
ejpam-5662	373	8	solutions	solution	NOUN
ejpam-5662	373	9	u(t	u(t	NOUN
ejpam-5662	373	10	)	)	PUNCT
ejpam-5662	373	11	and	and	CCONJ
ejpam-5662	373	12	v(t	v(t	NOUN
ejpam-5662	373	13	)	)	PUNCT
ejpam-5662	373	14	conferring	confer	VERB
ejpam-5662	373	15	to	to	ADP
ejpam-5662	373	16	eq	eq	NOUN
ejpam-5662	373	17	.	.	PUNCT
ejpam-5662	374	1	(	(	PUNCT
ejpam-5662	374	2	28	28	NUM
ejpam-5662	374	3	)	)	PUNCT
ejpam-5662	374	4	are	be	AUX
ejpam-5662	374	5	considered	consider	VERB
ejpam-5662	374	6	for	for	ADP
ejpam-5662	374	7	altered	altered	ADJ
ejpam-5662	374	8	values	value	NOUN
ejpam-5662	374	9	of	of	ADP
ejpam-5662	374	10	the	the	DET
ejpam-5662	374	11	nonlinear	nonlinear	ADJ
ejpam-5662	374	12	damping	damp	VERB
ejpam-5662	374	13	coefficients	coefficient	NOUN
ejpam-5662	374	14	α1	α1	PROPN
ejpam-5662	374	15	and	and	CCONJ
ejpam-5662	374	16	α2	α2	ADJ
ejpam-5662	374	17	as	as	SCONJ
ejpam-5662	374	18	detected	detect	VERB
ejpam-5662	374	19	in	in	ADP
ejpam-5662	374	20	figs	fig	NOUN
ejpam-5662	374	21	.	.	PUNCT
ejpam-5662	375	1	13	13	NUM
ejpam-5662	375	2	and	and	CCONJ
ejpam-5662	375	3	14	14	NUM
ejpam-5662	375	4	.	.	PUNCT
ejpam-5662	376	1	these	these	DET
ejpam-5662	376	2	illustrations	illustration	NOUN
ejpam-5662	376	3	comprehend	comprehend	VERB
ejpam-5662	376	4	the	the	DET
ejpam-5662	376	5	polarplots	polarplot	NOUN
ejpam-5662	376	6	of	of	ADP
ejpam-5662	376	7	the	the	DET
ejpam-5662	376	8	equal	equal	ADJ
ejpam-5662	376	9	solutions	solution	NOUN
ejpam-5662	376	10	with	with	ADP
ejpam-5662	376	11	a	a	DET
ejpam-5662	376	12	small	small	ADJ
ejpam-5662	376	13	variation	variation	NOUN
ejpam-5662	376	14	in	in	ADP
ejpam-5662	376	15	the	the	DET
ejpam-5662	376	16	nonlinear	nonlinear	ADJ
ejpam-5662	376	17	damping	damp	VERB
ejpam-5662	376	18	coefficients	coefficient	NOUN
ejpam-5662	376	19	.	.	PUNCT
ejpam-5662	377	1	one	one	PRON
ejpam-5662	377	2	can	can	AUX
ejpam-5662	377	3	notice	notice	VERB
ejpam-5662	377	4	that	that	SCONJ
ejpam-5662	377	5	the	the	DET
ejpam-5662	377	6	impacts	impact	NOUN
ejpam-5662	377	7	of	of	ADP
ejpam-5662	377	8	α1	α1	PROPN
ejpam-5662	377	9	and	and	CCONJ
ejpam-5662	377	10	α2	α2	NOUN
ejpam-5662	377	11	are	be	AUX
ejpam-5662	377	12	similar	similar	ADJ
ejpam-5662	377	13	to	to	ADP
ejpam-5662	377	14	those	those	PRON
ejpam-5662	377	15	of	of	ADP
ejpam-5662	377	16	the	the	DET
ejpam-5662	377	17	linear	linear	PROPN
ejpam-5662	377	18	ones	one	NOUN
ejpam-5662	377	19	µ1	µ1	ADJ
ejpam-5662	377	20	and	and	CCONJ
ejpam-5662	377	21	µ2	µ2	PROPN
ejpam-5662	377	22	,	,	PUNCT
ejpam-5662	377	23	approximately	approximately	ADV
ejpam-5662	377	24	they	they	PRON
ejpam-5662	377	25	give	give	VERB
ejpam-5662	377	26	the	the	DET
ejpam-5662	377	27	same	same	ADJ
ejpam-5662	377	28	distributed	distribute	VERB
ejpam-5662	377	29	circular	circular	ADJ
ejpam-5662	377	30	curves	curve	NOUN
ejpam-5662	377	31	.	.	PUNCT
ejpam-5662	378	1	these	these	DET
ejpam-5662	378	2	created	create	VERB
ejpam-5662	378	3	curves	curve	NOUN
ejpam-5662	378	4	are	be	AUX
ejpam-5662	378	5	exposed	expose	VERB
ejpam-5662	378	6	to	to	PART
ejpam-5662	378	7	spin	spin	VERB
ejpam-5662	378	8	in	in	ADP
ejpam-5662	378	9	repeated	repeat	VERB
ejpam-5662	378	10	pathways	pathway	NOUN
ejpam-5662	378	11	,	,	PUNCT
ejpam-5662	378	12	resulting	result	VERB
ejpam-5662	378	13	in	in	ADP
ejpam-5662	378	14	remarkable	remarkable	ADJ
ejpam-5662	378	15	spin	spin	NOUN
ejpam-5662	378	16	structures	structure	NOUN
ejpam-5662	378	17	that	that	PRON
ejpam-5662	378	18	are	be	AUX
ejpam-5662	378	19	symmetrical	symmetrical	ADJ
ejpam-5662	378	20	around	around	ADP
ejpam-5662	378	21	their	their	PRON
ejpam-5662	378	22	center	center	NOUN
ejpam-5662	378	23	,	,	PUNCT
ejpam-5662	378	24	which	which	PRON
ejpam-5662	378	25	validates	validate	VERB
ejpam-5662	378	26	the	the	DET
ejpam-5662	378	27	dominance	dominance	NOUN
ejpam-5662	378	28	of	of	ADP
ejpam-5662	378	29	the	the	DET
ejpam-5662	378	30	stable	stable	ADJ
ejpam-5662	378	31	mode	mode	NOUN
ejpam-5662	378	32	in	in	ADP
ejpam-5662	378	33	the	the	DET
ejpam-5662	378	34	current	current	ADJ
ejpam-5662	378	35	model	model	NOUN
ejpam-5662	378	36	with	with	ADP
ejpam-5662	378	37	the	the	DET
ejpam-5662	378	38	applicable	applicable	ADJ
ejpam-5662	378	39	importance	importance	NOUN
ejpam-5662	378	40	of	of	ADP
ejpam-5662	378	41	this	this	DET
ejpam-5662	378	42	conclusion	conclusion	NOUN
ejpam-5662	378	43	.	.	PUNCT
ejpam-5662	379	1	due	due	ADP
ejpam-5662	379	2	to	to	ADP
ejpam-5662	379	3	the	the	DET
ejpam-5662	379	4	similarity	similarity	NOUN
ejpam-5662	379	5	between	between	ADP
ejpam-5662	379	6	the	the	DET
ejpam-5662	379	7	cubic	cubic	ADJ
ejpam-5662	379	8	and	and	CCONJ
ejpam-5662	379	9	quintic	quintic	ADJ
ejpam-5662	379	10	coefficients	coefficient	NOUN
ejpam-5662	379	11	impacts	impact	NOUN
ejpam-5662	379	12	,	,	PUNCT
ejpam-5662	379	13	as	as	SCONJ
ejpam-5662	379	14	seen	see	VERB
ejpam-5662	379	15	before	before	ADV
ejpam-5662	379	16	,	,	PUNCT
ejpam-5662	379	17	it	it	PRON
ejpam-5662	379	18	is	be	AUX
ejpam-5662	379	19	adequate	adequate	ADJ
ejpam-5662	379	20	to	to	PART
ejpam-5662	379	21	study	study	VERB
ejpam-5662	379	22	the	the	DET
ejpam-5662	379	23	influence	influence	NOUN
ejpam-5662	379	24	of	of	ADP
ejpam-5662	379	25	one	one	NUM
ejpam-5662	379	26	of	of	ADP
ejpam-5662	379	27	them	they	PRON
ejpam-5662	379	28	.	.	PUNCT
ejpam-5662	380	1	consequently	consequently	ADV
ejpam-5662	380	2	,	,	PUNCT
ejpam-5662	380	3	figs	fig	NOUN
ejpam-5662	380	4	.	.	PUNCT
ejpam-5662	381	1	15	15	NUM
ejpam-5662	381	2	and	and	CCONJ
ejpam-5662	381	3	16	16	NUM
ejpam-5662	381	4	are	be	AUX
ejpam-5662	381	5	graphed	graph	VERB
ejpam-5662	381	6	to	to	PART
ejpam-5662	381	7	illustrate	illustrate	VERB
ejpam-5662	381	8	the	the	DET
ejpam-5662	381	9	impacts	impact	NOUN
ejpam-5662	381	10	of	of	ADP
ejpam-5662	381	11	the	the	DET
ejpam-5662	381	12	quintic	quintic	ADJ
ejpam-5662	381	13	coefficients	coefficient	NOUN
ejpam-5662	381	14	λ1	λ1	ADJ
ejpam-5662	381	15	and	and	CCONJ
ejpam-5662	381	16	λ2	λ2	NOUN
ejpam-5662	381	17	,	,	PUNCT
ejpam-5662	381	18	as	as	SCONJ
ejpam-5662	381	19	new	new	ADJ
ejpam-5662	381	20	terms	term	NOUN
ejpam-5662	381	21	added	add	VERB
ejpam-5662	381	22	in	in	ADP
ejpam-5662	381	23	the	the	DET
ejpam-5662	381	24	current	current	ADJ
ejpam-5662	381	25	study	study	NOUN
ejpam-5662	381	26	contrary	contrary	ADV
ejpam-5662	381	27	to	to	ADP
ejpam-5662	381	28	the	the	DET
ejpam-5662	381	29	previous	previous	ADJ
ejpam-5662	381	30	[	[	X
ejpam-5662	381	31	38	38	NUM
ejpam-5662	381	32	]	]	PUNCT
ejpam-5662	381	33	.	.	PUNCT
ejpam-5662	382	1	it	it	PRON
ejpam-5662	382	2	is	be	AUX
ejpam-5662	382	3	noticed	notice	VERB
ejpam-5662	382	4	that	that	SCONJ
ejpam-5662	382	5	the	the	DET
ejpam-5662	382	6	number	number	NOUN
ejpam-5662	382	7	of	of	ADP
ejpam-5662	382	8	loops	loop	NOUN
ejpam-5662	382	9	is	be	AUX
ejpam-5662	382	10	growing	grow	VERB
ejpam-5662	382	11	with	with	ADP
ejpam-5662	382	12	the	the	DET
ejpam-5662	382	13	rise	rise	NOUN
ejpam-5662	382	14	of	of	ADP
ejpam-5662	382	15	λ1	λ1	PROPN
ejpam-5662	382	16	and	and	CCONJ
ejpam-5662	382	17	λ2	λ2	PROPN
ejpam-5662	382	18	,	,	PUNCT
ejpam-5662	382	19	which	which	PRON
ejpam-5662	382	20	indicates	indicate	VERB
ejpam-5662	382	21	that	that	SCONJ
ejpam-5662	382	22	the	the	DET
ejpam-5662	382	23	current	current	ADJ
ejpam-5662	382	24	system	system	NOUN
ejpam-5662	382	25	in	in	ADP
ejpam-5662	382	26	general	general	ADJ
ejpam-5662	382	27	verifies	verifie	NOUN
ejpam-5662	382	28	the	the	DET
ejpam-5662	382	29	stability	stability	NOUN
ejpam-5662	382	30	manner	manner	NOUN
ejpam-5662	382	31	.	.	PUNCT
ejpam-5662	383	1	all	all	DET
ejpam-5662	383	2	these	these	DET
ejpam-5662	383	3	curves	curve	NOUN
ejpam-5662	383	4	have	have	VERB
ejpam-5662	383	5	a	a	DET
ejpam-5662	383	6	variety	variety	NOUN
ejpam-5662	383	7	of	of	ADP
ejpam-5662	383	8	closed	closed	ADJ
ejpam-5662	383	9	or	or	CCONJ
ejpam-5662	383	10	semi	semi	ADJ
ejpam-5662	383	11	-	-	ADJ
ejpam-5662	383	12	closed	closed	ADJ
ejpam-5662	383	13	elliptical	elliptical	ADJ
ejpam-5662	383	14	trajectories	trajectory	NOUN
ejpam-5662	383	15	that	that	PRON
ejpam-5662	383	16	distribute	distribute	VERB
ejpam-5662	383	17	steadily	steadily	ADV
ejpam-5662	383	18	around	around	ADP
ejpam-5662	383	19	the	the	DET
ejpam-5662	383	20	center	center	NOUN
ejpam-5662	383	21	point	point	NOUN
ejpam-5662	383	22	giving	give	VERB
ejpam-5662	383	23	these	these	DET
ejpam-5662	383	24	amazing	amazing	ADJ
ejpam-5662	383	25	shapes	shape	NOUN
ejpam-5662	383	26	.	.	PUNCT
ejpam-5662	384	1	because	because	SCONJ
ejpam-5662	384	2	of	of	ADP
ejpam-5662	384	3	the	the	DET
ejpam-5662	384	4	similarity	similarity	NOUN
ejpam-5662	384	5	of	of	ADP
ejpam-5662	384	6	data	datum	NOUN
ejpam-5662	384	7	used	use	VERB
ejpam-5662	384	8	to	to	PART
ejpam-5662	384	9	create	create	VERB
ejpam-5662	384	10	some	some	DET
ejpam-5662	384	11	figures	figure	NOUN
ejpam-5662	384	12	,	,	PUNCT
ejpam-5662	384	13	it	it	PRON
ejpam-5662	384	14	is	be	AUX
ejpam-5662	384	15	found	find	VERB
ejpam-5662	384	16	that	that	SCONJ
ejpam-5662	384	17	some	some	DET
ejpam-5662	384	18	parts	part	NOUN
ejpam-5662	384	19	of	of	ADP
ejpam-5662	384	20	them	they	PRON
ejpam-5662	384	21	are	be	AUX
ejpam-5662	384	22	comparable	comparable	ADJ
ejpam-5662	384	23	.	.	PUNCT
ejpam-5662	385	1	a.	a.	PROPN
ejpam-5662	385	2	alanazy	alanazy	PROPN
ejpam-5662	385	3	,	,	PUNCT
ejpam-5662	385	4	g.	g.	PROPN
ejpam-5662	385	5	m.	m.	PROPN
ejpam-5662	385	6	moatimid	moatimid	PROPN
ejpam-5662	385	7	,	,	PUNCT
ejpam-5662	385	8	m.	m.	PROPN
ejpam-5662	385	9	a.	a.	PROPN
ejpam-5662	385	10	a.	a.	PROPN
ejpam-5662	385	11	mohamed	mohamed	PROPN
ejpam-5662	385	12	/	/	SYM
ejpam-5662	385	13	eur	eur	PROPN
ejpam-5662	385	14	.	.	PUNCT
ejpam-5662	386	1	j.	j.	PROPN
ejpam-5662	386	2	pure	pure	PROPN
ejpam-5662	386	3	appl	appl	PROPN
ejpam-5662	386	4	.	.	PROPN
ejpam-5662	386	5	math	math	PROPN
ejpam-5662	386	6	,	,	PUNCT
ejpam-5662	386	7	18	18	NUM
ejpam-5662	386	8	(	(	PUNCT
ejpam-5662	386	9	2	2	NUM
ejpam-5662	386	10	)	)	PUNCT
ejpam-5662	386	11	(	(	PUNCT
ejpam-5662	386	12	2025	2025	NUM
ejpam-5662	386	13	)	)	PUNCT
ejpam-5662	386	14	,	,	PUNCT
ejpam-5662	386	15	5662	5662	NUM
ejpam-5662	386	16	19	19	NUM
ejpam-5662	386	17	of	of	ADP
ejpam-5662	386	18	36	36	NUM
ejpam-5662	386	19	figure	figure	NOUN
ejpam-5662	386	20	9	9	NUM
ejpam-5662	386	21	:	:	PUNCT
ejpam-5662	386	22	displays	display	VERB
ejpam-5662	386	23	the	the	DET
ejpam-5662	386	24	polarplot	polarplot	NOUN
ejpam-5662	386	25	of	of	ADP
ejpam-5662	386	26	u(t	u(t	NOUN
ejpam-5662	386	27	)	)	PUNCT
ejpam-5662	386	28	for	for	ADP
ejpam-5662	386	29	different	different	ADJ
ejpam-5662	386	30	measures	measure	NOUN
ejpam-5662	386	31	of	of	ADP
ejpam-5662	386	32	the	the	DET
ejpam-5662	386	33	x	x	ADJ
ejpam-5662	386	34	-	-	ADJ
ejpam-5662	386	35	oscillator	oscillator	ADJ
ejpam-5662	386	36	natural	natural	ADJ
ejpam-5662	386	37	frequency	frequency	NOUN
ejpam-5662	386	38	ω1	ω1	PROPN
ejpam-5662	386	39	.	.	PUNCT
ejpam-5662	386	40	figure	figure	NOUN
ejpam-5662	386	41	10	10	NUM
ejpam-5662	386	42	:	:	PUNCT
ejpam-5662	386	43	displays	display	VERB
ejpam-5662	386	44	the	the	DET
ejpam-5662	386	45	polarplot	polarplot	NOUN
ejpam-5662	386	46	of	of	ADP
ejpam-5662	386	47	v(t	v(t	NOUN
ejpam-5662	386	48	)	)	PUNCT
ejpam-5662	386	49	for	for	ADP
ejpam-5662	386	50	different	different	ADJ
ejpam-5662	386	51	measures	measure	NOUN
ejpam-5662	386	52	of	of	ADP
ejpam-5662	386	53	the	the	DET
ejpam-5662	386	54	y	y	PROPN
ejpam-5662	386	55	-	-	PUNCT
ejpam-5662	386	56	oscillator	oscillator	NOUN
ejpam-5662	386	57	natural	natural	ADJ
ejpam-5662	386	58	frequency	frequency	NOUN
ejpam-5662	386	59	ω2	ω2	PROPN
ejpam-5662	386	60	.	.	PUNCT
ejpam-5662	387	1	figure	figure	NOUN
ejpam-5662	387	2	11	11	NUM
ejpam-5662	387	3	:	:	PUNCT
ejpam-5662	387	4	displays	display	VERB
ejpam-5662	387	5	the	the	DET
ejpam-5662	387	6	polarplot	polarplot	NOUN
ejpam-5662	387	7	of	of	ADP
ejpam-5662	387	8	u(t	u(t	NOUN
ejpam-5662	387	9	)	)	PUNCT
ejpam-5662	387	10	for	for	ADP
ejpam-5662	387	11	different	different	ADJ
ejpam-5662	387	12	measures	measure	NOUN
ejpam-5662	387	13	of	of	ADP
ejpam-5662	387	14	the	the	DET
ejpam-5662	387	15	x	x	ADJ
ejpam-5662	387	16	-	-	NOUN
ejpam-5662	387	17	oscillator	oscillator	ADJ
ejpam-5662	387	18	damping	damp	VERB
ejpam-5662	387	19	coefficient	coefficient	NOUN
ejpam-5662	387	20	µ1	µ1	PROPN
ejpam-5662	387	21	.	.	PUNCT
ejpam-5662	387	22	a.	a.	PROPN
ejpam-5662	387	23	alanazy	alanazy	PROPN
ejpam-5662	387	24	,	,	PUNCT
ejpam-5662	388	1	g.	g.	PROPN
ejpam-5662	388	2	m.	m.	PROPN
ejpam-5662	388	3	moatimid	moatimid	PROPN
ejpam-5662	388	4	,	,	PUNCT
ejpam-5662	388	5	m.	m.	PROPN
ejpam-5662	388	6	a.	a.	PROPN
ejpam-5662	388	7	a.	a.	PROPN
ejpam-5662	388	8	mohamed	mohamed	PROPN
ejpam-5662	388	9	/	/	SYM
ejpam-5662	388	10	eur	eur	PROPN
ejpam-5662	388	11	.	.	PUNCT
ejpam-5662	389	1	j.	j.	PROPN
ejpam-5662	389	2	pure	pure	PROPN
ejpam-5662	389	3	appl	appl	PROPN
ejpam-5662	389	4	.	.	PROPN
ejpam-5662	389	5	math	math	PROPN
ejpam-5662	389	6	,	,	PUNCT
ejpam-5662	389	7	18	18	NUM
ejpam-5662	389	8	(	(	PUNCT
ejpam-5662	389	9	2	2	NUM
ejpam-5662	389	10	)	)	PUNCT
ejpam-5662	389	11	(	(	PUNCT
ejpam-5662	389	12	2025	2025	NUM
ejpam-5662	389	13	)	)	PUNCT
ejpam-5662	389	14	,	,	PUNCT
ejpam-5662	389	15	5662	5662	NUM
ejpam-5662	389	16	20	20	NUM
ejpam-5662	389	17	of	of	ADP
ejpam-5662	389	18	36	36	NUM
ejpam-5662	389	19	figure	figure	NOUN
ejpam-5662	389	20	12	12	NUM
ejpam-5662	389	21	:	:	PUNCT
ejpam-5662	389	22	displays	display	VERB
ejpam-5662	389	23	the	the	DET
ejpam-5662	389	24	polarplot	polarplot	NOUN
ejpam-5662	389	25	of	of	ADP
ejpam-5662	389	26	v(t	v(t	NOUN
ejpam-5662	389	27	)	)	PUNCT
ejpam-5662	389	28	for	for	ADP
ejpam-5662	389	29	different	different	ADJ
ejpam-5662	389	30	measures	measure	NOUN
ejpam-5662	389	31	of	of	ADP
ejpam-5662	389	32	the	the	DET
ejpam-5662	389	33	y	y	PROPN
ejpam-5662	389	34	-	-	PUNCT
ejpam-5662	389	35	oscillator	oscillator	NOUN
ejpam-5662	389	36	damping	damp	VERB
ejpam-5662	389	37	coefficient	coefficient	NOUN
ejpam-5662	389	38	µ2	µ2	PROPN
ejpam-5662	389	39	.	.	PUNCT
ejpam-5662	389	40	figure	figure	NOUN
ejpam-5662	389	41	13	13	NUM
ejpam-5662	389	42	:	:	PUNCT
ejpam-5662	389	43	displays	display	VERB
ejpam-5662	389	44	the	the	DET
ejpam-5662	389	45	polarplot	polarplot	NOUN
ejpam-5662	389	46	of	of	ADP
ejpam-5662	389	47	u(t	u(t	NOUN
ejpam-5662	389	48	)	)	PUNCT
ejpam-5662	389	49	for	for	ADP
ejpam-5662	389	50	different	different	ADJ
ejpam-5662	389	51	measures	measure	NOUN
ejpam-5662	389	52	of	of	ADP
ejpam-5662	389	53	the	the	DET
ejpam-5662	389	54	x	x	ADJ
ejpam-5662	389	55	-	-	ADJ
ejpam-5662	389	56	oscillator	oscillator	ADJ
ejpam-5662	389	57	cubic	cubic	ADJ
ejpam-5662	389	58	coefficient	coefficient	NOUN
ejpam-5662	389	59	α1	α1	PROPN
ejpam-5662	389	60	.	.	PUNCT
ejpam-5662	390	1	figure	figure	NOUN
ejpam-5662	390	2	14	14	NUM
ejpam-5662	390	3	:	:	PUNCT
ejpam-5662	390	4	displays	display	VERB
ejpam-5662	390	5	the	the	DET
ejpam-5662	390	6	polarplot	polarplot	NOUN
ejpam-5662	390	7	of	of	ADP
ejpam-5662	390	8	v(t	v(t	NOUN
ejpam-5662	390	9	)	)	PUNCT
ejpam-5662	390	10	for	for	ADP
ejpam-5662	390	11	different	different	ADJ
ejpam-5662	390	12	measures	measure	NOUN
ejpam-5662	390	13	of	of	ADP
ejpam-5662	390	14	the	the	DET
ejpam-5662	390	15	y	y	PROPN
ejpam-5662	390	16	-	-	PUNCT
ejpam-5662	390	17	oscillator	oscillator	NOUN
ejpam-5662	390	18	cubic	cubic	ADJ
ejpam-5662	390	19	coefficient	coefficient	NOUN
ejpam-5662	390	20	α2	α2	PROPN
ejpam-5662	390	21	.	.	PUNCT
ejpam-5662	391	1	a.	a.	PROPN
ejpam-5662	391	2	alanazy	alanazy	PROPN
ejpam-5662	391	3	,	,	PUNCT
ejpam-5662	391	4	g.	g.	PROPN
ejpam-5662	391	5	m.	m.	PROPN
ejpam-5662	391	6	moatimid	moatimid	PROPN
ejpam-5662	391	7	,	,	PUNCT
ejpam-5662	391	8	m.	m.	PROPN
ejpam-5662	391	9	a.	a.	PROPN
ejpam-5662	391	10	a.	a.	PROPN
ejpam-5662	391	11	mohamed	mohamed	PROPN
ejpam-5662	391	12	/	/	SYM
ejpam-5662	391	13	eur	eur	PROPN
ejpam-5662	391	14	.	.	PUNCT
ejpam-5662	392	1	j.	j.	PROPN
ejpam-5662	392	2	pure	pure	PROPN
ejpam-5662	392	3	appl	appl	PROPN
ejpam-5662	392	4	.	.	PROPN
ejpam-5662	392	5	math	math	PROPN
ejpam-5662	392	6	,	,	PUNCT
ejpam-5662	392	7	18	18	NUM
ejpam-5662	392	8	(	(	PUNCT
ejpam-5662	392	9	2	2	NUM
ejpam-5662	392	10	)	)	PUNCT
ejpam-5662	392	11	(	(	PUNCT
ejpam-5662	392	12	2025	2025	NUM
ejpam-5662	392	13	)	)	PUNCT
ejpam-5662	392	14	,	,	PUNCT
ejpam-5662	392	15	5662	5662	NUM
ejpam-5662	392	16	21	21	NUM
ejpam-5662	392	17	of	of	ADP
ejpam-5662	392	18	36	36	NUM
ejpam-5662	392	19	figure	figure	NOUN
ejpam-5662	392	20	15	15	NUM
ejpam-5662	392	21	:	:	PUNCT
ejpam-5662	392	22	displays	display	VERB
ejpam-5662	392	23	the	the	DET
ejpam-5662	392	24	polarplot	polarplot	NOUN
ejpam-5662	392	25	of	of	ADP
ejpam-5662	392	26	u(t	u(t	NOUN
ejpam-5662	392	27	)	)	PUNCT
ejpam-5662	392	28	for	for	ADP
ejpam-5662	392	29	different	different	ADJ
ejpam-5662	392	30	measures	measure	NOUN
ejpam-5662	392	31	of	of	ADP
ejpam-5662	392	32	the	the	DET
ejpam-5662	392	33	x	x	ADJ
ejpam-5662	392	34	-	-	ADJ
ejpam-5662	392	35	oscillator	oscillator	ADJ
ejpam-5662	392	36	quinitic	quinitic	ADJ
ejpam-5662	392	37	coefficient	coefficient	NOUN
ejpam-5662	392	38	λ1	λ1	PROPN
ejpam-5662	392	39	.	.	PUNCT
ejpam-5662	393	1	figure	figure	NOUN
ejpam-5662	393	2	16	16	NUM
ejpam-5662	393	3	:	:	PUNCT
ejpam-5662	393	4	displays	display	VERB
ejpam-5662	393	5	the	the	DET
ejpam-5662	393	6	polarplot	polarplot	NOUN
ejpam-5662	393	7	of	of	ADP
ejpam-5662	393	8	v(t	v(t	NOUN
ejpam-5662	393	9	)	)	PUNCT
ejpam-5662	393	10	for	for	ADP
ejpam-5662	393	11	different	different	ADJ
ejpam-5662	393	12	measures	measure	NOUN
ejpam-5662	393	13	of	of	ADP
ejpam-5662	393	14	the	the	DET
ejpam-5662	393	15	y	y	PROPN
ejpam-5662	393	16	-	-	PUNCT
ejpam-5662	393	17	oscillator	oscillator	NOUN
ejpam-5662	393	18	quinitic	quinitic	ADJ
ejpam-5662	393	19	coefficient	coefficient	NOUN
ejpam-5662	393	20	λ2	λ2	NOUN
ejpam-5662	393	21	.	.	PUNCT
ejpam-5662	394	1	5	5	NUM
ejpam-5662	394	2	.	.	X
ejpam-5662	395	1	the	the	DET
ejpam-5662	395	2	un	un	PROPN
ejpam-5662	395	3	-	-	ADJ
ejpam-5662	395	4	damped	damped	ADJ
ejpam-5662	395	5	tdof	tdof	NOUN
ejpam-5662	395	6	of	of	ADP
ejpam-5662	395	7	mdo	mdo	PROPN
ejpam-5662	395	8	inspecting	inspect	VERB
ejpam-5662	395	9	the	the	DET
ejpam-5662	395	10	conventional	conventional	ADJ
ejpam-5662	395	11	situation	situation	NOUN
ejpam-5662	395	12	of	of	ADP
ejpam-5662	395	13	the	the	DET
ejpam-5662	395	14	coupled	couple	VERB
ejpam-5662	395	15	system	system	NOUN
ejpam-5662	395	16	as	as	SCONJ
ejpam-5662	395	17	given	give	VERB
ejpam-5662	395	18	in	in	ADP
ejpam-5662	395	19	eqs	eqs	PROPN
ejpam-5662	395	20	.	.	PUNCT
ejpam-5662	396	1	(	(	PUNCT
ejpam-5662	396	2	18	18	NUM
ejpam-5662	396	3	)	)	PUNCT
ejpam-5662	396	4	and	and	CCONJ
ejpam-5662	396	5	(	(	PUNCT
ejpam-5662	396	6	19	19	NUM
ejpam-5662	396	7	)	)	PUNCT
ejpam-5662	396	8	,	,	PUNCT
ejpam-5662	396	9	in	in	ADP
ejpam-5662	396	10	the	the	DET
ejpam-5662	396	11	case	case	NOUN
ejpam-5662	396	12	of	of	ADP
ejpam-5662	396	13	nonexistence	nonexistence	NOUN
ejpam-5662	396	14	of	of	ADP
ejpam-5662	396	15	damping	damp	VERB
ejpam-5662	396	16	terms	term	NOUN
ejpam-5662	396	17	(	(	PUNCT
ejpam-5662	396	18	µ1	µ1	NOUN
ejpam-5662	396	19	=	=	SYM
ejpam-5662	396	20	µ2	µ2	NOUN
ejpam-5662	396	21	=	=	PROPN
ejpam-5662	396	22	α1	α1	PROPN
ejpam-5662	396	23	=	=	SYM
ejpam-5662	396	24	α2	α2	NOUN
ejpam-5662	396	25	=	=	SYM
ejpam-5662	396	26	0	0	NUM
ejpam-5662	396	27	)	)	PUNCT
ejpam-5662	396	28	.	.	PUNCT
ejpam-5662	397	1	the	the	DET
ejpam-5662	397	2	absence	absence	NOUN
ejpam-5662	397	3	of	of	ADP
ejpam-5662	397	4	damping	damp	VERB
ejpam-5662	397	5	in	in	ADP
ejpam-5662	397	6	the	the	DET
ejpam-5662	397	7	un	un	PROPN
ejpam-5662	397	8	-	-	ADJ
ejpam-5662	397	9	damped	damped	ADJ
ejpam-5662	397	10	situation	situation	NOUN
ejpam-5662	397	11	of	of	ADP
ejpam-5662	397	12	a	a	DET
ejpam-5662	397	13	tdof	tdof	NOUN
ejpam-5662	397	14	of	of	ADP
ejpam-5662	397	15	mdo	mdo	PROPN
ejpam-5662	397	16	prevents	prevent	VERB
ejpam-5662	397	17	energy	energy	NOUN
ejpam-5662	397	18	from	from	ADP
ejpam-5662	397	19	dissipating	dissipate	VERB
ejpam-5662	397	20	over	over	ADP
ejpam-5662	397	21	time	time	NOUN
ejpam-5662	397	22	.	.	PUNCT
ejpam-5662	398	1	this	this	DET
ejpam-5662	398	2	lack	lack	NOUN
ejpam-5662	398	3	of	of	ADP
ejpam-5662	398	4	damping	damp	VERB
ejpam-5662	398	5	considerably	considerably	ADV
ejpam-5662	398	6	changes	change	VERB
ejpam-5662	398	7	the	the	DET
ejpam-5662	398	8	dynamics	dynamic	NOUN
ejpam-5662	398	9	of	of	ADP
ejpam-5662	398	10	the	the	DET
ejpam-5662	398	11	system	system	NOUN
ejpam-5662	398	12	,	,	PUNCT
ejpam-5662	398	13	resulting	result	VERB
ejpam-5662	398	14	in	in	ADP
ejpam-5662	398	15	more	more	ADV
ejpam-5662	398	16	noticeable	noticeable	ADJ
ejpam-5662	398	17	nonlinear	nonlinear	ADJ
ejpam-5662	398	18	effects	effect	NOUN
ejpam-5662	398	19	due	due	ADJ
ejpam-5662	398	20	to	to	ADP
ejpam-5662	398	21	the	the	DET
ejpam-5662	398	22	existence	existence	NOUN
ejpam-5662	398	23	of	of	ADP
ejpam-5662	398	24	the	the	DET
ejpam-5662	398	25	cubic	cubic	ADJ
ejpam-5662	398	26	and	and	CCONJ
ejpam-5662	398	27	quintic	quintic	ADJ
ejpam-5662	398	28	terms	term	NOUN
ejpam-5662	398	29	,	,	PUNCT
ejpam-5662	398	30	magnified	magnify	VERB
ejpam-5662	398	31	reactions	reaction	NOUN
ejpam-5662	398	32	close	close	ADJ
ejpam-5662	398	33	to	to	ADP
ejpam-5662	398	34	resonance	resonance	NOUN
ejpam-5662	398	35	,	,	PUNCT
ejpam-5662	398	36	and	and	CCONJ
ejpam-5662	398	37	persistent	persistent	ADJ
ejpam-5662	398	38	oscillations	oscillation	NOUN
ejpam-5662	398	39	.	.	PUNCT
ejpam-5662	399	1	in	in	ADP
ejpam-5662	399	2	this	this	DET
ejpam-5662	399	3	case	case	NOUN
ejpam-5662	399	4	,	,	PUNCT
ejpam-5662	399	5	if	if	SCONJ
ejpam-5662	399	6	the	the	DET
ejpam-5662	399	7	system	system	NOUN
ejpam-5662	399	8	is	be	AUX
ejpam-5662	399	9	close	close	ADJ
ejpam-5662	399	10	to	to	ADP
ejpam-5662	399	11	resonance	resonance	NOUN
ejpam-5662	399	12	conditions	condition	NOUN
ejpam-5662	399	13	,	,	PUNCT
ejpam-5662	399	14	continuous	continuous	ADJ
ejpam-5662	399	15	large	large	ADJ
ejpam-5662	399	16	-	-	PUNCT
ejpam-5662	399	17	amplitude	amplitude	NOUN
ejpam-5662	399	18	oscillations	oscillation	NOUN
ejpam-5662	399	19	will	will	AUX
ejpam-5662	399	20	result	result	VERB
ejpam-5662	399	21	from	from	ADP
ejpam-5662	399	22	oscillations	oscillation	NOUN
ejpam-5662	399	23	in	in	ADP
ejpam-5662	399	24	both	both	DET
ejpam-5662	399	25	degrees	degree	NOUN
ejpam-5662	399	26	of	of	ADP
ejpam-5662	399	27	freedom	freedom	NOUN
ejpam-5662	399	28	.	.	PUNCT
ejpam-5662	400	1	furthermore	furthermore	ADV
ejpam-5662	400	2	,	,	PUNCT
ejpam-5662	400	3	strong	strong	ADJ
ejpam-5662	400	4	coupling	coupling	NOUN
ejpam-5662	400	5	and	and	CCONJ
ejpam-5662	400	6	possible	possible	ADJ
ejpam-5662	400	7	internal	internal	ADJ
ejpam-5662	400	8	resonance	resonance	NOUN
ejpam-5662	400	9	effects	effect	NOUN
ejpam-5662	400	10	result	result	VERB
ejpam-5662	400	11	from	from	ADP
ejpam-5662	400	12	the	the	DET
ejpam-5662	400	13	free	free	ADJ
ejpam-5662	400	14	flow	flow	NOUN
ejpam-5662	400	15	of	of	ADP
ejpam-5662	400	16	energy	energy	NOUN
ejpam-5662	400	17	between	between	ADP
ejpam-5662	400	18	modes	mode	NOUN
ejpam-5662	400	19	.	.	PUNCT
ejpam-5662	401	1	for	for	ADP
ejpam-5662	401	2	these	these	DET
ejpam-5662	401	3	important	important	ADJ
ejpam-5662	401	4	aspects	aspect	NOUN
ejpam-5662	401	5	,	,	PUNCT
ejpam-5662	401	6	we	we	PRON
ejpam-5662	401	7	are	be	AUX
ejpam-5662	401	8	going	go	VERB
ejpam-5662	401	9	to	to	PART
ejpam-5662	401	10	illustrate	illustrate	VERB
ejpam-5662	401	11	the	the	DET
ejpam-5662	401	12	tdof	tdof	NOUN
ejpam-5662	401	13	of	of	ADP
ejpam-5662	401	14	mdo	mdo	PROPN
ejpam-5662	401	15	without	without	ADP
ejpam-5662	401	16	the	the	DET
ejpam-5662	401	17	damping	damp	VERB
ejpam-5662	401	18	parameters	parameter	NOUN
ejpam-5662	401	19	.	.	PUNCT
ejpam-5662	402	1	the	the	DET
ejpam-5662	402	2	coupled	couple	VERB
ejpam-5662	402	3	harmonic	harmonic	PROPN
ejpam-5662	402	4	mdo	mdo	PROPN
ejpam-5662	402	5	(	(	PUNCT
ejpam-5662	402	6	18	18	NUM
ejpam-5662	402	7	)	)	PUNCT
ejpam-5662	402	8	and	and	CCONJ
ejpam-5662	402	9	(	(	PUNCT
ejpam-5662	402	10	19	19	NUM
ejpam-5662	402	11	)	)	PUNCT
ejpam-5662	402	12	in	in	ADP
ejpam-5662	402	13	this	this	DET
ejpam-5662	402	14	case	case	NOUN
ejpam-5662	402	15	is	be	AUX
ejpam-5662	402	16	identified	identify	VERB
ejpam-5662	402	17	as	as	SCONJ
ejpam-5662	402	18	follows	follow	VERB
ejpam-5662	402	19	:	:	PUNCT
ejpam-5662	402	20	ẍ+	ẍ+	PROPN
ejpam-5662	402	21	ω2	ω2	ADJ
ejpam-5662	402	22	1x+	1x+	NUM
ejpam-5662	402	23	γ1x	γ1x	NOUN
ejpam-5662	402	24	3	3	NUM
ejpam-5662	402	25	+	+	CCONJ
ejpam-5662	402	26	λ1x	λ1x	PUNCT
ejpam-5662	402	27	5	5	NUM
ejpam-5662	402	28	+	+	NUM
ejpam-5662	402	29	η11x	η11x	NOUN
ejpam-5662	402	30	cosωpt+	cosωpt+	X
ejpam-5662	402	31	η12y	η12y	PROPN
ejpam-5662	402	32	cosωpt	cosωpt	NOUN
ejpam-5662	402	33	=	=	NOUN
ejpam-5662	402	34	0	0	PROPN
ejpam-5662	402	35	,	,	PUNCT
ejpam-5662	402	36	(	(	PUNCT
ejpam-5662	402	37	39	39	NUM
ejpam-5662	402	38	)	)	PUNCT
ejpam-5662	402	39	and	and	CCONJ
ejpam-5662	402	40	ÿ	ÿ	PROPN
ejpam-5662	402	41	+	+	CCONJ
ejpam-5662	402	42	ω2	ω2	ADJ
ejpam-5662	402	43	2y	2y	PROPN
ejpam-5662	402	44	+	+	CCONJ
ejpam-5662	402	45	γ2y	γ2y	PROPN
ejpam-5662	402	46	3	3	NUM
ejpam-5662	402	47	+	+	CCONJ
ejpam-5662	402	48	λ2y	λ2y	PROPN
ejpam-5662	402	49	5	5	NUM
ejpam-5662	402	50	+	+	NUM
ejpam-5662	402	51	η21x	η21x	PROPN
ejpam-5662	402	52	cosωpt+	cosωpt+	INTJ
ejpam-5662	402	53	η22y	η22y	ADV
ejpam-5662	402	54	cosωpt	cosωpt	NOUN
ejpam-5662	402	55	=	=	SYM
ejpam-5662	402	56	0	0	NUM
ejpam-5662	402	57	,	,	PUNCT
ejpam-5662	402	58	(	(	PUNCT
ejpam-5662	402	59	40	40	NUM
ejpam-5662	402	60	)	)	PUNCT
ejpam-5662	402	61	a.	a.	NOUN
ejpam-5662	402	62	alanazy	alanazy	NOUN
ejpam-5662	402	63	,	,	PUNCT
ejpam-5662	402	64	g.	g.	PROPN
ejpam-5662	402	65	m.	m.	PROPN
ejpam-5662	402	66	moatimid	moatimid	PROPN
ejpam-5662	402	67	,	,	PUNCT
ejpam-5662	402	68	m.	m.	PROPN
ejpam-5662	402	69	a.	a.	PROPN
ejpam-5662	402	70	a.	a.	PROPN
ejpam-5662	402	71	mohamed	mohamed	PROPN
ejpam-5662	402	72	/	/	SYM
ejpam-5662	402	73	eur	eur	PROPN
ejpam-5662	402	74	.	.	PUNCT
ejpam-5662	403	1	j.	j.	PROPN
ejpam-5662	403	2	pure	pure	PROPN
ejpam-5662	403	3	appl	appl	PROPN
ejpam-5662	403	4	.	.	PROPN
ejpam-5662	403	5	math	math	PROPN
ejpam-5662	403	6	,	,	PUNCT
ejpam-5662	403	7	18	18	NUM
ejpam-5662	403	8	(	(	PUNCT
ejpam-5662	403	9	2	2	NUM
ejpam-5662	403	10	)	)	PUNCT
ejpam-5662	403	11	(	(	PUNCT
ejpam-5662	403	12	2025	2025	NUM
ejpam-5662	403	13	)	)	PUNCT
ejpam-5662	403	14	,	,	PUNCT
ejpam-5662	403	15	5662	5662	NUM
ejpam-5662	403	16	22	22	NUM
ejpam-5662	403	17	of	of	ADP
ejpam-5662	403	18	36	36	NUM
ejpam-5662	403	19	as	as	ADP
ejpam-5662	403	20	usual	usual	ADJ
ejpam-5662	403	21	,	,	PUNCT
ejpam-5662	403	22	the	the	DET
ejpam-5662	403	23	suggested	suggest	VERB
ejpam-5662	403	24	ics	ic	NOUN
ejpam-5662	403	25	of	of	ADP
ejpam-5662	403	26	eq	eq	PROPN
ejpam-5662	403	27	.	.	PUNCT
ejpam-5662	404	1	(	(	PUNCT
ejpam-5662	404	2	39	39	NUM
ejpam-5662	404	3	)	)	PUNCT
ejpam-5662	404	4	and	and	CCONJ
ejpam-5662	404	5	(	(	PUNCT
ejpam-5662	404	6	40	40	NUM
ejpam-5662	404	7	)	)	PUNCT
ejpam-5662	404	8	are	be	AUX
ejpam-5662	404	9	supposed	suppose	VERB
ejpam-5662	404	10	as	as	ADP
ejpam-5662	404	11	:	:	PUNCT
ejpam-5662	404	12	x(0	x(0	PROPN
ejpam-5662	404	13	)	)	PUNCT
ejpam-5662	405	1	=	=	SYM
ejpam-5662	405	2	c	c	X
ejpam-5662	405	3	,	,	PUNCT
ejpam-5662	405	4	y(0	y(0	PROPN
ejpam-5662	405	5	)	)	PUNCT
ejpam-5662	405	6	=	=	SYM
ejpam-5662	405	7	d	d	PROPN
ejpam-5662	405	8	,	,	PUNCT
ejpam-5662	405	9	ẋ(0	ẋ(0	X
ejpam-5662	405	10	)	)	PUNCT
ejpam-5662	405	11	=	=	SYM
ejpam-5662	405	12	0	0	NUM
ejpam-5662	405	13	,	,	PUNCT
ejpam-5662	405	14	ẏ(0	ẏ(0	NOUN
ejpam-5662	405	15	)	)	PUNCT
ejpam-5662	405	16	=	=	SYM
ejpam-5662	405	17	0	0	PUNCT
ejpam-5662	405	18	=	=	SYM
ejpam-5662	405	19	α1	α1	PROPN
ejpam-5662	405	20	=	=	SYM
ejpam-5662	405	21	0	0	NUM
ejpam-5662	405	22	(	(	PUNCT
ejpam-5662	405	23	41	41	NUM
ejpam-5662	405	24	)	)	PUNCT
ejpam-5662	405	25	eqs	eqs	PROPN
ejpam-5662	405	26	.	.	PUNCT
ejpam-5662	406	1	(	(	PUNCT
ejpam-5662	406	2	39	39	NUM
ejpam-5662	406	3	)	)	PUNCT
ejpam-5662	406	4	and	and	CCONJ
ejpam-5662	406	5	(	(	PUNCT
ejpam-5662	406	6	40	40	NUM
ejpam-5662	406	7	)	)	PUNCT
ejpam-5662	406	8	could	could	AUX
ejpam-5662	406	9	be	be	AUX
ejpam-5662	406	10	reconstructed	reconstruct	VERB
ejpam-5662	406	11	as	as	ADP
ejpam-5662	406	12	:	:	PUNCT
ejpam-5662	406	13	ẍ+	ẍ+	PROPN
ejpam-5662	406	14	f1(x	f1(x	PROPN
ejpam-5662	406	15	,	,	PUNCT
ejpam-5662	406	16	ẋ	ẋ	PROPN
ejpam-5662	406	17	,	,	PUNCT
ejpam-5662	406	18	ẍ	ẍ	PROPN
ejpam-5662	406	19	,	,	PUNCT
ejpam-5662	406	20	y	y	PROPN
ejpam-5662	406	21	,	,	PUNCT
ejpam-5662	406	22	ẏ	ẏ	PROPN
ejpam-5662	406	23	,	,	PUNCT
ejpam-5662	406	24	ÿ	ÿ	ADJ
ejpam-5662	406	25	)	)	PUNCT
ejpam-5662	406	26	=	=	SYM
ejpam-5662	406	27	0	0	NUM
ejpam-5662	406	28	,	,	PUNCT
ejpam-5662	406	29	(	(	PUNCT
ejpam-5662	406	30	42	42	NUM
ejpam-5662	406	31	)	)	PUNCT
ejpam-5662	406	32	and	and	CCONJ
ejpam-5662	406	33	ÿ	ÿ	PROPN
ejpam-5662	406	34	+	+	PROPN
ejpam-5662	406	35	h1(y	h1(y	PROPN
ejpam-5662	406	36	,	,	PUNCT
ejpam-5662	406	37	ẏ	ẏ	PROPN
ejpam-5662	406	38	,	,	PUNCT
ejpam-5662	406	39	ÿ	ÿ	PROPN
ejpam-5662	406	40	,	,	PUNCT
ejpam-5662	406	41	x	x	X
ejpam-5662	406	42	,	,	PUNCT
ejpam-5662	406	43	ẋ	ẋ	PROPN
ejpam-5662	406	44	,	,	PUNCT
ejpam-5662	406	45	ẍ	ẍ	X
ejpam-5662	406	46	)	)	PUNCT
ejpam-5662	407	1	=	=	SYM
ejpam-5662	407	2	0	0	NUM
ejpam-5662	407	3	,	,	PUNCT
ejpam-5662	407	4	(	(	PUNCT
ejpam-5662	407	5	43	43	NUM
ejpam-5662	407	6	)	)	PUNCT
ejpam-5662	407	7	where	where	SCONJ
ejpam-5662	407	8	f1(x	f1(x	VERB
ejpam-5662	407	9	,	,	PUNCT
ejpam-5662	407	10	ẋ	ẋ	PROPN
ejpam-5662	407	11	,	,	PUNCT
ejpam-5662	407	12	ẍ	ẍ	PROPN
ejpam-5662	407	13	,	,	PUNCT
ejpam-5662	407	14	y	y	PROPN
ejpam-5662	407	15	,	,	PUNCT
ejpam-5662	407	16	ẏ	ẏ	PROPN
ejpam-5662	407	17	,	,	PUNCT
ejpam-5662	407	18	ÿ	ÿ	PROPN
ejpam-5662	407	19	)	)	PUNCT
ejpam-5662	407	20	and	and	CCONJ
ejpam-5662	407	21	h1(x	h1(x	NOUN
ejpam-5662	407	22	,	,	PUNCT
ejpam-5662	407	23	ẋ	ẋ	PROPN
ejpam-5662	407	24	,	,	PUNCT
ejpam-5662	407	25	ẍ	ẍ	PROPN
ejpam-5662	407	26	,	,	PUNCT
ejpam-5662	407	27	y	y	PROPN
ejpam-5662	407	28	,	,	PUNCT
ejpam-5662	407	29	ẏ	ẏ	PROPN
ejpam-5662	407	30	,	,	PUNCT
ejpam-5662	407	31	ÿ	ÿ	ADJ
ejpam-5662	407	32	)	)	PUNCT
ejpam-5662	407	33	are	be	AUX
ejpam-5662	407	34	the	the	DET
ejpam-5662	407	35	odd	odd	ADJ
ejpam-5662	407	36	secular	secular	ADJ
ejpam-5662	407	37	terms	term	NOUN
ejpam-5662	407	38	in	in	ADP
ejpam-5662	407	39	the	the	DET
ejpam-5662	407	40	two	two	NUM
ejpam-5662	407	41	oscillators	oscillator	NOUN
ejpam-5662	407	42	,	,	PUNCT
ejpam-5662	407	43	which	which	PRON
ejpam-5662	407	44	are	be	AUX
ejpam-5662	407	45	defined	define	VERB
ejpam-5662	407	46	previously	previously	ADV
ejpam-5662	407	47	in	in	ADP
ejpam-5662	407	48	eqs	eqs	PROPN
ejpam-5662	407	49	.	.	PUNCT
ejpam-5662	408	1	(	(	PUNCT
ejpam-5662	408	2	23	23	NUM
ejpam-5662	408	3	)	)	PUNCT
ejpam-5662	408	4	and	and	CCONJ
ejpam-5662	408	5	(	(	PUNCT
ejpam-5662	408	6	25	25	NUM
ejpam-5662	408	7	)	)	PUNCT
ejpam-5662	408	8	.	.	PUNCT
ejpam-5662	409	1	the	the	DET
ejpam-5662	409	2	trial	trial	NOUN
ejpam-5662	409	3	solutions	solution	NOUN
ejpam-5662	409	4	of	of	ADP
ejpam-5662	409	5	the	the	DET
ejpam-5662	409	6	system	system	NOUN
ejpam-5662	409	7	of	of	ADP
ejpam-5662	409	8	eqs	eqs	PROPN
ejpam-5662	409	9	.	.	PUNCT
ejpam-5662	410	1	(	(	PUNCT
ejpam-5662	410	2	21	21	NUM
ejpam-5662	410	3	)	)	PUNCT
ejpam-5662	410	4	and	and	CCONJ
ejpam-5662	410	5	(	(	PUNCT
ejpam-5662	410	6	22	22	NUM
ejpam-5662	410	7	)	)	PUNCT
ejpam-5662	410	8	are	be	AUX
ejpam-5662	410	9	assumed	assume	VERB
ejpam-5662	410	10	,	,	PUNCT
ejpam-5662	410	11	as	as	ADP
ejpam-5662	410	12	per	per	ADP
ejpam-5662	410	13	the	the	DET
ejpam-5662	410	14	npa	npa	NOUN
ejpam-5662	410	15	method	method	NOUN
ejpam-5662	410	16	,	,	PUNCT
ejpam-5662	410	17	as	as	ADP
ejpam-5662	410	18	:	:	PUNCT
ejpam-5662	410	19	w̃	w̃	PROPN
ejpam-5662	410	20	=	=	SYM
ejpam-5662	410	21	c	c	PROPN
ejpam-5662	410	22	cosω3	cosω3	PROPN
ejpam-5662	410	23	t	t	PROPN
ejpam-5662	410	24	,	,	PUNCT
ejpam-5662	410	25	g̃	g̃	PROPN
ejpam-5662	410	26	=	=	SYM
ejpam-5662	411	1	d	d	PRON
ejpam-5662	411	2	cosω4	cosω4	PROPN
ejpam-5662	411	3	t	t	PROPN
ejpam-5662	411	4	,	,	PUNCT
ejpam-5662	411	5	(	(	PUNCT
ejpam-5662	411	6	44	44	NUM
ejpam-5662	411	7	)	)	PUNCT
ejpam-5662	411	8	where	where	SCONJ
ejpam-5662	411	9	c	c	NOUN
ejpam-5662	411	10	and	and	CCONJ
ejpam-5662	411	11	d	d	PROPN
ejpam-5662	411	12	represent	represent	VERB
ejpam-5662	411	13	the	the	DET
ejpam-5662	411	14	amplitudes	amplitude	NOUN
ejpam-5662	411	15	of	of	ADP
ejpam-5662	411	16	the	the	DET
ejpam-5662	411	17	equivalent	equivalent	ADJ
ejpam-5662	411	18	solutions	solution	NOUN
ejpam-5662	411	19	in	in	ADP
ejpam-5662	411	20	this	this	DET
ejpam-5662	411	21	case	case	NOUN
ejpam-5662	411	22	,	,	PUNCT
ejpam-5662	411	23	whereas	whereas	SCONJ
ejpam-5662	411	24	ω3	ω3	ADJ
ejpam-5662	411	25	and	and	CCONJ
ejpam-5662	411	26	ω4	ω4	NUM
ejpam-5662	411	27	are	be	AUX
ejpam-5662	411	28	the	the	DET
ejpam-5662	411	29	total	total	ADJ
ejpam-5662	411	30	frequencies	frequency	NOUN
ejpam-5662	411	31	to	to	PART
ejpam-5662	411	32	be	be	AUX
ejpam-5662	411	33	valued	value	VERB
ejpam-5662	411	34	later	later	ADV
ejpam-5662	411	35	.	.	PUNCT
ejpam-5662	412	1	moreover	moreover	ADV
ejpam-5662	412	2	,	,	PUNCT
ejpam-5662	412	3	the	the	DET
ejpam-5662	412	4	functions	function	NOUN
ejpam-5662	412	5	w	w	VERB
ejpam-5662	412	6	and	and	CCONJ
ejpam-5662	412	7	g	g	PROPN
ejpam-5662	412	8	satisfy	satisfy	VERB
ejpam-5662	412	9	the	the	DET
ejpam-5662	412	10	corresponding	corresponding	ADJ
ejpam-5662	412	11	system	system	NOUN
ejpam-5662	412	12	:	:	PUNCT
ejpam-5662	412	13	{	{	PUNCT
ejpam-5662	412	14	ẅ	ẅ	PUNCT
ejpam-5662	413	1	+	+	ADP
ejpam-5662	413	2	ϖ2	ϖ2	NOUN
ejpam-5662	413	3	3w	3w	NUM
ejpam-5662	413	4	=	=	SYM
ejpam-5662	413	5	0	0	NUM
ejpam-5662	413	6	g̈	g̈	X
ejpam-5662	414	1	+	+	PUNCT
ejpam-5662	414	2	ϖ2	ϖ2	NOUN
ejpam-5662	414	3	4	4	NUM
ejpam-5662	414	4	g	g	NOUN
ejpam-5662	414	5	=	=	SYM
ejpam-5662	414	6	0	0	NUM
ejpam-5662	414	7	.	.	PUNCT
ejpam-5662	415	1	(	(	PUNCT
ejpam-5662	415	2	45	45	NUM
ejpam-5662	415	3	)	)	PUNCT
ejpam-5662	415	4	one	one	NOUN
ejpam-5662	415	5	may	may	AUX
ejpam-5662	415	6	anticipate	anticipate	VERB
ejpam-5662	415	7	that	that	SCONJ
ejpam-5662	415	8	the	the	DET
ejpam-5662	415	9	solutions	solution	NOUN
ejpam-5662	415	10	’	'	PUNCT
ejpam-5662	415	11	behavior	behavior	NOUN
ejpam-5662	415	12	for	for	ADP
ejpam-5662	415	13	the	the	DET
ejpam-5662	415	14	system	system	NOUN
ejpam-5662	415	15	equations	equation	NOUN
ejpam-5662	415	16	(	(	PUNCT
ejpam-5662	415	17	39	39	NUM
ejpam-5662	415	18	)	)	PUNCT
ejpam-5662	415	19	and	and	CCONJ
ejpam-5662	415	20	(	(	PUNCT
ejpam-5662	415	21	40	40	NUM
ejpam-5662	415	22	)	)	PUNCT
ejpam-5662	415	23	will	will	AUX
ejpam-5662	415	24	exhibit	exhibit	VERB
ejpam-5662	415	25	an	an	DET
ejpam-5662	415	26	un	un	ADJ
ejpam-5662	415	27	-	-	ADJ
ejpam-5662	415	28	damping	damp	VERB
ejpam-5662	415	29	form	form	NOUN
ejpam-5662	415	30	across	across	ADP
ejpam-5662	415	31	the	the	DET
ejpam-5662	415	32	investigated	investigate	VERB
ejpam-5662	415	33	period	period	NOUN
ejpam-5662	415	34	of	of	ADP
ejpam-5662	415	35	time	time	NOUN
ejpam-5662	415	36	based	base	VERB
ejpam-5662	415	37	on	on	ADP
ejpam-5662	415	38	this	this	DET
ejpam-5662	415	39	system	system	NOUN
ejpam-5662	415	40	’s	’s	PART
ejpam-5662	415	41	examination	examination	NOUN
ejpam-5662	415	42	.	.	PUNCT
ejpam-5662	416	1	the	the	DET
ejpam-5662	416	2	elements	element	NOUN
ejpam-5662	416	3	ϖ3	ϖ3	NOUN
ejpam-5662	416	4	and	and	CCONJ
ejpam-5662	416	5	ϖ4	ϖ4	NOUN
ejpam-5662	416	6	are	be	AUX
ejpam-5662	416	7	identified	identify	VERB
ejpam-5662	416	8	by	by	ADP
ejpam-5662	416	9	equivalent	equivalent	ADJ
ejpam-5662	416	10	frequency	frequency	NOUN
ejpam-5662	416	11	coefficients	coefficient	NOUN
ejpam-5662	416	12	,	,	PUNCT
ejpam-5662	416	13	which	which	PRON
ejpam-5662	416	14	are	be	AUX
ejpam-5662	416	15	defined	define	VERB
ejpam-5662	416	16	as	as	SCONJ
ejpam-5662	416	17	follows	follow	VERB
ejpam-5662	416	18	:	:	PUNCT
ejpam-5662	416	19	ϖ2	ϖ2	NOUN
ejpam-5662	416	20	3	3	NUM
ejpam-5662	416	21	=	=	SYM
ejpam-5662	416	22	∫	∫	PROPN
ejpam-5662	416	23	2π	2π	NOUN
ejpam-5662	416	24	/	/	SYM
ejpam-5662	417	1	ω3	ω3	ADJ
ejpam-5662	417	2	0	0	PUNCT
ejpam-5662	418	1	w̃f1(w̃	w̃f1(w̃	NOUN
ejpam-5662	418	2	,	,	PUNCT
ejpam-5662	418	3	˙̃w	˙̃w	PROPN
ejpam-5662	418	4	,	,	PUNCT
ejpam-5662	418	5	¨̃w	¨̃w	PROPN
ejpam-5662	418	6	,	,	PUNCT
ejpam-5662	418	7	g̃	g̃	PROPN
ejpam-5662	418	8	,	,	PUNCT
ejpam-5662	418	9	˙̃g	˙̃g	PROPN
ejpam-5662	418	10	,	,	PUNCT
ejpam-5662	418	11	¨̃g	¨̃g	NOUN
ejpam-5662	418	12	)	)	PUNCT
ejpam-5662	418	13	dt/	dt/	VERB
ejpam-5662	418	14	∫	∫	PROPN
ejpam-5662	418	15	2π	2π	NOUN
ejpam-5662	418	16	/	/	SYM
ejpam-5662	418	17	ω3	ω3	ADJ
ejpam-5662	418	18	0	0	NUM
ejpam-5662	418	19	w̃2dt	w̃2dt	NOUN
ejpam-5662	418	20	=	=	PUNCT
ejpam-5662	418	21	b1	b1	NOUN
ejpam-5662	418	22	+	+	CCONJ
ejpam-5662	418	23	ω2	ω2	ADJ
ejpam-5662	418	24	1	1	NUM
ejpam-5662	418	25	+	+	NUM
ejpam-5662	418	26	b2	b2	NOUN
ejpam-5662	418	27	sin	sin	NOUN
ejpam-5662	418	28	(	(	PUNCT
ejpam-5662	418	29	2πωp	2πωp	NUM
ejpam-5662	418	30	ω3	ω3	NOUN
ejpam-5662	418	31	)	)	PUNCT
ejpam-5662	419	1	+	+	CCONJ
ejpam-5662	419	2	b3	b3	PROPN
ejpam-5662	419	3	sin	sin	NOUN
ejpam-5662	419	4	(	(	PUNCT
ejpam-5662	419	5	2π(ω4	2π(ω4	NUM
ejpam-5662	419	6	−	−	ADP
ejpam-5662	419	7	ωp	ωp	NOUN
ejpam-5662	419	8	)	)	PUNCT
ejpam-5662	419	9	ω3	ω3	NOUN
ejpam-5662	419	10	)	)	PUNCT
ejpam-5662	420	1	+	+	CCONJ
ejpam-5662	420	2	b4	b4	NOUN
ejpam-5662	420	3	sin	sin	NOUN
ejpam-5662	420	4	(	(	PUNCT
ejpam-5662	420	5	2π(ω4	2π(ω4	NUM
ejpam-5662	420	6	−	−	ADP
ejpam-5662	420	7	ωp	ωp	NOUN
ejpam-5662	420	8	)	)	PUNCT
ejpam-5662	420	9	ω3	ω3	PROPN
ejpam-5662	420	10	)	)	PUNCT
ejpam-5662	420	11	,	,	PUNCT
ejpam-5662	420	12	(	(	PUNCT
ejpam-5662	420	13	46	46	X
ejpam-5662	420	14	)	)	PUNCT
ejpam-5662	420	15	ϖ2	ϖ2	NOUN
ejpam-5662	420	16	4	4	NUM
ejpam-5662	420	17	=	=	SYM
ejpam-5662	420	18	∫	∫	PROPN
ejpam-5662	420	19	2π	2π	NOUN
ejpam-5662	420	20	/	/	SYM
ejpam-5662	420	21	ω4	ω4	NUM
ejpam-5662	420	22	0	0	NUM
ejpam-5662	421	1	g̃h1(w̃	g̃h1(w̃	NOUN
ejpam-5662	421	2	,	,	PUNCT
ejpam-5662	421	3	˙̃w	˙̃w	PROPN
ejpam-5662	421	4	,	,	PUNCT
ejpam-5662	421	5	¨̃w	¨̃w	PROPN
ejpam-5662	421	6	,	,	PUNCT
ejpam-5662	421	7	g̃	g̃	PROPN
ejpam-5662	421	8	,	,	PUNCT
ejpam-5662	421	9	˙̃g	˙̃g	PROPN
ejpam-5662	421	10	,	,	PUNCT
ejpam-5662	421	11	¨̃g	¨̃g	NOUN
ejpam-5662	421	12	)	)	PUNCT
ejpam-5662	421	13	dt/	dt/	VERB
ejpam-5662	421	14	∫	∫	PROPN
ejpam-5662	421	15	2π	2π	NOUN
ejpam-5662	421	16	/	/	SYM
ejpam-5662	421	17	ω4	ω4	NUM
ejpam-5662	421	18	0	0	NUM
ejpam-5662	421	19	g̃2dt	g̃2dt	NOUN
ejpam-5662	421	20	=	=	SYM
ejpam-5662	421	21	b5	b5	PROPN
ejpam-5662	421	22	+	+	CCONJ
ejpam-5662	421	23	ω2	ω2	ADJ
ejpam-5662	421	24	2	2	NUM
ejpam-5662	421	25	+	+	NOUN
ejpam-5662	421	26	b6	b6	NOUN
ejpam-5662	421	27	sin	sin	NOUN
ejpam-5662	421	28	(	(	PUNCT
ejpam-5662	421	29	2πωp	2πωp	NUM
ejpam-5662	421	30	ω4	ω4	NUM
ejpam-5662	421	31	)	)	PUNCT
ejpam-5662	422	1	+	+	CCONJ
ejpam-5662	422	2	b7	b7	PROPN
ejpam-5662	422	3	sin	sin	NOUN
ejpam-5662	422	4	(	(	PUNCT
ejpam-5662	422	5	2π(ω3	2π(ω3	NUM
ejpam-5662	422	6	−	−	PROPN
ejpam-5662	422	7	ωp	ωp	NOUN
ejpam-5662	422	8	)	)	PUNCT
ejpam-5662	422	9	ω4	ω4	NOUN
ejpam-5662	422	10	)	)	PUNCT
ejpam-5662	423	1	+	+	CCONJ
ejpam-5662	423	2	b8	b8	PROPN
ejpam-5662	423	3	sin	sin	NOUN
ejpam-5662	423	4	(	(	PUNCT
ejpam-5662	423	5	2π(ω3	2π(ω3	NUM
ejpam-5662	423	6	−	−	PROPN
ejpam-5662	423	7	ωp	ωp	NOUN
ejpam-5662	423	8	)	)	PUNCT
ejpam-5662	423	9	ω4	ω4	NUM
ejpam-5662	423	10	)	)	PUNCT
ejpam-5662	423	11	,	,	PUNCT
ejpam-5662	423	12	(	(	PUNCT
ejpam-5662	423	13	47	47	NUM
ejpam-5662	423	14	)	)	PUNCT
ejpam-5662	423	15	where	where	SCONJ
ejpam-5662	423	16	the	the	DET
ejpam-5662	423	17	coefficients	coefficient	NOUN
ejpam-5662	423	18	b1	b1	PROPN
ejpam-5662	423	19	→	→	SYM
ejpam-5662	423	20	b8	b8	PROPN
ejpam-5662	423	21	are	be	AUX
ejpam-5662	423	22	defined	define	VERB
ejpam-5662	423	23	through	through	ADP
ejpam-5662	423	24	the	the	DET
ejpam-5662	423	25	appendix	appendix	NOUN
ejpam-5662	423	26	.	.	PUNCT
ejpam-5662	424	1	it	it	PRON
ejpam-5662	424	2	should	should	AUX
ejpam-5662	424	3	be	be	AUX
ejpam-5662	424	4	noted	note	VERB
ejpam-5662	424	5	that	that	SCONJ
ejpam-5662	424	6	the	the	DET
ejpam-5662	424	7	equivalent	equivalent	ADJ
ejpam-5662	424	8	frequencies	frequency	NOUN
ejpam-5662	424	9	ϖ3	ϖ3	NOUN
ejpam-5662	424	10	,	,	PUNCT
ejpam-5662	424	11	and	and	CCONJ
ejpam-5662	424	12	ϖ4	ϖ4	NOUN
ejpam-5662	424	13	are	be	AUX
ejpam-5662	424	14	expected	expect	VERB
ejpam-5662	424	15	to	to	PART
ejpam-5662	424	16	be	be	AUX
ejpam-5662	424	17	equal	equal	ADJ
ejpam-5662	424	18	to	to	ADP
ejpam-5662	424	19	the	the	DET
ejpam-5662	424	20	total	total	ADJ
ejpam-5662	424	21	frequencies	frequency	NOUN
ejpam-5662	424	22	ω3	ω3	VERB
ejpam-5662	424	23	,	,	PUNCT
ejpam-5662	424	24	and	and	CCONJ
ejpam-5662	424	25	ω4	ω4	NOUN
ejpam-5662	424	26	here	here	ADV
ejpam-5662	424	27	due	due	ADP
ejpam-5662	424	28	to	to	ADP
ejpam-5662	424	29	the	the	DET
ejpam-5662	424	30	absence	absence	NOUN
ejpam-5662	424	31	of	of	ADP
ejpam-5662	424	32	the	the	DET
ejpam-5662	424	33	damping	damp	VERB
ejpam-5662	424	34	coefficients	coefficient	NOUN
ejpam-5662	424	35	.	.	PUNCT
ejpam-5662	425	1	in	in	ADP
ejpam-5662	425	2	this	this	DET
ejpam-5662	425	3	case	case	NOUN
ejpam-5662	425	4	,	,	PUNCT
ejpam-5662	425	5	there	there	PRON
ejpam-5662	425	6	is	be	VERB
ejpam-5662	425	7	no	no	DET
ejpam-5662	425	8	need	need	NOUN
ejpam-5662	425	9	to	to	PART
ejpam-5662	425	10	utilize	utilize	VERB
ejpam-5662	425	11	the	the	DET
ejpam-5662	425	12	standard	standard	ADJ
ejpam-5662	425	13	normalized	normalize	VERB
ejpam-5662	425	14	technique	technique	NOUN
ejpam-5662	425	15	and	and	CCONJ
ejpam-5662	425	16	the	the	DET
ejpam-5662	425	17	two	two	NUM
ejpam-5662	425	18	equations	equation	NOUN
ejpam-5662	425	19	(	(	PUNCT
ejpam-5662	425	20	45	45	NUM
ejpam-5662	425	21	)	)	PUNCT
ejpam-5662	425	22	will	will	AUX
ejpam-5662	425	23	be	be	AUX
ejpam-5662	425	24	scrutinized	scrutinize	VERB
ejpam-5662	425	25	directly	directly	ADV
ejpam-5662	425	26	.	.	PUNCT
ejpam-5662	426	1	the	the	DET
ejpam-5662	426	2	objective	objective	NOUN
ejpam-5662	426	3	of	of	ADP
ejpam-5662	426	4	the	the	DET
ejpam-5662	426	5	current	current	ADJ
ejpam-5662	426	6	case	case	NOUN
ejpam-5662	426	7	is	be	AUX
ejpam-5662	426	8	to	to	PART
ejpam-5662	426	9	follow	follow	VERB
ejpam-5662	426	10	the	the	DET
ejpam-5662	426	11	above	above	ADJ
ejpam-5662	426	12	procedures	procedure	NOUN
ejpam-5662	426	13	to	to	PART
ejpam-5662	426	14	study	study	VERB
ejpam-5662	426	15	other	other	ADJ
ejpam-5662	426	16	linear	linear	PROPN
ejpam-5662	426	17	odes	ode	NOUN
ejpam-5662	426	18	instead	instead	ADV
ejpam-5662	426	19	of	of	ADP
ejpam-5662	426	20	the	the	DET
ejpam-5662	426	21	non	non	ADJ
ejpam-5662	426	22	-	-	ADJ
ejpam-5662	426	23	linear	linear	ADJ
ejpam-5662	426	24	odes	ode	NOUN
ejpam-5662	426	25	described	describe	VERB
ejpam-5662	426	26	by	by	ADP
ejpam-5662	426	27	eqs	eqs	PROPN
ejpam-5662	426	28	.	.	PUNCT
ejpam-5662	427	1	(	(	PUNCT
ejpam-5662	427	2	39	39	NUM
ejpam-5662	427	3	)	)	PUNCT
ejpam-5662	427	4	and	and	CCONJ
ejpam-5662	427	5	(	(	PUNCT
ejpam-5662	427	6	40	40	NUM
ejpam-5662	427	7	)	)	PUNCT
ejpam-5662	427	8	.	.	PUNCT
ejpam-5662	428	1	this	this	DET
ejpam-5662	428	2	equivalent	equivalent	ADJ
ejpam-5662	428	3	a.	a.	NOUN
ejpam-5662	428	4	alanazy	alanazy	NOUN
ejpam-5662	428	5	,	,	PUNCT
ejpam-5662	428	6	g.	g.	PROPN
ejpam-5662	428	7	m.	m.	PROPN
ejpam-5662	428	8	moatimid	moatimid	PROPN
ejpam-5662	428	9	,	,	PUNCT
ejpam-5662	428	10	m.	m.	PROPN
ejpam-5662	428	11	a.	a.	PROPN
ejpam-5662	428	12	a.	a.	PROPN
ejpam-5662	428	13	mohamed	mohamed	PROPN
ejpam-5662	428	14	/	/	SYM
ejpam-5662	428	15	eur	eur	PROPN
ejpam-5662	428	16	.	.	PUNCT
ejpam-5662	429	1	j.	j.	PROPN
ejpam-5662	429	2	pure	pure	PROPN
ejpam-5662	429	3	appl	appl	PROPN
ejpam-5662	429	4	.	.	PROPN
ejpam-5662	429	5	math	math	PROPN
ejpam-5662	429	6	,	,	PUNCT
ejpam-5662	429	7	18	18	NUM
ejpam-5662	429	8	(	(	PUNCT
ejpam-5662	429	9	2	2	NUM
ejpam-5662	429	10	)	)	PUNCT
ejpam-5662	429	11	(	(	PUNCT
ejpam-5662	429	12	2025	2025	NUM
ejpam-5662	429	13	)	)	PUNCT
ejpam-5662	429	14	,	,	PUNCT
ejpam-5662	429	15	5662	5662	NUM
ejpam-5662	429	16	23	23	NUM
ejpam-5662	429	17	of	of	ADP
ejpam-5662	429	18	36	36	NUM
ejpam-5662	429	19	system	system	NOUN
ejpam-5662	429	20	as	as	SCONJ
ejpam-5662	429	21	defined	define	VERB
ejpam-5662	429	22	by	by	ADP
ejpam-5662	429	23	(	(	PUNCT
ejpam-5662	429	24	45	45	NUM
ejpam-5662	429	25	)	)	PUNCT
ejpam-5662	429	26	is	be	AUX
ejpam-5662	429	27	investigating	investigate	VERB
ejpam-5662	429	28	utilizing	utilize	VERB
ejpam-5662	429	29	the	the	DET
ejpam-5662	429	30	forms	form	NOUN
ejpam-5662	429	31	(	(	PUNCT
ejpam-5662	429	32	46	46	NUM
ejpam-5662	429	33	)	)	PUNCT
ejpam-5662	429	34	and	and	CCONJ
ejpam-5662	429	35	(	(	PUNCT
ejpam-5662	429	36	47	47	NUM
ejpam-5662	429	37	)	)	PUNCT
ejpam-5662	429	38	and	and	CCONJ
ejpam-5662	429	39	the	the	DET
ejpam-5662	429	40	following	follow	VERB
ejpam-5662	429	41	figs	fig	NOUN
ejpam-5662	429	42	and	and	CCONJ
ejpam-5662	429	43	tables	table	NOUN
ejpam-5662	429	44	validate	validate	VERB
ejpam-5662	429	45	the	the	DET
ejpam-5662	429	46	extreme	extreme	ADJ
ejpam-5662	429	47	matching	matching	NOUN
ejpam-5662	429	48	between	between	ADP
ejpam-5662	429	49	the	the	DET
ejpam-5662	429	50	two	two	NUM
ejpam-5662	429	51	solutions	solution	NOUN
ejpam-5662	429	52	,	,	PUNCT
ejpam-5662	429	53	approving	approve	VERB
ejpam-5662	429	54	the	the	DET
ejpam-5662	429	55	methodology	methodology	NOUN
ejpam-5662	429	56	’s	’s	PART
ejpam-5662	429	57	correctness	correctness	NOUN
ejpam-5662	429	58	and	and	CCONJ
ejpam-5662	429	59	awareness	awareness	NOUN
ejpam-5662	429	60	.	.	PUNCT
ejpam-5662	430	1	given	give	VERB
ejpam-5662	430	2	the	the	DET
ejpam-5662	430	3	aforementioned	aforementioned	ADJ
ejpam-5662	430	4	values	value	NOUN
ejpam-5662	430	5	of	of	ADP
ejpam-5662	430	6	the	the	DET
ejpam-5662	430	7	system	system	NOUN
ejpam-5662	430	8	coefficients	coefficient	NOUN
ejpam-5662	430	9	,	,	PUNCT
ejpam-5662	430	10	the	the	DET
ejpam-5662	430	11	numerical	numerical	ADJ
ejpam-5662	430	12	solutions	solution	NOUN
ejpam-5662	430	13	of	of	ADP
ejpam-5662	430	14	these	these	DET
ejpam-5662	430	15	two	two	NUM
ejpam-5662	430	16	systems	system	NOUN
ejpam-5662	430	17	are	be	AUX
ejpam-5662	430	18	compared	compare	VERB
ejpam-5662	430	19	using	use	VERB
ejpam-5662	430	20	the	the	DET
ejpam-5662	430	21	(	(	PUNCT
ejpam-5662	430	22	ndsolve	ndsolve	NOUN
ejpam-5662	430	23	)	)	PUNCT
ejpam-5662	430	24	command	command	NOUN
ejpam-5662	430	25	in	in	ADP
ejpam-5662	430	26	combination	combination	NOUN
ejpam-5662	430	27	with	with	ADP
ejpam-5662	430	28	the	the	DET
ejpam-5662	430	29	ms	ms	PROPN
ejpam-5662	430	30	.	.	PROPN
ejpam-5662	430	31	figs	figs	PROPN
ejpam-5662	430	32	.	.	PUNCT
ejpam-5662	431	1	17	17	NUM
ejpam-5662	431	2	and	and	CCONJ
ejpam-5662	431	3	18	18	NUM
ejpam-5662	431	4	and	and	CCONJ
ejpam-5662	431	5	tables	table	NOUN
ejpam-5662	431	6	3	3	NUM
ejpam-5662	431	7	and	and	CCONJ
ejpam-5662	431	8	4	4	NUM
ejpam-5662	431	9	are	be	AUX
ejpam-5662	431	10	designed	design	VERB
ejpam-5662	431	11	to	to	PART
ejpam-5662	431	12	achieve	achieve	VERB
ejpam-5662	431	13	this	this	DET
ejpam-5662	431	14	convergence	convergence	NOUN
ejpam-5662	431	15	.	.	PUNCT
ejpam-5662	432	1	as	as	SCONJ
ejpam-5662	432	2	can	can	AUX
ejpam-5662	432	3	be	be	AUX
ejpam-5662	432	4	noticed	notice	VERB
ejpam-5662	432	5	through	through	ADP
ejpam-5662	432	6	these	these	DET
ejpam-5662	432	7	figs	fig	NOUN
ejpam-5662	432	8	.	.	PUNCT
ejpam-5662	433	1	and	and	CCONJ
ejpam-5662	433	2	tables	table	NOUN
ejpam-5662	433	3	,	,	PUNCT
ejpam-5662	433	4	there	there	PRON
ejpam-5662	433	5	is	be	VERB
ejpam-5662	433	6	a	a	DET
ejpam-5662	433	7	noteworthy	noteworthy	ADJ
ejpam-5662	433	8	conjunction	conjunction	NOUN
ejpam-5662	433	9	between	between	ADP
ejpam-5662	433	10	the	the	DET
ejpam-5662	433	11	numerical	numerical	ADJ
ejpam-5662	433	12	solutions	solution	NOUN
ejpam-5662	433	13	of	of	ADP
ejpam-5662	433	14	the	the	DET
ejpam-5662	433	15	original	original	ADJ
ejpam-5662	433	16	and	and	CCONJ
ejpam-5662	433	17	equivalent	equivalent	ADJ
ejpam-5662	433	18	systems	system	NOUN
ejpam-5662	433	19	.	.	PUNCT
ejpam-5662	434	1	as	as	SCONJ
ejpam-5662	434	2	estimated	estimate	VERB
ejpam-5662	434	3	by	by	ADP
ejpam-5662	434	4	the	the	DET
ejpam-5662	434	5	ms	ms	PROPN
ejpam-5662	434	6	,	,	PUNCT
ejpam-5662	434	7	the	the	DET
ejpam-5662	434	8	assessed	assessed	ADJ
ejpam-5662	434	9	absolute	absolute	ADJ
ejpam-5662	434	10	error	error	NOUN
ejpam-5662	434	11	equals	equal	VERB
ejpam-5662	434	12	0.0108	0.0108	NUM
ejpam-5662	434	13	for	for	ADP
ejpam-5662	434	14	x	x	NOUN
ejpam-5662	434	15	distribution	distribution	NOUN
ejpam-5662	434	16	and	and	CCONJ
ejpam-5662	434	17	0.0135	0.0135	NUM
ejpam-5662	434	18	for	for	ADP
ejpam-5662	434	19	y	y	NOUN
ejpam-5662	434	20	distribution	distribution	NOUN
ejpam-5662	434	21	in	in	ADP
ejpam-5662	434	22	view	view	NOUN
ejpam-5662	434	23	of	of	ADP
ejpam-5662	434	24	the	the	DET
ejpam-5662	434	25	following	follow	VERB
ejpam-5662	434	26	data	data	PROPN
ejpam-5662	434	27	:	:	PUNCT
ejpam-5662	434	28	ω1	ω1	PROPN
ejpam-5662	434	29	=	=	SYM
ejpam-5662	434	30	2	2	NUM
ejpam-5662	434	31	,	,	PUNCT
ejpam-5662	434	32	ω2	ω2	NOUN
ejpam-5662	434	33	=	=	SYM
ejpam-5662	434	34	1.5	1.5	NUM
ejpam-5662	434	35	,	,	PUNCT
ejpam-5662	434	36	γ1	γ1	NOUN
ejpam-5662	434	37	=	=	NOUN
ejpam-5662	434	38	0.3	0.3	NUM
ejpam-5662	434	39	,	,	PUNCT
ejpam-5662	434	40	γ2	γ2	PROPN
ejpam-5662	434	41	=	=	NUM
ejpam-5662	434	42	0.3	0.3	NUM
ejpam-5662	434	43	,	,	PUNCT
ejpam-5662	434	44	η11	η11	NOUN
ejpam-5662	434	45	=	=	SYM
ejpam-5662	434	46	0.1	0.1	NUM
ejpam-5662	434	47	,	,	PUNCT
ejpam-5662	434	48	η12	η12	VERB
ejpam-5662	434	49	=	=	NOUN
ejpam-5662	434	50	0.2	0.2	NUM
ejpam-5662	434	51	,	,	PUNCT
ejpam-5662	434	52	η21	η21	NOUN
ejpam-5662	434	53	=	=	SYM
ejpam-5662	434	54	0.1	0.1	NUM
ejpam-5662	434	55	,	,	PUNCT
ejpam-5662	434	56	η22	η22	PROPN
ejpam-5662	434	57	=	=	SYM
ejpam-5662	434	58	0.2,ωp	0.2,ωp	NUM
ejpam-5662	434	59	=	=	SYM
ejpam-5662	434	60	0.5	0.5	NUM
ejpam-5662	434	61	,	,	PUNCT
ejpam-5662	434	62	λ1	λ1	PROPN
ejpam-5662	434	63	=	=	SYM
ejpam-5662	434	64	0.2	0.2	NUM
ejpam-5662	434	65	,	,	PUNCT
ejpam-5662	434	66	λ12	λ12	ADJ
ejpam-5662	434	67	=	=	NUM
ejpam-5662	434	68	0.3	0.3	NUM
ejpam-5662	434	69	,	,	PUNCT
ejpam-5662	434	70	a	a	DET
ejpam-5662	434	71	=	=	NOUN
ejpam-5662	434	72	0.05	0.05	NUM
ejpam-5662	434	73	and	and	CCONJ
ejpam-5662	434	74	b	b	NOUN
ejpam-5662	434	75	=	=	SYM
ejpam-5662	434	76	0.05	0.05	NUM
ejpam-5662	434	77	.	.	PUNCT
ejpam-5662	434	78	figure	figure	NOUN
ejpam-5662	434	79	17	17	NUM
ejpam-5662	434	80	:	:	PUNCT
ejpam-5662	434	81	demonstrates	demonstrate	VERB
ejpam-5662	434	82	the	the	DET
ejpam-5662	434	83	matching	matching	NOUN
ejpam-5662	434	84	between	between	ADP
ejpam-5662	434	85	the	the	DET
ejpam-5662	434	86	solutions	solution	NOUN
ejpam-5662	434	87	of	of	ADP
ejpam-5662	434	88	the	the	DET
ejpam-5662	434	89	nonlinear	nonlinear	ADJ
ejpam-5662	434	90	dynamical	dynamical	ADJ
ejpam-5662	434	91	system	system	NOUN
ejpam-5662	434	92	as	as	SCONJ
ejpam-5662	434	93	given	give	VERB
ejpam-5662	434	94	in	in	ADP
ejpam-5662	434	95	eqs	eqs	PROPN
ejpam-5662	434	96	.	.	PUNCT
ejpam-5662	435	1	(	(	PUNCT
ejpam-5662	435	2	39	39	NUM
ejpam-5662	435	3	)	)	PUNCT
ejpam-5662	435	4	and	and	CCONJ
ejpam-5662	435	5	(	(	PUNCT
ejpam-5662	435	6	40	40	NUM
ejpam-5662	435	7	)	)	PUNCT
ejpam-5662	435	8	and	and	CCONJ
ejpam-5662	435	9	those	those	PRON
ejpam-5662	435	10	of	of	ADP
ejpam-5662	435	11	the	the	DET
ejpam-5662	435	12	npa	npa	NOUN
ejpam-5662	435	13	system	system	NOUN
ejpam-5662	435	14	(	(	PUNCT
ejpam-5662	435	15	45	45	NUM
ejpam-5662	435	16	)	)	PUNCT
ejpam-5662	435	17	for	for	ADP
ejpam-5662	435	18	the	the	DET
ejpam-5662	435	19	un	un	PROPN
ejpam-5662	435	20	-	-	ADJ
ejpam-5662	435	21	damped	damped	ADJ
ejpam-5662	435	22	x	x	NOUN
ejpam-5662	435	23	oscillator	oscillator	NOUN
ejpam-5662	435	24	.	.	PUNCT
ejpam-5662	436	1	a.	a.	PROPN
ejpam-5662	436	2	alanazy	alanazy	PROPN
ejpam-5662	436	3	,	,	PUNCT
ejpam-5662	436	4	g.	g.	PROPN
ejpam-5662	436	5	m.	m.	PROPN
ejpam-5662	436	6	moatimid	moatimid	PROPN
ejpam-5662	436	7	,	,	PUNCT
ejpam-5662	436	8	m.	m.	PROPN
ejpam-5662	436	9	a.	a.	PROPN
ejpam-5662	436	10	a.	a.	PROPN
ejpam-5662	436	11	mohamed	mohamed	PROPN
ejpam-5662	436	12	/	/	SYM
ejpam-5662	436	13	eur	eur	PROPN
ejpam-5662	436	14	.	.	PUNCT
ejpam-5662	437	1	j.	j.	PROPN
ejpam-5662	437	2	pure	pure	PROPN
ejpam-5662	437	3	appl	appl	PROPN
ejpam-5662	437	4	.	.	PROPN
ejpam-5662	437	5	math	math	PROPN
ejpam-5662	437	6	,	,	PUNCT
ejpam-5662	437	7	18	18	NUM
ejpam-5662	437	8	(	(	PUNCT
ejpam-5662	437	9	2	2	NUM
ejpam-5662	437	10	)	)	PUNCT
ejpam-5662	437	11	(	(	PUNCT
ejpam-5662	437	12	2025	2025	NUM
ejpam-5662	437	13	)	)	PUNCT
ejpam-5662	437	14	,	,	PUNCT
ejpam-5662	437	15	5662	5662	NUM
ejpam-5662	437	16	24	24	NUM
ejpam-5662	437	17	of	of	ADP
ejpam-5662	437	18	36	36	NUM
ejpam-5662	437	19	table	table	NOUN
ejpam-5662	437	20	3	3	NUM
ejpam-5662	437	21	:	:	PUNCT
ejpam-5662	437	22	validates	validate	VERB
ejpam-5662	437	23	the	the	DET
ejpam-5662	437	24	convergence	convergence	NOUN
ejpam-5662	437	25	of	of	ADP
ejpam-5662	437	26	the	the	DET
ejpam-5662	437	27	original	original	ADJ
ejpam-5662	437	28	and	and	CCONJ
ejpam-5662	437	29	npa	npa	NOUN
ejpam-5662	437	30	solutions	solution	NOUN
ejpam-5662	437	31	for	for	ADP
ejpam-5662	437	32	the	the	DET
ejpam-5662	437	33	un	un	PROPN
ejpam-5662	437	34	-	-	ADJ
ejpam-5662	437	35	damped	damped	ADJ
ejpam-5662	437	36	x	x	NOUN
ejpam-5662	437	37	oscillator	oscillator	NOUN
ejpam-5662	437	38	.	.	PUNCT
ejpam-5662	438	1	t	t	PROPN
ejpam-5662	438	2	real	real	ADJ
ejpam-5662	438	3	oscillator	oscillator	NOUN
ejpam-5662	438	4	approximate	approximate	ADJ
ejpam-5662	438	5	oscillator	oscillator	NOUN
ejpam-5662	438	6	absolute	absolute	ADJ
ejpam-5662	438	7	error	error	NOUN
ejpam-5662	438	8	0	0	NUM
ejpam-5662	438	9	0.05	0.05	NUM
ejpam-5662	438	10	0.05	0.05	NUM
ejpam-5662	438	11	0	0	NUM
ejpam-5662	438	12	.	.	NOUN
ejpam-5662	438	13	5	5	NUM
ejpam-5662	438	14	-0.0436541	-0.0436541	NOUN
ejpam-5662	438	15	-0.0425569	-0.0425569	PROPN
ejpam-5662	438	16	0.00109724	0.00109724	NUM
ejpam-5662	438	17	10	10	NUM
ejpam-5662	438	18	0.0188486	0.0188486	NUM
ejpam-5662	438	19	0.0224435	0.0224435	NUM
ejpam-5662	438	20	0.00359486	0.00359486	NUM
ejpam-5662	438	21	15	15	NUM
ejpam-5662	438	22	0.00600942	0.00600942	NUM
ejpam-5662	438	23	0.00435191	0.00435191	NUM
ejpam-5662	438	24	0.00165751	0.00165751	NUM
ejpam-5662	438	25	20	20	NUM
ejpam-5662	438	26	-0.0347072	-0.0347072	NOUN
ejpam-5662	438	27	-0.0298516	-0.0298516	VERB
ejpam-5662	438	28	0.0048556	0.0048556	NUM
ejpam-5662	438	29	25	25	NUM
ejpam-5662	439	1	0.0479366	0.0479366	NUM
ejpam-5662	439	2	0.0464638	0.0464638	NUM
ejpam-5662	439	3	0.00147285	0.00147285	NUM
ejpam-5662	439	4	30	30	NUM
ejpam-5662	439	5	-0.0492413	-0.0492413	NOUN
ejpam-5662	439	6	-0.0492425	-0.0492425	NOUN
ejpam-5662	439	7	1.22066	1.22066	NUM
ejpam-5662	439	8	∗	∗	NOUN
ejpam-5662	439	9	10−6	10−6	NUM
ejpam-5662	439	10	35	35	NUM
ejpam-5662	439	11	0.030144	0.030144	NUM
ejpam-5662	439	12	0.0373605	0.0373605	NUM
ejpam-5662	439	13	0.00721643	0.00721643	NUM
ejpam-5662	439	14	40	40	NUM
ejpam-5662	439	15	-0.00746833	-0.00746833	NOUN
ejpam-5662	439	16	-0.0143553	-0.0143553	NOUN
ejpam-5662	439	17	0.00688697	0.00688697	NUM
ejpam-5662	439	18	45	45	NUM
ejpam-5662	439	19	-0.0230729	-0.0230729	ADJ
ejpam-5662	439	20	-0.0129238	-0.0129238	NOUN
ejpam-5662	439	21	0.010149	0.010149	NUM
ejpam-5662	439	22	50	50	NUM
ejpam-5662	439	23	0.0419213	0.0419213	NUM
ejpam-5662	439	24	0.0363552	0.0363552	NUM
ejpam-5662	439	25	0.00556605	0.00556605	NUM
ejpam-5662	439	26	figure	figure	NOUN
ejpam-5662	439	27	18	18	NUM
ejpam-5662	439	28	:	:	PUNCT
ejpam-5662	439	29	demonstrates	demonstrate	VERB
ejpam-5662	439	30	the	the	DET
ejpam-5662	439	31	matching	matching	NOUN
ejpam-5662	439	32	between	between	ADP
ejpam-5662	439	33	the	the	DET
ejpam-5662	439	34	solutions	solution	NOUN
ejpam-5662	439	35	of	of	ADP
ejpam-5662	439	36	the	the	DET
ejpam-5662	439	37	nonlinear	nonlinear	ADJ
ejpam-5662	439	38	dynamical	dynamical	ADJ
ejpam-5662	439	39	system	system	NOUN
ejpam-5662	439	40	as	as	SCONJ
ejpam-5662	439	41	given	give	VERB
ejpam-5662	439	42	in	in	ADP
ejpam-5662	439	43	eqs	eqs	PROPN
ejpam-5662	439	44	.	.	PUNCT
ejpam-5662	440	1	(	(	PUNCT
ejpam-5662	440	2	39	39	NUM
ejpam-5662	440	3	)	)	PUNCT
ejpam-5662	440	4	and	and	CCONJ
ejpam-5662	440	5	(	(	PUNCT
ejpam-5662	440	6	40	40	NUM
ejpam-5662	440	7	)	)	PUNCT
ejpam-5662	440	8	and	and	CCONJ
ejpam-5662	440	9	those	those	PRON
ejpam-5662	440	10	of	of	ADP
ejpam-5662	440	11	the	the	DET
ejpam-5662	440	12	npa	npa	NOUN
ejpam-5662	440	13	system	system	NOUN
ejpam-5662	440	14	(	(	PUNCT
ejpam-5662	440	15	45	45	NUM
ejpam-5662	440	16	)	)	PUNCT
ejpam-5662	440	17	for	for	ADP
ejpam-5662	440	18	the	the	DET
ejpam-5662	440	19	un	un	PROPN
ejpam-5662	440	20	-	-	ADJ
ejpam-5662	440	21	damped	damped	ADJ
ejpam-5662	440	22	y	y	PROPN
ejpam-5662	440	23	oscillator	oscillator	NOUN
ejpam-5662	440	24	.	.	PUNCT
ejpam-5662	441	1	table	table	NOUN
ejpam-5662	441	2	4	4	NUM
ejpam-5662	441	3	:	:	PUNCT
ejpam-5662	441	4	validates	validate	VERB
ejpam-5662	441	5	the	the	DET
ejpam-5662	441	6	convergence	convergence	NOUN
ejpam-5662	441	7	of	of	ADP
ejpam-5662	441	8	the	the	DET
ejpam-5662	441	9	original	original	ADJ
ejpam-5662	441	10	and	and	CCONJ
ejpam-5662	441	11	npa	npa	NOUN
ejpam-5662	441	12	solutions	solution	NOUN
ejpam-5662	441	13	for	for	ADP
ejpam-5662	441	14	the	the	DET
ejpam-5662	441	15	un	un	PROPN
ejpam-5662	441	16	-	-	ADJ
ejpam-5662	441	17	damped	damped	ADJ
ejpam-5662	441	18	y	y	PROPN
ejpam-5662	441	19	oscillator	oscillator	NOUN
ejpam-5662	441	20	.	.	PUNCT
ejpam-5662	442	1	t	t	PROPN
ejpam-5662	442	2	real	real	ADJ
ejpam-5662	442	3	oscillator	oscillator	NOUN
ejpam-5662	442	4	approximate	approximate	ADJ
ejpam-5662	442	5	oscillator	oscillator	NOUN
ejpam-5662	442	6	absolute	absolute	ADJ
ejpam-5662	442	7	error	error	NOUN
ejpam-5662	442	8	0	0	NUM
ejpam-5662	442	9	0.05	0.05	NUM
ejpam-5662	442	10	0.05	0.05	NUM
ejpam-5662	442	11	0	0	NUM
ejpam-5662	442	12	.	.	PUNCT
ejpam-5662	442	13	5	5	NUM
ejpam-5662	442	14	0.0171072	0.0171072	NUM
ejpam-5662	442	15	0.0171218	0.0171218	NUM
ejpam-5662	442	16	0.0000145838	0.0000145838	NUM
ejpam-5662	442	17	10	10	NUM
ejpam-5662	442	18	-0.0418844	-0.0418844	NOUN
ejpam-5662	442	19	-0.0382738	-0.0382738	NOUN
ejpam-5662	442	20	0.00361066	0.00361066	NUM
ejpam-5662	442	21	15	15	NUM
ejpam-5662	442	22	-0.0495195	-0.0495195	NOUN
ejpam-5662	442	23	-0.0433344	-0.0433344	NOUN
ejpam-5662	442	24	0.00618507	0.00618507	NUM
ejpam-5662	443	1	20	20	NUM
ejpam-5662	443	2	0.00346055	0.00346055	NUM
ejpam-5662	443	3	0.00859528	0.00859528	NUM
ejpam-5662	443	4	0.00513473	0.00513473	NUM
ejpam-5662	443	5	25	25	NUM
ejpam-5662	443	6	0.0481834	0.0481834	NUM
ejpam-5662	443	7	0.0492211	0.0492211	NUM
ejpam-5662	443	8	0.00103769	0.00103769	NUM
ejpam-5662	443	9	30	30	NUM
ejpam-5662	443	10	0.0296473	0.0296473	NUM
ejpam-5662	443	11	0.0251148	0.0251148	NUM
ejpam-5662	443	12	0.00453244	0.00453244	NUM
ejpam-5662	443	13	35	35	NUM
ejpam-5662	443	14	-0.0316531	-0.0316531	NOUN
ejpam-5662	443	15	-0.0320206	-0.0320206	NOUN
ejpam-5662	443	16	0.000367506	0.000367506	NUM
ejpam-5662	443	17	40	40	NUM
ejpam-5662	443	18	-0.0541948	-0.0541948	NOUN
ejpam-5662	443	19	-0.0470448	-0.0470448	X
ejpam-5662	443	20	0.00714994	0.00714994	NUM
ejpam-5662	443	21	45	45	NUM
ejpam-5662	443	22	-0.0105252	-0.0105252	NOUN
ejpam-5662	443	23	-0.00019903	-0.00019903	NOUN
ejpam-5662	444	1	0.0103262	0.0103262	NUM
ejpam-5662	444	2	50	50	NUM
ejpam-5662	444	3	0.0428419	0.0428419	NUM
ejpam-5662	444	4	0.0469085	0.0469085	NUM
ejpam-5662	444	5	0.00406667	0.00406667	NUM
ejpam-5662	444	6	a.	a.	NOUN
ejpam-5662	444	7	alanazy	alanazy	NOUN
ejpam-5662	444	8	,	,	PUNCT
ejpam-5662	444	9	g.	g.	PROPN
ejpam-5662	444	10	m.	m.	PROPN
ejpam-5662	444	11	moatimid	moatimid	PROPN
ejpam-5662	444	12	,	,	PUNCT
ejpam-5662	444	13	m.	m.	PROPN
ejpam-5662	444	14	a.	a.	PROPN
ejpam-5662	444	15	a.	a.	PROPN
ejpam-5662	444	16	mohamed	mohamed	PROPN
ejpam-5662	444	17	/	/	SYM
ejpam-5662	444	18	eur	eur	PROPN
ejpam-5662	444	19	.	.	PUNCT
ejpam-5662	445	1	j.	j.	PROPN
ejpam-5662	445	2	pure	pure	PROPN
ejpam-5662	445	3	appl	appl	PROPN
ejpam-5662	445	4	.	.	PROPN
ejpam-5662	445	5	math	math	PROPN
ejpam-5662	445	6	,	,	PUNCT
ejpam-5662	445	7	18	18	NUM
ejpam-5662	445	8	(	(	PUNCT
ejpam-5662	445	9	2	2	NUM
ejpam-5662	445	10	)	)	PUNCT
ejpam-5662	445	11	(	(	PUNCT
ejpam-5662	445	12	2025	2025	NUM
ejpam-5662	445	13	)	)	PUNCT
ejpam-5662	445	14	,	,	PUNCT
ejpam-5662	445	15	5662	5662	NUM
ejpam-5662	445	16	25	25	NUM
ejpam-5662	445	17	of	of	ADP
ejpam-5662	445	18	36	36	NUM
ejpam-5662	445	19	the	the	DET
ejpam-5662	445	20	solutions	solution	NOUN
ejpam-5662	445	21	of	of	ADP
ejpam-5662	445	22	the	the	DET
ejpam-5662	445	23	un	un	ADJ
ejpam-5662	445	24	-	-	ADJ
ejpam-5662	445	25	damped	damped	ADJ
ejpam-5662	445	26	oscillators	oscillator	NOUN
ejpam-5662	445	27	’	'	PUNCT
ejpam-5662	445	28	eqs	eqs	X
ejpam-5662	445	29	.	.	PUNCT
ejpam-5662	445	30	(	(	PUNCT
ejpam-5662	445	31	39	39	NUM
ejpam-5662	445	32	)	)	PUNCT
ejpam-5662	445	33	and	and	CCONJ
ejpam-5662	445	34	(	(	PUNCT
ejpam-5662	445	35	40	40	NUM
ejpam-5662	445	36	)	)	PUNCT
ejpam-5662	445	37	utilizing	utilize	VERB
ejpam-5662	445	38	the	the	DET
ejpam-5662	445	39	npa	npa	NOUN
ejpam-5662	445	40	are	be	AUX
ejpam-5662	445	41	graphically	graphically	ADV
ejpam-5662	445	42	represented	represent	VERB
ejpam-5662	445	43	in	in	ADP
ejpam-5662	445	44	figs	fig	NOUN
ejpam-5662	445	45	.	.	PUNCT
ejpam-5662	446	1	19	19	NUM
ejpam-5662	446	2	-	-	SYM
ejpam-5662	446	3	30	30	NUM
ejpam-5662	446	4	,	,	PUNCT
ejpam-5662	446	5	when	when	SCONJ
ejpam-5662	446	6	the	the	DET
ejpam-5662	446	7	previously	previously	ADV
ejpam-5662	446	8	measured	measure	VERB
ejpam-5662	446	9	data	datum	NOUN
ejpam-5662	446	10	of	of	ADP
ejpam-5662	446	11	the	the	DET
ejpam-5662	446	12	parameters	parameter	NOUN
ejpam-5662	446	13	are	be	AUX
ejpam-5662	446	14	considered	consider	VERB
ejpam-5662	446	15	.	.	PUNCT
ejpam-5662	447	1	initially	initially	ADV
ejpam-5662	447	2	,	,	PUNCT
ejpam-5662	447	3	figs	fig	NOUN
ejpam-5662	447	4	.	.	PUNCT
ejpam-5662	448	1	19	19	NUM
ejpam-5662	448	2	-	-	SYM
ejpam-5662	448	3	24	24	NUM
ejpam-5662	448	4	are	be	AUX
ejpam-5662	448	5	schemed	scheme	VERB
ejpam-5662	448	6	to	to	PART
ejpam-5662	448	7	inspect	inspect	VERB
ejpam-5662	448	8	the	the	DET
ejpam-5662	448	9	impacts	impact	NOUN
ejpam-5662	448	10	of	of	ADP
ejpam-5662	448	11	the	the	DET
ejpam-5662	448	12	pertinent	pertinent	ADJ
ejpam-5662	448	13	factors	factor	NOUN
ejpam-5662	448	14	ω1	ω1	PROPN
ejpam-5662	448	15	,	,	PUNCT
ejpam-5662	448	16	ω2	ω2	ADJ
ejpam-5662	448	17	,	,	PUNCT
ejpam-5662	448	18	γ1	γ1	NOUN
ejpam-5662	448	19	,	,	PUNCT
ejpam-5662	448	20	γ2	γ2	PROPN
ejpam-5662	448	21	,	,	PUNCT
ejpam-5662	448	22	η11	η11	NOUN
ejpam-5662	448	23	,	,	PUNCT
ejpam-5662	448	24	η21	η21	PROPN
ejpam-5662	448	25	,	,	PUNCT
ejpam-5662	448	26	η12	η12	NOUN
ejpam-5662	448	27	,	,	PUNCT
ejpam-5662	448	28	η22	η22	PROPN
ejpam-5662	448	29	,	,	PUNCT
ejpam-5662	448	30	λ1	λ1	ADJ
ejpam-5662	448	31	,	,	PUNCT
ejpam-5662	448	32	λ2	λ2	NOUN
ejpam-5662	448	33	,	,	PUNCT
ejpam-5662	448	34	and	and	CCONJ
ejpam-5662	448	35	ωp	ωp	INTJ
ejpam-5662	448	36	,	,	PUNCT
ejpam-5662	448	37	the	the	DET
ejpam-5662	448	38	same	same	ADJ
ejpam-5662	448	39	parameters	parameter	NOUN
ejpam-5662	448	40	discussed	discuss	VERB
ejpam-5662	448	41	in	in	ADP
ejpam-5662	448	42	the	the	DET
ejpam-5662	448	43	damped	damped	NOUN
ejpam-5662	448	44	case	case	NOUN
ejpam-5662	448	45	,	,	PUNCT
ejpam-5662	448	46	on	on	ADP
ejpam-5662	448	47	the	the	DET
ejpam-5662	448	48	time	time	NOUN
ejpam-5662	448	49	deviation	deviation	NOUN
ejpam-5662	448	50	and	and	CCONJ
ejpam-5662	448	51	the	the	DET
ejpam-5662	448	52	polarplots	polarplot	NOUN
ejpam-5662	448	53	of	of	ADP
ejpam-5662	448	54	w(t	w(t	PROPN
ejpam-5662	448	55	)	)	PUNCT
ejpam-5662	448	56	and	and	CCONJ
ejpam-5662	448	57	g(t	g(t	PROPN
ejpam-5662	448	58	)	)	PUNCT
ejpam-5662	448	59	.	.	PUNCT
ejpam-5662	449	1	these	these	DET
ejpam-5662	449	2	parameters	parameter	NOUN
ejpam-5662	449	3	use	use	VERB
ejpam-5662	449	4	the	the	DET
ejpam-5662	449	5	previously	previously	ADV
ejpam-5662	449	6	stated	state	VERB
ejpam-5662	449	7	values	value	NOUN
ejpam-5662	449	8	,	,	PUNCT
ejpam-5662	449	9	which	which	PRON
ejpam-5662	449	10	change	change	VERB
ejpam-5662	449	11	depending	depend	VERB
ejpam-5662	449	12	on	on	ADP
ejpam-5662	449	13	how	how	SCONJ
ejpam-5662	449	14	each	each	DET
ejpam-5662	449	15	parameter	parameter	NOUN
ejpam-5662	449	16	under	under	ADP
ejpam-5662	449	17	study	study	NOUN
ejpam-5662	449	18	changes	change	NOUN
ejpam-5662	449	19	from	from	ADP
ejpam-5662	449	20	one	one	NUM
ejpam-5662	449	21	picture	picture	NOUN
ejpam-5662	449	22	to	to	ADP
ejpam-5662	449	23	another	another	PRON
ejpam-5662	449	24	.	.	PUNCT
ejpam-5662	450	1	it	it	PRON
ejpam-5662	450	2	is	be	AUX
ejpam-5662	450	3	evident	evident	ADJ
ejpam-5662	450	4	from	from	ADP
ejpam-5662	450	5	analyzing	analyze	VERB
ejpam-5662	450	6	the	the	DET
ejpam-5662	450	7	time	time	NOUN
ejpam-5662	450	8	history	history	NOUN
ejpam-5662	450	9	waves	wave	NOUN
ejpam-5662	450	10	that	that	PRON
ejpam-5662	450	11	they	they	PRON
ejpam-5662	450	12	display	display	VERB
ejpam-5662	450	13	damping	damp	VERB
ejpam-5662	450	14	periodic	periodic	ADJ
ejpam-5662	450	15	forms	form	NOUN
ejpam-5662	450	16	over	over	ADP
ejpam-5662	450	17	the	the	DET
ejpam-5662	450	18	whole	whole	ADJ
ejpam-5662	450	19	duration	duration	NOUN
ejpam-5662	450	20	.	.	PUNCT
ejpam-5662	451	1	the	the	DET
ejpam-5662	451	2	graphs	graph	NOUN
ejpam-5662	451	3	show	show	VERB
ejpam-5662	451	4	that	that	SCONJ
ejpam-5662	451	5	the	the	DET
ejpam-5662	451	6	oscillation	oscillation	NOUN
ejpam-5662	451	7	numbers	number	NOUN
ejpam-5662	451	8	for	for	ADP
ejpam-5662	451	9	both	both	DET
ejpam-5662	451	10	solutions	solution	NOUN
ejpam-5662	451	11	differ	differ	VERB
ejpam-5662	451	12	according	accord	VERB
ejpam-5662	451	13	to	to	ADP
ejpam-5662	451	14	the	the	DET
ejpam-5662	451	15	factors	factor	NOUN
ejpam-5662	451	16	at	at	ADP
ejpam-5662	451	17	play	play	NOUN
ejpam-5662	451	18	.	.	PUNCT
ejpam-5662	452	1	fig	fig	NOUN
ejpam-5662	452	2	.	.	PUNCT
ejpam-5662	453	1	19	19	NUM
ejpam-5662	453	2	illustrates	illustrate	VERB
ejpam-5662	453	3	the	the	DET
ejpam-5662	453	4	impact	impact	NOUN
ejpam-5662	453	5	of	of	ADP
ejpam-5662	453	6	the	the	DET
ejpam-5662	453	7	natural	natural	ADJ
ejpam-5662	453	8	frequencies	frequency	NOUN
ejpam-5662	453	9	ω1	ω1	ADJ
ejpam-5662	453	10	and	and	CCONJ
ejpam-5662	453	11	ω2	ω2	ADJ
ejpam-5662	453	12	on	on	ADP
ejpam-5662	453	13	the	the	DET
ejpam-5662	453	14	time	time	NOUN
ejpam-5662	453	15	distribution	distribution	NOUN
ejpam-5662	453	16	of	of	ADP
ejpam-5662	453	17	w(t	w(t	PROPN
ejpam-5662	453	18	)	)	PUNCT
ejpam-5662	453	19	and	and	CCONJ
ejpam-5662	453	20	g(t	g(t	PROPN
ejpam-5662	453	21	)	)	PUNCT
ejpam-5662	453	22	,	,	PUNCT
ejpam-5662	453	23	respectively	respectively	ADV
ejpam-5662	453	24	.	.	PUNCT
ejpam-5662	454	1	these	these	DET
ejpam-5662	454	2	figures	figure	NOUN
ejpam-5662	454	3	illustrate	illustrate	VERB
ejpam-5662	454	4	how	how	SCONJ
ejpam-5662	454	5	the	the	DET
ejpam-5662	454	6	wave	wave	NOUN
ejpam-5662	454	7	amplitudes	amplitude	NOUN
ejpam-5662	454	8	for	for	ADP
ejpam-5662	454	9	the	the	DET
ejpam-5662	454	10	two	two	NUM
ejpam-5662	454	11	solutions	solution	NOUN
ejpam-5662	454	12	remain	remain	VERB
ejpam-5662	454	13	constant	constant	ADJ
ejpam-5662	454	14	but	but	CCONJ
ejpam-5662	454	15	the	the	DET
ejpam-5662	454	16	number	number	NOUN
ejpam-5662	454	17	of	of	ADP
ejpam-5662	454	18	vibrations	vibration	NOUN
ejpam-5662	454	19	rises	rise	VERB
ejpam-5662	454	20	sharply	sharply	ADV
ejpam-5662	454	21	as	as	ADP
ejpam-5662	454	22	ω1	ω1	PROPN
ejpam-5662	454	23	and	and	CCONJ
ejpam-5662	454	24	ω2	ω2	ADJ
ejpam-5662	454	25	grows	grow	NOUN
ejpam-5662	454	26	.	.	PUNCT
ejpam-5662	455	1	additionally	additionally	ADV
ejpam-5662	455	2	,	,	PUNCT
ejpam-5662	455	3	when	when	SCONJ
ejpam-5662	455	4	these	these	DET
ejpam-5662	455	5	two	two	NUM
ejpam-5662	455	6	frequencies	frequency	NOUN
ejpam-5662	455	7	increase	increase	VERB
ejpam-5662	455	8	,	,	PUNCT
ejpam-5662	455	9	the	the	DET
ejpam-5662	455	10	wavelengths	wavelength	NOUN
ejpam-5662	455	11	get	get	VERB
ejpam-5662	455	12	smaller	small	ADJ
ejpam-5662	455	13	.	.	PUNCT
ejpam-5662	456	1	because	because	SCONJ
ejpam-5662	456	2	of	of	ADP
ejpam-5662	456	3	their	their	PRON
ejpam-5662	456	4	growth	growth	NOUN
ejpam-5662	456	5	,	,	PUNCT
ejpam-5662	456	6	waves	wave	NOUN
ejpam-5662	456	7	are	be	AUX
ejpam-5662	456	8	also	also	ADV
ejpam-5662	456	9	seen	see	VERB
ejpam-5662	456	10	to	to	PART
ejpam-5662	456	11	accelerate	accelerate	VERB
ejpam-5662	456	12	.	.	PUNCT
ejpam-5662	457	1	the	the	DET
ejpam-5662	457	2	presence	presence	NOUN
ejpam-5662	457	3	of	of	ADP
ejpam-5662	457	4	quintic	quintic	ADJ
ejpam-5662	457	5	and	and	CCONJ
ejpam-5662	457	6	cubic	cubic	ADJ
ejpam-5662	457	7	nonlinearities	nonlinearitie	NOUN
ejpam-5662	457	8	in	in	ADP
ejpam-5662	457	9	the	the	DET
ejpam-5662	457	10	mathieu	mathieu	PROPN
ejpam-5662	457	11	system	system	NOUN
ejpam-5662	457	12	,	,	PUNCT
ejpam-5662	457	13	especially	especially	ADV
ejpam-5662	457	14	at	at	ADP
ejpam-5662	457	15	large	large	ADJ
ejpam-5662	457	16	oscillation	oscillation	NOUN
ejpam-5662	457	17	amplitudes	amplitude	NOUN
ejpam-5662	457	18	,	,	PUNCT
ejpam-5662	457	19	alters	alter	VERB
ejpam-5662	457	20	naturally	naturally	ADV
ejpam-5662	457	21	occurring	occur	VERB
ejpam-5662	457	22	frequencies	frequency	NOUN
ejpam-5662	457	23	.	.	PUNCT
ejpam-5662	458	1	this	this	PRON
ejpam-5662	458	2	is	be	AUX
ejpam-5662	458	3	referred	refer	VERB
ejpam-5662	458	4	to	to	ADP
ejpam-5662	458	5	as	as	ADP
ejpam-5662	458	6	amplitude	amplitude	NOUN
ejpam-5662	458	7	-	-	PUNCT
ejpam-5662	458	8	dependent	dependent	ADJ
ejpam-5662	458	9	frequency	frequency	NOUN
ejpam-5662	458	10	or	or	CCONJ
ejpam-5662	458	11	nonlinear	nonlinear	ADJ
ejpam-5662	458	12	frequency	frequency	NOUN
ejpam-5662	458	13	shift	shift	NOUN
ejpam-5662	458	14	.	.	PUNCT
ejpam-5662	459	1	the	the	DET
ejpam-5662	459	2	npa	npa	NOUN
ejpam-5662	459	3	is	be	AUX
ejpam-5662	459	4	used	use	VERB
ejpam-5662	459	5	in	in	ADP
ejpam-5662	459	6	the	the	DET
ejpam-5662	459	7	current	current	ADJ
ejpam-5662	459	8	study	study	NOUN
ejpam-5662	459	9	to	to	PART
ejpam-5662	459	10	realize	realize	VERB
ejpam-5662	459	11	these	these	DET
ejpam-5662	459	12	new	new	ADJ
ejpam-5662	459	13	frequencies	frequency	NOUN
ejpam-5662	459	14	,	,	PUNCT
ejpam-5662	459	15	as	as	SCONJ
ejpam-5662	459	16	seen	see	VERB
ejpam-5662	459	17	above	above	ADV
ejpam-5662	459	18	.	.	PUNCT
ejpam-5662	460	1	in	in	ADP
ejpam-5662	460	2	a	a	DET
ejpam-5662	460	3	nonlinear	nonlinear	ADJ
ejpam-5662	460	4	system	system	NOUN
ejpam-5662	460	5	,	,	PUNCT
ejpam-5662	460	6	such	such	ADJ
ejpam-5662	460	7	as	as	ADP
ejpam-5662	460	8	the	the	DET
ejpam-5662	460	9	do	do	NOUN
ejpam-5662	460	10	,	,	PUNCT
ejpam-5662	460	11	nonlinear	nonlinear	ADJ
ejpam-5662	460	12	restoring	restore	VERB
ejpam-5662	460	13	forces	force	NOUN
ejpam-5662	460	14	cause	cause	VERB
ejpam-5662	460	15	the	the	DET
ejpam-5662	460	16	effective	effective	ADJ
ejpam-5662	460	17	natural	natural	ADJ
ejpam-5662	460	18	frequency	frequency	NOUN
ejpam-5662	460	19	to	to	PART
ejpam-5662	460	20	change	change	VERB
ejpam-5662	460	21	with	with	ADP
ejpam-5662	460	22	the	the	DET
ejpam-5662	460	23	oscillation	oscillation	NOUN
ejpam-5662	460	24	amplitude	amplitude	NOUN
ejpam-5662	460	25	,	,	PUNCT
ejpam-5662	460	26	whereas	whereas	SCONJ
ejpam-5662	460	27	the	the	DET
ejpam-5662	460	28	natural	natural	ADJ
ejpam-5662	460	29	frequency	frequency	NOUN
ejpam-5662	460	30	remains	remain	VERB
ejpam-5662	460	31	constant	constant	ADJ
ejpam-5662	460	32	in	in	ADP
ejpam-5662	460	33	a	a	DET
ejpam-5662	460	34	fully	fully	ADV
ejpam-5662	460	35	linear	linear	ADJ
ejpam-5662	460	36	system	system	NOUN
ejpam-5662	460	37	.	.	PUNCT
ejpam-5662	461	1	furthermore	furthermore	ADV
ejpam-5662	461	2	,	,	PUNCT
ejpam-5662	461	3	figs	fig	NOUN
ejpam-5662	461	4	.	.	PUNCT
ejpam-5662	462	1	20	20	NUM
ejpam-5662	462	2	show	show	VERB
ejpam-5662	462	3	that	that	SCONJ
ejpam-5662	462	4	the	the	DET
ejpam-5662	462	5	number	number	NOUN
ejpam-5662	462	6	of	of	ADP
ejpam-5662	462	7	vibrations	vibration	NOUN
ejpam-5662	462	8	and	and	CCONJ
ejpam-5662	462	9	amplitudes	amplitude	NOUN
ejpam-5662	462	10	of	of	ADP
ejpam-5662	462	11	the	the	DET
ejpam-5662	462	12	waves	wave	NOUN
ejpam-5662	462	13	for	for	ADP
ejpam-5662	462	14	the	the	DET
ejpam-5662	462	15	two	two	NUM
ejpam-5662	462	16	solutions	solution	NOUN
ejpam-5662	462	17	are	be	AUX
ejpam-5662	462	18	roughly	roughly	ADV
ejpam-5662	462	19	constant	constant	ADJ
ejpam-5662	462	20	as	as	SCONJ
ejpam-5662	462	21	the	the	DET
ejpam-5662	462	22	cubic	cubic	ADJ
ejpam-5662	462	23	factors	factor	NOUN
ejpam-5662	462	24	γ1	γ1	NOUN
ejpam-5662	462	25	and	and	CCONJ
ejpam-5662	462	26	γ2	γ2	PROPN
ejpam-5662	462	27	are	be	AUX
ejpam-5662	462	28	increased	increase	VERB
ejpam-5662	462	29	.	.	PUNCT
ejpam-5662	463	1	the	the	DET
ejpam-5662	463	2	influence	influence	NOUN
ejpam-5662	463	3	of	of	ADP
ejpam-5662	463	4	γ1	γ1	PROPN
ejpam-5662	463	5	and	and	CCONJ
ejpam-5662	463	6	γ2	γ2	NOUN
ejpam-5662	463	7	is	be	AUX
ejpam-5662	463	8	shown	show	VERB
ejpam-5662	463	9	to	to	PART
ejpam-5662	463	10	have	have	VERB
ejpam-5662	463	11	little	little	ADJ
ejpam-5662	463	12	effect	effect	NOUN
ejpam-5662	463	13	on	on	ADP
ejpam-5662	463	14	the	the	DET
ejpam-5662	463	15	wavelengths	wavelength	NOUN
ejpam-5662	463	16	,	,	PUNCT
ejpam-5662	463	17	but	but	CCONJ
ejpam-5662	463	18	the	the	DET
ejpam-5662	463	19	growth	growth	NOUN
ejpam-5662	463	20	of	of	ADP
ejpam-5662	463	21	these	these	DET
ejpam-5662	463	22	cubic	cubic	ADJ
ejpam-5662	463	23	coefficients	coefficient	NOUN
ejpam-5662	463	24	in	in	ADP
ejpam-5662	463	25	figs	fig	NOUN
ejpam-5662	463	26	.	.	PUNCT
ejpam-5662	464	1	4	4	NUM
ejpam-5662	464	2	results	result	NOUN
ejpam-5662	464	3	in	in	ADP
ejpam-5662	464	4	a	a	DET
ejpam-5662	464	5	noticeable	noticeable	ADJ
ejpam-5662	464	6	delay	delay	NOUN
ejpam-5662	464	7	in	in	ADP
ejpam-5662	464	8	the	the	DET
ejpam-5662	464	9	waves	wave	NOUN
ejpam-5662	464	10	.	.	PUNCT
ejpam-5662	465	1	unlike	unlike	ADP
ejpam-5662	465	2	linear	linear	PROPN
ejpam-5662	465	3	systems	system	NOUN
ejpam-5662	465	4	,	,	PUNCT
ejpam-5662	465	5	systems	system	NOUN
ejpam-5662	465	6	with	with	ADP
ejpam-5662	465	7	cubic	cubic	ADJ
ejpam-5662	465	8	nonlinearities	nonlinearitie	NOUN
ejpam-5662	465	9	do	do	AUX
ejpam-5662	465	10	not	not	PART
ejpam-5662	465	11	have	have	VERB
ejpam-5662	465	12	a	a	DET
ejpam-5662	465	13	fixed	fix	VERB
ejpam-5662	465	14	natural	natural	ADJ
ejpam-5662	465	15	frequency	frequency	NOUN
ejpam-5662	465	16	of	of	ADP
ejpam-5662	465	17	oscillation	oscillation	NOUN
ejpam-5662	465	18	.	.	PUNCT
ejpam-5662	466	1	rather	rather	ADV
ejpam-5662	466	2	,	,	PUNCT
ejpam-5662	466	3	the	the	DET
ejpam-5662	466	4	intrinsic	intrinsic	ADJ
ejpam-5662	466	5	frequency	frequency	NOUN
ejpam-5662	466	6	begins	begin	VERB
ejpam-5662	466	7	to	to	PART
ejpam-5662	466	8	determine	determine	VERB
ejpam-5662	466	9	the	the	DET
ejpam-5662	466	10	amplitude	amplitude	NOUN
ejpam-5662	466	11	.	.	PUNCT
ejpam-5662	467	1	the	the	DET
ejpam-5662	467	2	complicated	complicated	ADJ
ejpam-5662	467	3	behavior	behavior	NOUN
ejpam-5662	467	4	and	and	CCONJ
ejpam-5662	467	5	improved	improved	ADJ
ejpam-5662	467	6	system	system	NOUN
ejpam-5662	467	7	dynamics	dynamic	NOUN
ejpam-5662	467	8	are	be	AUX
ejpam-5662	467	9	provided	provide	VERB
ejpam-5662	467	10	by	by	ADP
ejpam-5662	467	11	cubic	cubic	ADJ
ejpam-5662	467	12	nonlinearities	nonlinearitie	NOUN
ejpam-5662	467	13	,	,	PUNCT
ejpam-5662	467	14	which	which	PRON
ejpam-5662	467	15	are	be	AUX
ejpam-5662	467	16	not	not	PART
ejpam-5662	467	17	possible	possible	ADJ
ejpam-5662	467	18	in	in	ADP
ejpam-5662	467	19	simply	simply	ADV
ejpam-5662	467	20	linear	linear	PROPN
ejpam-5662	467	21	systems	system	NOUN
ejpam-5662	467	22	.	.	PUNCT
ejpam-5662	468	1	figs	fig	NOUN
ejpam-5662	468	2	.	.	PUNCT
ejpam-5662	469	1	21	21	NUM
ejpam-5662	469	2	and	and	CCONJ
ejpam-5662	469	3	22	22	NUM
ejpam-5662	469	4	are	be	AUX
ejpam-5662	469	5	plotted	plot	VERB
ejpam-5662	469	6	to	to	PART
ejpam-5662	469	7	examine	examine	VERB
ejpam-5662	469	8	the	the	DET
ejpam-5662	469	9	influence	influence	NOUN
ejpam-5662	469	10	of	of	ADP
ejpam-5662	469	11	the	the	DET
ejpam-5662	469	12	coefficients	coefficient	NOUN
ejpam-5662	469	13	of	of	ADP
ejpam-5662	469	14	the	the	DET
ejpam-5662	469	15	excited	excited	ADJ
ejpam-5662	469	16	amplitudes	amplitude	NOUN
ejpam-5662	469	17	of	of	ADP
ejpam-5662	469	18	x	x	X
ejpam-5662	469	19	and	and	CCONJ
ejpam-5662	469	20	y	y	PROPN
ejpam-5662	469	21	,	,	PUNCT
ejpam-5662	469	22	η11	η11	NOUN
ejpam-5662	469	23	,	,	PUNCT
ejpam-5662	469	24	η21,η12	η21,η12	NOUN
ejpam-5662	469	25	,	,	PUNCT
ejpam-5662	469	26	and	and	CCONJ
ejpam-5662	469	27	η22	η22	PROPN
ejpam-5662	469	28	,	,	PUNCT
ejpam-5662	469	29	in	in	ADP
ejpam-5662	469	30	the	the	DET
ejpam-5662	469	31	nonlinear	nonlinear	ADJ
ejpam-5662	469	32	system	system	NOUN
ejpam-5662	469	33	of	of	ADP
ejpam-5662	469	34	non	non	ADJ
ejpam-5662	469	35	-	-	ADJ
ejpam-5662	469	36	damped	damped	ADJ
ejpam-5662	469	37	mathieu	mathieu	PROPN
ejpam-5662	469	38	eqs	eqs	PROPN
ejpam-5662	469	39	.	.	PUNCT
ejpam-5662	470	1	(	(	PUNCT
ejpam-5662	470	2	39	39	NUM
ejpam-5662	470	3	)	)	PUNCT
ejpam-5662	470	4	and	and	CCONJ
ejpam-5662	470	5	(	(	PUNCT
ejpam-5662	470	6	40	40	NUM
ejpam-5662	470	7	)	)	PUNCT
ejpam-5662	470	8	,	,	PUNCT
ejpam-5662	470	9	on	on	ADP
ejpam-5662	470	10	both	both	DET
ejpam-5662	470	11	w(t	w(t	PROPN
ejpam-5662	470	12	)	)	PUNCT
ejpam-5662	470	13	and	and	CCONJ
ejpam-5662	470	14	g(t	g(t	PROPN
ejpam-5662	470	15	)	)	PUNCT
ejpam-5662	470	16	,	,	PUNCT
ejpam-5662	470	17	respectively	respectively	ADV
ejpam-5662	470	18	.	.	PUNCT
ejpam-5662	471	1	from	from	ADP
ejpam-5662	471	2	these	these	DET
ejpam-5662	471	3	figures	figure	NOUN
ejpam-5662	471	4	,	,	PUNCT
ejpam-5662	471	5	one	one	PRON
ejpam-5662	471	6	can	can	AUX
ejpam-5662	471	7	see	see	VERB
ejpam-5662	471	8	that	that	SCONJ
ejpam-5662	471	9	the	the	DET
ejpam-5662	471	10	amplitudes	amplitude	NOUN
ejpam-5662	471	11	of	of	ADP
ejpam-5662	471	12	the	the	DET
ejpam-5662	471	13	waves	wave	NOUN
ejpam-5662	471	14	are	be	AUX
ejpam-5662	471	15	stay	stay	VERB
ejpam-5662	471	16	stable	stable	ADJ
ejpam-5662	471	17	,	,	PUNCT
ejpam-5662	471	18	meanwhile	meanwhile	ADV
ejpam-5662	471	19	,	,	PUNCT
ejpam-5662	471	20	the	the	DET
ejpam-5662	471	21	wavelengths	wavelength	NOUN
ejpam-5662	471	22	are	be	AUX
ejpam-5662	471	23	shrinking	shrink	VERB
ejpam-5662	471	24	for	for	ADP
ejpam-5662	471	25	w(t	w(t	PROPN
ejpam-5662	471	26	)	)	PUNCT
ejpam-5662	471	27	and	and	CCONJ
ejpam-5662	471	28	g(t	g(t	PROPN
ejpam-5662	471	29	)	)	PUNCT
ejpam-5662	471	30	with	with	ADP
ejpam-5662	471	31	the	the	DET
ejpam-5662	471	32	rise	rise	NOUN
ejpam-5662	471	33	of	of	ADP
ejpam-5662	471	34	η11	η11	NOUN
ejpam-5662	471	35	,	,	PUNCT
ejpam-5662	471	36	η21	η21	PROPN
ejpam-5662	471	37	,	,	PUNCT
ejpam-5662	471	38	η12	η12	NOUN
ejpam-5662	471	39	,	,	PUNCT
ejpam-5662	471	40	and	and	CCONJ
ejpam-5662	471	41	η22	η22	PROPN
ejpam-5662	471	42	.	.	PUNCT
ejpam-5662	472	1	the	the	DET
ejpam-5662	472	2	oscillations	oscillation	NOUN
ejpam-5662	472	3	are	be	AUX
ejpam-5662	472	4	swinging	swinge	VERB
ejpam-5662	472	5	between	between	ADP
ejpam-5662	472	6	delays	delay	NOUN
ejpam-5662	472	7	and	and	CCONJ
ejpam-5662	472	8	enhance	enhance	VERB
ejpam-5662	472	9	with	with	ADP
ejpam-5662	472	10	the	the	DET
ejpam-5662	472	11	varying	varying	NOUN
ejpam-5662	472	12	of	of	ADP
ejpam-5662	472	13	these	these	DET
ejpam-5662	472	14	parameters	parameter	NOUN
ejpam-5662	472	15	.	.	PUNCT
ejpam-5662	473	1	physically	physically	ADV
ejpam-5662	473	2	,	,	PUNCT
ejpam-5662	473	3	parametric	parametric	ADJ
ejpam-5662	473	4	resonance	resonance	NOUN
ejpam-5662	473	5	is	be	AUX
ejpam-5662	473	6	made	make	VERB
ejpam-5662	473	7	possible	possible	ADJ
ejpam-5662	473	8	by	by	ADP
ejpam-5662	473	9	the	the	DET
ejpam-5662	473	10	growth	growth	NOUN
ejpam-5662	473	11	in	in	ADP
ejpam-5662	473	12	stimulated	stimulated	ADJ
ejpam-5662	473	13	amplitudes	amplitude	NOUN
ejpam-5662	473	14	.	.	PUNCT
ejpam-5662	474	1	nonlinear	nonlinear	ADJ
ejpam-5662	474	2	phenomena	phenomenon	NOUN
ejpam-5662	474	3	including	include	VERB
ejpam-5662	474	4	amplitude	amplitude	NOUN
ejpam-5662	474	5	-	-	PUNCT
ejpam-5662	474	6	dependent	dependent	ADJ
ejpam-5662	474	7	resonance	resonance	NOUN
ejpam-5662	474	8	,	,	PUNCT
ejpam-5662	474	9	large	large	ADJ
ejpam-5662	474	10	amplitude	amplitude	NOUN
ejpam-5662	474	11	oscillations	oscillation	NOUN
ejpam-5662	474	12	,	,	PUNCT
ejpam-5662	474	13	and	and	CCONJ
ejpam-5662	474	14	perhaps	perhaps	ADV
ejpam-5662	474	15	instability	instability	NOUN
ejpam-5662	474	16	can	can	AUX
ejpam-5662	474	17	result	result	VERB
ejpam-5662	474	18	from	from	ADP
ejpam-5662	474	19	this	this	PRON
ejpam-5662	474	20	.	.	PUNCT
ejpam-5662	475	1	the	the	DET
ejpam-5662	475	2	instability	instability	NOUN
ejpam-5662	475	3	zones	zone	NOUN
ejpam-5662	475	4	are	be	AUX
ejpam-5662	475	5	expanded	expand	VERB
ejpam-5662	475	6	by	by	ADP
ejpam-5662	475	7	higher	high	ADJ
ejpam-5662	475	8	stimulation	stimulation	NOUN
ejpam-5662	475	9	amplitudes	amplitude	NOUN
ejpam-5662	475	10	,	,	PUNCT
ejpam-5662	475	11	which	which	PRON
ejpam-5662	475	12	also	also	ADV
ejpam-5662	475	13	make	make	VERB
ejpam-5662	475	14	the	the	DET
ejpam-5662	475	15	system	system	NOUN
ejpam-5662	475	16	more	more	ADV
ejpam-5662	475	17	vulnerable	vulnerable	ADJ
ejpam-5662	475	18	to	to	ADP
ejpam-5662	475	19	massive	massive	ADJ
ejpam-5662	475	20	oscillations	oscillation	NOUN
ejpam-5662	475	21	and	and	CCONJ
ejpam-5662	475	22	parametric	parametric	ADJ
ejpam-5662	475	23	resonance	resonance	NOUN
ejpam-5662	475	24	.	.	PUNCT
ejpam-5662	476	1	to	to	PART
ejpam-5662	476	2	examine	examine	VERB
ejpam-5662	476	3	the	the	DET
ejpam-5662	476	4	impact	impact	NOUN
ejpam-5662	476	5	of	of	ADP
ejpam-5662	476	6	the	the	DET
ejpam-5662	476	7	quintic	quintic	ADJ
ejpam-5662	476	8	coefficients	coefficient	NOUN
ejpam-5662	476	9	λ1	λ1	ADJ
ejpam-5662	476	10	and	and	CCONJ
ejpam-5662	476	11	λ2	λ2	NOUN
ejpam-5662	476	12	on	on	ADP
ejpam-5662	476	13	the	the	DET
ejpam-5662	476	14	linked	link	VERB
ejpam-5662	476	15	system	system	NOUN
ejpam-5662	476	16	as	as	SCONJ
ejpam-5662	476	17	given	give	VERB
ejpam-5662	476	18	in	in	ADP
ejpam-5662	476	19	eqs	eqs	PROPN
ejpam-5662	476	20	.	.	PUNCT
ejpam-5662	477	1	(	(	PUNCT
ejpam-5662	477	2	39	39	NUM
ejpam-5662	477	3	)	)	PUNCT
ejpam-5662	477	4	and	and	CCONJ
ejpam-5662	477	5	(	(	PUNCT
ejpam-5662	477	6	40	40	NUM
ejpam-5662	477	7	)	)	PUNCT
ejpam-5662	477	8	,	,	PUNCT
ejpam-5662	477	9	fig	fig	NOUN
ejpam-5662	477	10	.	.	PUNCT
ejpam-5662	478	1	23	23	NUM
ejpam-5662	478	2	is	be	AUX
ejpam-5662	478	3	shown	show	VERB
ejpam-5662	478	4	.	.	PUNCT
ejpam-5662	479	1	both	both	CCONJ
ejpam-5662	479	2	the	the	DET
ejpam-5662	479	3	wave	wave	NOUN
ejpam-5662	479	4	amplitudes	amplitude	NOUN
ejpam-5662	479	5	and	and	CCONJ
ejpam-5662	479	6	the	the	DET
ejpam-5662	479	7	number	number	NOUN
ejpam-5662	479	8	of	of	ADP
ejpam-5662	479	9	vibrations	vibration	NOUN
ejpam-5662	479	10	for	for	ADP
ejpam-5662	479	11	the	the	DET
ejpam-5662	479	12	two	two	NUM
ejpam-5662	479	13	solutions	solution	NOUN
ejpam-5662	479	14	stay	stay	VERB
ejpam-5662	479	15	constant	constant	ADJ
ejpam-5662	479	16	as	as	SCONJ
ejpam-5662	479	17	these	these	DET
ejpam-5662	479	18	quinitic	quinitic	ADJ
ejpam-5662	479	19	factors	factor	NOUN
ejpam-5662	479	20	increase	increase	VERB
ejpam-5662	479	21	.	.	PUNCT
ejpam-5662	480	1	the	the	DET
ejpam-5662	480	2	a.	a.	NOUN
ejpam-5662	480	3	alanazy	alanazy	NOUN
ejpam-5662	480	4	,	,	PUNCT
ejpam-5662	480	5	g.	g.	PROPN
ejpam-5662	480	6	m.	m.	PROPN
ejpam-5662	480	7	moatimid	moatimid	PROPN
ejpam-5662	480	8	,	,	PUNCT
ejpam-5662	480	9	m.	m.	PROPN
ejpam-5662	480	10	a.	a.	PROPN
ejpam-5662	480	11	a.	a.	PROPN
ejpam-5662	480	12	mohamed	mohamed	PROPN
ejpam-5662	480	13	/	/	SYM
ejpam-5662	480	14	eur	eur	PROPN
ejpam-5662	480	15	.	.	PUNCT
ejpam-5662	481	1	j.	j.	PROPN
ejpam-5662	481	2	pure	pure	PROPN
ejpam-5662	481	3	appl	appl	PROPN
ejpam-5662	481	4	.	.	PROPN
ejpam-5662	481	5	math	math	PROPN
ejpam-5662	481	6	,	,	PUNCT
ejpam-5662	481	7	18	18	NUM
ejpam-5662	481	8	(	(	PUNCT
ejpam-5662	481	9	2	2	NUM
ejpam-5662	481	10	)	)	PUNCT
ejpam-5662	481	11	(	(	PUNCT
ejpam-5662	481	12	2025	2025	NUM
ejpam-5662	481	13	)	)	PUNCT
ejpam-5662	481	14	,	,	PUNCT
ejpam-5662	481	15	5662	5662	NUM
ejpam-5662	481	16	26	26	NUM
ejpam-5662	481	17	of	of	ADP
ejpam-5662	481	18	36	36	NUM
ejpam-5662	481	19	influence	influence	NOUN
ejpam-5662	481	20	of	of	ADP
ejpam-5662	481	21	and	and	CCONJ
ejpam-5662	481	22	is	be	AUX
ejpam-5662	481	23	shown	show	VERB
ejpam-5662	481	24	to	to	PART
ejpam-5662	481	25	have	have	VERB
ejpam-5662	481	26	little	little	ADJ
ejpam-5662	481	27	effect	effect	NOUN
ejpam-5662	481	28	on	on	ADP
ejpam-5662	481	29	the	the	DET
ejpam-5662	481	30	wavelengths	wavelength	NOUN
ejpam-5662	481	31	,	,	PUNCT
ejpam-5662	481	32	but	but	CCONJ
ejpam-5662	481	33	the	the	DET
ejpam-5662	481	34	growth	growth	NOUN
ejpam-5662	481	35	of	of	ADP
ejpam-5662	481	36	these	these	DET
ejpam-5662	481	37	quintic	quintic	ADJ
ejpam-5662	481	38	coefficients	coefficient	NOUN
ejpam-5662	481	39	in	in	ADP
ejpam-5662	481	40	figs	fig	NOUN
ejpam-5662	481	41	.	.	PUNCT
ejpam-5662	482	1	23	23	NUM
ejpam-5662	482	2	results	result	NOUN
ejpam-5662	482	3	in	in	ADP
ejpam-5662	482	4	a	a	DET
ejpam-5662	482	5	negligible	negligible	ADJ
ejpam-5662	482	6	delay	delay	NOUN
ejpam-5662	482	7	in	in	ADP
ejpam-5662	482	8	the	the	DET
ejpam-5662	482	9	waves	wave	NOUN
ejpam-5662	482	10	.	.	PUNCT
ejpam-5662	483	1	quintic	quintic	ADJ
ejpam-5662	483	2	nonlinearities	nonlinearitie	NOUN
ejpam-5662	483	3	complicate	complicate	VERB
ejpam-5662	483	4	the	the	DET
ejpam-5662	483	5	dynamic	dynamic	ADJ
ejpam-5662	483	6	behavior	behavior	NOUN
ejpam-5662	483	7	of	of	ADP
ejpam-5662	483	8	a	a	DET
ejpam-5662	483	9	tdof	tdof	NOUN
ejpam-5662	483	10	of	of	ADP
ejpam-5662	483	11	mdo	mdo	PROPN
ejpam-5662	483	12	,	,	PUNCT
ejpam-5662	483	13	especially	especially	ADV
ejpam-5662	483	14	when	when	SCONJ
ejpam-5662	483	15	combined	combine	VERB
ejpam-5662	483	16	with	with	ADP
ejpam-5662	483	17	additional	additional	ADJ
ejpam-5662	483	18	nonlinear	nonlinear	ADJ
ejpam-5662	483	19	effects	effect	NOUN
ejpam-5662	483	20	such	such	ADJ
ejpam-5662	483	21	as	as	ADP
ejpam-5662	483	22	cubic	cubic	ADJ
ejpam-5662	483	23	terms	term	NOUN
ejpam-5662	483	24	and	and	CCONJ
ejpam-5662	483	25	parametric	parametric	ADJ
ejpam-5662	483	26	excitation	excitation	NOUN
ejpam-5662	483	27	.	.	PUNCT
ejpam-5662	484	1	the	the	DET
ejpam-5662	484	2	quintic	quintic	ADJ
ejpam-5662	484	3	terms	term	NOUN
ejpam-5662	484	4	introduce	introduce	VERB
ejpam-5662	484	5	higher	high	ADJ
ejpam-5662	484	6	-	-	PUNCT
ejpam-5662	484	7	order	order	NOUN
ejpam-5662	484	8	stiffness	stiffness	ADJ
ejpam-5662	484	9	effects	effect	NOUN
ejpam-5662	484	10	that	that	PRON
ejpam-5662	484	11	impact	impact	VERB
ejpam-5662	484	12	the	the	DET
ejpam-5662	484	13	system	system	NOUN
ejpam-5662	484	14	’s	’s	PART
ejpam-5662	484	15	oscillations	oscillation	NOUN
ejpam-5662	484	16	,	,	PUNCT
ejpam-5662	484	17	bifurcation	bifurcation	NOUN
ejpam-5662	484	18	structures	structure	NOUN
ejpam-5662	484	19	,	,	PUNCT
ejpam-5662	484	20	and	and	CCONJ
ejpam-5662	484	21	stability	stability	NOUN
ejpam-5662	484	22	.	.	PUNCT
ejpam-5662	485	1	the	the	DET
ejpam-5662	485	2	quintic	quintic	ADJ
ejpam-5662	485	3	term	term	NOUN
ejpam-5662	485	4	can	can	AUX
ejpam-5662	485	5	interact	interact	VERB
ejpam-5662	485	6	with	with	ADP
ejpam-5662	485	7	cubic	cubic	ADJ
ejpam-5662	485	8	nonlinearities	nonlinearitie	NOUN
ejpam-5662	485	9	and	and	CCONJ
ejpam-5662	485	10	parametric	parametric	ADJ
ejpam-5662	485	11	excitation	excitation	NOUN
ejpam-5662	485	12	to	to	PART
ejpam-5662	485	13	produce	produce	VERB
ejpam-5662	485	14	complex	complex	ADJ
ejpam-5662	485	15	dynamics	dynamic	NOUN
ejpam-5662	485	16	,	,	PUNCT
ejpam-5662	485	17	and	and	CCONJ
ejpam-5662	485	18	they	they	PRON
ejpam-5662	485	19	change	change	VERB
ejpam-5662	485	20	the	the	DET
ejpam-5662	485	21	behavior	behavior	NOUN
ejpam-5662	485	22	of	of	ADP
ejpam-5662	485	23	the	the	DET
ejpam-5662	485	24	system	system	NOUN
ejpam-5662	485	25	at	at	ADP
ejpam-5662	485	26	greater	great	ADJ
ejpam-5662	485	27	oscillation	oscillation	NOUN
ejpam-5662	485	28	amplitudes	amplitude	NOUN
ejpam-5662	485	29	.	.	PUNCT
ejpam-5662	486	1	similar	similar	ADJ
ejpam-5662	486	2	to	to	ADP
ejpam-5662	486	3	cubic	cubic	ADJ
ejpam-5662	486	4	nonlinearities	nonlinearitie	NOUN
ejpam-5662	486	5	,	,	PUNCT
ejpam-5662	486	6	quintic	quintic	ADJ
ejpam-5662	486	7	nonlinearities	nonlinearitie	NOUN
ejpam-5662	486	8	cause	cause	VERB
ejpam-5662	486	9	the	the	DET
ejpam-5662	486	10	system	system	NOUN
ejpam-5662	486	11	’s	’s	PART
ejpam-5662	486	12	natural	natural	ADJ
ejpam-5662	486	13	frequencies	frequency	NOUN
ejpam-5662	486	14	to	to	PART
ejpam-5662	486	15	alter	alter	VERB
ejpam-5662	486	16	as	as	SCONJ
ejpam-5662	486	17	the	the	DET
ejpam-5662	486	18	amplitude	amplitude	NOUN
ejpam-5662	486	19	rises	rise	VERB
ejpam-5662	486	20	.	.	PUNCT
ejpam-5662	487	1	at	at	ADP
ejpam-5662	487	2	larger	large	ADJ
ejpam-5662	487	3	amplitudes	amplitude	NOUN
ejpam-5662	487	4	,	,	PUNCT
ejpam-5662	487	5	the	the	DET
ejpam-5662	487	6	frequency	frequency	NOUN
ejpam-5662	487	7	amplitude	amplitude	NOUN
ejpam-5662	487	8	dependency	dependency	NOUN
ejpam-5662	487	9	is	be	AUX
ejpam-5662	487	10	more	more	ADV
ejpam-5662	487	11	apparent	apparent	ADJ
ejpam-5662	487	12	due	due	ADP
ejpam-5662	487	13	to	to	ADP
ejpam-5662	487	14	the	the	DET
ejpam-5662	487	15	higher	high	ADJ
ejpam-5662	487	16	-	-	PUNCT
ejpam-5662	487	17	order	order	NOUN
ejpam-5662	487	18	frequency	frequency	NOUN
ejpam-5662	487	19	shift	shift	NOUN
ejpam-5662	487	20	produced	produce	VERB
ejpam-5662	487	21	by	by	ADP
ejpam-5662	487	22	the	the	DET
ejpam-5662	487	23	quintic	quintic	ADJ
ejpam-5662	487	24	components	component	NOUN
ejpam-5662	487	25	.	.	PUNCT
ejpam-5662	488	1	moreover	moreover	ADV
ejpam-5662	488	2	,	,	PUNCT
ejpam-5662	488	3	figs	fig	NOUN
ejpam-5662	488	4	.	.	PUNCT
ejpam-5662	489	1	24	24	NUM
ejpam-5662	489	2	illustrate	illustrate	VERB
ejpam-5662	489	3	how	how	SCONJ
ejpam-5662	489	4	the	the	DET
ejpam-5662	489	5	distributions	distribution	NOUN
ejpam-5662	489	6	are	be	AUX
ejpam-5662	489	7	affected	affect	VERB
ejpam-5662	489	8	by	by	ADP
ejpam-5662	489	9	the	the	DET
ejpam-5662	489	10	excited	excited	ADJ
ejpam-5662	489	11	frequency	frequency	NOUN
ejpam-5662	489	12	ωp	ωp	NOUN
ejpam-5662	489	13	of	of	ADP
ejpam-5662	489	14	the	the	DET
ejpam-5662	489	15	two	two	NUM
ejpam-5662	489	16	un	un	ADJ
ejpam-5662	489	17	-	-	ADJ
ejpam-5662	489	18	damped	damped	ADJ
ejpam-5662	489	19	waves	wave	NOUN
ejpam-5662	489	20	x	x	PUNCT
ejpam-5662	489	21	and	and	CCONJ
ejpam-5662	489	22	y	y	PROPN
ejpam-5662	489	23	and	and	CCONJ
ejpam-5662	489	24	that	that	PRON
ejpam-5662	489	25	characterizes	characterize	VERB
ejpam-5662	489	26	the	the	DET
ejpam-5662	489	27	two	two	NUM
ejpam-5662	489	28	linked	link	VERB
ejpam-5662	489	29	oscillators	oscillator	NOUN
ejpam-5662	489	30	by	by	ADP
ejpam-5662	489	31	the	the	DET
ejpam-5662	489	32	functions	function	NOUN
ejpam-5662	489	33	w(t	w(t	PROPN
ejpam-5662	489	34	)	)	PUNCT
ejpam-5662	489	35	and	and	CCONJ
ejpam-5662	489	36	g(t	g(t	PROPN
ejpam-5662	489	37	)	)	PUNCT
ejpam-5662	489	38	.	.	PUNCT
ejpam-5662	490	1	these	these	DET
ejpam-5662	490	2	figures	figure	NOUN
ejpam-5662	490	3	likewise	likewise	ADV
ejpam-5662	490	4	show	show	VERB
ejpam-5662	490	5	that	that	SCONJ
ejpam-5662	490	6	the	the	DET
ejpam-5662	490	7	number	number	NOUN
ejpam-5662	490	8	of	of	ADP
ejpam-5662	490	9	waves	wave	NOUN
ejpam-5662	490	10	and	and	CCONJ
ejpam-5662	490	11	wavelengths	wavelength	NOUN
ejpam-5662	490	12	do	do	AUX
ejpam-5662	490	13	not	not	PART
ejpam-5662	490	14	change	change	VERB
ejpam-5662	490	15	,	,	PUNCT
ejpam-5662	490	16	however	however	ADV
ejpam-5662	490	17	,	,	PUNCT
ejpam-5662	490	18	fig	fig	NOUN
ejpam-5662	490	19	.	.	PUNCT
ejpam-5662	491	1	24	24	NUM
ejpam-5662	491	2	shows	show	VERB
ejpam-5662	491	3	a	a	DET
ejpam-5662	491	4	notable	notable	ADJ
ejpam-5662	491	5	improvement	improvement	NOUN
ejpam-5662	491	6	in	in	ADP
ejpam-5662	491	7	the	the	DET
ejpam-5662	491	8	waves	wave	NOUN
ejpam-5662	491	9	with	with	ADP
ejpam-5662	491	10	the	the	DET
ejpam-5662	491	11	increase	increase	NOUN
ejpam-5662	491	12	of	of	ADP
ejpam-5662	491	13	ωp	ωp	PROPN
ejpam-5662	491	14	.	.	PUNCT
ejpam-5662	492	1	a	a	DET
ejpam-5662	492	2	tdof	tdof	NOUN
ejpam-5662	492	3	of	of	ADP
ejpam-5662	492	4	mdo	mdo	PROPN
ejpam-5662	492	5	’s	’s	PART
ejpam-5662	492	6	excited	excited	ADJ
ejpam-5662	492	7	frequency	frequency	NOUN
ejpam-5662	492	8	plays	play	VERB
ejpam-5662	492	9	a	a	DET
ejpam-5662	492	10	critical	critical	ADJ
ejpam-5662	492	11	role	role	NOUN
ejpam-5662	492	12	in	in	ADP
ejpam-5662	492	13	shaping	shape	VERB
ejpam-5662	492	14	the	the	DET
ejpam-5662	492	15	system	system	NOUN
ejpam-5662	492	16	’s	’s	PART
ejpam-5662	492	17	response	response	NOUN
ejpam-5662	492	18	to	to	ADP
ejpam-5662	492	19	parametric	parametric	ADJ
ejpam-5662	492	20	stimulation	stimulation	NOUN
ejpam-5662	492	21	.	.	PUNCT
ejpam-5662	493	1	the	the	DET
ejpam-5662	493	2	excited	excited	ADJ
ejpam-5662	493	3	frequency	frequency	NOUN
ejpam-5662	493	4	affects	affect	VERB
ejpam-5662	493	5	bifurcations	bifurcation	NOUN
ejpam-5662	493	6	,	,	PUNCT
ejpam-5662	493	7	oscillation	oscillation	NOUN
ejpam-5662	493	8	amplitude	amplitude	NOUN
ejpam-5662	493	9	,	,	PUNCT
ejpam-5662	493	10	stability	stability	NOUN
ejpam-5662	493	11	,	,	PUNCT
ejpam-5662	493	12	the	the	DET
ejpam-5662	493	13	onset	onset	NOUN
ejpam-5662	493	14	of	of	ADP
ejpam-5662	493	15	parametric	parametric	ADJ
ejpam-5662	493	16	resonance	resonance	NOUN
ejpam-5662	493	17	,	,	PUNCT
ejpam-5662	493	18	and	and	CCONJ
ejpam-5662	493	19	the	the	DET
ejpam-5662	493	20	transition	transition	NOUN
ejpam-5662	493	21	to	to	ADP
ejpam-5662	493	22	complex	complex	ADJ
ejpam-5662	493	23	and	and	CCONJ
ejpam-5662	493	24	chaotic	chaotic	ADJ
ejpam-5662	493	25	dynamics	dynamic	NOUN
ejpam-5662	493	26	.	.	PUNCT
ejpam-5662	494	1	the	the	DET
ejpam-5662	494	2	system	system	NOUN
ejpam-5662	494	3	’s	’s	PART
ejpam-5662	494	4	response	response	NOUN
ejpam-5662	494	5	amplitude	amplitude	NOUN
ejpam-5662	494	6	is	be	AUX
ejpam-5662	494	7	significantly	significantly	ADV
ejpam-5662	494	8	influenced	influence	VERB
ejpam-5662	494	9	by	by	ADP
ejpam-5662	494	10	the	the	DET
ejpam-5662	494	11	stimulated	stimulated	ADJ
ejpam-5662	494	12	frequency	frequency	NOUN
ejpam-5662	494	13	ωp	ωp	NOUN
ejpam-5662	494	14	.	.	PUNCT
ejpam-5662	495	1	around	around	ADP
ejpam-5662	495	2	resonant	resonant	ADJ
ejpam-5662	495	3	frequencies	frequency	NOUN
ejpam-5662	495	4	,	,	PUNCT
ejpam-5662	495	5	even	even	ADV
ejpam-5662	495	6	little	little	ADJ
ejpam-5662	495	7	parametric	parametric	ADJ
ejpam-5662	495	8	stimulation	stimulation	NOUN
ejpam-5662	495	9	can	can	AUX
ejpam-5662	495	10	produce	produce	VERB
ejpam-5662	495	11	large	large	ADJ
ejpam-5662	495	12	oscillations	oscillation	NOUN
ejpam-5662	495	13	.	.	PUNCT
ejpam-5662	496	1	the	the	DET
ejpam-5662	496	2	relationship	relationship	NOUN
ejpam-5662	496	3	between	between	ADP
ejpam-5662	496	4	and	and	CCONJ
ejpam-5662	496	5	the	the	DET
ejpam-5662	496	6	system	system	NOUN
ejpam-5662	496	7	’s	’s	PART
ejpam-5662	496	8	intrinsic	intrinsic	ADJ
ejpam-5662	496	9	frequencies	frequency	NOUN
ejpam-5662	496	10	determines	determine	VERB
ejpam-5662	496	11	the	the	DET
ejpam-5662	496	12	size	size	NOUN
ejpam-5662	496	13	of	of	ADP
ejpam-5662	496	14	its	its	PRON
ejpam-5662	496	15	oscillatory	oscillatory	ADJ
ejpam-5662	496	16	response	response	NOUN
ejpam-5662	496	17	.	.	PUNCT
ejpam-5662	497	1	based	base	VERB
ejpam-5662	497	2	on	on	ADP
ejpam-5662	497	3	the	the	DET
ejpam-5662	497	4	facts	fact	NOUN
ejpam-5662	497	5	presented	present	VERB
ejpam-5662	497	6	above	above	ADV
ejpam-5662	497	7	and	and	CCONJ
ejpam-5662	497	8	as	as	SCONJ
ejpam-5662	497	9	stated	state	VERB
ejpam-5662	497	10	in	in	ADP
ejpam-5662	497	11	the	the	DET
ejpam-5662	497	12	damped	damped	NOUN
ejpam-5662	497	13	instance	instance	NOUN
ejpam-5662	497	14	,	,	PUNCT
ejpam-5662	497	15	it	it	PRON
ejpam-5662	497	16	is	be	AUX
ejpam-5662	497	17	possible	possible	ADJ
ejpam-5662	497	18	to	to	PART
ejpam-5662	497	19	realize	realize	VERB
ejpam-5662	497	20	the	the	DET
ejpam-5662	497	21	conclusion	conclusion	NOUN
ejpam-5662	497	22	that	that	SCONJ
ejpam-5662	497	23	these	these	DET
ejpam-5662	497	24	results	result	NOUN
ejpam-5662	497	25	can	can	AUX
ejpam-5662	497	26	help	help	VERB
ejpam-5662	497	27	with	with	ADP
ejpam-5662	497	28	the	the	DET
ejpam-5662	497	29	construction	construction	NOUN
ejpam-5662	497	30	and	and	CCONJ
ejpam-5662	497	31	management	management	NOUN
ejpam-5662	497	32	of	of	ADP
ejpam-5662	497	33	systems	system	NOUN
ejpam-5662	497	34	that	that	PRON
ejpam-5662	497	35	depend	depend	VERB
ejpam-5662	497	36	on	on	ADP
ejpam-5662	497	37	periodic	periodic	ADJ
ejpam-5662	497	38	solutions	solution	NOUN
ejpam-5662	497	39	.	.	PUNCT
ejpam-5662	498	1	to	to	PART
ejpam-5662	498	2	improve	improve	VERB
ejpam-5662	498	3	system	system	NOUN
ejpam-5662	498	4	performance	performance	NOUN
ejpam-5662	498	5	or	or	CCONJ
ejpam-5662	498	6	design	design	NOUN
ejpam-5662	498	7	systems	system	NOUN
ejpam-5662	498	8	that	that	PRON
ejpam-5662	498	9	operate	operate	VERB
ejpam-5662	498	10	well	well	ADV
ejpam-5662	498	11	at	at	ADP
ejpam-5662	498	12	particular	particular	ADJ
ejpam-5662	498	13	frequencies	frequency	NOUN
ejpam-5662	498	14	,	,	PUNCT
ejpam-5662	498	15	engineers	engineer	NOUN
ejpam-5662	498	16	could	could	AUX
ejpam-5662	498	17	,	,	PUNCT
ejpam-5662	498	18	for	for	ADP
ejpam-5662	498	19	instance	instance	NOUN
ejpam-5662	498	20	,	,	PUNCT
ejpam-5662	498	21	leverage	leverage	VERB
ejpam-5662	498	22	periodic	periodic	ADJ
ejpam-5662	498	23	behavior	behavior	NOUN
ejpam-5662	498	24	in	in	ADP
ejpam-5662	498	25	mechanical	mechanical	ADJ
ejpam-5662	498	26	systems	system	NOUN
ejpam-5662	498	27	.	.	PUNCT
ejpam-5662	499	1	nonlinearities	nonlinearitie	NOUN
ejpam-5662	499	2	,	,	PUNCT
ejpam-5662	499	3	parametric	parametric	ADJ
ejpam-5662	499	4	excitation	excitation	NOUN
ejpam-5662	499	5	,	,	PUNCT
ejpam-5662	499	6	and	and	CCONJ
ejpam-5662	499	7	excitation	excitation	NOUN
ejpam-5662	499	8	frequency	frequency	NOUN
ejpam-5662	499	9	interact	interact	VERB
ejpam-5662	499	10	to	to	PART
ejpam-5662	499	11	produce	produce	VERB
ejpam-5662	499	12	the	the	DET
ejpam-5662	499	13	system	system	NOUN
ejpam-5662	499	14	’s	’s	PART
ejpam-5662	499	15	complicated	complicated	ADJ
ejpam-5662	499	16	behavior	behavior	NOUN
ejpam-5662	499	17	.	.	PUNCT
ejpam-5662	500	1	the	the	DET
ejpam-5662	500	2	system	system	NOUN
ejpam-5662	500	3	may	may	AUX
ejpam-5662	500	4	exhibit	exhibit	VERB
ejpam-5662	500	5	bifurcations	bifurcation	NOUN
ejpam-5662	500	6	,	,	PUNCT
ejpam-5662	500	7	nonlinear	nonlinear	ADJ
ejpam-5662	500	8	frequency	frequency	NOUN
ejpam-5662	500	9	changes	change	NOUN
ejpam-5662	500	10	,	,	PUNCT
ejpam-5662	500	11	heightened	heighten	VERB
ejpam-5662	500	12	oscillations	oscillation	NOUN
ejpam-5662	500	13	,	,	PUNCT
ejpam-5662	500	14	or	or	CCONJ
ejpam-5662	500	15	even	even	ADV
ejpam-5662	500	16	chaotic	chaotic	ADJ
ejpam-5662	500	17	motion	motion	NOUN
ejpam-5662	500	18	close	close	ADJ
ejpam-5662	500	19	to	to	ADP
ejpam-5662	500	20	resonances	resonance	NOUN
ejpam-5662	500	21	.	.	PUNCT
ejpam-5662	501	1	the	the	DET
ejpam-5662	501	2	quintic	quintic	ADJ
ejpam-5662	501	3	term	term	NOUN
ejpam-5662	501	4	improves	improve	VERB
ejpam-5662	501	5	the	the	DET
ejpam-5662	501	6	amplitude	amplitude	NOUN
ejpam-5662	501	7	dependency	dependency	NOUN
ejpam-5662	501	8	of	of	ADP
ejpam-5662	501	9	these	these	DET
ejpam-5662	501	10	effects	effect	NOUN
ejpam-5662	501	11	,	,	PUNCT
ejpam-5662	501	12	especially	especially	ADV
ejpam-5662	501	13	when	when	SCONJ
ejpam-5662	501	14	there	there	PRON
ejpam-5662	501	15	are	be	VERB
ejpam-5662	501	16	large	large	ADJ
ejpam-5662	501	17	oscillations	oscillation	NOUN
ejpam-5662	501	18	.	.	PUNCT
ejpam-5662	502	1	a.	a.	PROPN
ejpam-5662	502	2	alanazy	alanazy	PROPN
ejpam-5662	502	3	,	,	PUNCT
ejpam-5662	502	4	g.	g.	PROPN
ejpam-5662	502	5	m.	m.	PROPN
ejpam-5662	502	6	moatimid	moatimid	PROPN
ejpam-5662	502	7	,	,	PUNCT
ejpam-5662	502	8	m.	m.	PROPN
ejpam-5662	502	9	a.	a.	PROPN
ejpam-5662	502	10	a.	a.	PROPN
ejpam-5662	502	11	mohamed	mohamed	PROPN
ejpam-5662	502	12	/	/	SYM
ejpam-5662	502	13	eur	eur	PROPN
ejpam-5662	502	14	.	.	PUNCT
ejpam-5662	503	1	j.	j.	PROPN
ejpam-5662	503	2	pure	pure	PROPN
ejpam-5662	503	3	appl	appl	PROPN
ejpam-5662	503	4	.	.	PROPN
ejpam-5662	503	5	math	math	PROPN
ejpam-5662	503	6	,	,	PUNCT
ejpam-5662	503	7	18	18	NUM
ejpam-5662	503	8	(	(	PUNCT
ejpam-5662	503	9	2	2	NUM
ejpam-5662	503	10	)	)	PUNCT
ejpam-5662	503	11	(	(	PUNCT
ejpam-5662	503	12	2025	2025	NUM
ejpam-5662	503	13	)	)	PUNCT
ejpam-5662	503	14	,	,	PUNCT
ejpam-5662	503	15	5662	5662	NUM
ejpam-5662	503	16	27	27	NUM
ejpam-5662	503	17	of	of	ADP
ejpam-5662	503	18	36	36	NUM
ejpam-5662	503	19	figure	figure	NOUN
ejpam-5662	503	20	19	19	NUM
ejpam-5662	503	21	:	:	PUNCT
ejpam-5662	503	22	the	the	DET
ejpam-5662	503	23	effect	effect	NOUN
ejpam-5662	503	24	of	of	ADP
ejpam-5662	503	25	the	the	DET
ejpam-5662	503	26	natural	natural	ADJ
ejpam-5662	503	27	frequencies	frequency	NOUN
ejpam-5662	503	28	ω1	ω1	ADJ
ejpam-5662	503	29	and	and	CCONJ
ejpam-5662	503	30	ω2	ω2	ADJ
ejpam-5662	503	31	on	on	ADP
ejpam-5662	503	32	the	the	DET
ejpam-5662	503	33	time	time	NOUN
ejpam-5662	503	34	-	-	PUNCT
ejpam-5662	503	35	dependent	dependent	ADJ
ejpam-5662	503	36	variation	variation	NOUN
ejpam-5662	503	37	of	of	ADP
ejpam-5662	503	38	w(t	w(t	PROPN
ejpam-5662	503	39	)	)	PUNCT
ejpam-5662	503	40	and	and	CCONJ
ejpam-5662	503	41	g(t	g(t	PROPN
ejpam-5662	503	42	)	)	PUNCT
ejpam-5662	503	43	.	.	PUNCT
ejpam-5662	504	1	figure	figure	NOUN
ejpam-5662	504	2	20	20	NUM
ejpam-5662	504	3	:	:	PUNCT
ejpam-5662	504	4	the	the	DET
ejpam-5662	504	5	effect	effect	NOUN
ejpam-5662	504	6	of	of	ADP
ejpam-5662	504	7	the	the	DET
ejpam-5662	504	8	cubic	cubic	ADJ
ejpam-5662	504	9	coefficients	coefficient	NOUN
ejpam-5662	504	10	γ1	γ1	NOUN
ejpam-5662	504	11	and	and	CCONJ
ejpam-5662	504	12	γ2	γ2	NOUN
ejpam-5662	504	13	on	on	ADP
ejpam-5662	504	14	the	the	DET
ejpam-5662	504	15	time	time	NOUN
ejpam-5662	504	16	-	-	PUNCT
ejpam-5662	504	17	dependent	dependent	ADJ
ejpam-5662	504	18	variation	variation	NOUN
ejpam-5662	504	19	of	of	ADP
ejpam-5662	504	20	w(t	w(t	PROPN
ejpam-5662	504	21	)	)	PUNCT
ejpam-5662	504	22	and	and	CCONJ
ejpam-5662	504	23	g(t	g(t	PROPN
ejpam-5662	504	24	)	)	PUNCT
ejpam-5662	504	25	.	.	PUNCT
ejpam-5662	505	1	figure	figure	NOUN
ejpam-5662	505	2	21	21	NUM
ejpam-5662	505	3	:	:	PUNCT
ejpam-5662	505	4	the	the	DET
ejpam-5662	505	5	effect	effect	NOUN
ejpam-5662	505	6	of	of	ADP
ejpam-5662	505	7	the	the	DET
ejpam-5662	505	8	excited	excited	ADJ
ejpam-5662	505	9	amplitudes	amplitude	NOUN
ejpam-5662	505	10	η11	η11	NOUN
ejpam-5662	505	11	and	and	CCONJ
ejpam-5662	505	12	η21	η21	NOUN
ejpam-5662	505	13	on	on	ADP
ejpam-5662	505	14	the	the	DET
ejpam-5662	505	15	time	time	NOUN
ejpam-5662	505	16	-	-	PUNCT
ejpam-5662	505	17	dependent	dependent	ADJ
ejpam-5662	505	18	deviation	deviation	NOUN
ejpam-5662	505	19	of	of	ADP
ejpam-5662	505	20	w(t	w(t	PROPN
ejpam-5662	505	21	)	)	PUNCT
ejpam-5662	505	22	and	and	CCONJ
ejpam-5662	505	23	g(t	g(t	PROPN
ejpam-5662	505	24	)	)	PUNCT
ejpam-5662	505	25	.	.	PUNCT
ejpam-5662	506	1	a.	a.	PROPN
ejpam-5662	506	2	alanazy	alanazy	PROPN
ejpam-5662	506	3	,	,	PUNCT
ejpam-5662	506	4	g.	g.	PROPN
ejpam-5662	506	5	m.	m.	PROPN
ejpam-5662	506	6	moatimid	moatimid	PROPN
ejpam-5662	506	7	,	,	PUNCT
ejpam-5662	506	8	m.	m.	PROPN
ejpam-5662	506	9	a.	a.	PROPN
ejpam-5662	506	10	a.	a.	PROPN
ejpam-5662	506	11	mohamed	mohamed	PROPN
ejpam-5662	506	12	/	/	SYM
ejpam-5662	506	13	eur	eur	PROPN
ejpam-5662	506	14	.	.	PUNCT
ejpam-5662	507	1	j.	j.	PROPN
ejpam-5662	507	2	pure	pure	PROPN
ejpam-5662	507	3	appl	appl	PROPN
ejpam-5662	507	4	.	.	PROPN
ejpam-5662	507	5	math	math	PROPN
ejpam-5662	507	6	,	,	PUNCT
ejpam-5662	507	7	18	18	NUM
ejpam-5662	507	8	(	(	PUNCT
ejpam-5662	507	9	2	2	NUM
ejpam-5662	507	10	)	)	PUNCT
ejpam-5662	507	11	(	(	PUNCT
ejpam-5662	507	12	2025	2025	NUM
ejpam-5662	507	13	)	)	PUNCT
ejpam-5662	507	14	,	,	PUNCT
ejpam-5662	507	15	5662	5662	NUM
ejpam-5662	507	16	28	28	NUM
ejpam-5662	507	17	of	of	ADP
ejpam-5662	507	18	36	36	NUM
ejpam-5662	507	19	figure	figure	NOUN
ejpam-5662	507	20	22	22	NUM
ejpam-5662	507	21	:	:	PUNCT
ejpam-5662	507	22	the	the	DET
ejpam-5662	507	23	effect	effect	NOUN
ejpam-5662	507	24	of	of	ADP
ejpam-5662	507	25	the	the	DET
ejpam-5662	507	26	excited	excited	ADJ
ejpam-5662	507	27	amplitudes	amplitude	NOUN
ejpam-5662	507	28	η12	η12	VERB
ejpam-5662	507	29	and	and	CCONJ
ejpam-5662	507	30	η22	η22	NOUN
ejpam-5662	507	31	on	on	ADP
ejpam-5662	507	32	the	the	DET
ejpam-5662	507	33	time	time	NOUN
ejpam-5662	507	34	-	-	PUNCT
ejpam-5662	507	35	dependent	dependent	ADJ
ejpam-5662	507	36	deviation	deviation	NOUN
ejpam-5662	507	37	of	of	ADP
ejpam-5662	507	38	w(t	w(t	PROPN
ejpam-5662	507	39	)	)	PUNCT
ejpam-5662	507	40	and	and	CCONJ
ejpam-5662	507	41	g(t	g(t	PROPN
ejpam-5662	507	42	)	)	PUNCT
ejpam-5662	507	43	.	.	PUNCT
ejpam-5662	508	1	figure	figure	VERB
ejpam-5662	508	2	23	23	NUM
ejpam-5662	508	3	:	:	PUNCT
ejpam-5662	508	4	the	the	DET
ejpam-5662	508	5	effect	effect	NOUN
ejpam-5662	508	6	of	of	ADP
ejpam-5662	508	7	the	the	DET
ejpam-5662	508	8	quinitic	quinitic	ADJ
ejpam-5662	508	9	coefficients	coefficient	NOUN
ejpam-5662	508	10	λ1	λ1	ADJ
ejpam-5662	508	11	and	and	CCONJ
ejpam-5662	508	12	λ2	λ2	NOUN
ejpam-5662	508	13	on	on	ADP
ejpam-5662	508	14	the	the	DET
ejpam-5662	508	15	time	time	NOUN
ejpam-5662	508	16	-	-	PUNCT
ejpam-5662	508	17	dependent	dependent	ADJ
ejpam-5662	508	18	distribution	distribution	NOUN
ejpam-5662	508	19	of	of	ADP
ejpam-5662	508	20	w(t	w(t	PROPN
ejpam-5662	508	21	)	)	PUNCT
ejpam-5662	508	22	and	and	CCONJ
ejpam-5662	508	23	g(t	g(t	PROPN
ejpam-5662	508	24	)	)	PUNCT
ejpam-5662	508	25	.	.	PUNCT
ejpam-5662	509	1	figure	figure	NOUN
ejpam-5662	509	2	24	24	NUM
ejpam-5662	509	3	:	:	PUNCT
ejpam-5662	509	4	the	the	DET
ejpam-5662	509	5	effect	effect	NOUN
ejpam-5662	509	6	of	of	ADP
ejpam-5662	509	7	the	the	DET
ejpam-5662	509	8	excited	excited	ADJ
ejpam-5662	509	9	frequency	frequency	NOUN
ejpam-5662	509	10	ωp	ωp	PRON
ejpam-5662	509	11	on	on	ADP
ejpam-5662	509	12	the	the	DET
ejpam-5662	509	13	time	time	NOUN
ejpam-5662	509	14	-	-	PUNCT
ejpam-5662	509	15	dependent	dependent	ADJ
ejpam-5662	509	16	distribution	distribution	NOUN
ejpam-5662	509	17	of	of	ADP
ejpam-5662	509	18	w(t	w(t	PROPN
ejpam-5662	509	19	)	)	PUNCT
ejpam-5662	509	20	and	and	CCONJ
ejpam-5662	509	21	g(t	g(t	PROPN
ejpam-5662	509	22	)	)	PUNCT
ejpam-5662	509	23	.	.	PUNCT
ejpam-5662	510	1	once	once	ADV
ejpam-5662	510	2	more	more	ADJ
ejpam-5662	510	3	,	,	PUNCT
ejpam-5662	510	4	figs	fig	NOUN
ejpam-5662	510	5	.	.	PUNCT
ejpam-5662	511	1	25	25	NUM
ejpam-5662	511	2	-	-	SYM
ejpam-5662	511	3	30	30	NUM
ejpam-5662	511	4	designate	designate	ADJ
ejpam-5662	511	5	the	the	DET
ejpam-5662	511	6	polarplots	polarplot	NOUN
ejpam-5662	511	7	of	of	ADP
ejpam-5662	511	8	the	the	DET
ejpam-5662	511	9	proposed	propose	VERB
ejpam-5662	511	10	solutions	solution	NOUN
ejpam-5662	511	11	as	as	SCONJ
ejpam-5662	511	12	given	give	VERB
ejpam-5662	511	13	in	in	ADP
ejpam-5662	511	14	eq	eq	ADP
ejpam-5662	511	15	.	.	PUNCT
ejpam-5662	512	1	(	(	PUNCT
ejpam-5662	512	2	45	45	NUM
ejpam-5662	512	3	)	)	PUNCT
ejpam-5662	512	4	over	over	ADP
ejpam-5662	512	5	the	the	DET
ejpam-5662	512	6	time	time	NOUN
ejpam-5662	512	7	interval[0	interval[0	NOUN
ejpam-5662	512	8	,	,	PUNCT
ejpam-5662	512	9	50π	50π	NUM
ejpam-5662	512	10	]	]	PUNCT
ejpam-5662	512	11	with	with	ADP
ejpam-5662	512	12	the	the	DET
ejpam-5662	512	13	difference	difference	NOUN
ejpam-5662	512	14	of	of	ADP
ejpam-5662	512	15	the	the	DET
ejpam-5662	512	16	factors	factor	NOUN
ejpam-5662	512	17	ω1	ω1	PROPN
ejpam-5662	512	18	,	,	PUNCT
ejpam-5662	512	19	ω2	ω2	ADJ
ejpam-5662	512	20	,	,	PUNCT
ejpam-5662	512	21	α1	α1	PROPN
ejpam-5662	512	22	,	,	PUNCT
ejpam-5662	512	23	α2	α2	ADJ
ejpam-5662	512	24	,	,	PUNCT
ejpam-5662	512	25	λ1	λ1	ADJ
ejpam-5662	512	26	,	,	PUNCT
ejpam-5662	512	27	and	and	CCONJ
ejpam-5662	512	28	λ2	λ2	NOUN
ejpam-5662	512	29	to	to	PART
ejpam-5662	512	30	demonstrate	demonstrate	VERB
ejpam-5662	512	31	the	the	DET
ejpam-5662	512	32	polarization	polarization	NOUN
ejpam-5662	512	33	performance	performance	NOUN
ejpam-5662	512	34	of	of	ADP
ejpam-5662	512	35	the	the	DET
ejpam-5662	512	36	functions	function	NOUN
ejpam-5662	512	37	w(t	w(t	PROPN
ejpam-5662	512	38	)	)	PUNCT
ejpam-5662	512	39	and	and	CCONJ
ejpam-5662	512	40	g(t	g(t	PROPN
ejpam-5662	512	41	)	)	PUNCT
ejpam-5662	512	42	as	as	SCONJ
ejpam-5662	512	43	given	give	VERB
ejpam-5662	512	44	in	in	ADP
ejpam-5662	512	45	eq	eq	ADP
ejpam-5662	512	46	.	.	PUNCT
ejpam-5662	513	1	(	(	PUNCT
ejpam-5662	513	2	45	45	NUM
ejpam-5662	513	3	)	)	PUNCT
ejpam-5662	513	4	in	in	ADP
ejpam-5662	513	5	terms	term	NOUN
ejpam-5662	513	6	of	of	ADP
ejpam-5662	513	7	the	the	DET
ejpam-5662	513	8	total	total	ADJ
ejpam-5662	513	9	frequencies	frequency	NOUN
ejpam-5662	513	10	ω3	ω3	VERB
ejpam-5662	513	11	and	and	CCONJ
ejpam-5662	513	12	ω4	ω4	NUM
ejpam-5662	513	13	,	,	PUNCT
ejpam-5662	513	14	respectively	respectively	ADV
ejpam-5662	513	15	.	.	PUNCT
ejpam-5662	514	1	considering	consider	VERB
ejpam-5662	514	2	the	the	DET
ejpam-5662	514	3	identical	identical	ADJ
ejpam-5662	514	4	data	datum	NOUN
ejpam-5662	514	5	but	but	CCONJ
ejpam-5662	514	6	taking	take	VERB
ejpam-5662	514	7	c	c	NOUN
ejpam-5662	514	8	=	=	PUNCT
ejpam-5662	514	9	d	d	NOUN
ejpam-5662	514	10	=	=	SYM
ejpam-5662	514	11	0.5	0.5	NUM
ejpam-5662	514	12	,	,	PUNCT
ejpam-5662	514	13	which	which	PRON
ejpam-5662	514	14	differ	differ	VERB
ejpam-5662	514	15	from	from	ADP
ejpam-5662	514	16	one	one	NUM
ejpam-5662	514	17	figure	figure	NOUN
ejpam-5662	514	18	to	to	ADP
ejpam-5662	514	19	another	another	DET
ejpam-5662	514	20	rendering	rendering	NOUN
ejpam-5662	514	21	to	to	ADP
ejpam-5662	514	22	the	the	DET
ejpam-5662	514	23	deliberated	deliberate	VERB
ejpam-5662	514	24	stricture	stricture	NOUN
ejpam-5662	514	25	.	.	PUNCT
ejpam-5662	515	1	according	accord	VERB
ejpam-5662	515	2	to	to	ADP
ejpam-5662	515	3	the	the	DET
ejpam-5662	515	4	altered	altered	ADJ
ejpam-5662	515	5	values	value	NOUN
ejpam-5662	515	6	of	of	ADP
ejpam-5662	515	7	the	the	DET
ejpam-5662	515	8	natural	natural	ADJ
ejpam-5662	515	9	frequencies	frequency	NOUN
ejpam-5662	515	10	ω1	ω1	PROPN
ejpam-5662	515	11	and	and	CCONJ
ejpam-5662	515	12	ω2	ω2	ADJ
ejpam-5662	515	13	,	,	PUNCT
ejpam-5662	515	14	figs	fig	NOUN
ejpam-5662	515	15	.	.	PUNCT
ejpam-5662	516	1	25	25	NUM
ejpam-5662	516	2	and	and	CCONJ
ejpam-5662	516	3	26	26	NUM
ejpam-5662	516	4	are	be	AUX
ejpam-5662	516	5	displayed	display	VERB
ejpam-5662	516	6	.	.	PUNCT
ejpam-5662	517	1	these	these	DET
ejpam-5662	517	2	figures	figure	NOUN
ejpam-5662	517	3	reveal	reveal	VERB
ejpam-5662	517	4	that	that	SCONJ
ejpam-5662	517	5	as	as	ADP
ejpam-5662	517	6	ω1	ω1	PROPN
ejpam-5662	517	7	and	and	CCONJ
ejpam-5662	517	8	ω2	ω2	ADJ
ejpam-5662	517	9	rise	rise	NOUN
ejpam-5662	517	10	,	,	PUNCT
ejpam-5662	517	11	the	the	DET
ejpam-5662	517	12	curvilinear	curvilinear	PROPN
ejpam-5662	517	13	circles	circle	NOUN
ejpam-5662	517	14	control	control	NOUN
ejpam-5662	517	15	and	and	CCONJ
ejpam-5662	517	16	a.	a.	NOUN
ejpam-5662	517	17	alanazy	alanazy	PROPN
ejpam-5662	517	18	,	,	PUNCT
ejpam-5662	517	19	g.	g.	PROPN
ejpam-5662	517	20	m.	m.	PROPN
ejpam-5662	517	21	moatimid	moatimid	PROPN
ejpam-5662	517	22	,	,	PUNCT
ejpam-5662	517	23	m.	m.	PROPN
ejpam-5662	517	24	a.	a.	PROPN
ejpam-5662	517	25	a.	a.	PROPN
ejpam-5662	517	26	mohamed	mohamed	PROPN
ejpam-5662	517	27	/	/	SYM
ejpam-5662	517	28	eur	eur	PROPN
ejpam-5662	517	29	.	.	PUNCT
ejpam-5662	518	1	j.	j.	PROPN
ejpam-5662	518	2	pure	pure	PROPN
ejpam-5662	518	3	appl	appl	PROPN
ejpam-5662	518	4	.	.	PROPN
ejpam-5662	518	5	math	math	PROPN
ejpam-5662	518	6	,	,	PUNCT
ejpam-5662	518	7	18	18	NUM
ejpam-5662	518	8	(	(	PUNCT
ejpam-5662	518	9	2	2	NUM
ejpam-5662	518	10	)	)	PUNCT
ejpam-5662	518	11	(	(	PUNCT
ejpam-5662	518	12	2025	2025	NUM
ejpam-5662	518	13	)	)	PUNCT
ejpam-5662	518	14	,	,	PUNCT
ejpam-5662	518	15	5662	5662	NUM
ejpam-5662	518	16	29	29	NUM
ejpam-5662	518	17	of	of	ADP
ejpam-5662	518	18	36	36	NUM
ejpam-5662	518	19	gather	gather	NOUN
ejpam-5662	518	20	around	around	ADP
ejpam-5662	518	21	the	the	DET
ejpam-5662	518	22	center	center	NOUN
ejpam-5662	518	23	more	more	ADV
ejpam-5662	518	24	consistently	consistently	ADV
ejpam-5662	518	25	.	.	PUNCT
ejpam-5662	519	1	these	these	DET
ejpam-5662	519	2	results	result	NOUN
ejpam-5662	519	3	are	be	AUX
ejpam-5662	519	4	supported	support	VERB
ejpam-5662	519	5	by	by	ADP
ejpam-5662	519	6	the	the	DET
ejpam-5662	519	7	parameters	parameter	NOUN
ejpam-5662	519	8	’	’	PART
ejpam-5662	519	9	stimulating	stimulate	VERB
ejpam-5662	519	10	effects	effect	NOUN
ejpam-5662	519	11	that	that	PRON
ejpam-5662	519	12	are	be	AUX
ejpam-5662	519	13	shown	show	VERB
ejpam-5662	519	14	in	in	ADP
ejpam-5662	519	15	fig	fig	NOUN
ejpam-5662	519	16	.	.	PUNCT
ejpam-5662	520	1	19	19	NUM
ejpam-5662	520	2	.	.	PUNCT
ejpam-5662	521	1	in	in	ADP
ejpam-5662	521	2	this	this	DET
ejpam-5662	521	3	idea	idea	NOUN
ejpam-5662	521	4	,	,	PUNCT
ejpam-5662	521	5	a	a	DET
ejpam-5662	521	6	symmetric	symmetric	ADJ
ejpam-5662	521	7	distribution	distribution	NOUN
ejpam-5662	521	8	encircles	encircle	VERB
ejpam-5662	521	9	the	the	DET
ejpam-5662	521	10	centers	center	NOUN
ejpam-5662	521	11	of	of	ADP
ejpam-5662	521	12	the	the	DET
ejpam-5662	521	13	rounded	rounded	ADJ
ejpam-5662	521	14	,	,	PUNCT
ejpam-5662	521	15	connected	connected	ADJ
ejpam-5662	521	16	curves	curve	NOUN
ejpam-5662	521	17	.	.	PUNCT
ejpam-5662	522	1	this	this	DET
ejpam-5662	522	2	dispersion	dispersion	NOUN
ejpam-5662	522	3	may	may	AUX
ejpam-5662	522	4	be	be	AUX
ejpam-5662	522	5	used	use	VERB
ejpam-5662	522	6	to	to	PART
ejpam-5662	522	7	determine	determine	VERB
ejpam-5662	522	8	the	the	DET
ejpam-5662	522	9	stable	stable	ADJ
ejpam-5662	522	10	form	form	NOUN
ejpam-5662	522	11	in	in	ADP
ejpam-5662	522	12	which	which	PRON
ejpam-5662	522	13	these	these	DET
ejpam-5662	522	14	curves	curve	NOUN
ejpam-5662	522	15	operate	operate	VERB
ejpam-5662	522	16	.	.	PUNCT
ejpam-5662	523	1	the	the	DET
ejpam-5662	523	2	impact	impact	NOUN
ejpam-5662	523	3	of	of	ADP
ejpam-5662	523	4	the	the	DET
ejpam-5662	523	5	modifying	modify	VERB
ejpam-5662	523	6	elements	element	NOUN
ejpam-5662	523	7	determines	determine	VERB
ejpam-5662	523	8	how	how	SCONJ
ejpam-5662	523	9	much	much	ADJ
ejpam-5662	523	10	the	the	DET
ejpam-5662	523	11	intersecting	intersecting	NOUN
ejpam-5662	523	12	plots	plot	NOUN
ejpam-5662	523	13	circulate	circulate	VERB
ejpam-5662	523	14	.	.	PUNCT
ejpam-5662	524	1	additionally	additionally	ADV
ejpam-5662	524	2	,	,	PUNCT
ejpam-5662	524	3	the	the	DET
ejpam-5662	524	4	polarplots	polarplot	NOUN
ejpam-5662	524	5	of	of	ADP
ejpam-5662	524	6	the	the	DET
ejpam-5662	524	7	recommended	recommend	VERB
ejpam-5662	524	8	solutions	solution	NOUN
ejpam-5662	524	9	w(t	w(t	PROPN
ejpam-5662	524	10	)	)	PUNCT
ejpam-5662	524	11	and	and	CCONJ
ejpam-5662	524	12	g(t	g(t	PROPN
ejpam-5662	524	13	)	)	PUNCT
ejpam-5662	524	14	conferring	confer	VERB
ejpam-5662	524	15	to	to	ADP
ejpam-5662	524	16	eqs	eqs	PROPN
ejpam-5662	524	17	.	.	PUNCT
ejpam-5662	525	1	(	(	PUNCT
ejpam-5662	525	2	45	45	NUM
ejpam-5662	525	3	)	)	PUNCT
ejpam-5662	525	4	are	be	AUX
ejpam-5662	525	5	considered	consider	VERB
ejpam-5662	525	6	for	for	ADP
ejpam-5662	525	7	altered	altered	ADJ
ejpam-5662	525	8	values	value	NOUN
ejpam-5662	525	9	of	of	ADP
ejpam-5662	525	10	the	the	DET
ejpam-5662	525	11	coefficients	coefficient	NOUN
ejpam-5662	525	12	of	of	ADP
ejpam-5662	525	13	the	the	DET
ejpam-5662	525	14	excited	excited	ADJ
ejpam-5662	525	15	amplitude	amplitude	NOUN
ejpam-5662	525	16	η11	η11	NOUN
ejpam-5662	525	17	and	and	CCONJ
ejpam-5662	525	18	η21	η21	NOUN
ejpam-5662	525	19	as	as	SCONJ
ejpam-5662	525	20	detected	detect	VERB
ejpam-5662	525	21	in	in	ADP
ejpam-5662	525	22	figs	fig	NOUN
ejpam-5662	525	23	.	.	PUNCT
ejpam-5662	526	1	27	27	NUM
ejpam-5662	526	2	and	and	CCONJ
ejpam-5662	526	3	28	28	NUM
ejpam-5662	526	4	.	.	PUNCT
ejpam-5662	527	1	these	these	DET
ejpam-5662	527	2	illustrations	illustration	NOUN
ejpam-5662	527	3	comprehend	comprehend	VERB
ejpam-5662	527	4	the	the	DET
ejpam-5662	527	5	polarplots	polarplot	NOUN
ejpam-5662	527	6	of	of	ADP
ejpam-5662	527	7	the	the	DET
ejpam-5662	527	8	equivalent	equivalent	ADJ
ejpam-5662	527	9	solutions	solution	NOUN
ejpam-5662	527	10	w(t	w(t	PROPN
ejpam-5662	527	11	)	)	PUNCT
ejpam-5662	527	12	and	and	CCONJ
ejpam-5662	527	13	g(t	g(t	PROPN
ejpam-5662	527	14	)	)	PUNCT
ejpam-5662	527	15	with	with	ADP
ejpam-5662	527	16	a	a	DET
ejpam-5662	527	17	small	small	ADJ
ejpam-5662	527	18	variation	variation	NOUN
ejpam-5662	527	19	in	in	ADP
ejpam-5662	527	20	the	the	DET
ejpam-5662	527	21	excited	excited	ADJ
ejpam-5662	527	22	amplitudes	amplitude	NOUN
ejpam-5662	527	23	coefficients	coefficient	NOUN
ejpam-5662	527	24	of	of	ADP
ejpam-5662	527	25	the	the	DET
ejpam-5662	527	26	x	x	ADJ
ejpam-5662	527	27	oscillator	oscillator	NOUN
ejpam-5662	527	28	,	,	PUNCT
ejpam-5662	527	29	where	where	SCONJ
ejpam-5662	527	30	the	the	DET
ejpam-5662	527	31	effects	effect	NOUN
ejpam-5662	527	32	of	of	ADP
ejpam-5662	527	33	the	the	DET
ejpam-5662	527	34	other	other	ADJ
ejpam-5662	527	35	two	two	NUM
ejpam-5662	527	36	excited	excited	ADJ
ejpam-5662	527	37	amplitudes	amplitude	NOUN
ejpam-5662	527	38	of	of	ADP
ejpam-5662	527	39	the	the	DET
ejpam-5662	527	40	yoscillator	yoscillator	NOUN
ejpam-5662	527	41	η12	η12	NOUN
ejpam-5662	527	42	and	and	CCONJ
ejpam-5662	527	43	η22	η22	PROPN
ejpam-5662	527	44	are	be	AUX
ejpam-5662	527	45	excluded	exclude	VERB
ejpam-5662	527	46	here	here	ADV
ejpam-5662	527	47	due	due	ADP
ejpam-5662	527	48	to	to	ADP
ejpam-5662	527	49	their	their	PRON
ejpam-5662	527	50	similarity	similarity	NOUN
ejpam-5662	527	51	with	with	ADP
ejpam-5662	527	52	the	the	DET
ejpam-5662	527	53	effects	effect	NOUN
ejpam-5662	527	54	of	of	ADP
ejpam-5662	527	55	η11	η11	NOUN
ejpam-5662	527	56	and	and	CCONJ
ejpam-5662	527	57	η21	η21	NOUN
ejpam-5662	527	58	.	.	PUNCT
ejpam-5662	528	1	one	one	PRON
ejpam-5662	528	2	can	can	AUX
ejpam-5662	528	3	notice	notice	VERB
ejpam-5662	528	4	that	that	SCONJ
ejpam-5662	528	5	the	the	DET
ejpam-5662	528	6	impacts	impact	NOUN
ejpam-5662	528	7	of	of	ADP
ejpam-5662	528	8	the	the	DET
ejpam-5662	528	9	excited	excited	ADJ
ejpam-5662	528	10	amplitudes	amplitude	NOUN
ejpam-5662	528	11	are	be	AUX
ejpam-5662	528	12	similar	similar	ADJ
ejpam-5662	528	13	for	for	ADP
ejpam-5662	528	14	both	both	DET
ejpam-5662	528	15	w(t	w(t	PROPN
ejpam-5662	528	16	)	)	PUNCT
ejpam-5662	528	17	andg(t	andg(t	PROPN
ejpam-5662	528	18	)	)	PUNCT
ejpam-5662	528	19	,	,	PUNCT
ejpam-5662	528	20	almost	almost	ADV
ejpam-5662	528	21	they	they	PRON
ejpam-5662	528	22	give	give	VERB
ejpam-5662	528	23	the	the	DET
ejpam-5662	528	24	same	same	ADJ
ejpam-5662	528	25	dispersed	disperse	VERB
ejpam-5662	528	26	circular	circular	ADJ
ejpam-5662	528	27	curves	curve	NOUN
ejpam-5662	528	28	.	.	PUNCT
ejpam-5662	529	1	when	when	SCONJ
ejpam-5662	529	2	these	these	DET
ejpam-5662	529	3	generated	generate	VERB
ejpam-5662	529	4	curves	curve	NOUN
ejpam-5662	529	5	are	be	AUX
ejpam-5662	529	6	subjected	subject	VERB
ejpam-5662	529	7	to	to	PART
ejpam-5662	529	8	swirl	swirl	VERB
ejpam-5662	529	9	in	in	ADP
ejpam-5662	529	10	recurring	recur	VERB
ejpam-5662	529	11	tracks	track	NOUN
ejpam-5662	529	12	,	,	PUNCT
ejpam-5662	529	13	amazing	amazing	ADJ
ejpam-5662	529	14	gyration	gyration	ADJ
ejpam-5662	529	15	constructions	construction	NOUN
ejpam-5662	529	16	are	be	AUX
ejpam-5662	529	17	constructed	construct	VERB
ejpam-5662	529	18	,	,	PUNCT
ejpam-5662	529	19	which	which	PRON
ejpam-5662	529	20	are	be	AUX
ejpam-5662	529	21	regular	regular	ADJ
ejpam-5662	529	22	about	about	ADP
ejpam-5662	529	23	their	their	PRON
ejpam-5662	529	24	center	center	NOUN
ejpam-5662	529	25	.	.	PUNCT
ejpam-5662	530	1	it	it	PRON
ejpam-5662	530	2	is	be	AUX
ejpam-5662	530	3	sufficient	sufficient	ADJ
ejpam-5662	530	4	to	to	PART
ejpam-5662	530	5	examine	examine	VERB
ejpam-5662	530	6	the	the	DET
ejpam-5662	530	7	impact	impact	NOUN
ejpam-5662	530	8	of	of	ADP
ejpam-5662	530	9	one	one	NUM
ejpam-5662	530	10	of	of	ADP
ejpam-5662	530	11	the	the	DET
ejpam-5662	530	12	cubic	cubic	ADJ
ejpam-5662	530	13	and	and	CCONJ
ejpam-5662	530	14	quintic	quintic	ADJ
ejpam-5662	530	15	factors	factor	NOUN
ejpam-5662	530	16	because	because	SCONJ
ejpam-5662	530	17	of	of	ADP
ejpam-5662	530	18	their	their	PRON
ejpam-5662	530	19	similarities	similarity	NOUN
ejpam-5662	530	20	,	,	PUNCT
ejpam-5662	530	21	as	as	SCONJ
ejpam-5662	530	22	previously	previously	ADV
ejpam-5662	530	23	shown	show	VERB
ejpam-5662	530	24	.	.	PUNCT
ejpam-5662	531	1	in	in	ADP
ejpam-5662	531	2	order	order	NOUN
ejpam-5662	531	3	to	to	PART
ejpam-5662	531	4	show	show	VERB
ejpam-5662	531	5	the	the	DET
ejpam-5662	531	6	effects	effect	NOUN
ejpam-5662	531	7	of	of	ADP
ejpam-5662	531	8	the	the	DET
ejpam-5662	531	9	quinitic	quinitic	ADJ
ejpam-5662	531	10	coefficients	coefficient	NOUN
ejpam-5662	531	11	λ1	λ1	ADJ
ejpam-5662	531	12	and	and	CCONJ
ejpam-5662	531	13	λ2	λ2	PROPN
ejpam-5662	531	14	,	,	PUNCT
ejpam-5662	531	15	a	a	DET
ejpam-5662	531	16	new	new	ADJ
ejpam-5662	531	17	term	term	NOUN
ejpam-5662	531	18	included	include	VERB
ejpam-5662	531	19	in	in	ADP
ejpam-5662	531	20	the	the	DET
ejpam-5662	531	21	current	current	ADJ
ejpam-5662	531	22	research	research	NOUN
ejpam-5662	531	23	in	in	ADP
ejpam-5662	531	24	contrast	contrast	NOUN
ejpam-5662	531	25	to	to	ADP
ejpam-5662	531	26	the	the	DET
ejpam-5662	531	27	previous	previous	ADJ
ejpam-5662	531	28	one	one	NUM
ejpam-5662	531	29	[	[	X
ejpam-5662	531	30	38	38	NUM
ejpam-5662	531	31	]	]	PUNCT
ejpam-5662	531	32	,	,	PUNCT
ejpam-5662	531	33	figs	fig	NOUN
ejpam-5662	531	34	.	.	X
ejpam-5662	531	35	29	29	NUM
ejpam-5662	531	36	and	and	CCONJ
ejpam-5662	531	37	30	30	NUM
ejpam-5662	531	38	are	be	AUX
ejpam-5662	531	39	graphed	graph	VERB
ejpam-5662	531	40	.	.	PUNCT
ejpam-5662	532	1	the	the	DET
ejpam-5662	532	2	number	number	NOUN
ejpam-5662	532	3	of	of	ADP
ejpam-5662	532	4	loops	loop	NOUN
ejpam-5662	532	5	is	be	AUX
ejpam-5662	532	6	observed	observe	VERB
ejpam-5662	532	7	to	to	PART
ejpam-5662	532	8	increase	increase	VERB
ejpam-5662	532	9	as	as	ADP
ejpam-5662	532	10	and	and	CCONJ
ejpam-5662	532	11	rises	rise	NOUN
ejpam-5662	532	12	,	,	PUNCT
ejpam-5662	532	13	indicating	indicate	VERB
ejpam-5662	532	14	that	that	SCONJ
ejpam-5662	532	15	the	the	DET
ejpam-5662	532	16	existing	exist	VERB
ejpam-5662	532	17	system	system	NOUN
ejpam-5662	532	18	generally	generally	ADV
ejpam-5662	532	19	verifies	verify	VERB
ejpam-5662	532	20	the	the	DET
ejpam-5662	532	21	stability	stability	NOUN
ejpam-5662	532	22	method	method	NOUN
ejpam-5662	532	23	.	.	PUNCT
ejpam-5662	533	1	all	all	PRON
ejpam-5662	533	2	of	of	ADP
ejpam-5662	533	3	these	these	DET
ejpam-5662	533	4	curves	curve	NOUN
ejpam-5662	533	5	have	have	VERB
ejpam-5662	533	6	a	a	DET
ejpam-5662	533	7	variety	variety	NOUN
ejpam-5662	533	8	of	of	ADP
ejpam-5662	533	9	closed	closed	ADJ
ejpam-5662	533	10	or	or	CCONJ
ejpam-5662	533	11	semi	semi	ADJ
ejpam-5662	533	12	-	-	ADJ
ejpam-5662	533	13	closed	closed	ADJ
ejpam-5662	533	14	elliptical	elliptical	ADJ
ejpam-5662	533	15	trajectories	trajectory	NOUN
ejpam-5662	533	16	that	that	PRON
ejpam-5662	533	17	,	,	PUNCT
ejpam-5662	533	18	when	when	SCONJ
ejpam-5662	533	19	they	they	PRON
ejpam-5662	533	20	progressively	progressively	ADV
ejpam-5662	533	21	spread	spread	VERB
ejpam-5662	533	22	out	out	ADP
ejpam-5662	533	23	around	around	ADP
ejpam-5662	533	24	the	the	DET
ejpam-5662	533	25	center	center	NOUN
ejpam-5662	533	26	point	point	NOUN
ejpam-5662	533	27	,	,	PUNCT
ejpam-5662	533	28	produce	produce	VERB
ejpam-5662	533	29	these	these	DET
ejpam-5662	533	30	amazing	amazing	ADJ
ejpam-5662	533	31	shapes	shape	NOUN
ejpam-5662	533	32	.	.	PUNCT
ejpam-5662	534	1	because	because	SCONJ
ejpam-5662	534	2	the	the	DET
ejpam-5662	534	3	data	datum	NOUN
ejpam-5662	534	4	used	use	VERB
ejpam-5662	534	5	to	to	PART
ejpam-5662	534	6	create	create	VERB
ejpam-5662	534	7	the	the	DET
ejpam-5662	534	8	figures	figure	NOUN
ejpam-5662	534	9	is	be	AUX
ejpam-5662	534	10	similar	similar	ADJ
ejpam-5662	534	11	,	,	PUNCT
ejpam-5662	534	12	some	some	PRON
ejpam-5662	534	13	of	of	ADP
ejpam-5662	534	14	its	its	PRON
ejpam-5662	534	15	components	component	NOUN
ejpam-5662	534	16	are	be	AUX
ejpam-5662	534	17	deemed	deem	VERB
ejpam-5662	534	18	comparable	comparable	ADJ
ejpam-5662	534	19	.	.	PUNCT
ejpam-5662	535	1	a.	a.	PROPN
ejpam-5662	535	2	alanazy	alanazy	PROPN
ejpam-5662	535	3	,	,	PUNCT
ejpam-5662	535	4	g.	g.	PROPN
ejpam-5662	535	5	m.	m.	PROPN
ejpam-5662	535	6	moatimid	moatimid	PROPN
ejpam-5662	535	7	,	,	PUNCT
ejpam-5662	535	8	m.	m.	PROPN
ejpam-5662	535	9	a.	a.	PROPN
ejpam-5662	535	10	a.	a.	PROPN
ejpam-5662	535	11	mohamed	mohamed	PROPN
ejpam-5662	535	12	/	/	SYM
ejpam-5662	535	13	eur	eur	PROPN
ejpam-5662	535	14	.	.	PUNCT
ejpam-5662	536	1	j.	j.	PROPN
ejpam-5662	536	2	pure	pure	PROPN
ejpam-5662	536	3	appl	appl	PROPN
ejpam-5662	536	4	.	.	PROPN
ejpam-5662	536	5	math	math	PROPN
ejpam-5662	536	6	,	,	PUNCT
ejpam-5662	536	7	18	18	NUM
ejpam-5662	536	8	(	(	PUNCT
ejpam-5662	536	9	2	2	NUM
ejpam-5662	536	10	)	)	PUNCT
ejpam-5662	536	11	(	(	PUNCT
ejpam-5662	536	12	2025	2025	NUM
ejpam-5662	536	13	)	)	PUNCT
ejpam-5662	536	14	,	,	PUNCT
ejpam-5662	536	15	5662	5662	NUM
ejpam-5662	536	16	30	30	NUM
ejpam-5662	536	17	of	of	ADP
ejpam-5662	536	18	36	36	NUM
ejpam-5662	536	19	figure	figure	NOUN
ejpam-5662	536	20	25	25	NUM
ejpam-5662	536	21	:	:	PUNCT
ejpam-5662	536	22	displays	display	VERB
ejpam-5662	536	23	the	the	DET
ejpam-5662	536	24	polarplot	polarplot	NOUN
ejpam-5662	536	25	of	of	ADP
ejpam-5662	536	26	w(t	w(t	PROPN
ejpam-5662	536	27	)	)	PUNCT
ejpam-5662	536	28	for	for	ADP
ejpam-5662	536	29	different	different	ADJ
ejpam-5662	536	30	measures	measure	NOUN
ejpam-5662	536	31	of	of	ADP
ejpam-5662	536	32	the	the	DET
ejpam-5662	536	33	x	x	ADJ
ejpam-5662	536	34	-	-	ADJ
ejpam-5662	536	35	oscillator	oscillator	ADJ
ejpam-5662	536	36	natural	natural	ADJ
ejpam-5662	536	37	frequency	frequency	NOUN
ejpam-5662	536	38	ω1	ω1	PROPN
ejpam-5662	536	39	.	.	PUNCT
ejpam-5662	536	40	figure	figure	NOUN
ejpam-5662	536	41	26	26	NUM
ejpam-5662	536	42	:	:	PUNCT
ejpam-5662	536	43	displays	display	VERB
ejpam-5662	536	44	the	the	DET
ejpam-5662	536	45	polarplot	polarplot	NOUN
ejpam-5662	536	46	of	of	ADP
ejpam-5662	536	47	g(t	g(t	PROPN
ejpam-5662	536	48	)	)	PUNCT
ejpam-5662	536	49	for	for	ADP
ejpam-5662	536	50	different	different	ADJ
ejpam-5662	536	51	measures	measure	NOUN
ejpam-5662	536	52	of	of	ADP
ejpam-5662	536	53	the	the	DET
ejpam-5662	536	54	y	y	PROPN
ejpam-5662	536	55	-	-	PUNCT
ejpam-5662	536	56	oscillator	oscillator	NOUN
ejpam-5662	536	57	natural	natural	ADJ
ejpam-5662	536	58	frequency	frequency	NOUN
ejpam-5662	536	59	ω2	ω2	PROPN
ejpam-5662	536	60	.	.	PUNCT
ejpam-5662	537	1	figure	figure	NOUN
ejpam-5662	537	2	27	27	NUM
ejpam-5662	537	3	:	:	PUNCT
ejpam-5662	537	4	displays	display	VERB
ejpam-5662	537	5	the	the	DET
ejpam-5662	537	6	polarplot	polarplot	NOUN
ejpam-5662	537	7	of	of	ADP
ejpam-5662	537	8	w(t	w(t	PROPN
ejpam-5662	537	9	)	)	PUNCT
ejpam-5662	537	10	for	for	ADP
ejpam-5662	537	11	different	different	ADJ
ejpam-5662	537	12	measures	measure	NOUN
ejpam-5662	537	13	of	of	ADP
ejpam-5662	537	14	the	the	DET
ejpam-5662	537	15	x	x	ADJ
ejpam-5662	537	16	-	-	ADJ
ejpam-5662	537	17	oscillator	oscillator	ADJ
ejpam-5662	537	18	excited	excite	VERB
ejpam-5662	537	19	amplitude	amplitude	NOUN
ejpam-5662	537	20	coefficient	coefficient	NOUN
ejpam-5662	537	21	η11	η11	NOUN
ejpam-5662	537	22	.	.	PUNCT
ejpam-5662	538	1	a.	a.	PROPN
ejpam-5662	538	2	alanazy	alanazy	PROPN
ejpam-5662	538	3	,	,	PUNCT
ejpam-5662	538	4	g.	g.	PROPN
ejpam-5662	538	5	m.	m.	PROPN
ejpam-5662	538	6	moatimid	moatimid	PROPN
ejpam-5662	538	7	,	,	PUNCT
ejpam-5662	538	8	m.	m.	PROPN
ejpam-5662	538	9	a.	a.	PROPN
ejpam-5662	538	10	a.	a.	PROPN
ejpam-5662	538	11	mohamed	mohamed	PROPN
ejpam-5662	538	12	/	/	SYM
ejpam-5662	538	13	eur	eur	PROPN
ejpam-5662	538	14	.	.	PUNCT
ejpam-5662	539	1	j.	j.	PROPN
ejpam-5662	539	2	pure	pure	PROPN
ejpam-5662	539	3	appl	appl	PROPN
ejpam-5662	539	4	.	.	PROPN
ejpam-5662	539	5	math	math	PROPN
ejpam-5662	539	6	,	,	PUNCT
ejpam-5662	539	7	18	18	NUM
ejpam-5662	539	8	(	(	PUNCT
ejpam-5662	539	9	2	2	NUM
ejpam-5662	539	10	)	)	PUNCT
ejpam-5662	539	11	(	(	PUNCT
ejpam-5662	539	12	2025	2025	NUM
ejpam-5662	539	13	)	)	PUNCT
ejpam-5662	539	14	,	,	PUNCT
ejpam-5662	539	15	5662	5662	NUM
ejpam-5662	539	16	31	31	NUM
ejpam-5662	539	17	of	of	ADP
ejpam-5662	539	18	36	36	NUM
ejpam-5662	539	19	figure	figure	NOUN
ejpam-5662	539	20	28	28	NUM
ejpam-5662	539	21	:	:	PUNCT
ejpam-5662	539	22	displays	display	VERB
ejpam-5662	539	23	the	the	DET
ejpam-5662	539	24	polarplot	polarplot	NOUN
ejpam-5662	539	25	of	of	ADP
ejpam-5662	539	26	g(t	g(t	PROPN
ejpam-5662	539	27	)	)	PUNCT
ejpam-5662	539	28	for	for	ADP
ejpam-5662	539	29	different	different	ADJ
ejpam-5662	539	30	measures	measure	NOUN
ejpam-5662	539	31	of	of	ADP
ejpam-5662	539	32	the	the	DET
ejpam-5662	539	33	excited	excited	ADJ
ejpam-5662	539	34	amplitude	amplitude	NOUN
ejpam-5662	539	35	coefficient	coefficient	NOUN
ejpam-5662	539	36	η21	η21	PROPN
ejpam-5662	539	37	.	.	PUNCT
ejpam-5662	540	1	figure	figure	NOUN
ejpam-5662	540	2	29	29	NUM
ejpam-5662	540	3	:	:	PUNCT
ejpam-5662	540	4	displays	display	VERB
ejpam-5662	540	5	the	the	DET
ejpam-5662	540	6	polarplot	polarplot	NOUN
ejpam-5662	540	7	of	of	ADP
ejpam-5662	540	8	w(t	w(t	PROPN
ejpam-5662	540	9	)	)	PUNCT
ejpam-5662	540	10	for	for	ADP
ejpam-5662	540	11	different	different	ADJ
ejpam-5662	540	12	measures	measure	NOUN
ejpam-5662	540	13	of	of	ADP
ejpam-5662	540	14	the	the	DET
ejpam-5662	540	15	x	x	ADJ
ejpam-5662	540	16	-	-	ADJ
ejpam-5662	540	17	oscillator	oscillator	ADJ
ejpam-5662	540	18	quinitic	quinitic	ADJ
ejpam-5662	540	19	coefficient	coefficient	NOUN
ejpam-5662	540	20	λ1	λ1	PROPN
ejpam-5662	540	21	.	.	PUNCT
ejpam-5662	541	1	figure	figure	NOUN
ejpam-5662	541	2	30	30	NUM
ejpam-5662	541	3	:	:	PUNCT
ejpam-5662	541	4	displays	display	VERB
ejpam-5662	541	5	the	the	DET
ejpam-5662	541	6	polarplot	polarplot	NOUN
ejpam-5662	541	7	of	of	ADP
ejpam-5662	541	8	g(t	g(t	PROPN
ejpam-5662	541	9	)	)	PUNCT
ejpam-5662	541	10	for	for	ADP
ejpam-5662	541	11	different	different	ADJ
ejpam-5662	541	12	measures	measure	NOUN
ejpam-5662	541	13	of	of	ADP
ejpam-5662	541	14	the	the	DET
ejpam-5662	541	15	y	y	PROPN
ejpam-5662	541	16	-	-	PUNCT
ejpam-5662	541	17	oscillator	oscillator	NOUN
ejpam-5662	541	18	quinitic	quinitic	ADJ
ejpam-5662	541	19	coefficient	coefficient	NOUN
ejpam-5662	541	20	λ2	λ2	PROPN
ejpam-5662	541	21	.	.	PUNCT
ejpam-5662	542	1	6	6	NUM
ejpam-5662	542	2	.	.	X
ejpam-5662	542	3	concluding	conclude	VERB
ejpam-5662	542	4	remarks	remark	VERB
ejpam-5662	542	5	the	the	DET
ejpam-5662	542	6	mdo	mdo	PROPN
ejpam-5662	542	7	served	serve	VERB
ejpam-5662	542	8	as	as	ADP
ejpam-5662	542	9	a	a	DET
ejpam-5662	542	10	foundational	foundational	ADJ
ejpam-5662	542	11	model	model	NOUN
ejpam-5662	542	12	in	in	ADP
ejpam-5662	542	13	a	a	DET
ejpam-5662	542	14	parametrically	parametrically	ADV
ejpam-5662	542	15	excited	excited	ADJ
ejpam-5662	542	16	system	system	NOUN
ejpam-5662	542	17	that	that	PRON
ejpam-5662	542	18	distinguished	distinguish	VERB
ejpam-5662	542	19	by	by	ADP
ejpam-5662	542	20	the	the	DET
ejpam-5662	542	21	nonlinearities	nonlinearitie	NOUN
ejpam-5662	542	22	.	.	PUNCT
ejpam-5662	543	1	this	this	DET
ejpam-5662	543	2	matter	matter	NOUN
ejpam-5662	543	3	is	be	AUX
ejpam-5662	543	4	crucial	crucial	ADJ
ejpam-5662	543	5	for	for	ADP
ejpam-5662	543	6	understanding	understand	VERB
ejpam-5662	543	7	complex	complex	ADJ
ejpam-5662	543	8	,	,	PUNCT
ejpam-5662	543	9	nonlinear	nonlinear	ADJ
ejpam-5662	543	10	dynamical	dynamical	ADJ
ejpam-5662	543	11	behavior	behavior	NOUN
ejpam-5662	543	12	,	,	PUNCT
ejpam-5662	543	13	including	include	VERB
ejpam-5662	543	14	bifurcations	bifurcation	NOUN
ejpam-5662	543	15	,	,	PUNCT
ejpam-5662	543	16	chaos	chaos	NOUN
ejpam-5662	543	17	,	,	PUNCT
ejpam-5662	543	18	and	and	CCONJ
ejpam-5662	543	19	resonance	resonance	NOUN
ejpam-5662	543	20	phenomena	phenomenon	NOUN
ejpam-5662	543	21	,	,	PUNCT
ejpam-5662	543	22	a.	a.	NOUN
ejpam-5662	543	23	alanazy	alanazy	NOUN
ejpam-5662	543	24	,	,	PUNCT
ejpam-5662	543	25	g.	g.	PROPN
ejpam-5662	543	26	m.	m.	PROPN
ejpam-5662	543	27	moatimid	moatimid	PROPN
ejpam-5662	543	28	,	,	PUNCT
ejpam-5662	543	29	m.	m.	PROPN
ejpam-5662	543	30	a.	a.	PROPN
ejpam-5662	543	31	a.	a.	PROPN
ejpam-5662	543	32	mohamed	mohamed	PROPN
ejpam-5662	543	33	/	/	SYM
ejpam-5662	543	34	eur	eur	PROPN
ejpam-5662	543	35	.	.	PUNCT
ejpam-5662	544	1	j.	j.	PROPN
ejpam-5662	544	2	pure	pure	PROPN
ejpam-5662	544	3	appl	appl	PROPN
ejpam-5662	544	4	.	.	PROPN
ejpam-5662	544	5	math	math	PROPN
ejpam-5662	544	6	,	,	PUNCT
ejpam-5662	544	7	18	18	NUM
ejpam-5662	544	8	(	(	PUNCT
ejpam-5662	544	9	2	2	NUM
ejpam-5662	544	10	)	)	PUNCT
ejpam-5662	544	11	(	(	PUNCT
ejpam-5662	544	12	2025	2025	NUM
ejpam-5662	544	13	)	)	PUNCT
ejpam-5662	544	14	,	,	PUNCT
ejpam-5662	544	15	5662	5662	NUM
ejpam-5662	544	16	32	32	NUM
ejpam-5662	544	17	of	of	ADP
ejpam-5662	544	18	36	36	NUM
ejpam-5662	544	19	relevant	relevant	ADJ
ejpam-5662	544	20	to	to	ADP
ejpam-5662	544	21	engineering	engineering	NOUN
ejpam-5662	544	22	and	and	CCONJ
ejpam-5662	544	23	physics	physics	NOUN
ejpam-5662	544	24	for	for	ADP
ejpam-5662	544	25	systems	system	NOUN
ejpam-5662	544	26	affected	affect	VERB
ejpam-5662	544	27	by	by	ADP
ejpam-5662	544	28	periodic	periodic	ADJ
ejpam-5662	544	29	external	external	ADJ
ejpam-5662	544	30	stimuli	stimulus	NOUN
ejpam-5662	544	31	.	.	PUNCT
ejpam-5662	545	1	a	a	DET
ejpam-5662	545	2	universal	universal	ADJ
ejpam-5662	545	3	tdof	tdof	ADJ
ejpam-5662	545	4	model	model	NOUN
ejpam-5662	545	5	of	of	ADP
ejpam-5662	545	6	dynamic	dynamic	ADJ
ejpam-5662	545	7	optimization	optimization	NOUN
ejpam-5662	545	8	was	be	AUX
ejpam-5662	545	9	analyzed	analyze	VERB
ejpam-5662	545	10	.	.	PUNCT
ejpam-5662	546	1	this	this	DET
ejpam-5662	546	2	work	work	NOUN
ejpam-5662	546	3	employed	employ	VERB
ejpam-5662	546	4	an	an	DET
ejpam-5662	546	5	application	application	NOUN
ejpam-5662	546	6	of	of	ADP
ejpam-5662	546	7	the	the	DET
ejpam-5662	546	8	npa	npa	NOUN
ejpam-5662	546	9	to	to	PART
ejpam-5662	546	10	analyze	analyze	VERB
ejpam-5662	546	11	a	a	DET
ejpam-5662	546	12	coupled	couple	VERB
ejpam-5662	546	13	system	system	NOUN
ejpam-5662	546	14	of	of	ADP
ejpam-5662	546	15	mdo	mdo	PROPN
ejpam-5662	546	16	and	and	CCONJ
ejpam-5662	546	17	assess	assess	VERB
ejpam-5662	546	18	the	the	DET
ejpam-5662	546	19	efficacy	efficacy	NOUN
ejpam-5662	546	20	of	of	ADP
ejpam-5662	546	21	a	a	DET
ejpam-5662	546	22	parametric	parametric	ADJ
ejpam-5662	546	23	nonlinear	nonlinear	ADJ
ejpam-5662	546	24	oscillatory	oscillatory	ADJ
ejpam-5662	546	25	system	system	NOUN
ejpam-5662	546	26	in	in	ADP
ejpam-5662	546	27	the	the	DET
ejpam-5662	546	28	damped	damped	NOUN
ejpam-5662	546	29	and	and	CCONJ
ejpam-5662	546	30	non	non	ADJ
ejpam-5662	546	31	-	-	ADJ
ejpam-5662	546	32	damped	damped	ADJ
ejpam-5662	546	33	cases	case	NOUN
ejpam-5662	546	34	.	.	PUNCT
ejpam-5662	547	1	the	the	DET
ejpam-5662	547	2	npa	npa	NOUN
ejpam-5662	547	3	primarily	primarily	ADV
ejpam-5662	547	4	relies	rely	VERB
ejpam-5662	547	5	on	on	ADP
ejpam-5662	547	6	the	the	DET
ejpam-5662	547	7	hff	hff	NOUN
ejpam-5662	547	8	.	.	PUNCT
ejpam-5662	548	1	therefore	therefore	ADV
ejpam-5662	548	2	,	,	PUNCT
ejpam-5662	548	3	the	the	DET
ejpam-5662	548	4	current	current	ADJ
ejpam-5662	548	5	study	study	NOUN
ejpam-5662	548	6	aims	aim	VERB
ejpam-5662	548	7	to	to	PART
ejpam-5662	548	8	move	move	VERB
ejpam-5662	548	9	away	away	ADV
ejpam-5662	548	10	from	from	ADP
ejpam-5662	548	11	conventional	conventional	ADJ
ejpam-5662	548	12	perturbation	perturbation	NOUN
ejpam-5662	548	13	techniques	technique	NOUN
ejpam-5662	548	14	and	and	CCONJ
ejpam-5662	548	15	provide	provide	VERB
ejpam-5662	548	16	approximated	approximate	VERB
ejpam-5662	548	17	solutions	solution	NOUN
ejpam-5662	548	18	for	for	ADP
ejpam-5662	548	19	small	small	ADJ
ejpam-5662	548	20	amplitude	amplitude	NOUN
ejpam-5662	548	21	parametric	parametric	ADJ
ejpam-5662	548	22	components	component	NOUN
ejpam-5662	548	23	without	without	ADP
ejpam-5662	548	24	limitations	limitation	NOUN
ejpam-5662	548	25	.	.	PUNCT
ejpam-5662	549	1	moreover	moreover	ADV
ejpam-5662	549	2	,	,	PUNCT
ejpam-5662	549	3	the	the	DET
ejpam-5662	549	4	technique	technique	NOUN
ejpam-5662	549	5	is	be	AUX
ejpam-5662	549	6	expanded	expand	VERB
ejpam-5662	549	7	to	to	PART
ejpam-5662	549	8	determine	determine	VERB
ejpam-5662	549	9	optimal	optimal	ADJ
ejpam-5662	549	10	solutions	solution	NOUN
ejpam-5662	549	11	for	for	ADP
ejpam-5662	549	12	nonlinear	nonlinear	ADJ
ejpam-5662	549	13	large	large	ADJ
ejpam-5662	549	14	amplitude	amplitude	NOUN
ejpam-5662	549	15	fluctuations	fluctuation	NOUN
ejpam-5662	549	16	.	.	PUNCT
ejpam-5662	550	1	the	the	DET
ejpam-5662	550	2	ms	ms	PROPN
ejpam-5662	550	3	was	be	AUX
ejpam-5662	550	4	utilized	utilize	VERB
ejpam-5662	550	5	to	to	PART
ejpam-5662	550	6	validate	validate	VERB
ejpam-5662	550	7	the	the	DET
ejpam-5662	550	8	resulting	result	VERB
ejpam-5662	550	9	parametric	parametric	ADJ
ejpam-5662	550	10	equation	equation	NOUN
ejpam-5662	550	11	,	,	PUNCT
ejpam-5662	550	12	which	which	PRON
ejpam-5662	550	13	exhibits	exhibit	VERB
ejpam-5662	550	14	substantial	substantial	ADJ
ejpam-5662	550	15	agreement	agreement	NOUN
ejpam-5662	550	16	with	with	ADP
ejpam-5662	550	17	the	the	DET
ejpam-5662	550	18	original	original	ADJ
ejpam-5662	550	19	equation	equation	NOUN
ejpam-5662	550	20	.	.	PUNCT
ejpam-5662	551	1	the	the	DET
ejpam-5662	551	2	current	current	ADJ
ejpam-5662	551	3	methodology	methodology	NOUN
ejpam-5662	551	4	was	be	AUX
ejpam-5662	551	5	defined	define	VERB
ejpam-5662	551	6	by	by	ADP
ejpam-5662	551	7	explicit	explicit	ADJ
ejpam-5662	551	8	principles	principle	NOUN
ejpam-5662	551	9	,	,	PUNCT
ejpam-5662	551	10	suitability	suitability	NOUN
ejpam-5662	551	11	,	,	PUNCT
ejpam-5662	551	12	ease	ease	NOUN
ejpam-5662	551	13	of	of	ADP
ejpam-5662	551	14	use	use	NOUN
ejpam-5662	551	15	,	,	PUNCT
ejpam-5662	551	16	and	and	CCONJ
ejpam-5662	551	17	remarkable	remarkable	ADJ
ejpam-5662	551	18	numerical	numerical	ADJ
ejpam-5662	551	19	accuracy	accuracy	NOUN
ejpam-5662	551	20	.	.	PUNCT
ejpam-5662	552	1	the	the	DET
ejpam-5662	552	2	existing	exist	VERB
ejpam-5662	552	3	approach	approach	NOUN
ejpam-5662	552	4	diminishes	diminish	VERB
ejpam-5662	552	5	mathematical	mathematical	ADJ
ejpam-5662	552	6	complexity	complexity	NOUN
ejpam-5662	552	7	,	,	PUNCT
ejpam-5662	552	8	rendering	render	VERB
ejpam-5662	552	9	it	it	PRON
ejpam-5662	552	10	beneficial	beneficial	ADJ
ejpam-5662	552	11	for	for	ADP
ejpam-5662	552	12	tackling	tackle	VERB
ejpam-5662	552	13	nonlinear	nonlinear	ADJ
ejpam-5662	552	14	parametric	parametric	ADJ
ejpam-5662	552	15	issues	issue	NOUN
ejpam-5662	552	16	.	.	PUNCT
ejpam-5662	553	1	the	the	DET
ejpam-5662	553	2	main	main	ADJ
ejpam-5662	553	3	key	key	ADJ
ejpam-5662	553	4	outcomes	outcome	NOUN
ejpam-5662	553	5	of	of	ADP
ejpam-5662	553	6	the	the	DET
ejpam-5662	553	7	current	current	NOUN
ejpam-5662	553	8	may	may	AUX
ejpam-5662	553	9	be	be	AUX
ejpam-5662	553	10	summarized	summarize	VERB
ejpam-5662	553	11	as	as	SCONJ
ejpam-5662	553	12	follows	follow	VERB
ejpam-5662	553	13	:	:	PUNCT
ejpam-5662	554	1	1	1	X
ejpam-5662	554	2	.	.	PUNCT
ejpam-5662	554	3	the	the	DET
ejpam-5662	554	4	npa	npa	NOUN
ejpam-5662	554	5	was	be	AUX
ejpam-5662	554	6	adapted	adapt	VERB
ejpam-5662	554	7	to	to	PART
ejpam-5662	554	8	find	find	VERB
ejpam-5662	554	9	equivalent	equivalent	ADJ
ejpam-5662	554	10	linear	linear	ADJ
ejpam-5662	554	11	odes	ode	NOUN
ejpam-5662	554	12	.	.	PUNCT
ejpam-5662	555	1	an	an	DET
ejpam-5662	555	2	excellent	excellent	ADJ
ejpam-5662	555	3	matching	matching	NOUN
ejpam-5662	555	4	between	between	ADP
ejpam-5662	555	5	the	the	DET
ejpam-5662	555	6	original	original	ADJ
ejpam-5662	555	7	nonlinear	nonlinear	ADJ
ejpam-5662	555	8	system	system	NOUN
ejpam-5662	555	9	and	and	CCONJ
ejpam-5662	555	10	the	the	DET
ejpam-5662	555	11	corresponding	corresponding	ADJ
ejpam-5662	555	12	linear	linear	ADJ
ejpam-5662	555	13	one	one	NUM
ejpam-5662	555	14	was	be	AUX
ejpam-5662	555	15	found	find	VERB
ejpam-5662	555	16	and	and	CCONJ
ejpam-5662	555	17	validated	validate	VERB
ejpam-5662	555	18	through	through	ADP
ejpam-5662	555	19	some	some	DET
ejpam-5662	555	20	graphs	graph	NOUN
ejpam-5662	555	21	and	and	CCONJ
ejpam-5662	555	22	error	error	NOUN
ejpam-5662	555	23	tables	table	NOUN
ejpam-5662	555	24	.	.	PUNCT
ejpam-5662	556	1	2	2	X
ejpam-5662	556	2	.	.	X
ejpam-5662	556	3	the	the	DET
ejpam-5662	556	4	stability	stability	NOUN
ejpam-5662	556	5	of	of	ADP
ejpam-5662	556	6	the	the	DET
ejpam-5662	556	7	various	various	ADJ
ejpam-5662	556	8	states	state	NOUN
ejpam-5662	556	9	was	be	AUX
ejpam-5662	556	10	guaranteed	guarantee	VERB
ejpam-5662	556	11	by	by	ADP
ejpam-5662	556	12	time	time	NOUN
ejpam-5662	556	13	-	-	PUNCT
ejpam-5662	556	14	dependent	dependent	ADJ
ejpam-5662	556	15	plots	plot	NOUN
ejpam-5662	556	16	and	and	CCONJ
ejpam-5662	556	17	polarplots	polarplot	NOUN
ejpam-5662	556	18	of	of	ADP
ejpam-5662	556	19	these	these	DET
ejpam-5662	556	20	equivalent	equivalent	ADJ
ejpam-5662	556	21	solutions	solution	NOUN
ejpam-5662	556	22	with	with	ADP
ejpam-5662	556	23	the	the	DET
ejpam-5662	556	24	variation	variation	NOUN
ejpam-5662	556	25	of	of	ADP
ejpam-5662	556	26	the	the	DET
ejpam-5662	556	27	multiple	multiple	ADJ
ejpam-5662	556	28	pertinent	pertinent	ADJ
ejpam-5662	556	29	coefficients	coefficient	NOUN
ejpam-5662	556	30	.	.	PUNCT
ejpam-5662	557	1	3	3	X
ejpam-5662	557	2	.	.	X
ejpam-5662	557	3	regular	regular	ADJ
ejpam-5662	557	4	reduction	reduction	NOUN
ejpam-5662	557	5	conduct	conduct	NOUN
ejpam-5662	557	6	in	in	ADP
ejpam-5662	557	7	the	the	DET
ejpam-5662	557	8	time	time	NOUN
ejpam-5662	557	9	histories	history	NOUN
ejpam-5662	557	10	of	of	ADP
ejpam-5662	557	11	these	these	DET
ejpam-5662	557	12	solutions	solution	NOUN
ejpam-5662	557	13	indicates	indicate	VERB
ejpam-5662	557	14	stable	stable	ADJ
ejpam-5662	557	15	modes	mode	NOUN
ejpam-5662	557	16	.	.	PUNCT
ejpam-5662	558	1	4	4	X
ejpam-5662	558	2	.	.	PUNCT
ejpam-5662	558	3	additionally	additionally	ADV
ejpam-5662	558	4	,	,	PUNCT
ejpam-5662	558	5	the	the	DET
ejpam-5662	558	6	polarplots	polarplot	NOUN
ejpam-5662	558	7	curves	curve	NOUN
ejpam-5662	558	8	displayed	display	VERB
ejpam-5662	558	9	continued	continue	VERB
ejpam-5662	558	10	uniform	uniform	ADJ
ejpam-5662	558	11	spirals	spiral	NOUN
ejpam-5662	558	12	meeting	meet	VERB
ejpam-5662	558	13	at	at	ADP
ejpam-5662	558	14	a	a	DET
ejpam-5662	558	15	central	central	ADJ
ejpam-5662	558	16	point	point	NOUN
ejpam-5662	558	17	.	.	PUNCT
ejpam-5662	559	1	5	5	X
ejpam-5662	559	2	.	.	X
ejpam-5662	559	3	periodic	periodic	ADJ
ejpam-5662	559	4	behaviors	behavior	NOUN
ejpam-5662	559	5	were	be	AUX
ejpam-5662	559	6	detected	detect	VERB
ejpam-5662	559	7	in	in	ADP
ejpam-5662	559	8	all	all	DET
ejpam-5662	559	9	cases	case	NOUN
ejpam-5662	559	10	with	with	ADP
ejpam-5662	559	11	the	the	DET
ejpam-5662	559	12	variation	variation	NOUN
ejpam-5662	559	13	of	of	ADP
ejpam-5662	559	14	several	several	ADJ
ejpam-5662	559	15	parameters	parameter	NOUN
ejpam-5662	559	16	.	.	PUNCT
ejpam-5662	560	1	the	the	DET
ejpam-5662	560	2	current	current	ADJ
ejpam-5662	560	3	study	study	NOUN
ejpam-5662	560	4	will	will	AUX
ejpam-5662	560	5	be	be	AUX
ejpam-5662	560	6	enhanced	enhance	VERB
ejpam-5662	560	7	in	in	ADP
ejpam-5662	560	8	the	the	DET
ejpam-5662	560	9	subsequent	subsequent	ADJ
ejpam-5662	560	10	work	work	NOUN
ejpam-5662	560	11	to	to	PART
ejpam-5662	560	12	include	include	VERB
ejpam-5662	560	13	the	the	DET
ejpam-5662	560	14	stability	stability	NOUN
ejpam-5662	560	15	conditions	condition	NOUN
ejpam-5662	560	16	profile	profile	VERB
ejpam-5662	560	17	,	,	PUNCT
ejpam-5662	560	18	the	the	DET
ejpam-5662	560	19	resonance	resonance	NOUN
ejpam-5662	560	20	,	,	PUNCT
ejpam-5662	560	21	the	the	DET
ejpam-5662	560	22	bifurcation	bifurcation	NOUN
ejpam-5662	560	23	,	,	PUNCT
ejpam-5662	560	24	and	and	CCONJ
ejpam-5662	560	25	the	the	DET
ejpam-5662	560	26	chaotic	chaotic	ADJ
ejpam-5662	560	27	behavior	behavior	NOUN
ejpam-5662	560	28	of	of	ADP
ejpam-5662	560	29	coupled	couple	VERB
ejpam-5662	560	30	and	and	CCONJ
ejpam-5662	560	31	multiple	multiple	ADJ
ejpam-5662	560	32	systems	system	NOUN
ejpam-5662	560	33	.	.	PUNCT
ejpam-5662	561	1	acknowledgements	acknowledgement	NOUN
ejpam-5662	561	2	the	the	DET
ejpam-5662	561	3	authors	author	NOUN
ejpam-5662	561	4	extend	extend	VERB
ejpam-5662	561	5	their	their	PRON
ejpam-5662	561	6	appreciation	appreciation	NOUN
ejpam-5662	561	7	to	to	ADP
ejpam-5662	561	8	the	the	DET
ejpam-5662	561	9	deanship	deanship	NOUN
ejpam-5662	561	10	of	of	ADP
ejpam-5662	561	11	scientific	scientific	ADJ
ejpam-5662	561	12	research	research	NOUN
ejpam-5662	561	13	at	at	ADP
ejpam-5662	561	14	northern	northern	ADJ
ejpam-5662	561	15	border	border	NOUN
ejpam-5662	561	16	university	university	PROPN
ejpam-5662	561	17	,	,	PUNCT
ejpam-5662	561	18	arar	arar	PROPN
ejpam-5662	561	19	,	,	PUNCT
ejpam-5662	561	20	ksa	ksa	PROPN
ejpam-5662	561	21	for	for	ADP
ejpam-5662	561	22	funding	fund	VERB
ejpam-5662	561	23	this	this	DET
ejpam-5662	561	24	research	research	NOUN
ejpam-5662	561	25	work	work	NOUN
ejpam-5662	561	26	through	through	ADP
ejpam-5662	561	27	the	the	DET
ejpam-5662	561	28	project	project	NOUN
ejpam-5662	561	29	number	number	NOUN
ejpam-5662	561	30	”	"	PUNCT
ejpam-5662	561	31	nbu	nbu	NOUN
ejpam-5662	561	32	-	-	PUNCT
ejpam-5662	561	33	ffr-2024	ffr-2024	NOUN
ejpam-5662	561	34	-	-	PUNCT
ejpam-5662	561	35	912	912	NUM
ejpam-5662	561	36	-	-	PUNCT
ejpam-5662	561	37	04	04	NUM
ejpam-5662	561	38	”	"	PUNCT
ejpam-5662	561	39	author	author	NOUN
ejpam-5662	561	40	contributions	contribution	NOUN
ejpam-5662	561	41	asma	asma	PROPN
ejpam-5662	561	42	alanazy	alanazy	PROPN
ejpam-5662	561	43	:	:	PUNCT
ejpam-5662	561	44	resources	resource	NOUN
ejpam-5662	561	45	,	,	PUNCT
ejpam-5662	561	46	methodology	methodology	NOUN
ejpam-5662	561	47	,	,	PUNCT
ejpam-5662	561	48	formal	formal	ADJ
ejpam-5662	561	49	analysis	analysis	NOUN
ejpam-5662	561	50	,	,	PUNCT
ejpam-5662	561	51	validation	validation	NOUN
ejpam-5662	561	52	,	,	PUNCT
ejpam-5662	561	53	visualization	visualization	NOUN
ejpam-5662	561	54	and	and	CCONJ
ejpam-5662	561	55	reviewing	reviewing	NOUN
ejpam-5662	561	56	.	.	PUNCT
ejpam-5662	562	1	galal	galal	PROPN
ejpam-5662	562	2	m.	m.	PROPN
ejpam-5662	562	3	moatimid	moatimid	PROPN
ejpam-5662	562	4	:	:	PUNCT
ejpam-5662	562	5	conceptualization	conceptualization	NOUN
ejpam-5662	562	6	,	,	PUNCT
ejpam-5662	562	7	resources	resource	NOUN
ejpam-5662	562	8	,	,	PUNCT
ejpam-5662	562	9	methodology	methodology	NOUN
ejpam-5662	562	10	,	,	PUNCT
ejpam-5662	562	11	formal	formal	ADJ
ejpam-5662	562	12	analysis	analysis	NOUN
ejpam-5662	562	13	,	,	PUNCT
ejpam-5662	562	14	validation	validation	NOUN
ejpam-5662	562	15	,	,	PUNCT
ejpam-5662	562	16	writing	writing	NOUN
ejpam-5662	562	17	-	-	PUNCT
ejpam-5662	562	18	original	original	ADJ
ejpam-5662	562	19	draft	draft	NOUN
ejpam-5662	562	20	preparation	preparation	NOUN
ejpam-5662	562	21	,	,	PUNCT
ejpam-5662	562	22	visualization	visualization	NOUN
ejpam-5662	562	23	and	and	CCONJ
ejpam-5662	562	24	reviewing	reviewing	NOUN
ejpam-5662	562	25	.	.	PUNCT
ejpam-5662	563	1	a.	a.	PROPN
ejpam-5662	563	2	alanazy	alanazy	PROPN
ejpam-5662	563	3	,	,	PUNCT
ejpam-5662	563	4	g.	g.	PROPN
ejpam-5662	563	5	m.	m.	PROPN
ejpam-5662	563	6	moatimid	moatimid	PROPN
ejpam-5662	563	7	,	,	PUNCT
ejpam-5662	563	8	m.	m.	PROPN
ejpam-5662	563	9	a.	a.	PROPN
ejpam-5662	563	10	a.	a.	PROPN
ejpam-5662	563	11	mohamed	mohamed	PROPN
ejpam-5662	563	12	/	/	SYM
ejpam-5662	563	13	eur	eur	PROPN
ejpam-5662	563	14	.	.	PUNCT
ejpam-5662	564	1	j.	j.	PROPN
ejpam-5662	564	2	pure	pure	PROPN
ejpam-5662	564	3	appl	appl	PROPN
ejpam-5662	564	4	.	.	PROPN
ejpam-5662	564	5	math	math	PROPN
ejpam-5662	564	6	,	,	PUNCT
ejpam-5662	564	7	18	18	NUM
ejpam-5662	564	8	(	(	PUNCT
ejpam-5662	564	9	2	2	NUM
ejpam-5662	564	10	)	)	PUNCT
ejpam-5662	564	11	(	(	PUNCT
ejpam-5662	564	12	2025	2025	NUM
ejpam-5662	564	13	)	)	PUNCT
ejpam-5662	564	14	,	,	PUNCT
ejpam-5662	564	15	5662	5662	NUM
ejpam-5662	564	16	33	33	NUM
ejpam-5662	564	17	of	of	ADP
ejpam-5662	564	18	36	36	NUM
ejpam-5662	564	19	mona	mona	PROPN
ejpam-5662	564	20	a.	a.	PROPN
ejpam-5662	564	21	a.	a.	PROPN
ejpam-5662	564	22	mohamed	mohamed	PROPN
ejpam-5662	564	23	:	:	PUNCT
ejpam-5662	565	1	investigation	investigation	NOUN
ejpam-5662	565	2	,	,	PUNCT
ejpam-5662	565	3	methodology	methodology	NOUN
ejpam-5662	565	4	,	,	PUNCT
ejpam-5662	565	5	data	data	NOUN
ejpam-5662	565	6	duration	duration	NOUN
ejpam-5662	565	7	,	,	PUNCT
ejpam-5662	565	8	examination	examination	NOUN
ejpam-5662	565	9	,	,	PUNCT
ejpam-5662	565	10	organization	organization	NOUN
ejpam-5662	565	11	,	,	PUNCT
ejpam-5662	565	12	validation	validation	NOUN
ejpam-5662	565	13	,	,	PUNCT
ejpam-5662	565	14	reviewing	reviewing	NOUN
ejpam-5662	565	15	and	and	CCONJ
ejpam-5662	565	16	editing	editing	NOUN
ejpam-5662	565	17	.	.	PUNCT
ejpam-5662	566	1	all	all	DET
ejpam-5662	566	2	authors	author	NOUN
ejpam-5662	566	3	have	have	AUX
ejpam-5662	566	4	read	read	VERB
ejpam-5662	566	5	and	and	CCONJ
ejpam-5662	566	6	agreed	agree	VERB
ejpam-5662	566	7	to	to	ADP
ejpam-5662	566	8	the	the	DET
ejpam-5662	566	9	published	publish	VERB
ejpam-5662	566	10	version	version	NOUN
ejpam-5662	566	11	of	of	ADP
ejpam-5662	566	12	the	the	DET
ejpam-5662	566	13	manuscript	manuscript	NOUN
ejpam-5662	566	14	.	.	PUNCT
ejpam-5662	567	1	data	datum	NOUN
ejpam-5662	567	2	availability	availability	NOUN
ejpam-5662	567	3	statement	statement	NOUN
ejpam-5662	567	4	all	all	DET
ejpam-5662	567	5	data	datum	NOUN
ejpam-5662	567	6	generated	generate	VERB
ejpam-5662	567	7	or	or	CCONJ
ejpam-5662	567	8	analyzed	analyze	VERB
ejpam-5662	567	9	during	during	ADP
ejpam-5662	567	10	this	this	DET
ejpam-5662	567	11	study	study	NOUN
ejpam-5662	567	12	are	be	AUX
ejpam-5662	567	13	included	include	VERB
ejpam-5662	567	14	in	in	ADP
ejpam-5662	567	15	this	this	DET
ejpam-5662	567	16	article	article	NOUN
ejpam-5662	567	17	.	.	PUNCT
ejpam-5662	568	1	conflicts	conflict	NOUN
ejpam-5662	568	2	of	of	ADP
ejpam-5662	568	3	interest	interest	NOUN
ejpam-5662	568	4	:	:	PUNCT
ejpam-5662	568	5	the	the	DET
ejpam-5662	568	6	authors	author	NOUN
ejpam-5662	568	7	have	have	AUX
ejpam-5662	568	8	disclosed	disclose	VERB
ejpam-5662	568	9	no	no	DET
ejpam-5662	568	10	competing	compete	VERB
ejpam-5662	568	11	interests	interest	NOUN
ejpam-5662	568	12	.	.	PUNCT
ejpam-5662	569	1	references	reference	NOUN
ejpam-5662	569	2	[	[	X
ejpam-5662	569	3	1	1	NUM
ejpam-5662	569	4	]	]	PUNCT
ejpam-5662	569	5	rhoads	rhoads	PROPN
ejpam-5662	569	6	j.f	j.f	PROPN
ejpam-5662	569	7	.	.	PROPN
ejpam-5662	569	8	,	,	PUNCT
ejpam-5662	569	9	guo	guo	PROPN
ejpam-5662	569	10	c.	c.	PROPN
ejpam-5662	569	11	,	,	PUNCT
ejpam-5662	569	12	and	and	CCONJ
ejpam-5662	569	13	fedder	fedder	PROPN
ejpam-5662	569	14	g.k	g.k	PROPN
ejpam-5662	569	15	.	.	PROPN
ejpam-5662	569	16	,	,	PUNCT
ejpam-5662	569	17	parametrically	parametrically	ADV
ejpam-5662	569	18	excited	excited	ADJ
ejpam-5662	569	19	microand	microand	NOUN
ejpam-5662	569	20	nanosystems	nanosystem	NOUN
ejpam-5662	569	21	.	.	PUNCT
ejpam-5662	570	1	in	in	ADP
ejpam-5662	570	2	:	:	PUNCT
ejpam-5662	570	3	resonant	resonant	ADJ
ejpam-5662	570	4	mems	mem	NOUN
ejpam-5662	570	5	,	,	PUNCT
ejpam-5662	570	6	principles	principle	NOUN
ejpam-5662	570	7	,	,	PUNCT
ejpam-5662	570	8	modeling	modeling	NOUN
ejpam-5662	570	9	,	,	PUNCT
ejpam-5662	570	10	implementation	implementation	NOUN
ejpam-5662	570	11	,	,	PUNCT
ejpam-5662	570	12	and	and	CCONJ
ejpam-5662	570	13	applications	application	NOUN
ejpam-5662	570	14	,	,	PUNCT
ejpam-5662	570	15	pp	pp	ADJ
ejpam-5662	570	16	.	.	PUNCT
ejpam-5662	571	1	73–95	73–95	NUM
ejpam-5662	571	2	.	.	PUNCT
ejpam-5662	572	1	wiley	wiley	PROPN
ejpam-5662	572	2	-	-	PUNCT
ejpam-5662	572	3	vch	vch	PROPN
ejpam-5662	572	4	verlag	verlag	PROPN
ejpam-5662	572	5	(	(	PUNCT
ejpam-5662	572	6	2015	2015	NUM
ejpam-5662	572	7	)	)	PUNCT
ejpam-5662	572	8	.	.	PUNCT
ejpam-5662	573	1	[	[	X
ejpam-5662	573	2	2	2	NUM
ejpam-5662	573	3	]	]	PUNCT
ejpam-5662	573	4	cerullo	cerullo	PROPN
ejpam-5662	573	5	g.	g.	PROPN
ejpam-5662	573	6	,	,	PUNCT
ejpam-5662	573	7	de	de	PROPN
ejpam-5662	573	8	silvestri	silvestri	PROPN
ejpam-5662	573	9	s.	s.	PROPN
ejpam-5662	573	10	,	,	PUNCT
ejpam-5662	573	11	ultrafast	ultrafast	ADJ
ejpam-5662	573	12	optical	optical	ADJ
ejpam-5662	573	13	parametric	parametric	PROPN
ejpam-5662	573	14	amplifiers	amplifier	NOUN
ejpam-5662	573	15	,	,	PUNCT
ejpam-5662	573	16	review	review	NOUN
ejpam-5662	573	17	of	of	ADP
ejpam-5662	573	18	scientific	scientific	ADJ
ejpam-5662	573	19	instruments	instrument	NOUN
ejpam-5662	573	20	,	,	PUNCT
ejpam-5662	573	21	74(1	74(1	NOUN
ejpam-5662	573	22	)	)	PUNCT
ejpam-5662	573	23	,	,	PUNCT
ejpam-5662	573	24	1–18	1–18	PROPN
ejpam-5662	573	25	(	(	PUNCT
ejpam-5662	573	26	2003	2003	NUM
ejpam-5662	573	27	)	)	PUNCT
ejpam-5662	573	28	.	.	PUNCT
ejpam-5662	574	1	[	[	X
ejpam-5662	574	2	3	3	X
ejpam-5662	574	3	]	]	PUNCT
ejpam-5662	574	4	aumentado	aumentado	PROPN
ejpam-5662	574	5	j.	j.	PROPN
ejpam-5662	574	6	,	,	PUNCT
ejpam-5662	574	7	superconducting	superconducte	VERB
ejpam-5662	574	8	parametric	parametric	ADJ
ejpam-5662	574	9	amplifiers	amplifier	NOUN
ejpam-5662	574	10	:	:	PUNCT
ejpam-5662	574	11	the	the	DET
ejpam-5662	574	12	state	state	NOUN
ejpam-5662	574	13	of	of	ADP
ejpam-5662	574	14	the	the	DET
ejpam-5662	574	15	art	art	NOUN
ejpam-5662	574	16	in	in	ADP
ejpam-5662	574	17	josephson	josephson	PROPN
ejpam-5662	574	18	parametric	parametric	PROPN
ejpam-5662	574	19	amplifiers	amplifiers	PROPN
ejpam-5662	574	20	,	,	PUNCT
ejpam-5662	574	21	ieee	ieee	NOUN
ejpam-5662	574	22	microwave	microwave	PROPN
ejpam-5662	574	23	magazine	magazine	PROPN
ejpam-5662	574	24	,	,	PUNCT
ejpam-5662	574	25	21(8	21(8	NUM
ejpam-5662	574	26	)	)	PUNCT
ejpam-5662	574	27	,	,	PUNCT
ejpam-5662	574	28	45–59	45–59	NUM
ejpam-5662	574	29	(	(	PUNCT
ejpam-5662	574	30	2020	2020	NUM
ejpam-5662	574	31	)	)	PUNCT
ejpam-5662	574	32	.	.	PUNCT
ejpam-5662	575	1	[	[	X
ejpam-5662	575	2	4	4	X
ejpam-5662	575	3	]	]	PUNCT
ejpam-5662	575	4	gemelke	gemelke	ADJ
ejpam-5662	575	5	n.	n.	NOUN
ejpam-5662	575	6	,	,	PUNCT
ejpam-5662	575	7	sarajlic	sarajlic	PROPN
ejpam-5662	575	8	e.	e.	PROPN
ejpam-5662	575	9	,	,	PUNCT
ejpam-5662	575	10	bidel	bidel	PROPN
ejpam-5662	575	11	y.	y.	PROPN
ejpam-5662	575	12	,	,	PUNCT
ejpam-5662	575	13	hong	hong	PROPN
ejpam-5662	575	14	s.	s.	PROPN
ejpam-5662	575	15	,	,	PUNCT
ejpam-5662	575	16	and	and	CCONJ
ejpam-5662	575	17	chu	chu	PROPN
ejpam-5662	575	18	s.	s.	PROPN
ejpam-5662	575	19	,	,	PUNCT
ejpam-5662	575	20	parametric	parametric	ADJ
ejpam-5662	575	21	amplification	amplification	NOUN
ejpam-5662	575	22	of	of	ADP
ejpam-5662	575	23	matter	matter	ADJ
ejpam-5662	575	24	waves	wave	NOUN
ejpam-5662	575	25	in	in	ADP
ejpam-5662	575	26	periodically	periodically	ADV
ejpam-5662	575	27	translated	translate	VERB
ejpam-5662	575	28	optical	optical	ADJ
ejpam-5662	575	29	lattices	lattice	NOUN
ejpam-5662	575	30	,	,	PUNCT
ejpam-5662	575	31	physical	physical	ADJ
ejpam-5662	575	32	review	review	NOUN
ejpam-5662	575	33	letters	letter	NOUN
ejpam-5662	575	34	,	,	PUNCT
ejpam-5662	575	35	95(17	95(17	NUM
ejpam-5662	575	36	)	)	PUNCT
ejpam-5662	575	37	,	,	PUNCT
ejpam-5662	575	38	170404	170404	NUM
ejpam-5662	575	39	(	(	PUNCT
ejpam-5662	575	40	2005	2005	NUM
ejpam-5662	575	41	)	)	PUNCT
ejpam-5662	575	42	.	.	PUNCT
ejpam-5662	576	1	[	[	X
ejpam-5662	576	2	5	5	NUM
ejpam-5662	576	3	]	]	PUNCT
ejpam-5662	576	4	rhoads	rhoads	PROPN
ejpam-5662	576	5	j.f	j.f	PROPN
ejpam-5662	576	6	.	.	PROPN
ejpam-5662	576	7	,	,	PUNCT
ejpam-5662	576	8	shaw	shaw	PROPN
ejpam-5662	576	9	s.w	s.w	PROPN
ejpam-5662	576	10	.	.	PROPN
ejpam-5662	576	11	,	,	PUNCT
ejpam-5662	576	12	and	and	CCONJ
ejpam-5662	576	13	turner	turner	PROPN
ejpam-5662	576	14	k.l	k.l	PROPN
ejpam-5662	576	15	.	.	PROPN
ejpam-5662	576	16	,	,	PUNCT
ejpam-5662	576	17	nonlinear	nonlinear	ADJ
ejpam-5662	576	18	dynamics	dynamic	NOUN
ejpam-5662	576	19	and	and	CCONJ
ejpam-5662	576	20	its	its	PRON
ejpam-5662	576	21	applications	application	NOUN
ejpam-5662	576	22	in	in	ADP
ejpam-5662	576	23	micro	micro	NOUN
ejpam-5662	576	24	-	-	ADJ
ejpam-5662	576	25	and	and	CCONJ
ejpam-5662	576	26	nanoresonators	nanoresonator	NOUN
ejpam-5662	576	27	,	,	PUNCT
ejpam-5662	576	28	journal	journal	NOUN
ejpam-5662	576	29	of	of	ADP
ejpam-5662	576	30	dynamic	dynamic	ADJ
ejpam-5662	576	31	systems	system	NOUN
ejpam-5662	576	32	,	,	PUNCT
ejpam-5662	576	33	measurement	measurement	NOUN
ejpam-5662	576	34	,	,	PUNCT
ejpam-5662	576	35	and	and	CCONJ
ejpam-5662	576	36	control	control	NOUN
ejpam-5662	576	37	,	,	PUNCT
ejpam-5662	576	38	132(3	132(3	NUM
ejpam-5662	576	39	)	)	PUNCT
ejpam-5662	576	40	,	,	PUNCT
ejpam-5662	576	41	1–14	1–14	PROPN
ejpam-5662	576	42	(	(	PUNCT
ejpam-5662	576	43	2010	2010	NUM
ejpam-5662	576	44	)	)	PUNCT
ejpam-5662	576	45	.	.	PUNCT
ejpam-5662	577	1	[	[	X
ejpam-5662	577	2	6	6	NUM
ejpam-5662	577	3	]	]	X
ejpam-5662	577	4	kovacic	kovacic	PROPN
ejpam-5662	577	5	i.	i.	PROPN
ejpam-5662	577	6	,	,	PUNCT
ejpam-5662	577	7	rand	rand	PROPN
ejpam-5662	577	8	r.	r.	PROPN
ejpam-5662	577	9	,	,	PUNCT
ejpam-5662	577	10	sah	sah	PROPN
ejpam-5662	577	11	s.m	s.m	PROPN
ejpam-5662	577	12	.	.	PROPN
ejpam-5662	577	13	,	,	PUNCT
ejpam-5662	577	14	mathieu	mathieu	PROPN
ejpam-5662	577	15	’s	’s	PART
ejpam-5662	577	16	equation	equation	NOUN
ejpam-5662	577	17	and	and	CCONJ
ejpam-5662	577	18	its	its	PRON
ejpam-5662	577	19	generalizations	generalization	NOUN
ejpam-5662	577	20	:	:	PUNCT
ejpam-5662	577	21	overview	overview	NOUN
ejpam-5662	577	22	of	of	ADP
ejpam-5662	577	23	stability	stability	NOUN
ejpam-5662	577	24	charts	chart	NOUN
ejpam-5662	577	25	and	and	CCONJ
ejpam-5662	577	26	their	their	PRON
ejpam-5662	577	27	features	feature	NOUN
ejpam-5662	577	28	,	,	PUNCT
ejpam-5662	577	29	applied	apply	VERB
ejpam-5662	577	30	mechanics	mechanic	NOUN
ejpam-5662	577	31	reviews	review	NOUN
ejpam-5662	577	32	,	,	PUNCT
ejpam-5662	577	33	70(2	70(2	PROPN
ejpam-5662	577	34	)	)	PUNCT
ejpam-5662	577	35	,	,	PUNCT
ejpam-5662	577	36	020802	020802	NUM
ejpam-5662	577	37	(	(	PUNCT
ejpam-5662	577	38	2018	2018	NUM
ejpam-5662	577	39	)	)	PUNCT
ejpam-5662	577	40	.	.	PUNCT
ejpam-5662	578	1	[	[	X
ejpam-5662	578	2	7	7	X
ejpam-5662	578	3	]	]	X
ejpam-5662	578	4	nayfeh	nayfeh	ADJ
ejpam-5662	578	5	a.h	a.h	PROPN
ejpam-5662	578	6	.	.	PROPN
ejpam-5662	578	7	,	,	PUNCT
ejpam-5662	578	8	and	and	CCONJ
ejpam-5662	578	9	mook	mook	PROPN
ejpam-5662	578	10	d.t	d.t	PROPN
ejpam-5662	578	11	.	.	PROPN
ejpam-5662	578	12	,	,	PUNCT
ejpam-5662	578	13	nonlinear	nonlinear	ADJ
ejpam-5662	578	14	oscillations	oscillation	NOUN
ejpam-5662	578	15	,	,	PUNCT
ejpam-5662	578	16	wiley	wiley	PROPN
ejpam-5662	578	17	&	&	CCONJ
ejpam-5662	578	18	sons	son	NOUN
ejpam-5662	578	19	,	,	PUNCT
ejpam-5662	578	20	new	new	PROPN
ejpam-5662	578	21	york	york	PROPN
ejpam-5662	578	22	(	(	PUNCT
ejpam-5662	578	23	1979	1979	NUM
ejpam-5662	578	24	)	)	PUNCT
ejpam-5662	578	25	.	.	PUNCT
ejpam-5662	579	1	[	[	X
ejpam-5662	579	2	8	8	NUM
ejpam-5662	579	3	]	]	X
ejpam-5662	579	4	mclachlan	mclachlan	PROPN
ejpam-5662	579	5	n.w	n.w	PROPN
ejpam-5662	579	6	.	.	PROPN
ejpam-5662	579	7	,	,	PUNCT
ejpam-5662	579	8	theory	theory	NOUN
ejpam-5662	579	9	and	and	CCONJ
ejpam-5662	579	10	applications	application	NOUN
ejpam-5662	579	11	of	of	ADP
ejpam-5662	579	12	mathieu	mathieu	PROPN
ejpam-5662	579	13	functions	function	NOUN
ejpam-5662	579	14	,	,	PUNCT
ejpam-5662	579	15	clarendon	clarendon	PROPN
ejpam-5662	579	16	press	press	NOUN
ejpam-5662	579	17	,	,	PUNCT
ejpam-5662	579	18	oxford	oxford	PROPN
ejpam-5662	579	19	,	,	PUNCT
ejpam-5662	579	20	uk	uk	PROPN
ejpam-5662	579	21	,	,	PUNCT
ejpam-5662	579	22	(	(	PUNCT
ejpam-5662	579	23	1947	1947	NUM
ejpam-5662	579	24	)	)	PUNCT
ejpam-5662	579	25	.	.	PUNCT
ejpam-5662	580	1	[	[	X
ejpam-5662	580	2	9	9	X
ejpam-5662	580	3	]	]	X
ejpam-5662	580	4	achala	achala	PROPN
ejpam-5662	580	5	l.n	l.n	PROPN
ejpam-5662	580	6	.	.	PROPN
ejpam-5662	580	7	,	,	PUNCT
ejpam-5662	580	8	mathematical	mathematical	ADJ
ejpam-5662	580	9	analysis	analysis	NOUN
ejpam-5662	580	10	and	and	CCONJ
ejpam-5662	580	11	applications	application	NOUN
ejpam-5662	580	12	of	of	ADP
ejpam-5662	580	13	mathieu	mathieu	PROPN
ejpam-5662	580	14	’s	’s	PART
ejpam-5662	580	15	equation	equation	NOUN
ejpam-5662	580	16	revisited	revisit	VERB
ejpam-5662	580	17	,	,	PUNCT
ejpam-5662	580	18	international	international	ADJ
ejpam-5662	580	19	journal	journal	NOUN
ejpam-5662	580	20	of	of	ADP
ejpam-5662	580	21	mathematics	mathematic	NOUN
ejpam-5662	580	22	and	and	CCONJ
ejpam-5662	580	23	its	its	PRON
ejpam-5662	580	24	applications	application	NOUN
ejpam-5662	580	25	,	,	PUNCT
ejpam-5662	580	26	9(2	9(2	NUM
ejpam-5662	580	27	)	)	PUNCT
ejpam-5662	580	28	,	,	PUNCT
ejpam-5662	580	29	49	49	NUM
ejpam-5662	580	30	-	-	SYM
ejpam-5662	580	31	54	54	NUM
ejpam-5662	580	32	(	(	PUNCT
ejpam-5662	580	33	2021	2021	NUM
ejpam-5662	580	34	)	)	PUNCT
ejpam-5662	580	35	.	.	PUNCT
ejpam-5662	581	1	[	[	X
ejpam-5662	581	2	10	10	NUM
ejpam-5662	581	3	]	]	X
ejpam-5662	581	4	kovacic	kovacic	PROPN
ejpam-5662	581	5	i.	i.	PROPN
ejpam-5662	581	6	,	,	PUNCT
ejpam-5662	581	7	rand	rand	PROPN
ejpam-5662	581	8	r.	r.	PROPN
ejpam-5662	581	9	,	,	PUNCT
ejpam-5662	581	10	and	and	CCONJ
ejpam-5662	581	11	sah	sah	PROPN
ejpam-5662	581	12	s.m	s.m	PROPN
ejpam-5662	581	13	.	.	PROPN
ejpam-5662	581	14	,	,	PUNCT
ejpam-5662	581	15	mathieu	mathieu	PROPN
ejpam-5662	581	16	’s	’s	PART
ejpam-5662	581	17	equation	equation	NOUN
ejpam-5662	581	18	and	and	CCONJ
ejpam-5662	581	19	its	its	PRON
ejpam-5662	581	20	generalizations	generalization	NOUN
ejpam-5662	581	21	:	:	PUNCT
ejpam-5662	581	22	overview	overview	NOUN
ejpam-5662	581	23	of	of	ADP
ejpam-5662	581	24	stability	stability	NOUN
ejpam-5662	581	25	charts	chart	NOUN
ejpam-5662	581	26	and	and	CCONJ
ejpam-5662	581	27	their	their	PRON
ejpam-5662	581	28	features	feature	NOUN
ejpam-5662	581	29	,	,	PUNCT
ejpam-5662	581	30	applied	apply	VERB
ejpam-5662	581	31	mechanics	mechanic	NOUN
ejpam-5662	581	32	reviews	review	NOUN
ejpam-5662	581	33	,	,	PUNCT
ejpam-5662	581	34	70	70	NUM
ejpam-5662	581	35	,	,	PUNCT
ejpam-5662	581	36	020802	020802	NUM
ejpam-5662	581	37	(	(	PUNCT
ejpam-5662	581	38	22	22	NUM
ejpam-5662	581	39	pages	page	NOUN
ejpam-5662	581	40	)	)	PUNCT
ejpam-5662	581	41	(	(	PUNCT
ejpam-5662	581	42	2018	2018	NUM
ejpam-5662	581	43	)	)	PUNCT
ejpam-5662	581	44	.	.	PUNCT
ejpam-5662	582	1	[	[	X
ejpam-5662	582	2	11	11	NUM
ejpam-5662	582	3	]	]	PUNCT
ejpam-5662	582	4	ramani	ramani	PROPN
ejpam-5662	582	5	d.v	d.v	PROPN
ejpam-5662	582	6	.	.	PROPN
ejpam-5662	582	7	,	,	PUNCT
ejpam-5662	582	8	keith	keith	PROPN
ejpam-5662	582	9	wl	wl	PROPN
ejpam-5662	582	10	,	,	PUNCT
ejpam-5662	582	11	and	and	CCONJ
ejpam-5662	582	12	rand	rand	NOUN
ejpam-5662	582	13	r.h	r.h	PROPN
ejpam-5662	582	14	..	..	NOUN
ejpam-5662	582	15	perturbation	perturbation	NOUN
ejpam-5662	582	16	solution	solution	NOUN
ejpam-5662	582	17	for	for	ADP
ejpam-5662	582	18	secondary	secondary	ADJ
ejpam-5662	582	19	bifurcation	bifurcation	NOUN
ejpam-5662	582	20	in	in	ADP
ejpam-5662	582	21	the	the	DET
ejpam-5662	582	22	quadratically	quadratically	ADV
ejpam-5662	582	23	-	-	PUNCT
ejpam-5662	582	24	damped	damp	VERB
ejpam-5662	582	25	mathieu	mathieu	PROPN
ejpam-5662	582	26	equation	equation	NOUN
ejpam-5662	582	27	,	,	PUNCT
ejpam-5662	582	28	international	international	ADJ
ejpam-5662	582	29	journal	journal	NOUN
ejpam-5662	582	30	of	of	ADP
ejpam-5662	582	31	non	non	ADJ
ejpam-5662	582	32	-	-	ADJ
ejpam-5662	582	33	linear	linear	ADJ
ejpam-5662	582	34	mechanics	mechanic	NOUN
ejpam-5662	582	35	,	,	PUNCT
ejpam-5662	582	36	39	39	NUM
ejpam-5662	582	37	(	(	PUNCT
ejpam-5662	582	38	3	3	NUM
ejpam-5662	582	39	)	)	PUNCT
ejpam-5662	582	40	,	,	PUNCT
ejpam-5662	582	41	491	491	NUM
ejpam-5662	582	42	-	-	SYM
ejpam-5662	582	43	502	502	NUM
ejpam-5662	582	44	(	(	PUNCT
ejpam-5662	582	45	2004	2004	NUM
ejpam-5662	582	46	)	)	PUNCT
ejpam-5662	582	47	.	.	PUNCT
ejpam-5662	583	1	[	[	X
ejpam-5662	583	2	12	12	NUM
ejpam-5662	583	3	]	]	PUNCT
ejpam-5662	583	4	nayfeh	nayfeh	ADJ
ejpam-5662	583	5	a.h	a.h	PROPN
ejpam-5662	583	6	.	.	PROPN
ejpam-5662	583	7	,	,	PUNCT
ejpam-5662	583	8	introduction	introduction	NOUN
ejpam-5662	583	9	to	to	ADP
ejpam-5662	583	10	perturbation	perturbation	NOUN
ejpam-5662	583	11	techniques	technique	NOUN
ejpam-5662	583	12	,	,	PUNCT
ejpam-5662	583	13	new	new	PROPN
ejpam-5662	583	14	york	york	PROPN
ejpam-5662	583	15	,	,	PUNCT
ejpam-5662	583	16	wiley	wiley	PROPN
ejpam-5662	583	17	&	&	CCONJ
ejpam-5662	583	18	sons	son	NOUN
ejpam-5662	583	19	(	(	PUNCT
ejpam-5662	583	20	1981	1981	NUM
ejpam-5662	583	21	)	)	PUNCT
ejpam-5662	583	22	.	.	PUNCT
ejpam-5662	584	1	[	[	X
ejpam-5662	584	2	13	13	NUM
ejpam-5662	584	3	]	]	PUNCT
ejpam-5662	584	4	nayfeh	nayfeh	ADJ
ejpam-5662	584	5	a.h	a.h	PROPN
ejpam-5662	584	6	.	.	PROPN
ejpam-5662	584	7	,	,	PUNCT
ejpam-5662	584	8	and	and	CCONJ
ejpam-5662	584	9	zavodney	zavodney	PROPN
ejpam-5662	584	10	l.d	l.d	PROPN
ejpam-5662	584	11	.	.	PROPN
ejpam-5662	584	12	,	,	PUNCT
ejpam-5662	584	13	the	the	DET
ejpam-5662	584	14	response	response	NOUN
ejpam-5662	584	15	of	of	ADP
ejpam-5662	584	16	two	two	NUM
ejpam-5662	584	17	-	-	PUNCT
ejpam-5662	584	18	degree	degree	NOUN
ejpam-5662	584	19	-	-	PUNCT
ejpam-5662	584	20	of	of	ADP
ejpam-5662	584	21	-	-	PUNCT
ejpam-5662	584	22	freedom	freedom	NOUN
ejpam-5662	584	23	systems	system	NOUN
ejpam-5662	584	24	with	with	ADP
ejpam-5662	584	25	quadratic	quadratic	ADJ
ejpam-5662	584	26	non	non	NOUN
ejpam-5662	584	27	-	-	NOUN
ejpam-5662	584	28	linearities	linearity	NOUN
ejpam-5662	584	29	to	to	ADP
ejpam-5662	584	30	a	a	DET
ejpam-5662	584	31	combination	combination	NOUN
ejpam-5662	584	32	parametric	parametric	ADJ
ejpam-5662	584	33	resonance	resonance	NOUN
ejpam-5662	584	34	,	,	PUNCT
ejpam-5662	584	35	journal	journal	NOUN
ejpam-5662	584	36	of	of	ADP
ejpam-5662	584	37	sound	sound	NOUN
ejpam-5662	584	38	and	and	CCONJ
ejpam-5662	584	39	vibration	vibration	NOUN
ejpam-5662	584	40	,	,	PUNCT
ejpam-5662	584	41	107(2	107(2	NUM
ejpam-5662	584	42	)	)	PUNCT
ejpam-5662	584	43	,	,	PUNCT
ejpam-5662	584	44	329–350	329–350	NUM
ejpam-5662	584	45	(	(	PUNCT
ejpam-5662	584	46	1986	1986	NUM
ejpam-5662	584	47	)	)	PUNCT
ejpam-5662	584	48	.	.	PUNCT
ejpam-5662	585	1	[	[	X
ejpam-5662	585	2	14	14	NUM
ejpam-5662	585	3	]	]	X
ejpam-5662	585	4	nayfeh	nayfeh	ADJ
ejpam-5662	585	5	a.h	a.h	PROPN
ejpam-5662	585	6	.	.	PROPN
ejpam-5662	585	7	,	,	PUNCT
ejpam-5662	585	8	chin	chin	PROPN
ejpam-5662	585	9	c.	c.	PROPN
ejpam-5662	585	10	,	,	PUNCT
ejpam-5662	585	11	and	and	CCONJ
ejpam-5662	585	12	mook	mook	PROPN
ejpam-5662	585	13	d.t	d.t	PROPN
ejpam-5662	585	14	.	.	PROPN
ejpam-5662	585	15	,	,	PUNCT
ejpam-5662	585	16	parametrically	parametrically	ADV
ejpam-5662	585	17	excited	excite	VERB
ejpam-5662	585	18	nonlinear	nonlinear	ADJ
ejpam-5662	585	19	two	two	NUM
ejpam-5662	585	20	-	-	PUNCT
ejpam-5662	585	21	degreea	degreea	NOUN
ejpam-5662	585	22	.	.	PUNCT
ejpam-5662	586	1	alanazy	alanazy	NOUN
ejpam-5662	586	2	,	,	PUNCT
ejpam-5662	586	3	g.	g.	PROPN
ejpam-5662	586	4	m.	m.	PROPN
ejpam-5662	586	5	moatimid	moatimid	PROPN
ejpam-5662	586	6	,	,	PUNCT
ejpam-5662	586	7	m.	m.	PROPN
ejpam-5662	586	8	a.	a.	PROPN
ejpam-5662	586	9	a.	a.	PROPN
ejpam-5662	586	10	mohamed	mohamed	PROPN
ejpam-5662	586	11	/	/	SYM
ejpam-5662	586	12	eur	eur	PROPN
ejpam-5662	586	13	.	.	PUNCT
ejpam-5662	587	1	j.	j.	PROPN
ejpam-5662	587	2	pure	pure	PROPN
ejpam-5662	587	3	appl	appl	PROPN
ejpam-5662	587	4	.	.	PROPN
ejpam-5662	587	5	math	math	PROPN
ejpam-5662	587	6	,	,	PUNCT
ejpam-5662	587	7	18	18	NUM
ejpam-5662	587	8	(	(	PUNCT
ejpam-5662	587	9	2	2	NUM
ejpam-5662	587	10	)	)	PUNCT
ejpam-5662	587	11	(	(	PUNCT
ejpam-5662	587	12	2025	2025	NUM
ejpam-5662	587	13	)	)	PUNCT
ejpam-5662	587	14	,	,	PUNCT
ejpam-5662	587	15	5662	5662	NUM
ejpam-5662	587	16	34	34	NUM
ejpam-5662	587	17	of	of	ADP
ejpam-5662	587	18	36	36	NUM
ejpam-5662	587	19	of	of	ADP
ejpam-5662	587	20	-	-	PUNCT
ejpam-5662	587	21	freedom	freedom	NOUN
ejpam-5662	587	22	systems	system	NOUN
ejpam-5662	587	23	with	with	ADP
ejpam-5662	587	24	repeated	repeat	VERB
ejpam-5662	587	25	natural	natural	ADJ
ejpam-5662	587	26	frequencies	frequency	NOUN
ejpam-5662	587	27	,	,	PUNCT
ejpam-5662	587	28	shock	shock	NOUN
ejpam-5662	587	29	and	and	CCONJ
ejpam-5662	587	30	vibration	vibration	NOUN
ejpam-5662	587	31	,	,	PUNCT
ejpam-5662	587	32	2(1	2(1	NUM
ejpam-5662	587	33	)	)	PUNCT
ejpam-5662	587	34	,	,	PUNCT
ejpam-5662	587	35	43–57	43–57	NUM
ejpam-5662	587	36	(	(	PUNCT
ejpam-5662	587	37	1995	1995	NUM
ejpam-5662	587	38	)	)	PUNCT
ejpam-5662	587	39	.	.	PUNCT
ejpam-5662	588	1	[	[	X
ejpam-5662	588	2	15	15	NUM
ejpam-5662	588	3	]	]	PUNCT
ejpam-5662	588	4	sinha	sinha	PROPN
ejpam-5662	588	5	s.c	s.c	PROPN
ejpam-5662	588	6	.	.	PROPN
ejpam-5662	588	7	,	,	PUNCT
ejpam-5662	588	8	and	and	CCONJ
ejpam-5662	588	9	wu	wu	PROPN
ejpam-5662	588	10	d.h	d.h	PROPN
ejpam-5662	588	11	.	.	PROPN
ejpam-5662	588	12	,	,	PUNCT
ejpam-5662	588	13	an	an	DET
ejpam-5662	588	14	efficient	efficient	ADJ
ejpam-5662	588	15	computational	computational	ADJ
ejpam-5662	588	16	scheme	scheme	NOUN
ejpam-5662	588	17	for	for	ADP
ejpam-5662	588	18	the	the	DET
ejpam-5662	588	19	analysis	analysis	NOUN
ejpam-5662	588	20	of	of	ADP
ejpam-5662	588	21	periodic	periodic	ADJ
ejpam-5662	588	22	systems	system	NOUN
ejpam-5662	588	23	,	,	PUNCT
ejpam-5662	588	24	journal	journal	NOUN
ejpam-5662	588	25	of	of	ADP
ejpam-5662	588	26	sound	sound	NOUN
ejpam-5662	588	27	and	and	CCONJ
ejpam-5662	588	28	vibration	vibration	NOUN
ejpam-5662	588	29	,	,	PUNCT
ejpam-5662	588	30	151(1	151(1	NUM
ejpam-5662	588	31	)	)	PUNCT
ejpam-5662	588	32	,	,	PUNCT
ejpam-5662	588	33	91–117	91–117	PROPN
ejpam-5662	588	34	(	(	PUNCT
ejpam-5662	588	35	1991	1991	NUM
ejpam-5662	588	36	)	)	PUNCT
ejpam-5662	588	37	.	.	PUNCT
ejpam-5662	589	1	[	[	X
ejpam-5662	589	2	16	16	NUM
ejpam-5662	589	3	]	]	X
ejpam-5662	589	4	dohnal	dohnal	PROPN
ejpam-5662	589	5	f.	f.	PROPN
ejpam-5662	589	6	,	,	PUNCT
ejpam-5662	589	7	experimental	experimental	ADJ
ejpam-5662	589	8	studies	study	NOUN
ejpam-5662	589	9	on	on	ADP
ejpam-5662	589	10	damping	damp	VERB
ejpam-5662	589	11	by	by	ADP
ejpam-5662	589	12	parametric	parametric	ADJ
ejpam-5662	589	13	excitation	excitation	NOUN
ejpam-5662	589	14	using	use	VERB
ejpam-5662	589	15	electromagnets	electromagnet	NOUN
ejpam-5662	589	16	,	,	PUNCT
ejpam-5662	589	17	proceedings	proceeding	NOUN
ejpam-5662	589	18	of	of	ADP
ejpam-5662	589	19	the	the	DET
ejpam-5662	589	20	institution	institution	NOUN
ejpam-5662	589	21	of	of	ADP
ejpam-5662	589	22	mechanical	mechanical	ADJ
ejpam-5662	589	23	engineers	engineer	NOUN
ejpam-5662	589	24	,	,	PUNCT
ejpam-5662	589	25	part	part	NOUN
ejpam-5662	589	26	c	c	NOUN
ejpam-5662	589	27	:	:	PUNCT
ejpam-5662	589	28	journal	journal	NOUN
ejpam-5662	589	29	of	of	ADP
ejpam-5662	589	30	mechanical	mechanical	ADJ
ejpam-5662	589	31	engineering	engineering	NOUN
ejpam-5662	589	32	science	science	NOUN
ejpam-5662	589	33	,	,	PUNCT
ejpam-5662	589	34	226(8	226(8	NUM
ejpam-5662	589	35	)	)	PUNCT
ejpam-5662	589	36	,	,	PUNCT
ejpam-5662	589	37	2015–2027	2015–2027	NUM
ejpam-5662	589	38	(	(	PUNCT
ejpam-5662	589	39	2012	2012	NUM
ejpam-5662	589	40	)	)	PUNCT
ejpam-5662	589	41	.	.	PUNCT
ejpam-5662	590	1	[	[	X
ejpam-5662	590	2	17	17	NUM
ejpam-5662	590	3	]	]	X
ejpam-5662	590	4	zaghari	zaghari	PROPN
ejpam-5662	590	5	b.	b.	PROPN
ejpam-5662	590	6	,	,	PUNCT
ejpam-5662	590	7	dynamic	dynamic	ADJ
ejpam-5662	590	8	analysis	analysis	NOUN
ejpam-5662	590	9	of	of	ADP
ejpam-5662	590	10	a	a	DET
ejpam-5662	590	11	nonlinear	nonlinear	ADJ
ejpam-5662	590	12	parametrically	parametrically	ADV
ejpam-5662	590	13	excited	excited	ADJ
ejpam-5662	590	14	system	system	NOUN
ejpam-5662	590	15	using	use	VERB
ejpam-5662	590	16	electromagnets	electromagnet	NOUN
ejpam-5662	590	17	,	,	PUNCT
ejpam-5662	590	18	ph.d	ph.d	PROPN
ejpam-5662	590	19	.	.	PUNCT
ejpam-5662	591	1	thesis	thesis	NOUN
ejpam-5662	591	2	,	,	PUNCT
ejpam-5662	591	3	university	university	PROPN
ejpam-5662	591	4	of	of	ADP
ejpam-5662	591	5	southampton	southampton	PROPN
ejpam-5662	591	6	(	(	PUNCT
ejpam-5662	591	7	2016	2016	NUM
ejpam-5662	591	8	)	)	PUNCT
ejpam-5662	591	9	.	.	PUNCT
ejpam-5662	592	1	[	[	X
ejpam-5662	592	2	18	18	NUM
ejpam-5662	592	3	]	]	X
ejpam-5662	592	4	ji	ji	PROPN
ejpam-5662	592	5	w.m	w.m	PROPN
ejpam-5662	592	6	.	.	PROPN
ejpam-5662	592	7	,	,	PUNCT
ejpam-5662	592	8	wang	wang	PROPN
ejpam-5662	592	9	h.	h.	PROPN
ejpam-5662	592	10	,	,	PUNCT
ejpam-5662	592	11	and	and	CCONJ
ejpam-5662	592	12	liu	liu	PROPN
ejpam-5662	592	13	m.	m.	NOUN
ejpam-5662	592	14	,	,	PUNCT
ejpam-5662	592	15	dynamics	dynamic	VERB
ejpam-5662	592	16	analysis	analysis	NOUN
ejpam-5662	592	17	of	of	ADP
ejpam-5662	592	18	an	an	DET
ejpam-5662	592	19	impulsive	impulsive	ADJ
ejpam-5662	592	20	stochastic	stochastic	ADJ
ejpam-5662	592	21	model	model	NOUN
ejpam-5662	592	22	for	for	ADP
ejpam-5662	592	23	spruce	spruce	NOUN
ejpam-5662	592	24	budworm	budworm	NOUN
ejpam-5662	592	25	growth	growth	NOUN
ejpam-5662	592	26	,	,	PUNCT
ejpam-5662	592	27	applied	apply	VERB
ejpam-5662	592	28	mathematics	mathematic	NOUN
ejpam-5662	592	29	and	and	CCONJ
ejpam-5662	592	30	computations	computation	NOUN
ejpam-5662	592	31	,	,	PUNCT
ejpam-5662	592	32	19	19	NUM
ejpam-5662	592	33	,	,	PUNCT
ejpam-5662	592	34	336–359	336–359	NUM
ejpam-5662	592	35	(	(	PUNCT
ejpam-5662	592	36	2021	2021	NUM
ejpam-5662	592	37	)	)	PUNCT
ejpam-5662	592	38	.	.	PUNCT
ejpam-5662	593	1	[	[	X
ejpam-5662	593	2	19	19	NUM
ejpam-5662	593	3	]	]	X
ejpam-5662	593	4	he	he	PRON
ejpam-5662	593	5	j.h	j.h	PROPN
ejpam-5662	593	6	,	,	PUNCT
ejpam-5662	593	7	homotopy	homotopy	VERB
ejpam-5662	593	8	perturbation	perturbation	NOUN
ejpam-5662	593	9	technique	technique	NOUN
ejpam-5662	593	10	,	,	PUNCT
ejpam-5662	593	11	computer	computer	NOUN
ejpam-5662	593	12	methods	method	NOUN
ejpam-5662	593	13	in	in	ADP
ejpam-5662	593	14	applied	applied	ADJ
ejpam-5662	593	15	mechanics	mechanic	NOUN
ejpam-5662	593	16	and	and	CCONJ
ejpam-5662	593	17	engineering	engineering	NOUN
ejpam-5662	593	18	,	,	PUNCT
ejpam-5662	593	19	178	178	NUM
ejpam-5662	593	20	,	,	PUNCT
ejpam-5662	593	21	257–262	257–262	NUM
ejpam-5662	593	22	(	(	PUNCT
ejpam-5662	593	23	1999	1999	NUM
ejpam-5662	593	24	)	)	PUNCT
ejpam-5662	593	25	.	.	PUNCT
ejpam-5662	594	1	[	[	X
ejpam-5662	594	2	20	20	NUM
ejpam-5662	594	3	]	]	X
ejpam-5662	594	4	moatimid	moatimid	PROPN
ejpam-5662	594	5	g.m	g.m	PROPN
ejpam-5662	594	6	.	.	PROPN
ejpam-5662	594	7	,	,	PUNCT
ejpam-5662	594	8	and	and	CCONJ
ejpam-5662	594	9	amer	amer	PROPN
ejpam-5662	594	10	t.s	t.s	PROPN
ejpam-5662	594	11	.	.	PROPN
ejpam-5662	594	12	analytical	analytical	ADJ
ejpam-5662	594	13	approximate	approximate	ADJ
ejpam-5662	594	14	solutions	solution	NOUN
ejpam-5662	594	15	of	of	ADP
ejpam-5662	594	16	a	a	DET
ejpam-5662	594	17	magnetic	magnetic	ADJ
ejpam-5662	594	18	spherical	spherical	ADJ
ejpam-5662	594	19	pendulum	pendulum	NOUN
ejpam-5662	594	20	:	:	PUNCT
ejpam-5662	594	21	stability	stability	NOUN
ejpam-5662	594	22	analysis	analysis	NOUN
ejpam-5662	594	23	,	,	PUNCT
ejpam-5662	594	24	journal	journal	NOUN
ejpam-5662	594	25	of	of	ADP
ejpam-5662	594	26	vibration	vibration	NOUN
ejpam-5662	594	27	engineering	engineering	NOUN
ejpam-5662	594	28	&	&	CCONJ
ejpam-5662	594	29	technologies	technology	NOUN
ejpam-5662	594	30	,	,	PUNCT
ejpam-5662	594	31	11	11	NUM
ejpam-5662	594	32	,	,	PUNCT
ejpam-5662	594	33	2155–2165	2155–2165	NUM
ejpam-5662	594	34	(	(	PUNCT
ejpam-5662	594	35	2023	2023	NUM
ejpam-5662	594	36	)	)	PUNCT
ejpam-5662	594	37	.	.	PUNCT
ejpam-5662	595	1	[	[	X
ejpam-5662	595	2	21	21	NUM
ejpam-5662	595	3	]	]	X
ejpam-5662	595	4	ghaleb	ghaleb	PROPN
ejpam-5662	595	5	a.f	a.f	PROPN
ejpam-5662	595	6	.	.	PROPN
ejpam-5662	595	7	,	,	PUNCT
ejpam-5662	595	8	abou	abou	PROPN
ejpam-5662	595	9	-	-	PUNCT
ejpam-5662	595	10	dina	dina	PROPN
ejpam-5662	595	11	m.s	m.s	PROPN
ejpam-5662	595	12	.	.	PROPN
ejpam-5662	595	13	,	,	PUNCT
ejpam-5662	595	14	moatimid	moatimid	PROPN
ejpam-5662	595	15	g.m	g.m	PROPN
ejpam-5662	595	16	.	.	PROPN
ejpam-5662	595	17	,	,	PUNCT
ejpam-5662	595	18	and	and	CCONJ
ejpam-5662	595	19	zekry	zekry	PROPN
ejpam-5662	595	20	m.h	m.h	PROPN
ejpam-5662	595	21	.	.	PROPN
ejpam-5662	595	22	,	,	PUNCT
ejpam-5662	595	23	analytic	analytic	ADJ
ejpam-5662	595	24	approximate	approximate	ADJ
ejpam-5662	595	25	solutions	solution	NOUN
ejpam-5662	595	26	of	of	ADP
ejpam-5662	595	27	the	the	DET
ejpam-5662	595	28	cubic	cubic	ADJ
ejpam-5662	595	29	-	-	PUNCT
ejpam-5662	595	30	quintic	quintic	ADJ
ejpam-5662	595	31	duffing	duffing	NOUN
ejpam-5662	595	32	van	van	PROPN
ejpam-5662	595	33	der	der	ADJ
ejpam-5662	595	34	pol	pol	NOUN
ejpam-5662	595	35	equation	equation	NOUN
ejpam-5662	595	36	with	with	ADP
ejpam-5662	595	37	two	two	NUM
ejpam-5662	595	38	-	-	PUNCT
ejpam-5662	595	39	external	external	ADJ
ejpam-5662	595	40	periodic	periodic	ADJ
ejpam-5662	595	41	forces	force	NOUN
ejpam-5662	595	42	terms	term	NOUN
ejpam-5662	595	43	:	:	PUNCT
ejpam-5662	595	44	stability	stability	NOUN
ejpam-5662	595	45	analysis	analysis	NOUN
ejpam-5662	595	46	,	,	PUNCT
ejpam-5662	595	47	mathematics	mathematic	NOUN
ejpam-5662	595	48	and	and	CCONJ
ejpam-5662	595	49	computers	computer	NOUN
ejpam-5662	595	50	in	in	ADP
ejpam-5662	595	51	simulation	simulation	NOUN
ejpam-5662	595	52	,	,	PUNCT
ejpam-5662	595	53	180	180	NUM
ejpam-5662	595	54	,	,	PUNCT
ejpam-5662	595	55	129	129	NUM
ejpam-5662	595	56	-	-	SYM
ejpam-5662	595	57	151	151	NUM
ejpam-5662	595	58	(	(	PUNCT
ejpam-5662	595	59	2021	2021	NUM
ejpam-5662	595	60	)	)	PUNCT
ejpam-5662	595	61	.	.	PUNCT
ejpam-5662	596	1	[	[	X
ejpam-5662	596	2	22	22	NUM
ejpam-5662	596	3	]	]	X
ejpam-5662	596	4	moatimid	moatimid	PROPN
ejpam-5662	596	5	g.m	g.m	PROPN
ejpam-5662	596	6	.	.	PROPN
ejpam-5662	596	7	,	,	PUNCT
ejpam-5662	596	8	el	el	PROPN
ejpam-5662	596	9	-	-	PROPN
ejpam-5662	596	10	dib	dib	PROPN
ejpam-5662	596	11	y.o	y.o	PROPN
ejpam-5662	596	12	.	.	PROPN
ejpam-5662	596	13	,	,	PUNCT
ejpam-5662	596	14	and	and	CCONJ
ejpam-5662	596	15	zekry	zekry	PROPN
ejpam-5662	596	16	m.h	m.h	PROPN
ejpam-5662	596	17	.	.	PROPN
ejpam-5662	596	18	,	,	PUNCT
ejpam-5662	596	19	stability	stability	NOUN
ejpam-5662	596	20	analysis	analysis	NOUN
ejpam-5662	596	21	using	use	VERB
ejpam-5662	596	22	multiple	multiple	ADJ
ejpam-5662	596	23	scales	scale	NOUN
ejpam-5662	596	24	homotopy	homotopy	NOUN
ejpam-5662	596	25	approach	approach	NOUN
ejpam-5662	596	26	of	of	ADP
ejpam-5662	596	27	coupled	couple	VERB
ejpam-5662	596	28	cylindrical	cylindrical	ADJ
ejpam-5662	596	29	interfaces	interface	NOUN
ejpam-5662	596	30	under	under	ADP
ejpam-5662	596	31	the	the	DET
ejpam-5662	596	32	influence	influence	NOUN
ejpam-5662	596	33	of	of	ADP
ejpam-5662	596	34	periodic	periodic	ADJ
ejpam-5662	596	35	electrostatic	electrostatic	ADJ
ejpam-5662	596	36	fields	field	NOUN
ejpam-5662	596	37	,	,	PUNCT
ejpam-5662	596	38	chinese	chinese	ADJ
ejpam-5662	596	39	journal	journal	PROPN
ejpam-5662	596	40	of	of	ADP
ejpam-5662	596	41	physics	physics	PROPN
ejpam-5662	596	42	,	,	PUNCT
ejpam-5662	596	43	56(5	56(5	NOUN
ejpam-5662	596	44	)	)	PUNCT
ejpam-5662	596	45	,	,	PUNCT
ejpam-5662	596	46	2507	2507	NUM
ejpam-5662	596	47	-	-	SYM
ejpam-5662	596	48	2522	2522	NUM
ejpam-5662	596	49	(	(	PUNCT
ejpam-5662	596	50	2018	2018	NUM
ejpam-5662	596	51	)	)	PUNCT
ejpam-5662	596	52	.	.	PUNCT
ejpam-5662	597	1	[	[	X
ejpam-5662	597	2	23	23	NUM
ejpam-5662	597	3	]	]	X
ejpam-5662	597	4	moatimid	moatimid	PROPN
ejpam-5662	597	5	g.m	g.m	PROPN
ejpam-5662	597	6	.	.	PROPN
ejpam-5662	597	7	,	,	PUNCT
ejpam-5662	597	8	sliding	slide	VERB
ejpam-5662	597	9	bead	bead	NOUN
ejpam-5662	597	10	on	on	ADP
ejpam-5662	597	11	a	a	DET
ejpam-5662	597	12	smooth	smooth	ADJ
ejpam-5662	597	13	vertical	vertical	ADJ
ejpam-5662	597	14	rotated	rotated	ADJ
ejpam-5662	597	15	parabola	parabola	PROPN
ejpam-5662	597	16	:	:	PUNCT
ejpam-5662	597	17	stability	stability	NOUN
ejpam-5662	597	18	configuration	configuration	NOUN
ejpam-5662	597	19	,	,	PUNCT
ejpam-5662	597	20	kuwait	kuwait	PROPN
ejpam-5662	597	21	journal	journal	PROPN
ejpam-5662	597	22	of	of	ADP
ejpam-5662	597	23	science	science	PROPN
ejpam-5662	597	24	,	,	PUNCT
ejpam-5662	597	25	47(2	47(2	PROPN
ejpam-5662	597	26	)	)	PUNCT
ejpam-5662	597	27	,	,	PUNCT
ejpam-5662	597	28	6	6	NUM
ejpam-5662	597	29	-	-	SYM
ejpam-5662	597	30	21	21	NUM
ejpam-5662	597	31	(	(	PUNCT
ejpam-5662	597	32	2020	2020	NUM
ejpam-5662	597	33	)	)	PUNCT
ejpam-5662	597	34	.	.	PUNCT
ejpam-5662	598	1	[	[	X
ejpam-5662	598	2	24	24	NUM
ejpam-5662	598	3	]	]	X
ejpam-5662	598	4	moatimid	moatimid	PROPN
ejpam-5662	598	5	g.m	g.m	PROPN
ejpam-5662	598	6	.	.	PROPN
ejpam-5662	598	7	,	,	PUNCT
ejpam-5662	598	8	and	and	CCONJ
ejpam-5662	598	9	amer	amer	PROPN
ejpam-5662	598	10	t.s	t.s	PROPN
ejpam-5662	598	11	.	.	PROPN
ejpam-5662	598	12	,	,	PUNCT
ejpam-5662	598	13	analytical	analytical	ADJ
ejpam-5662	598	14	solution	solution	NOUN
ejpam-5662	598	15	for	for	ADP
ejpam-5662	598	16	the	the	DET
ejpam-5662	598	17	motion	motion	NOUN
ejpam-5662	598	18	of	of	ADP
ejpam-5662	598	19	a	a	DET
ejpam-5662	598	20	pendulum	pendulum	NOUN
ejpam-5662	598	21	with	with	ADP
ejpam-5662	598	22	rolling	rolling	ADJ
ejpam-5662	598	23	wheel	wheel	NOUN
ejpam-5662	598	24	:	:	PUNCT
ejpam-5662	598	25	stability	stability	NOUN
ejpam-5662	598	26	analysis	analysis	NOUN
ejpam-5662	598	27	,	,	PUNCT
ejpam-5662	598	28	scientific	scientific	ADJ
ejpam-5662	598	29	reports	report	NOUN
ejpam-5662	598	30	,	,	PUNCT
ejpam-5662	598	31	12(1	12(1	NUM
ejpam-5662	598	32	)	)	PUNCT
ejpam-5662	598	33	,	,	PUNCT
ejpam-5662	598	34	12628	12628	NUM
ejpam-5662	598	35	(	(	PUNCT
ejpam-5662	598	36	2022	2022	NUM
ejpam-5662	598	37	)	)	PUNCT
ejpam-5662	598	38	.	.	PUNCT
ejpam-5662	599	1	[	[	X
ejpam-5662	599	2	25	25	NUM
ejpam-5662	599	3	]	]	X
ejpam-5662	599	4	zhang	zhang	PROPN
ejpam-5662	599	5	j	j	PROPN
ejpam-5662	599	6	-	-	PROPN
ejpam-5662	599	7	g.	g.	PROPN
ejpam-5662	599	8	,	,	PUNCT
ejpam-5662	599	9	song	song	NOUN
ejpam-5662	599	10	q	q	PROPN
ejpam-5662	599	11	-	-	PUNCT
ejpam-5662	599	12	r.	r.	PROPN
ejpam-5662	599	13	,	,	PUNCT
ejpam-5662	599	14	zhang	zhang	PROPN
ejpam-5662	599	15	j	j	PROPN
ejpam-5662	599	16	-	-	PUNCT
ejpam-5662	599	17	q.	q.	PROPN
ejpam-5662	599	18	,	,	PUNCT
ejpam-5662	599	19	and	and	CCONJ
ejpam-5662	599	20	wang	wang	PROPN
ejpam-5662	599	21	f.	f.	PROPN
ejpam-5662	599	22	,	,	PUNCT
ejpam-5662	599	23	application	application	NOUN
ejpam-5662	599	24	of	of	ADP
ejpam-5662	599	25	he	he	PRON
ejpam-5662	599	26	’s	’s	PART
ejpam-5662	599	27	frequency	frequency	NOUN
ejpam-5662	599	28	formula	formula	NOUN
ejpam-5662	599	29	to	to	PART
ejpam-5662	599	30	nonlinear	nonlinear	ADJ
ejpam-5662	599	31	oscillators	oscillator	NOUN
ejpam-5662	599	32	with	with	ADP
ejpam-5662	599	33	generalized	generalized	ADJ
ejpam-5662	599	34	initial	initial	ADJ
ejpam-5662	599	35	conditions	condition	NOUN
ejpam-5662	599	36	,	,	PUNCT
ejpam-5662	599	37	facta	facta	PROPN
ejpam-5662	599	38	universitatis	universitatis	PROPN
ejpam-5662	599	39	series	series	NOUN
ejpam-5662	599	40	:	:	PUNCT
ejpam-5662	599	41	mechanical	mechanical	ADJ
ejpam-5662	599	42	engineering	engineering	NOUN
ejpam-5662	599	43	,	,	PUNCT
ejpam-5662	599	44	21(4	21(4	NUM
ejpam-5662	599	45	)	)	PUNCT
ejpam-5662	599	46	,	,	PUNCT
ejpam-5662	599	47	701	701	NUM
ejpam-5662	599	48	-	-	SYM
ejpam-5662	599	49	712	712	NUM
ejpam-5662	599	50	(	(	PUNCT
ejpam-5662	599	51	2023	2023	NUM
ejpam-5662	599	52	)	)	PUNCT
ejpam-5662	599	53	.	.	PUNCT
ejpam-5662	600	1	[	[	X
ejpam-5662	600	2	26	26	NUM
ejpam-5662	600	3	]	]	X
ejpam-5662	600	4	ma	ma	PROPN
ejpam-5662	600	5	h.	h.	PROPN
ejpam-5662	600	6	,	,	PUNCT
ejpam-5662	600	7	a	a	DET
ejpam-5662	600	8	short	short	ADJ
ejpam-5662	600	9	remark	remark	NOUN
ejpam-5662	600	10	on	on	ADP
ejpam-5662	600	11	he	he	PRON
ejpam-5662	600	12	’s	’s	PART
ejpam-5662	600	13	frequency	frequency	NOUN
ejpam-5662	600	14	formulation	formulation	NOUN
ejpam-5662	600	15	,	,	PUNCT
ejpam-5662	600	16	journal	journal	NOUN
ejpam-5662	600	17	of	of	ADP
ejpam-5662	600	18	low	low	ADJ
ejpam-5662	600	19	frequency	frequency	NOUN
ejpam-5662	600	20	noise	noise	NOUN
ejpam-5662	600	21	,	,	PUNCT
ejpam-5662	600	22	vibration	vibration	NOUN
ejpam-5662	600	23	and	and	CCONJ
ejpam-5662	600	24	active	active	ADJ
ejpam-5662	600	25	control	control	NOUN
ejpam-5662	600	26	,	,	PUNCT
ejpam-5662	600	27	41(4	41(4	NUM
ejpam-5662	600	28	)	)	PUNCT
ejpam-5662	600	29	,	,	PUNCT
ejpam-5662	600	30	1380–1385	1380–1385	NUM
ejpam-5662	600	31	(	(	PUNCT
ejpam-5662	600	32	2022	2022	NUM
ejpam-5662	600	33	)	)	PUNCT
ejpam-5662	600	34	.	.	PUNCT
ejpam-5662	601	1	[	[	X
ejpam-5662	601	2	27	27	NUM
ejpam-5662	601	3	]	]	X
ejpam-5662	601	4	ma	ma	PROPN
ejpam-5662	601	5	h.	h.	PROPN
ejpam-5662	601	6	,	,	PUNCT
ejpam-5662	601	7	simplified	simplify	VERB
ejpam-5662	601	8	hamiltonian	hamiltonian	ADJ
ejpam-5662	601	9	-	-	PUNCT
ejpam-5662	601	10	based	base	VERB
ejpam-5662	601	11	frequency	frequency	NOUN
ejpam-5662	601	12	-	-	PUNCT
ejpam-5662	601	13	amplitude	amplitude	NOUN
ejpam-5662	601	14	formulation	formulation	NOUN
ejpam-5662	601	15	for	for	ADP
ejpam-5662	601	16	nonlinear	nonlinear	ADJ
ejpam-5662	601	17	vibration	vibration	NOUN
ejpam-5662	601	18	systems	system	NOUN
ejpam-5662	601	19	,	,	PUNCT
ejpam-5662	601	20	facta	facta	PROPN
ejpam-5662	601	21	universitatis	universitatis	PROPN
ejpam-5662	601	22	series	series	PROPN
ejpam-5662	601	23	mechanical	mechanical	ADJ
ejpam-5662	601	24	engineering	engineering	NOUN
ejpam-5662	601	25	,	,	PUNCT
ejpam-5662	601	26	20(2	20(2	NUM
ejpam-5662	601	27	)	)	PUNCT
ejpam-5662	601	28	,	,	PUNCT
ejpam-5662	601	29	445	445	NUM
ejpam-5662	601	30	-	-	SYM
ejpam-5662	601	31	455	455	NUM
ejpam-5662	601	32	(	(	PUNCT
ejpam-5662	601	33	2022	2022	NUM
ejpam-5662	601	34	)	)	PUNCT
ejpam-5662	601	35	.	.	PUNCT
ejpam-5662	602	1	[	[	X
ejpam-5662	602	2	28	28	NUM
ejpam-5662	602	3	]	]	PUNCT
ejpam-5662	602	4	he	he	PRON
ejpam-5662	602	5	j	j	PROPN
ejpam-5662	602	6	-	-	PROPN
ejpam-5662	602	7	h.	h.	PROPN
ejpam-5662	602	8	,	,	PUNCT
ejpam-5662	602	9	the	the	DET
ejpam-5662	602	10	simplest	simple	ADJ
ejpam-5662	602	11	approach	approach	NOUN
ejpam-5662	602	12	to	to	ADP
ejpam-5662	602	13	nonlinear	nonlinear	ADJ
ejpam-5662	602	14	oscillators	oscillator	NOUN
ejpam-5662	602	15	,	,	PUNCT
ejpam-5662	602	16	results	result	NOUN
ejpam-5662	602	17	in	in	ADP
ejpam-5662	602	18	physics	physics	NOUN
ejpam-5662	602	19	,	,	PUNCT
ejpam-5662	602	20	15	15	NUM
ejpam-5662	602	21	,	,	PUNCT
ejpam-5662	602	22	102546	102546	NUM
ejpam-5662	602	23	(	(	PUNCT
ejpam-5662	602	24	2019	2019	NUM
ejpam-5662	602	25	)	)	PUNCT
ejpam-5662	602	26	.	.	PUNCT
ejpam-5662	603	1	[	[	X
ejpam-5662	603	2	29	29	NUM
ejpam-5662	603	3	]	]	PUNCT
ejpam-5662	603	4	he	he	PRON
ejpam-5662	603	5	c	c	PROPN
ejpam-5662	603	6	-	-	PUNCT
ejpam-5662	603	7	h.	h.	NOUN
ejpam-5662	603	8	,	,	PUNCT
ejpam-5662	603	9	and	and	CCONJ
ejpam-5662	603	10	liu	liu	PROPN
ejpam-5662	603	11	c.	c.	PROPN
ejpam-5662	603	12	,	,	PUNCT
ejpam-5662	603	13	a	a	DET
ejpam-5662	603	14	modified	modify	VERB
ejpam-5662	603	15	frequency	frequency	NOUN
ejpam-5662	603	16	-	-	PUNCT
ejpam-5662	603	17	amplitude	amplitude	NOUN
ejpam-5662	603	18	formulation	formulation	NOUN
ejpam-5662	603	19	for	for	ADP
ejpam-5662	603	20	fractal	fractal	ADJ
ejpam-5662	603	21	vibration	vibration	NOUN
ejpam-5662	603	22	systems	system	NOUN
ejpam-5662	603	23	,	,	PUNCT
ejpam-5662	603	24	fractals	fractal	NOUN
ejpam-5662	603	25	,	,	PUNCT
ejpam-5662	603	26	30	30	NUM
ejpam-5662	603	27	(	(	PUNCT
ejpam-5662	603	28	03	03	NUM
ejpam-5662	603	29	)	)	PUNCT
ejpam-5662	603	30	,	,	PUNCT
ejpam-5662	603	31	2250046	2250046	NUM
ejpam-5662	603	32	(	(	PUNCT
ejpam-5662	603	33	2022	2022	NUM
ejpam-5662	603	34	)	)	PUNCT
ejpam-5662	603	35	.	.	PUNCT
ejpam-5662	604	1	[	[	X
ejpam-5662	604	2	30	30	NUM
ejpam-5662	604	3	]	]	X
ejpam-5662	604	4	niu	niu	PROPN
ejpam-5662	604	5	j	j	PROPN
ejpam-5662	604	6	-	-	PUNCT
ejpam-5662	604	7	y.	y.	PROPN
ejpam-5662	604	8	,	,	PUNCT
ejpam-5662	604	9	feng	feng	PROPN
ejpam-5662	604	10	g	g	PROPN
ejpam-5662	604	11	-	-	PUNCT
ejpam-5662	604	12	q.	q.	NOUN
ejpam-5662	604	13	,	,	PUNCT
ejpam-5662	604	14	and	and	CCONJ
ejpam-5662	604	15	gepreel	gepreel	PROPN
ejpam-5662	604	16	k.a	k.a	PROPN
ejpam-5662	604	17	.	.	PROPN
ejpam-5662	604	18	,	,	PUNCT
ejpam-5662	604	19	a	a	DET
ejpam-5662	604	20	simple	simple	ADJ
ejpam-5662	604	21	frequency	frequency	NOUN
ejpam-5662	604	22	formulation	formulation	NOUN
ejpam-5662	604	23	for	for	ADP
ejpam-5662	604	24	fractal	fractal	ADJ
ejpam-5662	604	25	–	–	PUNCT
ejpam-5662	604	26	fractional	fractional	ADJ
ejpam-5662	604	27	non	non	ADJ
ejpam-5662	604	28	-	-	ADJ
ejpam-5662	604	29	linear	linear	ADJ
ejpam-5662	604	30	oscillators	oscillator	NOUN
ejpam-5662	604	31	:	:	PUNCT
ejpam-5662	604	32	a	a	DET
ejpam-5662	604	33	promising	promising	ADJ
ejpam-5662	604	34	tool	tool	NOUN
ejpam-5662	604	35	and	and	CCONJ
ejpam-5662	604	36	its	its	PRON
ejpam-5662	604	37	future	future	ADJ
ejpam-5662	604	38	challenge	challenge	NOUN
ejpam-5662	604	39	,	,	PUNCT
ejpam-5662	604	40	frontiers	frontier	NOUN
ejpam-5662	604	41	in	in	ADP
ejpam-5662	604	42	physics	physics	NOUN
ejpam-5662	604	43	,	,	PUNCT
ejpam-5662	604	44	11	11	NUM
ejpam-5662	604	45	,	,	PUNCT
ejpam-5662	604	46	1158121	1158121	NUM
ejpam-5662	604	47	(	(	PUNCT
ejpam-5662	604	48	2023	2023	NUM
ejpam-5662	604	49	)	)	PUNCT
ejpam-5662	604	50	.	.	PUNCT
ejpam-5662	605	1	a.	a.	PROPN
ejpam-5662	605	2	alanazy	alanazy	PROPN
ejpam-5662	605	3	,	,	PUNCT
ejpam-5662	605	4	g.	g.	PROPN
ejpam-5662	605	5	m.	m.	PROPN
ejpam-5662	605	6	moatimid	moatimid	PROPN
ejpam-5662	605	7	,	,	PUNCT
ejpam-5662	605	8	m.	m.	PROPN
ejpam-5662	605	9	a.	a.	PROPN
ejpam-5662	605	10	a.	a.	PROPN
ejpam-5662	605	11	mohamed	mohamed	PROPN
ejpam-5662	605	12	/	/	SYM
ejpam-5662	605	13	eur	eur	PROPN
ejpam-5662	605	14	.	.	PUNCT
ejpam-5662	606	1	j.	j.	PROPN
ejpam-5662	606	2	pure	pure	PROPN
ejpam-5662	606	3	appl	appl	PROPN
ejpam-5662	606	4	.	.	PROPN
ejpam-5662	606	5	math	math	PROPN
ejpam-5662	606	6	,	,	PUNCT
ejpam-5662	606	7	18	18	NUM
ejpam-5662	606	8	(	(	PUNCT
ejpam-5662	606	9	2	2	NUM
ejpam-5662	606	10	)	)	PUNCT
ejpam-5662	606	11	(	(	PUNCT
ejpam-5662	606	12	2025	2025	NUM
ejpam-5662	606	13	)	)	PUNCT
ejpam-5662	606	14	,	,	PUNCT
ejpam-5662	606	15	5662	5662	NUM
ejpam-5662	606	16	35	35	NUM
ejpam-5662	606	17	of	of	ADP
ejpam-5662	606	18	36	36	NUM
ejpam-5662	606	19	[	[	X
ejpam-5662	606	20	31	31	NUM
ejpam-5662	606	21	]	]	X
ejpam-5662	606	22	moatimid	moatimid	PROPN
ejpam-5662	606	23	g.m	g.m	PROPN
ejpam-5662	606	24	.	.	PROPN
ejpam-5662	606	25	,	,	PUNCT
ejpam-5662	606	26	and	and	CCONJ
ejpam-5662	606	27	amer	amer	PROPN
ejpam-5662	606	28	t.s	t.s	PROPN
ejpam-5662	606	29	.	.	PROPN
ejpam-5662	606	30	,	,	PUNCT
ejpam-5662	606	31	dynamical	dynamical	ADJ
ejpam-5662	606	32	system	system	NOUN
ejpam-5662	606	33	of	of	ADP
ejpam-5662	606	34	a	a	DET
ejpam-5662	606	35	time	time	NOUN
ejpam-5662	606	36	-	-	PUNCT
ejpam-5662	606	37	delayed	delay	VERB
ejpam-5662	606	38	-van	-van	ADJ
ejpam-5662	606	39	der	der	ADJ
ejpam-5662	606	40	pole	pole	NOUN
ejpam-5662	606	41	oscillator	oscillator	NOUN
ejpam-5662	606	42	:	:	PUNCT
ejpam-5662	606	43	a	a	DET
ejpam-5662	606	44	non	non	ADJ
ejpam-5662	606	45	-	-	ADJ
ejpam-5662	606	46	perturbative	perturbative	ADJ
ejpam-5662	606	47	approach	approach	NOUN
ejpam-5662	606	48	,	,	PUNCT
ejpam-5662	606	49	scientific	scientific	ADJ
ejpam-5662	606	50	reports	report	NOUN
ejpam-5662	606	51	,	,	PUNCT
ejpam-5662	606	52	13	13	NUM
ejpam-5662	606	53	,	,	PUNCT
ejpam-5662	606	54	11942	11942	NUM
ejpam-5662	606	55	(	(	PUNCT
ejpam-5662	606	56	2023	2023	NUM
ejpam-5662	606	57	)	)	PUNCT
ejpam-5662	606	58	.	.	PUNCT
ejpam-5662	607	1	[	[	X
ejpam-5662	607	2	32	32	NUM
ejpam-5662	607	3	]	]	X
ejpam-5662	607	4	moatimid	moatimid	PROPN
ejpam-5662	607	5	g.m	g.m	PROPN
ejpam-5662	607	6	.	.	PROPN
ejpam-5662	607	7	,	,	PUNCT
ejpam-5662	607	8	amer	amer	PROPN
ejpam-5662	607	9	t.s	t.s	PROPN
ejpam-5662	607	10	.	.	PROPN
ejpam-5662	607	11	,	,	PUNCT
ejpam-5662	607	12	and	and	CCONJ
ejpam-5662	607	13	ellabban	ellabban	PROPN
ejpam-5662	607	14	y.y	y.y	PROPN
ejpam-5662	607	15	.	.	PROPN
ejpam-5662	607	16	,	,	PUNCT
ejpam-5662	607	17	a	a	DET
ejpam-5662	607	18	novel	novel	ADJ
ejpam-5662	607	19	methodology	methodology	NOUN
ejpam-5662	607	20	for	for	ADP
ejpam-5662	607	21	a	a	DET
ejpam-5662	607	22	timedelayed	timedelayed	ADJ
ejpam-5662	607	23	controller	controller	NOUN
ejpam-5662	607	24	to	to	PART
ejpam-5662	607	25	prevent	prevent	VERB
ejpam-5662	607	26	nonlinear	nonlinear	ADJ
ejpam-5662	607	27	system	system	NOUN
ejpam-5662	607	28	oscillations	oscillation	NOUN
ejpam-5662	607	29	,	,	PUNCT
ejpam-5662	607	30	journal	journal	NOUN
ejpam-5662	607	31	of	of	ADP
ejpam-5662	607	32	low	low	ADJ
ejpam-5662	607	33	frequency	frequency	NOUN
ejpam-5662	607	34	noise	noise	NOUN
ejpam-5662	607	35	,	,	PUNCT
ejpam-5662	607	36	vibration	vibration	NOUN
ejpam-5662	607	37	and	and	CCONJ
ejpam-5662	607	38	active	active	ADJ
ejpam-5662	607	39	control	control	NOUN
ejpam-5662	607	40	,	,	PUNCT
ejpam-5662	607	41	43(1	43(1	NOUN
ejpam-5662	607	42	)	)	PUNCT
ejpam-5662	607	43	,	,	PUNCT
ejpam-5662	607	44	525	525	NUM
ejpam-5662	607	45	-	-	SYM
ejpam-5662	607	46	542	542	NUM
ejpam-5662	607	47	(	(	PUNCT
ejpam-5662	607	48	2024	2024	NUM
ejpam-5662	607	49	)	)	PUNCT
ejpam-5662	607	50	.	.	PUNCT
ejpam-5662	608	1	[	[	X
ejpam-5662	608	2	33	33	NUM
ejpam-5662	608	3	]	]	X
ejpam-5662	608	4	moatimid	moatimid	PROPN
ejpam-5662	608	5	g.m	g.m	PROPN
ejpam-5662	608	6	.	.	PROPN
ejpam-5662	608	7	,	,	PUNCT
ejpam-5662	608	8	amer	amer	PROPN
ejpam-5662	608	9	t.s	t.s	PROPN
ejpam-5662	608	10	.	.	PROPN
ejpam-5662	608	11	,	,	PUNCT
ejpam-5662	608	12	and	and	CCONJ
ejpam-5662	608	13	galal	galal	PROPN
ejpam-5662	608	14	a.a	a.a	PROPN
ejpam-5662	608	15	.	.	PROPN
ejpam-5662	608	16	,	,	PUNCT
ejpam-5662	608	17	studying	study	VERB
ejpam-5662	608	18	highly	highly	ADV
ejpam-5662	608	19	nonlinear	nonlinear	ADJ
ejpam-5662	608	20	oscillators	oscillator	NOUN
ejpam-5662	608	21	using	use	VERB
ejpam-5662	608	22	the	the	DET
ejpam-5662	608	23	non	non	ADJ
ejpam-5662	608	24	-	-	ADJ
ejpam-5662	608	25	perturbative	perturbative	ADJ
ejpam-5662	608	26	methodology	methodology	NOUN
ejpam-5662	608	27	,	,	PUNCT
ejpam-5662	608	28	scientific	scientific	ADJ
ejpam-5662	608	29	reports	report	NOUN
ejpam-5662	608	30	,	,	PUNCT
ejpam-5662	608	31	13	13	NUM
ejpam-5662	608	32	,	,	PUNCT
ejpam-5662	608	33	20288	20288	NUM
ejpam-5662	608	34	(	(	PUNCT
ejpam-5662	608	35	2023	2023	NUM
ejpam-5662	608	36	)	)	PUNCT
ejpam-5662	608	37	.	.	PUNCT
ejpam-5662	609	1	[	[	X
ejpam-5662	609	2	34	34	NUM
ejpam-5662	609	3	]	]	X
ejpam-5662	609	4	moatimid	moatimid	PROPN
ejpam-5662	609	5	g.m	g.m	PROPN
ejpam-5662	609	6	.	.	PROPN
ejpam-5662	609	7	,	,	PUNCT
ejpam-5662	609	8	mohamed	mohamed	PROPN
ejpam-5662	609	9	m.	m.	PROPN
ejpam-5662	609	10	a.a	a.a	PROPN
ejpam-5662	609	11	.	.	PROPN
ejpam-5662	609	12	,	,	PUNCT
ejpam-5662	609	13	and	and	CCONJ
ejpam-5662	609	14	elagamy	elagamy	PROPN
ejpam-5662	609	15	kh	kh	PROPN
ejpam-5662	609	16	.	.	PROPN
ejpam-5662	609	17	,	,	PUNCT
ejpam-5662	609	18	nonlinear	nonlinear	PROPN
ejpam-5662	609	19	kelvin	kelvin	PROPN
ejpam-5662	609	20	-	-	PUNCT
ejpam-5662	609	21	helmholtz	helmholtz	PROPN
ejpam-5662	609	22	instability	instability	NOUN
ejpam-5662	609	23	of	of	ADP
ejpam-5662	609	24	a	a	DET
ejpam-5662	609	25	horizontal	horizontal	ADJ
ejpam-5662	609	26	interface	interface	NOUN
ejpam-5662	609	27	separating	separate	VERB
ejpam-5662	609	28	two	two	NUM
ejpam-5662	609	29	electrified	electrify	VERB
ejpam-5662	609	30	walters	walter	NOUN
ejpam-5662	609	31	’	'	PUNCT
ejpam-5662	609	32	b	b	PROPN
ejpam-5662	609	33	liquids	liquid	NOUN
ejpam-5662	609	34	:	:	PUNCT
ejpam-5662	609	35	a	a	DET
ejpam-5662	609	36	new	new	ADJ
ejpam-5662	609	37	approach	approach	NOUN
ejpam-5662	609	38	,	,	PUNCT
ejpam-5662	609	39	chinese	chinese	ADJ
ejpam-5662	609	40	journal	journal	PROPN
ejpam-5662	609	41	of	of	ADP
ejpam-5662	609	42	physics	physics	PROPN
ejpam-5662	609	43	,	,	PUNCT
ejpam-5662	609	44	85	85	NUM
ejpam-5662	609	45	,	,	PUNCT
ejpam-5662	609	46	629	629	NUM
ejpam-5662	609	47	-	-	SYM
ejpam-5662	609	48	648	648	NUM
ejpam-5662	609	49	(	(	PUNCT
ejpam-5662	609	50	2023	2023	NUM
ejpam-5662	609	51	)	)	PUNCT
ejpam-5662	609	52	.	.	PUNCT
ejpam-5662	610	1	[	[	X
ejpam-5662	610	2	35	35	NUM
ejpam-5662	610	3	]	]	X
ejpam-5662	610	4	moatimid	moatimid	PROPN
ejpam-5662	610	5	g.m	g.m	PROPN
ejpam-5662	610	6	.	.	PROPN
ejpam-5662	610	7	,	,	PUNCT
ejpam-5662	610	8	and	and	CCONJ
ejpam-5662	610	9	sayed	sayed	PROPN
ejpam-5662	610	10	a.	a.	PROPN
ejpam-5662	610	11	,	,	PUNCT
ejpam-5662	610	12	nonlinear	nonlinear	ADJ
ejpam-5662	610	13	ehd	ehd	NOUN
ejpam-5662	610	14	stability	stability	NOUN
ejpam-5662	610	15	of	of	ADP
ejpam-5662	610	16	a	a	DET
ejpam-5662	610	17	cylindrical	cylindrical	ADJ
ejpam-5662	610	18	interface	interface	NOUN
ejpam-5662	610	19	separating	separate	VERB
ejpam-5662	610	20	two	two	NUM
ejpam-5662	610	21	rivlin	rivlin	ADJ
ejpam-5662	610	22	-	-	PUNCT
ejpam-5662	610	23	ericksen	ericksen	ADJ
ejpam-5662	610	24	fluids	fluid	NOUN
ejpam-5662	610	25	:	:	PUNCT
ejpam-5662	610	26	a	a	DET
ejpam-5662	610	27	novel	novel	ADJ
ejpam-5662	610	28	analysis	analysis	NOUN
ejpam-5662	610	29	,	,	PUNCT
ejpam-5662	610	30	chinese	chinese	ADJ
ejpam-5662	610	31	journal	journal	PROPN
ejpam-5662	610	32	of	of	ADP
ejpam-5662	610	33	physics	physics	PROPN
ejpam-5662	610	34	,	,	PUNCT
ejpam-5662	610	35	87	87	NUM
ejpam-5662	610	36	,	,	PUNCT
ejpam-5662	610	37	379–397	379–397	NUM
ejpam-5662	610	38	(	(	PUNCT
ejpam-5662	610	39	2024	2024	NUM
ejpam-5662	610	40	)	)	PUNCT
ejpam-5662	610	41	.	.	PUNCT
ejpam-5662	611	1	[	[	X
ejpam-5662	611	2	36	36	NUM
ejpam-5662	611	3	]	]	X
ejpam-5662	611	4	moatimid	moatimid	PROPN
ejpam-5662	611	5	g.m	g.m	PROPN
ejpam-5662	611	6	.	.	PROPN
ejpam-5662	611	7	,	,	PUNCT
ejpam-5662	611	8	el	el	PROPN
ejpam-5662	611	9	-	-	PUNCT
ejpam-5662	611	10	sayed	say	VERB
ejpam-5662	611	11	a.t	a.t	PROPN
ejpam-5662	611	12	.	.	PROPN
ejpam-5662	611	13	,	,	PUNCT
ejpam-5662	611	14	and	and	CCONJ
ejpam-5662	611	15	salman	salman	PROPN
ejpam-5662	611	16	h.f	h.f	PROPN
ejpam-5662	611	17	.	.	PROPN
ejpam-5662	611	18	,	,	PUNCT
ejpam-5662	611	19	different	different	ADJ
ejpam-5662	611	20	controllers	controller	NOUN
ejpam-5662	611	21	for	for	ADP
ejpam-5662	611	22	suppressing	suppress	VERB
ejpam-5662	611	23	oscillations	oscillation	NOUN
ejpam-5662	611	24	of	of	ADP
ejpam-5662	611	25	a	a	DET
ejpam-5662	611	26	hybrid	hybrid	ADJ
ejpam-5662	611	27	oscillator	oscillator	NOUN
ejpam-5662	611	28	via	via	ADP
ejpam-5662	611	29	non	non	ADJ
ejpam-5662	611	30	-	-	ADJ
ejpam-5662	611	31	perturbative	perturbative	ADJ
ejpam-5662	611	32	analysis	analysis	NOUN
ejpam-5662	611	33	,	,	PUNCT
ejpam-5662	611	34	scientific	scientific	ADJ
ejpam-5662	611	35	reports	report	NOUN
ejpam-5662	611	36	,	,	PUNCT
ejpam-5662	611	37	14	14	NUM
ejpam-5662	611	38	,	,	PUNCT
ejpam-5662	611	39	307	307	NUM
ejpam-5662	611	40	(	(	PUNCT
ejpam-5662	611	41	2024	2024	NUM
ejpam-5662	611	42	)	)	PUNCT
ejpam-5662	611	43	.	.	PUNCT
ejpam-5662	612	1	[	[	X
ejpam-5662	612	2	37	37	NUM
ejpam-5662	612	3	]	]	X
ejpam-5662	612	4	moatimid	moatimid	PROPN
ejpam-5662	612	5	g.m	g.m	PROPN
ejpam-5662	612	6	.	.	PROPN
ejpam-5662	612	7	,	,	PUNCT
ejpam-5662	612	8	and	and	CCONJ
ejpam-5662	612	9	m.	m.	PROPN
ejpam-5662	612	10	mohamed	mohamed	PROPN
ejpam-5662	612	11	y.m	y.m	PROPN
ejpam-5662	612	12	.	.	PROPN
ejpam-5662	612	13	,	,	PUNCT
ejpam-5662	612	14	a	a	DET
ejpam-5662	612	15	novel	novel	ADJ
ejpam-5662	612	16	methodology	methodology	NOUN
ejpam-5662	612	17	in	in	ADP
ejpam-5662	612	18	analyzing	analyze	VERB
ejpam-5662	612	19	nonlinear	nonlinear	ADJ
ejpam-5662	612	20	stability	stability	NOUN
ejpam-5662	612	21	of	of	ADP
ejpam-5662	612	22	two	two	NUM
ejpam-5662	612	23	electrified	electrify	VERB
ejpam-5662	612	24	viscoelastic	viscoelastic	ADJ
ejpam-5662	612	25	liquids	liquid	NOUN
ejpam-5662	612	26	,	,	PUNCT
ejpam-5662	612	27	chinese	chinese	ADJ
ejpam-5662	612	28	journal	journal	PROPN
ejpam-5662	612	29	of	of	ADP
ejpam-5662	612	30	physics	physics	PROPN
ejpam-5662	612	31	,	,	PUNCT
ejpam-5662	612	32	89	89	NUM
ejpam-5662	612	33	,	,	PUNCT
ejpam-5662	612	34	679	679	NUM
ejpam-5662	612	35	-	-	SYM
ejpam-5662	612	36	706	706	NUM
ejpam-5662	612	37	(	(	PUNCT
ejpam-5662	612	38	2024	2024	NUM
ejpam-5662	612	39	)	)	PUNCT
ejpam-5662	612	40	.	.	PUNCT
ejpam-5662	613	1	[	[	X
ejpam-5662	613	2	38	38	NUM
ejpam-5662	613	3	]	]	PUNCT
ejpam-5662	613	4	moatimid	moatimid	PROPN
ejpam-5662	613	5	g.m	g.m	PROPN
ejpam-5662	613	6	.	.	PROPN
ejpam-5662	613	7	,	,	PUNCT
ejpam-5662	613	8	and	and	CCONJ
ejpam-5662	613	9	m.	m.	PROPN
ejpam-5662	613	10	mohamed	mohamed	PROPN
ejpam-5662	613	11	y.m	y.m	PROPN
ejpam-5662	613	12	.	.	PROPN
ejpam-5662	613	13	,	,	PUNCT
ejpam-5662	613	14	nonlinear	nonlinear	ADJ
ejpam-5662	613	15	electro	electro	ADJ
ejpam-5662	613	16	-	-	PUNCT
ejpam-5662	613	17	rheological	rheological	ADJ
ejpam-5662	613	18	instability	instability	NOUN
ejpam-5662	613	19	of	of	ADP
ejpam-5662	613	20	two	two	NUM
ejpam-5662	613	21	moving	move	VERB
ejpam-5662	613	22	cylindrical	cylindrical	ADJ
ejpam-5662	613	23	fluids	fluid	NOUN
ejpam-5662	613	24	:	:	PUNCT
ejpam-5662	613	25	an	an	DET
ejpam-5662	613	26	innovative	innovative	ADJ
ejpam-5662	613	27	approach	approach	NOUN
ejpam-5662	613	28	,	,	PUNCT
ejpam-5662	613	29	physics	physics	NOUN
ejpam-5662	613	30	of	of	ADP
ejpam-5662	613	31	fluids	fluid	NOUN
ejpam-5662	613	32	,	,	PUNCT
ejpam-5662	613	33	36	36	NUM
ejpam-5662	613	34	,	,	PUNCT
ejpam-5662	613	35	024110	024110	NUM
ejpam-5662	613	36	(	(	PUNCT
ejpam-5662	613	37	2024	2024	NUM
ejpam-5662	613	38	)	)	PUNCT
ejpam-5662	613	39	.	.	PUNCT
ejpam-5662	614	1	[	[	X
ejpam-5662	614	2	39	39	NUM
ejpam-5662	614	3	]	]	PUNCT
ejpam-5662	614	4	moatimid	moatimid	PROPN
ejpam-5662	614	5	g.m	g.m	PROPN
ejpam-5662	614	6	.	.	PROPN
ejpam-5662	614	7	,	,	PUNCT
ejpam-5662	614	8	mostafa	mostafa	PROPN
ejpam-5662	614	9	d.m	d.m	PROPN
ejpam-5662	614	10	.	.	PROPN
ejpam-5662	614	11	,	,	PUNCT
ejpam-5662	614	12	and	and	CCONJ
ejpam-5662	614	13	zekry	zekry	PROPN
ejpam-5662	614	14	m.h	m.h	PROPN
ejpam-5662	614	15	.	.	PROPN
ejpam-5662	614	16	,	,	PUNCT
ejpam-5662	614	17	a	a	DET
ejpam-5662	614	18	new	new	ADJ
ejpam-5662	614	19	methodology	methodology	NOUN
ejpam-5662	614	20	in	in	ADP
ejpam-5662	614	21	evaluating	evaluate	VERB
ejpam-5662	614	22	nonlinear	nonlinear	ADJ
ejpam-5662	614	23	eelectrohydrodynamic	eelectrohydrodynamic	ADJ
ejpam-5662	614	24	azimuthal	azimuthal	NOUN
ejpam-5662	614	25	stability	stability	NOUN
ejpam-5662	614	26	between	between	ADP
ejpam-5662	614	27	two	two	NUM
ejpam-5662	614	28	dusty	dusty	ADJ
ejpam-5662	614	29	viscous	viscous	ADJ
ejpam-5662	614	30	fluids	fluid	NOUN
ejpam-5662	614	31	,	,	PUNCT
ejpam-5662	614	32	chinese	chinese	ADJ
ejpam-5662	614	33	journal	journal	PROPN
ejpam-5662	614	34	of	of	ADP
ejpam-5662	614	35	physics	physics	PROPN
ejpam-5662	614	36	,	,	PUNCT
ejpam-5662	614	37	90	90	NUM
ejpam-5662	614	38	,	,	PUNCT
ejpam-5662	614	39	134–154	134–154	NUM
ejpam-5662	614	40	(	(	PUNCT
ejpam-5662	614	41	2024	2024	NUM
ejpam-5662	614	42	)	)	PUNCT
ejpam-5662	614	43	.	.	PUNCT
ejpam-5662	615	1	[	[	X
ejpam-5662	615	2	40	40	NUM
ejpam-5662	615	3	]	]	X
ejpam-5662	615	4	moatimid	moatimid	PROPN
ejpam-5662	615	5	g.m	g.m	PROPN
ejpam-5662	615	6	.	.	PROPN
ejpam-5662	615	7	,	,	PUNCT
ejpam-5662	615	8	and	and	CCONJ
ejpam-5662	615	9	mostafa	mostafa	PROPN
ejpam-5662	615	10	d.m	d.m	PROPN
ejpam-5662	615	11	.	.	PROPN
ejpam-5662	615	12	,	,	PUNCT
ejpam-5662	615	13	nonlinear	nonlinear	ADJ
ejpam-5662	615	14	stability	stability	NOUN
ejpam-5662	615	15	of	of	ADP
ejpam-5662	615	16	two	two	NUM
ejpam-5662	615	17	superimposed	superimpose	VERB
ejpam-5662	615	18	electrified	electrified	ADJ
ejpam-5662	615	19	dusty	dusty	ADJ
ejpam-5662	615	20	fluids	fluid	NOUN
ejpam-5662	615	21	of	of	ADP
ejpam-5662	615	22	type	type	NOUN
ejpam-5662	615	23	rivlin	rivlin	PROPN
ejpam-5662	615	24	-	-	PUNCT
ejpam-5662	615	25	ericksen	ericksen	ADJ
ejpam-5662	615	26	:	:	PUNCT
ejpam-5662	615	27	non	non	ADJ
ejpam-5662	615	28	-	-	ADJ
ejpam-5662	615	29	perturbative	perturbative	ADJ
ejpam-5662	615	30	approach	approach	NOUN
ejpam-5662	615	31	,	,	PUNCT
ejpam-5662	615	32	partial	partial	ADJ
ejpam-5662	615	33	differential	differential	ADJ
ejpam-5662	615	34	equations	equation	NOUN
ejpam-5662	615	35	in	in	ADP
ejpam-5662	615	36	applied	applied	ADJ
ejpam-5662	615	37	mathematics	mathematic	NOUN
ejpam-5662	615	38	,	,	PUNCT
ejpam-5662	615	39	10	10	NUM
ejpam-5662	615	40	,	,	PUNCT
ejpam-5662	615	41	100745	100745	NUM
ejpam-5662	615	42	(	(	PUNCT
ejpam-5662	615	43	2024	2024	NUM
ejpam-5662	615	44	)	)	PUNCT
ejpam-5662	615	45	.	.	PUNCT
ejpam-5662	616	1	[	[	X
ejpam-5662	616	2	41	41	NUM
ejpam-5662	616	3	]	]	X
ejpam-5662	616	4	moatimid	moatimid	PROPN
ejpam-5662	616	5	g.m	g.m	PROPN
ejpam-5662	616	6	.	.	PROPN
ejpam-5662	616	7	,	,	PUNCT
ejpam-5662	616	8	mohamed	mohamed	PROPN
ejpam-5662	616	9	m.	m.	PROPN
ejpam-5662	616	10	a.a	a.a	PROPN
ejpam-5662	616	11	.	.	PROPN
ejpam-5662	616	12	,	,	PUNCT
ejpam-5662	616	13	and	and	CCONJ
ejpam-5662	616	14	elagamy	elagamy	PROPN
ejpam-5662	616	15	kh	kh	PROPN
ejpam-5662	616	16	.	.	PROPN
ejpam-5662	616	17	,	,	PUNCT
ejpam-5662	616	18	insightful	insightful	ADJ
ejpam-5662	616	19	inspection	inspection	NOUN
ejpam-5662	616	20	of	of	ADP
ejpam-5662	616	21	the	the	DET
ejpam-5662	616	22	nonlinear	nonlinear	ADJ
ejpam-5662	616	23	instability	instability	NOUN
ejpam-5662	616	24	of	of	ADP
ejpam-5662	616	25	an	an	DET
ejpam-5662	616	26	azimuthal	azimuthal	ADJ
ejpam-5662	616	27	disturbance	disturbance	NOUN
ejpam-5662	616	28	separating	separate	VERB
ejpam-5662	616	29	two	two	NUM
ejpam-5662	616	30	rotating	rotate	VERB
ejpam-5662	616	31	magnetic	magnetic	ADJ
ejpam-5662	616	32	liquid	liquid	ADJ
ejpam-5662	616	33	columns	column	NOUN
ejpam-5662	616	34	,	,	PUNCT
ejpam-5662	616	35	the	the	DET
ejpam-5662	616	36	european	european	PROPN
ejpam-5662	616	37	physical	physical	PROPN
ejpam-5662	616	38	journal	journal	PROPN
ejpam-5662	616	39	plus	plus	CCONJ
ejpam-5662	616	40	,	,	PUNCT
ejpam-5662	616	41	139	139	NUM
ejpam-5662	616	42	,	,	PUNCT
ejpam-5662	616	43	590	590	NUM
ejpam-5662	616	44	(	(	PUNCT
ejpam-5662	616	45	2024	2024	NUM
ejpam-5662	616	46	)	)	PUNCT
ejpam-5662	616	47	.	.	PUNCT
ejpam-5662	617	1	[	[	X
ejpam-5662	617	2	42	42	NUM
ejpam-5662	617	3	]	]	X
ejpam-5662	617	4	ismail	ismail	PROPN
ejpam-5662	617	5	g.m	g.m	PROPN
ejpam-5662	617	6	.	.	PROPN
ejpam-5662	617	7	,	,	PUNCT
ejpam-5662	617	8	moatimid	moatimid	PROPN
ejpam-5662	617	9	g.m	g.m	PROPN
ejpam-5662	617	10	.	.	PROPN
ejpam-5662	617	11	,	,	PUNCT
ejpam-5662	617	12	yamani	yamani	PROPN
ejpam-5662	617	13	m.i	m.i	PROPN
ejpam-5662	617	14	.	.	PROPN
ejpam-5662	617	15	,	,	PUNCT
ejpam-5662	617	16	periodic	periodic	ADJ
ejpam-5662	617	17	solutions	solution	NOUN
ejpam-5662	617	18	of	of	ADP
ejpam-5662	617	19	strongly	strongly	ADV
ejpam-5662	617	20	nonlinear	nonlinear	ADJ
ejpam-5662	617	21	oscillators	oscillator	NOUN
ejpam-5662	617	22	using	use	VERB
ejpam-5662	617	23	he	he	PRON
ejpam-5662	617	24	’s	’s	PART
ejpam-5662	617	25	frequency	frequency	NOUN
ejpam-5662	617	26	formulation	formulation	NOUN
ejpam-5662	617	27	,	,	PUNCT
ejpam-5662	617	28	european	european	ADJ
ejpam-5662	617	29	journal	journal	NOUN
ejpam-5662	617	30	of	of	ADP
ejpam-5662	617	31	pure	pure	ADJ
ejpam-5662	617	32	and	and	CCONJ
ejpam-5662	617	33	applied	applied	ADJ
ejpam-5662	617	34	mathematics	mathematic	NOUN
ejpam-5662	617	35	,	,	PUNCT
ejpam-5662	617	36	17(3	17(3	NUM
ejpam-5662	617	37	)	)	PUNCT
ejpam-5662	617	38	,	,	PUNCT
ejpam-5662	617	39	2154	2154	NUM
ejpam-5662	617	40	-	-	SYM
ejpam-5662	617	41	2171	2171	NUM
ejpam-5662	617	42	(	(	PUNCT
ejpam-5662	617	43	2024	2024	NUM
ejpam-5662	617	44	)	)	PUNCT
ejpam-5662	617	45	.	.	PUNCT
ejpam-5662	618	1	[	[	X
ejpam-5662	618	2	43	43	NUM
ejpam-5662	618	3	]	]	X
ejpam-5662	618	4	alluhydan	alluhydan	PROPN
ejpam-5662	619	1	kh	kh	PROPN
ejpam-5662	619	2	.	.	PROPN
ejpam-5662	619	3	,	,	PUNCT
ejpam-5662	619	4	moatimid	moatimid	PROPN
ejpam-5662	619	5	g.m	g.m	PROPN
ejpam-5662	619	6	.	.	PROPN
ejpam-5662	619	7	,	,	PUNCT
ejpam-5662	619	8	and	and	CCONJ
ejpam-5662	619	9	amer	amer	PROPN
ejpam-5662	619	10	t.s	t.s	PROPN
ejpam-5662	619	11	.	.	PROPN
ejpam-5662	619	12	,	,	PUNCT
ejpam-5662	619	13	the	the	DET
ejpam-5662	619	14	non	non	ADJ
ejpam-5662	619	15	-	-	ADJ
ejpam-5662	619	16	perturbative	perturbative	ADJ
ejpam-5662	619	17	approach	approach	NOUN
ejpam-5662	619	18	in	in	ADP
ejpam-5662	619	19	examining	examine	VERB
ejpam-5662	619	20	the	the	DET
ejpam-5662	619	21	motion	motion	NOUN
ejpam-5662	619	22	of	of	ADP
ejpam-5662	619	23	a	a	DET
ejpam-5662	619	24	simple	simple	ADJ
ejpam-5662	619	25	pendulum	pendulum	NOUN
ejpam-5662	619	26	associated	associate	VERB
ejpam-5662	619	27	with	with	ADP
ejpam-5662	619	28	a	a	DET
ejpam-5662	619	29	rolling	rolling	ADJ
ejpam-5662	619	30	wheel	wheel	NOUN
ejpam-5662	619	31	with	with	ADP
ejpam-5662	619	32	a	a	DET
ejpam-5662	619	33	time	time	NOUN
ejpam-5662	619	34	-	-	PUNCT
ejpam-5662	619	35	delay	delay	NOUN
ejpam-5662	619	36	,	,	PUNCT
ejpam-5662	619	37	european	european	ADJ
ejpam-5662	619	38	journal	journal	PROPN
ejpam-5662	619	39	of	of	ADP
ejpam-5662	619	40	pure	pure	ADJ
ejpam-5662	619	41	and	and	CCONJ
ejpam-5662	619	42	applied	applied	ADJ
ejpam-5662	619	43	mathematics	mathematic	NOUN
ejpam-5662	619	44	,	,	PUNCT
ejpam-5662	619	45	17(4	17(4	NUM
ejpam-5662	619	46	)	)	PUNCT
ejpam-5662	619	47	,	,	PUNCT
ejpam-5662	619	48	3185	3185	NUM
ejpam-5662	619	49	-	-	SYM
ejpam-5662	619	50	3208	3208	NUM
ejpam-5662	619	51	(	(	PUNCT
ejpam-5662	619	52	2024	2024	NUM
ejpam-5662	619	53	)	)	PUNCT
ejpam-5662	619	54	.	.	PUNCT
ejpam-5662	620	1	[	[	X
ejpam-5662	620	2	44	44	NUM
ejpam-5662	620	3	]	]	PUNCT
ejpam-5662	620	4	alluhydan	alluhydan	PROPN
ejpam-5662	620	5	kh	kh	PROPN
ejpam-5662	620	6	.	.	PROPN
ejpam-5662	620	7	,	,	PUNCT
ejpam-5662	620	8	moatimid	moatimid	PROPN
ejpam-5662	620	9	g.m	g.m	PROPN
ejpam-5662	620	10	.	.	PROPN
ejpam-5662	620	11	,	,	PUNCT
ejpam-5662	620	12	amer	amer	PROPN
ejpam-5662	620	13	t.s	t.s	PROPN
ejpam-5662	620	14	.	.	PROPN
ejpam-5662	620	15	,	,	PUNCT
ejpam-5662	620	16	and	and	CCONJ
ejpam-5662	620	17	a.a	a.a	PROPN
ejpam-5662	620	18	.	.	PROPN
ejpam-5662	620	19	galal	galal	PROPN
ejpam-5662	620	20	,	,	PUNCT
ejpam-5662	620	21	a	a	DET
ejpam-5662	620	22	novel	novel	ADJ
ejpam-5662	620	23	inspection	inspection	NOUN
ejpam-5662	620	24	of	of	ADP
ejpam-5662	620	25	a	a	DET
ejpam-5662	620	26	time	time	NOUN
ejpam-5662	620	27	-	-	PUNCT
ejpam-5662	620	28	delayed	delay	VERB
ejpam-5662	620	29	rolling	rolling	NOUN
ejpam-5662	620	30	of	of	ADP
ejpam-5662	620	31	a	a	DET
ejpam-5662	620	32	rigid	rigid	ADJ
ejpam-5662	620	33	rod	rod	NOUN
ejpam-5662	620	34	,	,	PUNCT
ejpam-5662	620	35	european	european	ADJ
ejpam-5662	620	36	journal	journal	NOUN
ejpam-5662	620	37	of	of	ADP
ejpam-5662	620	38	pure	pure	ADJ
ejpam-5662	620	39	and	and	CCONJ
ejpam-5662	620	40	applied	applied	ADJ
ejpam-5662	620	41	mathematics	mathematic	NOUN
ejpam-5662	620	42	,	,	PUNCT
ejpam-5662	620	43	17(4	17(4	NUM
ejpam-5662	620	44	)	)	PUNCT
ejpam-5662	620	45	,	,	PUNCT
ejpam-5662	620	46	2878	2878	NUM
ejpam-5662	620	47	-	-	SYM
ejpam-5662	620	48	2895	2895	NUM
ejpam-5662	620	49	(	(	PUNCT
ejpam-5662	620	50	2024	2024	NUM
ejpam-5662	620	51	)	)	PUNCT
ejpam-5662	620	52	.	.	PUNCT
ejpam-5662	621	1	[	[	X
ejpam-5662	621	2	45	45	NUM
ejpam-5662	621	3	]	]	PUNCT
ejpam-5662	621	4	barakat	barakat	PROPN
ejpam-5662	621	5	a.a	a.a	PROPN
ejpam-5662	621	6	.	.	PROPN
ejpam-5662	621	7	,	,	PUNCT
ejpam-5662	621	8	weig	weig	PROPN
ejpam-5662	621	9	e.m	e.m	PROPN
ejpam-5662	621	10	.	.	PROPN
ejpam-5662	621	11	,	,	PUNCT
ejpam-5662	621	12	and	and	CCONJ
ejpam-5662	621	13	hagedorn	hagedorn	PROPN
ejpam-5662	621	14	p.	p.	PROPN
ejpam-5662	621	15	,	,	PUNCT
ejpam-5662	621	16	non	non	ADJ
ejpam-5662	621	17	-	-	ADJ
ejpam-5662	621	18	trivial	trivial	ADJ
ejpam-5662	621	19	solutions	solution	NOUN
ejpam-5662	621	20	and	and	CCONJ
ejpam-5662	621	21	their	their	PRON
ejpam-5662	621	22	stability	stability	NOUN
ejpam-5662	621	23	in	in	ADP
ejpam-5662	621	24	a	a	DET
ejpam-5662	621	25	two	two	NUM
ejpam-5662	621	26	-	-	PUNCT
ejpam-5662	621	27	degree	degree	NOUN
ejpam-5662	621	28	-	-	PUNCT
ejpam-5662	621	29	of	of	ADP
ejpam-5662	621	30	-	-	PUNCT
ejpam-5662	621	31	freedom	freedom	NOUN
ejpam-5662	621	32	mathieu	mathieu	PROPN
ejpam-5662	621	33	–	–	PUNCT
ejpam-5662	621	34	duffing	duffing	NOUN
ejpam-5662	621	35	system	system	NOUN
ejpam-5662	621	36	,	,	PUNCT
ejpam-5662	621	37	nonlinear	nonlinear	ADJ
ejpam-5662	621	38	dynamics	dynamic	NOUN
ejpam-5662	621	39	,	,	PUNCT
ejpam-5662	621	40	111	111	NUM
ejpam-5662	621	41	,	,	PUNCT
ejpam-5662	621	42	a.	a.	NOUN
ejpam-5662	621	43	alanazy	alanazy	NOUN
ejpam-5662	621	44	,	,	PUNCT
ejpam-5662	621	45	g.	g.	PROPN
ejpam-5662	621	46	m.	m.	PROPN
ejpam-5662	621	47	moatimid	moatimid	PROPN
ejpam-5662	621	48	,	,	PUNCT
ejpam-5662	621	49	m.	m.	PROPN
ejpam-5662	621	50	a.	a.	PROPN
ejpam-5662	621	51	a.	a.	PROPN
ejpam-5662	621	52	mohamed	mohamed	PROPN
ejpam-5662	621	53	/	/	SYM
ejpam-5662	621	54	eur	eur	PROPN
ejpam-5662	621	55	.	.	PUNCT
ejpam-5662	622	1	j.	j.	PROPN
ejpam-5662	622	2	pure	pure	PROPN
ejpam-5662	622	3	appl	appl	PROPN
ejpam-5662	622	4	.	.	PROPN
ejpam-5662	622	5	math	math	PROPN
ejpam-5662	622	6	,	,	PUNCT
ejpam-5662	622	7	18	18	NUM
ejpam-5662	622	8	(	(	PUNCT
ejpam-5662	622	9	2	2	NUM
ejpam-5662	622	10	)	)	PUNCT
ejpam-5662	622	11	(	(	PUNCT
ejpam-5662	622	12	2025	2025	NUM
ejpam-5662	622	13	)	)	PUNCT
ejpam-5662	622	14	,	,	PUNCT
ejpam-5662	622	15	5662	5662	NUM
ejpam-5662	622	16	36	36	NUM
ejpam-5662	622	17	of	of	ADP
ejpam-5662	622	18	36	36	NUM
ejpam-5662	622	19	22119–22136	22119–22136	NUM
ejpam-5662	622	20	(	(	PUNCT
ejpam-5662	622	21	2023	2023	NUM
ejpam-5662	622	22	)	)	PUNCT
ejpam-5662	622	23	.	.	PUNCT
ejpam-5662	623	1	[	[	X
ejpam-5662	623	2	46	46	NUM
ejpam-5662	623	3	]	]	X
ejpam-5662	623	4	moatimid	moatimid	PROPN
ejpam-5662	623	5	g.m	g.m	PROPN
ejpam-5662	623	6	.	.	PROPN
ejpam-5662	623	7	,	,	PUNCT
ejpam-5662	623	8	mohamed	mohamed	PROPN
ejpam-5662	623	9	m.a.a	m.a.a	PROPN
ejpam-5662	623	10	.	.	PUNCT
ejpam-5662	623	11	,	,	PUNCT
ejpam-5662	623	12	and	and	CCONJ
ejpam-5662	623	13	elagamy	elagamy	PROPN
ejpam-5662	623	14	kh	kh	PROPN
ejpam-5662	623	15	.	.	PROPN
ejpam-5662	623	16	,	,	PUNCT
ejpam-5662	623	17	an	an	DET
ejpam-5662	623	18	innovative	innovative	ADJ
ejpam-5662	623	19	approach	approach	NOUN
ejpam-5662	623	20	in	in	ADP
ejpam-5662	623	21	inspecting	inspect	VERB
ejpam-5662	623	22	a	a	DET
ejpam-5662	623	23	damped	damp	VERB
ejpam-5662	623	24	mathieu	mathieu	PROPN
ejpam-5662	623	25	cubic	cubic	ADJ
ejpam-5662	623	26	–	–	PUNCT
ejpam-5662	623	27	quintic	quintic	ADJ
ejpam-5662	623	28	duffing	duffing	NOUN
ejpam-5662	623	29	oscillator	oscillator	NOUN
ejpam-5662	623	30	,	,	PUNCT
ejpam-5662	623	31	journal	journal	NOUN
ejpam-5662	623	32	of	of	ADP
ejpam-5662	623	33	vibration	vibration	NOUN
ejpam-5662	623	34	engineering	engineering	NOUN
ejpam-5662	623	35	&	&	CCONJ
ejpam-5662	623	36	technologies	technology	NOUN
ejpam-5662	623	37	,	,	PUNCT
ejpam-5662	623	38	published	publish	VERB
ejpam-5662	623	39	online	online	ADV
ejpam-5662	623	40	:	:	PUNCT
ejpam-5662	623	41	23	23	NUM
ejpam-5662	623	42	july	july	PROPN
ejpam-5662	623	43	(	(	PUNCT
ejpam-5662	623	44	2024	2024	NUM
ejpam-5662	623	45	)	)	PUNCT
ejpam-5662	623	46	.	.	PUNCT
ejpam-5662	624	1	https://doi.org/10.1007/s42417-024-01506-w	https://doi.org/10.1007/s42417-024-01506-w	NOUN
ejpam-5662	624	2	appendix	appendix	VERB
ejpam-5662	624	3	the	the	DET
ejpam-5662	624	4	coefficients	coefficient	NOUN
ejpam-5662	624	5	defined	define	VERB
ejpam-5662	624	6	in	in	ADP
ejpam-5662	624	7	eqs	eqs	PROPN
ejpam-5662	624	8	.	.	PUNCT
ejpam-5662	625	1	(	(	PUNCT
ejpam-5662	625	2	29	29	NUM
ejpam-5662	625	3	)	)	PUNCT
ejpam-5662	625	4	and	and	CCONJ
ejpam-5662	625	5	(	(	PUNCT
ejpam-5662	625	6	28	28	NUM
ejpam-5662	625	7	)	)	PUNCT
ejpam-5662	625	8	as	as	SCONJ
ejpam-5662	625	9	evaluated	evaluate	VERB
ejpam-5662	625	10	by	by	ADP
ejpam-5662	625	11	ms	ms	PROPN
ejpam-5662	625	12	are	be	AUX
ejpam-5662	625	13	given	give	VERB
ejpam-5662	625	14	as	as	ADP
ejpam-5662	625	15	:	:	PUNCT
ejpam-5662	625	16	a1	a1	NOUN
ejpam-5662	625	17	=	=	NOUN
ejpam-5662	625	18	3	3	NUM
ejpam-5662	625	19	4	4	NUM
ejpam-5662	625	20	a2γ1	a2γ1	NOUN
ejpam-5662	626	1	+	+	NUM
ejpam-5662	626	2	5	5	NUM
ejpam-5662	626	3	8	8	NUM
ejpam-5662	626	4	a4λ1	a4λ1	NOUN
ejpam-5662	626	5	,	,	PUNCT
ejpam-5662	626	6	a2	a2	NOUN
ejpam-5662	626	7	=	=	PUNCT
ejpam-5662	626	8	η11ω1(−2ω2	η11ω1(−2ω2	PROPN
ejpam-5662	626	9	1	1	NUM
ejpam-5662	626	10	+	+	PROPN
ejpam-5662	626	11	ω2	ω2	PROPN
ejpam-5662	626	12	p	p	NOUN
ejpam-5662	626	13	)	)	PUNCT
ejpam-5662	626	14	π(−4ω2	π(−4ω2	NOUN
ejpam-5662	626	15	1ωp	1ωp	PUNCT
ejpam-5662	627	1	+	+	PROPN
ejpam-5662	627	2	ω3	ω3	NOUN
ejpam-5662	627	3	p	p	X
ejpam-5662	627	4	)	)	PUNCT
ejpam-5662	627	5	,	,	PUNCT
ejpam-5662	627	6	a3	a3	NOUN
ejpam-5662	627	7	=	=	SYM
ejpam-5662	627	8	bη12ω1	bη12ω1	NUM
ejpam-5662	627	9	2πa	2πa	NOUN
ejpam-5662	627	10	(	(	PUNCT
ejpam-5662	627	11	(	(	PUNCT
ejpam-5662	627	12	−ω2	−ω2	ADP
ejpam-5662	627	13	+	+	NOUN
ejpam-5662	627	14	ωp	ωp	NOUN
ejpam-5662	627	15	)	)	PUNCT
ejpam-5662	627	16	ω2	ω2	CCONJ
ejpam-5662	627	17	1	1	NUM
ejpam-5662	627	18	−	−	NOUN
ejpam-5662	627	19	ω2	ω2	ADJ
ejpam-5662	627	20	2	2	NUM
ejpam-5662	627	21	+	+	SYM
ejpam-5662	627	22	2ω2ωp	2ω2ωp	NUM
ejpam-5662	627	23	−	−	NOUN
ejpam-5662	627	24	ω2	ω2	ADJ
ejpam-5662	627	25	p	p	PROPN
ejpam-5662	627	26	)	)	PUNCT
ejpam-5662	627	27	,	,	PUNCT
ejpam-5662	627	28	a4	a4	NOUN
ejpam-5662	627	29	=	=	SYM
ejpam-5662	627	30	bη12ω1	bη12ω1	NUM
ejpam-5662	627	31	2πa	2πa	NOUN
ejpam-5662	627	32	(	(	PUNCT
ejpam-5662	627	33	(	(	PUNCT
ejpam-5662	627	34	ω2	ω2	ADJ
ejpam-5662	627	35	+	+	NOUN
ejpam-5662	627	36	ωp	ωp	NOUN
ejpam-5662	627	37	)	)	PUNCT
ejpam-5662	627	38	ω2	ω2	CCONJ
ejpam-5662	627	39	2	2	NUM
ejpam-5662	627	40	−	−	NOUN
ejpam-5662	627	41	ω2	ω2	ADJ
ejpam-5662	627	42	1	1	NUM
ejpam-5662	627	43	+	+	NUM
ejpam-5662	627	44	2ω2ωp	2ω2ωp	NUM
ejpam-5662	627	45	+	+	PROPN
ejpam-5662	627	46	ω2	ω2	PROPN
ejpam-5662	627	47	p	p	NOUN
ejpam-5662	627	48	)	)	PUNCT
ejpam-5662	627	49	,	,	PUNCT
ejpam-5662	627	50	a5	a5	PROPN
ejpam-5662	627	51	=	=	PUNCT
ejpam-5662	627	52	3	3	NUM
ejpam-5662	627	53	4	4	NUM
ejpam-5662	627	54	b2γ2	b2γ2	DET
ejpam-5662	627	55	+	+	CCONJ
ejpam-5662	627	56	5	5	NUM
ejpam-5662	627	57	8	8	NUM
ejpam-5662	627	58	b4λ′	b4λ′	NOUN
ejpam-5662	627	59	2a6	2a6	NUM
ejpam-5662	627	60	=	=	PUNCT
ejpam-5662	627	61	η22ω2(−2ω2	η22ω2(−2ω2	NOUN
ejpam-5662	627	62	2	2	NUM
ejpam-5662	627	63	+	+	PROPN
ejpam-5662	627	64	ω2	ω2	NOUN
ejpam-5662	627	65	p	p	NOUN
ejpam-5662	627	66	)	)	PUNCT
ejpam-5662	627	67	π(−4ω2	π(−4ω2	NOUN
ejpam-5662	627	68	2ωp	2ωp	PUNCT
ejpam-5662	628	1	+	+	PUNCT
ejpam-5662	628	2	ω3	ω3	ADJ
ejpam-5662	628	3	p	p	X
ejpam-5662	628	4	)	)	PUNCT
ejpam-5662	628	5	,	,	PUNCT
ejpam-5662	628	6	a7	a7	PROPN
ejpam-5662	628	7	=	=	SYM
ejpam-5662	628	8	aη21ω2	aη21ω2	PROPN
ejpam-5662	628	9	2πb	2πb	ADJ
ejpam-5662	628	10	(	(	PUNCT
ejpam-5662	628	11	(	(	PUNCT
ejpam-5662	628	12	ω1−ωp	ω1−ωp	NUM
ejpam-5662	628	13	)	)	PUNCT
ejpam-5662	628	14	ω2	ω2	NOUN
ejpam-5662	628	15	1−ω2	1−ω2	NUM
ejpam-5662	628	16	2−2ω1ωp+ω2	2−2ω1ωp+ω2	NUM
ejpam-5662	628	17	p	p	NOUN
ejpam-5662	628	18	)	)	PUNCT
ejpam-5662	628	19	,	,	PUNCT
ejpam-5662	628	20	and	and	CCONJ
ejpam-5662	628	21	a8	a8	PROPN
ejpam-5662	628	22	=	=	SYM
ejpam-5662	628	23	aη21ω2	aη21ω2	PROPN
ejpam-5662	628	24	2πb	2πb	ADJ
ejpam-5662	628	25	(	(	PUNCT
ejpam-5662	628	26	(	(	PUNCT
ejpam-5662	628	27	ω1+ωp	ω1+ωp	PROPN
ejpam-5662	628	28	)	)	PUNCT
ejpam-5662	628	29	ω2	ω2	CCONJ
ejpam-5662	628	30	1−ω2	1−ω2	NUM
ejpam-5662	628	31	2	2	NUM
ejpam-5662	628	32	+	+	PROPN
ejpam-5662	628	33	2ω1ωp+ω2	2ω1ωp+ω2	NUM
ejpam-5662	628	34	p	p	NOUN
ejpam-5662	628	35	)	)	PUNCT
ejpam-5662	628	36	.	.	PUNCT
ejpam-5662	629	1	the	the	DET
ejpam-5662	629	2	coefficients	coefficient	NOUN
ejpam-5662	629	3	defined	define	VERB
ejpam-5662	629	4	in	in	ADP
ejpam-5662	629	5	eqs	eqs	PROPN
ejpam-5662	629	6	.	.	PUNCT
ejpam-5662	630	1	(	(	PUNCT
ejpam-5662	630	2	46	46	NUM
ejpam-5662	630	3	)	)	PUNCT
ejpam-5662	630	4	and	and	CCONJ
ejpam-5662	630	5	(	(	PUNCT
ejpam-5662	630	6	47	47	NUM
ejpam-5662	630	7	)	)	PUNCT
ejpam-5662	630	8	as	as	SCONJ
ejpam-5662	630	9	evaluated	evaluate	VERB
ejpam-5662	630	10	by	by	ADP
ejpam-5662	630	11	ms	ms	PROPN
ejpam-5662	630	12	are	be	AUX
ejpam-5662	630	13	given	give	VERB
ejpam-5662	630	14	as	as	ADP
ejpam-5662	630	15	:	:	PUNCT
ejpam-5662	630	16	b1	b1	NOUN
ejpam-5662	630	17	=	=	SYM
ejpam-5662	630	18	3	3	NUM
ejpam-5662	630	19	4	4	NUM
ejpam-5662	630	20	c2γ1	c2γ1	NOUN
ejpam-5662	630	21	+	+	NOUN
ejpam-5662	630	22	5	5	NUM
ejpam-5662	630	23	8	8	NUM
ejpam-5662	630	24	c4λ1	c4λ1	NOUN
ejpam-5662	630	25	,	,	PUNCT
ejpam-5662	630	26	b2	b2	NOUN
ejpam-5662	630	27	=	=	SYM
ejpam-5662	630	28	η11ω3(−2ω2	η11ω3(−2ω2	NOUN
ejpam-5662	630	29	3	3	NUM
ejpam-5662	630	30	+	+	PROPN
ejpam-5662	630	31	ω2	ω2	NOUN
ejpam-5662	630	32	p	p	NOUN
ejpam-5662	630	33	)	)	PUNCT
ejpam-5662	630	34	π(−4ω2	π(−4ω2	NOUN
ejpam-5662	630	35	3ωp	3ωp	NOUN
ejpam-5662	631	1	+	+	PROPN
ejpam-5662	631	2	ω3	ω3	NOUN
ejpam-5662	631	3	p	p	X
ejpam-5662	631	4	)	)	PUNCT
ejpam-5662	631	5	,	,	PUNCT
ejpam-5662	631	6	b3	b3	PROPN
ejpam-5662	631	7	=	=	PUNCT
ejpam-5662	632	1	dη12ω3	dη12ω3	ADP
ejpam-5662	632	2	2πc	2πc	NOUN
ejpam-5662	632	3	(	(	PUNCT
ejpam-5662	632	4	(	(	PUNCT
ejpam-5662	632	5	−ω4	−ω4	PROPN
ejpam-5662	632	6	+	+	NOUN
ejpam-5662	632	7	ωp	ωp	NOUN
ejpam-5662	632	8	)	)	PUNCT
ejpam-5662	632	9	ω2	ω2	CCONJ
ejpam-5662	632	10	3	3	NUM
ejpam-5662	632	11	−	−	NOUN
ejpam-5662	632	12	ω2	ω2	ADJ
ejpam-5662	632	13	4	4	NUM
ejpam-5662	632	14	+	+	SYM
ejpam-5662	632	15	2ω4ωp	2ω4ωp	NUM
ejpam-5662	632	16	−	−	NOUN
ejpam-5662	632	17	ω2	ω2	PROPN
ejpam-5662	632	18	p	p	PROPN
ejpam-5662	632	19	)	)	PUNCT
ejpam-5662	632	20	,	,	PUNCT
ejpam-5662	632	21	b4	b4	NOUN
ejpam-5662	632	22	=	=	PUNCT
ejpam-5662	633	1	dη12ω3	dη12ω3	ADP
ejpam-5662	633	2	2πc	2πc	NOUN
ejpam-5662	633	3	(	(	PUNCT
ejpam-5662	633	4	(	(	PUNCT
ejpam-5662	633	5	ω4	ω4	NOUN
ejpam-5662	633	6	+	+	NOUN
ejpam-5662	633	7	ωp	ωp	NOUN
ejpam-5662	633	8	)	)	PUNCT
ejpam-5662	633	9	ω2	ω2	ADV
ejpam-5662	633	10	4	4	NUM
ejpam-5662	633	11	−	−	NOUN
ejpam-5662	633	12	ω2	ω2	ADJ
ejpam-5662	633	13	3	3	NUM
ejpam-5662	633	14	+	+	SYM
ejpam-5662	633	15	2ω4ωp	2ω4ωp	NUM
ejpam-5662	633	16	+	+	PROPN
ejpam-5662	633	17	ω2	ω2	PROPN
ejpam-5662	633	18	p	p	NOUN
ejpam-5662	633	19	)	)	PUNCT
ejpam-5662	633	20	,	,	PUNCT
ejpam-5662	633	21	b5	b5	PROPN
ejpam-5662	633	22	=	=	PUNCT
ejpam-5662	633	23	3	3	NUM
ejpam-5662	633	24	4	4	NUM
ejpam-5662	633	25	d2γ2	d2γ2	NOUN
ejpam-5662	633	26	+	+	CCONJ
ejpam-5662	633	27	5	5	NUM
ejpam-5662	633	28	8	8	NUM
ejpam-5662	633	29	d4λ′	d4λ′	NOUN
ejpam-5662	633	30	2b6	2b6	NUM
ejpam-5662	633	31	=	=	SYM
ejpam-5662	633	32	η22ω4(−2ω2	η22ω4(−2ω2	ADJ
ejpam-5662	633	33	4	4	NUM
ejpam-5662	633	34	+	+	NOUN
ejpam-5662	633	35	ω2	ω2	NOUN
ejpam-5662	633	36	p	p	NOUN
ejpam-5662	633	37	)	)	PUNCT
ejpam-5662	633	38	π(−4ω2	π(−4ω2	NOUN
ejpam-5662	633	39	4ωp	4ωp	PUNCT
ejpam-5662	634	1	+	+	PROPN
ejpam-5662	634	2	ω3	ω3	NOUN
ejpam-5662	634	3	p	p	X
ejpam-5662	634	4	)	)	PUNCT
ejpam-5662	634	5	,	,	PUNCT
ejpam-5662	634	6	b7	b7	PROPN
ejpam-5662	634	7	=	=	PROPN
ejpam-5662	634	8	cη21ω4	cη21ω4	PROPN
ejpam-5662	634	9	2πd	2πd	NOUN
ejpam-5662	635	1	(	(	PUNCT
ejpam-5662	635	2	(	(	PUNCT
ejpam-5662	635	3	ω3−ωp	ω3−ωp	NUM
ejpam-5662	635	4	)	)	PUNCT
ejpam-5662	635	5	ω2	ω2	NOUN
ejpam-5662	635	6	3−ω2	3−ω2	NUM
ejpam-5662	635	7	4−2ω3ωp+ω2	4−2ω3ωp+ω2	NUM
ejpam-5662	635	8	p	p	NOUN
ejpam-5662	635	9	)	)	PUNCT
ejpam-5662	635	10	,	,	PUNCT
ejpam-5662	635	11	and	and	CCONJ
ejpam-5662	635	12	b8	b8	PROPN
ejpam-5662	635	13	=	=	PROPN
ejpam-5662	635	14	cη21ω4	cη21ω4	PROPN
ejpam-5662	635	15	2πd	2πd	NOUN
ejpam-5662	635	16	(	(	PUNCT
ejpam-5662	635	17	(	(	PUNCT
ejpam-5662	635	18	ω3+ωp	ω3+ωp	PROPN
ejpam-5662	635	19	)	)	PUNCT
ejpam-5662	635	20	ω2	ω2	ADJ
ejpam-5662	635	21	3−ω2	3−ω2	NUM
ejpam-5662	635	22	4	4	NUM
ejpam-5662	635	23	+	+	PROPN
ejpam-5662	635	24	2ω3ωp+ω2	2ω3ωp+ω2	NUM
ejpam-5662	635	25	p	p	NOUN
ejpam-5662	635	26	)	)	PUNCT
ejpam-5662	635	27	.	.	PUNCT