id	sid	tid	token	lemma	pos
ejpam-5479	1	1	european	european	PROPN
ejpam-5479	1	2	journal	journal	PROPN
ejpam-5479	1	3	of	of	ADP
ejpam-5479	1	4	pure	pure	ADJ
ejpam-5479	1	5	and	and	CCONJ
ejpam-5479	1	6	applied	apply	VERB
ejpam-5479	1	7	mathematics	mathematic	NOUN
ejpam-5479	1	8	vol	vol	NOUN
ejpam-5479	1	9	.	.	PROPN
ejpam-5479	2	1	17	17	NUM
ejpam-5479	2	2	,	,	PUNCT
ejpam-5479	2	3	no	no	INTJ
ejpam-5479	2	4	.	.	NOUN
ejpam-5479	2	5	4	4	NUM
ejpam-5479	2	6	,	,	PUNCT
ejpam-5479	2	7	2024	2024	NUM
ejpam-5479	2	8	,	,	PUNCT
ejpam-5479	2	9	3185	3185	NUM
ejpam-5479	2	10	-	-	SYM
ejpam-5479	2	11	3208	3208	NUM
ejpam-5479	2	12	issn	issn	PROPN
ejpam-5479	2	13	1307	1307	NUM
ejpam-5479	2	14	-	-	SYM
ejpam-5479	2	15	5543	5543	NUM
ejpam-5479	2	16	–	–	PUNCT
ejpam-5479	2	17	ejpam.com	ejpam.com	X
ejpam-5479	2	18	published	publish	VERB
ejpam-5479	2	19	by	by	ADP
ejpam-5479	2	20	new	new	PROPN
ejpam-5479	2	21	york	york	PROPN
ejpam-5479	2	22	business	business	PROPN
ejpam-5479	2	23	global	global	PROPN
ejpam-5479	2	24	the	the	DET
ejpam-5479	2	25	non	non	ADJ
ejpam-5479	2	26	-	-	ADJ
ejpam-5479	2	27	perturbative	perturbative	ADJ
ejpam-5479	2	28	approach	approach	NOUN
ejpam-5479	2	29	in	in	ADP
ejpam-5479	2	30	examining	examine	VERB
ejpam-5479	2	31	the	the	DET
ejpam-5479	2	32	motion	motion	NOUN
ejpam-5479	2	33	of	of	ADP
ejpam-5479	2	34	a	a	DET
ejpam-5479	2	35	simple	simple	ADJ
ejpam-5479	2	36	pendulum	pendulum	NOUN
ejpam-5479	2	37	associated	associate	VERB
ejpam-5479	2	38	with	with	ADP
ejpam-5479	2	39	a	a	DET
ejpam-5479	2	40	rolling	rolling	ADJ
ejpam-5479	2	41	wheel	wheel	NOUN
ejpam-5479	2	42	with	with	ADP
ejpam-5479	2	43	a	a	DET
ejpam-5479	2	44	time	time	NOUN
ejpam-5479	2	45	-	-	PUNCT
ejpam-5479	2	46	delay	delay	NOUN
ejpam-5479	2	47	khalid	khalid	PROPN
ejpam-5479	2	48	alluhydan1,∗	alluhydan1,∗	PROPN
ejpam-5479	2	49	,	,	PUNCT
ejpam-5479	2	50	galal	galal	PROPN
ejpam-5479	2	51	m.	m.	NOUN
ejpam-5479	2	52	moatimid2	moatimid2	PROPN
ejpam-5479	2	53	,	,	PUNCT
ejpam-5479	2	54	t.	t.	PROPN
ejpam-5479	2	55	s.	s.	PROPN
ejpam-5479	2	56	amer3	amer3	PROPN
ejpam-5479	2	57	1	1	NUM
ejpam-5479	2	58	department	department	NOUN
ejpam-5479	2	59	of	of	ADP
ejpam-5479	2	60	mechanical	mechanical	ADJ
ejpam-5479	2	61	engineering	engineering	NOUN
ejpam-5479	2	62	,	,	PUNCT
ejpam-5479	2	63	college	college	NOUN
ejpam-5479	2	64	of	of	ADP
ejpam-5479	2	65	engineering	engineering	NOUN
ejpam-5479	2	66	,	,	PUNCT
ejpam-5479	2	67	king	king	PROPN
ejpam-5479	2	68	saud	saud	PROPN
ejpam-5479	2	69	university	university	PROPN
ejpam-5479	2	70	,	,	PUNCT
ejpam-5479	2	71	p.o	p.o	PROPN
ejpam-5479	2	72	box	box	PROPN
ejpam-5479	2	73	800	800	NUM
ejpam-5479	2	74	,	,	PUNCT
ejpam-5479	2	75	riyadh	riyadh	NOUN
ejpam-5479	2	76	11421	11421	NUM
ejpam-5479	2	77	,	,	PUNCT
ejpam-5479	2	78	saudi	saudi	PROPN
ejpam-5479	2	79	arabia	arabia	PROPN
ejpam-5479	2	80	2	2	NUM
ejpam-5479	2	81	department	department	NOUN
ejpam-5479	2	82	of	of	ADP
ejpam-5479	2	83	mathematics	mathematic	NOUN
ejpam-5479	2	84	,	,	PUNCT
ejpam-5479	2	85	faculty	faculty	NOUN
ejpam-5479	2	86	of	of	ADP
ejpam-5479	2	87	education	education	NOUN
ejpam-5479	2	88	,	,	PUNCT
ejpam-5479	2	89	ain	ain	PROPN
ejpam-5479	2	90	shams	shams	PROPN
ejpam-5479	2	91	university	university	PROPN
ejpam-5479	2	92	,	,	PUNCT
ejpam-5479	2	93	egypt	egypt	PROPN
ejpam-5479	2	94	3	3	NUM
ejpam-5479	2	95	department	department	NOUN
ejpam-5479	2	96	of	of	ADP
ejpam-5479	2	97	mathematics	mathematic	NOUN
ejpam-5479	2	98	,	,	PUNCT
ejpam-5479	2	99	faculty	faculty	NOUN
ejpam-5479	2	100	of	of	ADP
ejpam-5479	2	101	science	science	NOUN
ejpam-5479	2	102	,	,	PUNCT
ejpam-5479	2	103	tanta	tanta	PROPN
ejpam-5479	2	104	university	university	PROPN
ejpam-5479	2	105	,	,	PUNCT
ejpam-5479	2	106	tanta	tanta	PROPN
ejpam-5479	2	107	31527	31527	NUM
ejpam-5479	2	108	,	,	PUNCT
ejpam-5479	2	109	egypt	egypt	PROPN
ejpam-5479	2	110	abstract	abstract	PROPN
ejpam-5479	2	111	.	.	PUNCT
ejpam-5479	3	1	the	the	DET
ejpam-5479	3	2	present	present	ADJ
ejpam-5479	3	3	study	study	NOUN
ejpam-5479	3	4	aims	aim	VERB
ejpam-5479	3	5	to	to	PART
ejpam-5479	3	6	examine	examine	VERB
ejpam-5479	3	7	the	the	DET
ejpam-5479	3	8	movement	movement	NOUN
ejpam-5479	3	9	of	of	ADP
ejpam-5479	3	10	a	a	DET
ejpam-5479	3	11	simple	simple	ADJ
ejpam-5479	3	12	pendulum	pendulum	NOUN
ejpam-5479	3	13	that	that	PRON
ejpam-5479	3	14	is	be	AUX
ejpam-5479	3	15	connected	connect	VERB
ejpam-5479	3	16	by	by	ADP
ejpam-5479	3	17	a	a	DET
ejpam-5479	3	18	lightweight	lightweight	ADJ
ejpam-5479	3	19	spring	spring	NOUN
ejpam-5479	3	20	and	and	CCONJ
ejpam-5479	3	21	connected	connect	VERB
ejpam-5479	3	22	with	with	ADP
ejpam-5479	3	23	a	a	DET
ejpam-5479	3	24	rotating	rotate	VERB
ejpam-5479	3	25	wheel	wheel	NOUN
ejpam-5479	3	26	.	.	PUNCT
ejpam-5479	4	1	the	the	DET
ejpam-5479	4	2	motivation	motivation	NOUN
ejpam-5479	4	3	behind	behind	ADP
ejpam-5479	4	4	this	this	DET
ejpam-5479	4	5	topic	topic	NOUN
ejpam-5479	4	6	is	be	AUX
ejpam-5479	4	7	to	to	PART
ejpam-5479	4	8	gain	gain	VERB
ejpam-5479	4	9	a	a	DET
ejpam-5479	4	10	comprehensive	comprehensive	ADJ
ejpam-5479	4	11	understanding	understanding	NOUN
ejpam-5479	4	12	of	of	ADP
ejpam-5479	4	13	intricate	intricate	ADJ
ejpam-5479	4	14	dynamic	dynamic	ADJ
ejpam-5479	4	15	systems	system	NOUN
ejpam-5479	4	16	that	that	PRON
ejpam-5479	4	17	involve	involve	VERB
ejpam-5479	4	18	consistent	consistent	ADJ
ejpam-5479	4	19	mechanical	mechanical	ADJ
ejpam-5479	4	20	components	component	NOUN
ejpam-5479	4	21	and	and	CCONJ
ejpam-5479	4	22	response	response	NOUN
ejpam-5479	4	23	with	with	ADP
ejpam-5479	4	24	time	time	NOUN
ejpam-5479	4	25	delay	delay	NOUN
ejpam-5479	4	26	.	.	PUNCT
ejpam-5479	5	1	this	this	DET
ejpam-5479	5	2	system	system	NOUN
ejpam-5479	5	3	is	be	AUX
ejpam-5479	5	4	not	not	PART
ejpam-5479	5	5	only	only	ADV
ejpam-5479	5	6	theoretically	theoretically	ADV
ejpam-5479	5	7	attractive	attractive	ADJ
ejpam-5479	5	8	but	but	CCONJ
ejpam-5479	5	9	also	also	ADV
ejpam-5479	5	10	practically	practically	ADV
ejpam-5479	5	11	appropriate	appropriate	ADJ
ejpam-5479	5	12	in	in	ADP
ejpam-5479	5	13	domains	domain	NOUN
ejpam-5479	5	14	such	such	ADJ
ejpam-5479	5	15	as	as	ADP
ejpam-5479	5	16	robotics	robotic	NOUN
ejpam-5479	5	17	,	,	PUNCT
ejpam-5479	5	18	engineering	engineering	NOUN
ejpam-5479	5	19	,	,	PUNCT
ejpam-5479	5	20	and	and	CCONJ
ejpam-5479	5	21	control	control	NOUN
ejpam-5479	5	22	systems	system	NOUN
ejpam-5479	5	23	.	.	PUNCT
ejpam-5479	6	1	as	as	ADV
ejpam-5479	6	2	well	well	ADV
ejpam-5479	6	3	-	-	PUNCT
ejpam-5479	6	4	known	know	VERB
ejpam-5479	6	5	,	,	PUNCT
ejpam-5479	6	6	all	all	DET
ejpam-5479	6	7	classical	classical	ADJ
ejpam-5479	6	8	perturbation	perturbation	NOUN
ejpam-5479	6	9	methods	method	NOUN
ejpam-5479	6	10	exploit	exploit	VERB
ejpam-5479	6	11	taylor	taylor	NOUN
ejpam-5479	6	12	expansion	expansion	NOUN
ejpam-5479	6	13	to	to	PART
ejpam-5479	6	14	simplify	simplify	VERB
ejpam-5479	6	15	the	the	DET
ejpam-5479	6	16	practicality	practicality	NOUN
ejpam-5479	6	17	of	of	ADP
ejpam-5479	6	18	restoring	restore	VERB
ejpam-5479	6	19	forces	force	NOUN
ejpam-5479	6	20	.	.	PUNCT
ejpam-5479	7	1	in	in	ADP
ejpam-5479	7	2	contrast	contrast	NOUN
ejpam-5479	7	3	,	,	PUNCT
ejpam-5479	7	4	the	the	DET
ejpam-5479	7	5	non	non	ADJ
ejpam-5479	7	6	-	-	ADJ
ejpam-5479	7	7	perturbative	perturbative	ADJ
ejpam-5479	7	8	approach	approach	NOUN
ejpam-5479	7	9	,	,	PUNCT
ejpam-5479	7	10	as	as	ADP
ejpam-5479	7	11	a	a	DET
ejpam-5479	7	12	novel	novel	ADJ
ejpam-5479	7	13	methodology	methodology	NOUN
ejpam-5479	7	14	,	,	PUNCT
ejpam-5479	7	15	transforms	transform	VERB
ejpam-5479	7	16	any	any	DET
ejpam-5479	7	17	nonlinear	nonlinear	ADJ
ejpam-5479	7	18	ordinary	ordinary	ADJ
ejpam-5479	7	19	differential	differential	ADJ
ejpam-5479	7	20	equation	equation	NOUN
ejpam-5479	7	21	into	into	ADP
ejpam-5479	7	22	a	a	DET
ejpam-5479	7	23	linear	linear	ADJ
ejpam-5479	7	24	one	one	NUM
ejpam-5479	7	25	.	.	PUNCT
ejpam-5479	8	1	it	it	PRON
ejpam-5479	8	2	scrutinizes	scrutinize	VERB
ejpam-5479	8	3	the	the	DET
ejpam-5479	8	4	restoring	restore	VERB
ejpam-5479	8	5	forces	force	NOUN
ejpam-5479	8	6	,	,	PUNCT
ejpam-5479	8	7	away	away	ADV
ejpam-5479	8	8	from	from	ADP
ejpam-5479	8	9	employing	employ	VERB
ejpam-5479	8	10	taylor	taylor	NOUN
ejpam-5479	8	11	expansion	expansion	NOUN
ejpam-5479	8	12	;	;	PUNCT
ejpam-5479	8	13	hence	hence	ADV
ejpam-5479	8	14	it	it	PRON
ejpam-5479	8	15	eliminates	eliminate	VERB
ejpam-5479	8	16	the	the	DET
ejpam-5479	8	17	previous	previous	ADJ
ejpam-5479	8	18	weakness	weakness	NOUN
ejpam-5479	8	19	.	.	PUNCT
ejpam-5479	9	1	the	the	DET
ejpam-5479	9	2	concept	concept	NOUN
ejpam-5479	9	3	of	of	ADP
ejpam-5479	9	4	the	the	DET
ejpam-5479	9	5	non	non	ADJ
ejpam-5479	9	6	-	-	ADJ
ejpam-5479	9	7	perturbative	perturbative	ADJ
ejpam-5479	9	8	approach	approach	NOUN
ejpam-5479	9	9	is	be	AUX
ejpam-5479	9	10	based	base	VERB
ejpam-5479	9	11	mainly	mainly	ADV
ejpam-5479	9	12	on	on	ADP
ejpam-5479	9	13	the	the	DET
ejpam-5479	9	14	he	he	PRON
ejpam-5479	9	15	’s	’s	PART
ejpam-5479	9	16	frequency	frequency	NOUN
ejpam-5479	9	17	formula	formula	NOUN
ejpam-5479	9	18	.	.	PUNCT
ejpam-5479	10	1	the	the	DET
ejpam-5479	10	2	confidence	confidence	NOUN
ejpam-5479	10	3	of	of	ADP
ejpam-5479	10	4	the	the	DET
ejpam-5479	10	5	non	non	ADJ
ejpam-5479	10	6	-	-	ADJ
ejpam-5479	10	7	perturbative	perturbative	ADJ
ejpam-5479	10	8	approach	approach	NOUN
ejpam-5479	10	9	comes	come	VERB
ejpam-5479	10	10	from	from	ADP
ejpam-5479	10	11	the	the	DET
ejpam-5479	10	12	numerical	numerical	ADJ
ejpam-5479	10	13	compatibility	compatibility	NOUN
ejpam-5479	10	14	between	between	ADP
ejpam-5479	10	15	the	the	DET
ejpam-5479	10	16	nonlinear	nonlinear	ADJ
ejpam-5479	10	17	and	and	CCONJ
ejpam-5479	10	18	linear	linear	ADJ
ejpam-5479	10	19	ordinary	ordinary	ADJ
ejpam-5479	10	20	differential	differential	ADJ
ejpam-5479	10	21	equation	equation	NOUN
ejpam-5479	10	22	via	via	ADP
ejpam-5479	10	23	the	the	DET
ejpam-5479	10	24	mathematica	mathematica	PROPN
ejpam-5479	10	25	software	software	PROPN
ejpam-5479	10	26	.	.	PUNCT
ejpam-5479	11	1	therefore	therefore	ADV
ejpam-5479	11	2	,	,	PUNCT
ejpam-5479	11	3	instead	instead	ADV
ejpam-5479	11	4	of	of	ADP
ejpam-5479	11	5	handling	handle	VERB
ejpam-5479	11	6	the	the	DET
ejpam-5479	11	7	nonlinear	nonlinear	ADJ
ejpam-5479	11	8	ordinary	ordinary	ADJ
ejpam-5479	11	9	differential	differential	ADJ
ejpam-5479	11	10	equation	equation	NOUN
ejpam-5479	11	11	,	,	PUNCT
ejpam-5479	11	12	we	we	PRON
ejpam-5479	11	13	investigate	investigate	VERB
ejpam-5479	11	14	the	the	DET
ejpam-5479	11	15	linear	linear	ADJ
ejpam-5479	11	16	one	one	NUM
ejpam-5479	11	17	.	.	PUNCT
ejpam-5479	12	1	the	the	DET
ejpam-5479	12	2	achieved	achieve	VERB
ejpam-5479	12	3	response	response	NOUN
ejpam-5479	12	4	is	be	AUX
ejpam-5479	12	5	plotted	plot	VERB
ejpam-5479	12	6	over	over	ADP
ejpam-5479	12	7	time	time	NOUN
ejpam-5479	12	8	to	to	PART
ejpam-5479	12	9	show	show	VERB
ejpam-5479	12	10	the	the	DET
ejpam-5479	12	11	impact	impact	NOUN
ejpam-5479	12	12	of	of	ADP
ejpam-5479	12	13	the	the	DET
ejpam-5479	12	14	acted	act	VERB
ejpam-5479	12	15	parameters	parameter	NOUN
ejpam-5479	12	16	during	during	ADP
ejpam-5479	12	17	a	a	DET
ejpam-5479	12	18	specified	specified	ADJ
ejpam-5479	12	19	time	time	NOUN
ejpam-5479	12	20	interval	interval	NOUN
ejpam-5479	12	21	.	.	PUNCT
ejpam-5479	13	1	moreover	moreover	ADV
ejpam-5479	13	2	,	,	PUNCT
ejpam-5479	13	3	the	the	DET
ejpam-5479	13	4	phase	phase	NOUN
ejpam-5479	13	5	plane	plane	NOUN
ejpam-5479	13	6	curves	curve	NOUN
ejpam-5479	13	7	that	that	PRON
ejpam-5479	13	8	correspond	correspond	VERB
ejpam-5479	13	9	to	to	ADP
ejpam-5479	13	10	the	the	DET
ejpam-5479	13	11	plotted	plot	VERB
ejpam-5479	13	12	solution	solution	NOUN
ejpam-5479	13	13	are	be	AUX
ejpam-5479	13	14	presented	present	VERB
ejpam-5479	13	15	and	and	CCONJ
ejpam-5479	13	16	examined	examine	VERB
ejpam-5479	13	17	.	.	PUNCT
ejpam-5479	14	1	the	the	DET
ejpam-5479	14	2	stability	stability	NOUN
ejpam-5479	14	3	criteria	criterion	NOUN
ejpam-5479	14	4	of	of	ADP
ejpam-5479	14	5	the	the	DET
ejpam-5479	14	6	analogous	analogous	ADJ
ejpam-5479	14	7	linear	linear	ADJ
ejpam-5479	14	8	ordinary	ordinary	ADJ
ejpam-5479	14	9	differential	differential	ADJ
ejpam-5479	14	10	equation	equation	NOUN
ejpam-5479	14	11	are	be	AUX
ejpam-5479	14	12	provided	provide	VERB
ejpam-5479	14	13	and	and	CCONJ
ejpam-5479	14	14	drawn	draw	VERB
ejpam-5479	14	15	to	to	PART
ejpam-5479	14	16	explore	explore	VERB
ejpam-5479	14	17	the	the	DET
ejpam-5479	14	18	stability	stability	NOUN
ejpam-5479	14	19	/	/	SYM
ejpam-5479	14	20	instability	instability	NOUN
ejpam-5479	14	21	zones	zone	NOUN
ejpam-5479	14	22	.	.	PUNCT
ejpam-5479	15	1	the	the	DET
ejpam-5479	15	2	performance	performance	NOUN
ejpam-5479	15	3	is	be	AUX
ejpam-5479	15	4	applicable	applicable	ADJ
ejpam-5479	15	5	in	in	ADP
ejpam-5479	15	6	engineering	engineering	NOUN
ejpam-5479	15	7	and	and	CCONJ
ejpam-5479	15	8	other	other	ADJ
ejpam-5479	15	9	fields	field	NOUN
ejpam-5479	15	10	due	due	ADP
ejpam-5479	15	11	to	to	ADP
ejpam-5479	15	12	its	its	PRON
ejpam-5479	15	13	ease	ease	NOUN
ejpam-5479	15	14	of	of	ADP
ejpam-5479	15	15	adaptation	adaptation	NOUN
ejpam-5479	15	16	to	to	ADP
ejpam-5479	15	17	different	different	ADJ
ejpam-5479	15	18	nonlinear	nonlinear	ADJ
ejpam-5479	15	19	systems	system	NOUN
ejpam-5479	15	20	.	.	PUNCT
ejpam-5479	16	1	therefore	therefore	ADV
ejpam-5479	16	2	,	,	PUNCT
ejpam-5479	16	3	the	the	DET
ejpam-5479	16	4	non	non	ADJ
ejpam-5479	16	5	-	-	ADJ
ejpam-5479	16	6	perturbative	perturbative	ADJ
ejpam-5479	16	7	approach	approach	NOUN
ejpam-5479	16	8	can	can	AUX
ejpam-5479	16	9	be	be	AUX
ejpam-5479	16	10	regarded	regard	VERB
ejpam-5479	16	11	as	as	ADP
ejpam-5479	16	12	substantial	substantial	ADJ
ejpam-5479	16	13	,	,	PUNCT
ejpam-5479	16	14	successful	successful	ADJ
ejpam-5479	16	15	,	,	PUNCT
ejpam-5479	16	16	and	and	CCONJ
ejpam-5479	16	17	interesting	interesting	ADJ
ejpam-5479	16	18	and	and	CCONJ
ejpam-5479	16	19	can	can	AUX
ejpam-5479	16	20	extended	extend	VERB
ejpam-5479	16	21	to	to	PART
ejpam-5479	16	22	be	be	AUX
ejpam-5479	16	23	applied	apply	VERB
ejpam-5479	16	24	in	in	ADP
ejpam-5479	16	25	further	further	ADJ
ejpam-5479	16	26	categories	category	NOUN
ejpam-5479	16	27	within	within	ADP
ejpam-5479	16	28	the	the	DET
ejpam-5479	16	29	field	field	NOUN
ejpam-5479	16	30	of	of	ADP
ejpam-5479	16	31	couples	couple	NOUN
ejpam-5479	16	32	dynamical	dynamical	ADJ
ejpam-5479	16	33	systems	system	NOUN
ejpam-5479	16	34	.	.	PUNCT
ejpam-5479	17	1	2020	2020	NUM
ejpam-5479	17	2	mathematics	mathematic	NOUN
ejpam-5479	17	3	subject	subject	NOUN
ejpam-5479	17	4	classifications	classification	NOUN
ejpam-5479	17	5	:	:	PUNCT
ejpam-5479	17	6	34c15	34c15	NUM
ejpam-5479	17	7	,	,	PUNCT
ejpam-5479	17	8	34d20	34d20	NUM
ejpam-5479	17	9	,	,	PUNCT
ejpam-5479	17	10	70k20	70k20	NUM
ejpam-5479	17	11	,	,	PUNCT
ejpam-5479	17	12	37c75	37c75	NUM
ejpam-5479	17	13	,	,	PUNCT
ejpam-5479	17	14	93c10	93c10	NOUN
ejpam-5479	17	15	key	key	ADJ
ejpam-5479	17	16	words	word	NOUN
ejpam-5479	17	17	and	and	CCONJ
ejpam-5479	17	18	phrases	phrase	NOUN
ejpam-5479	17	19	:	:	PUNCT
ejpam-5479	17	20	simple	simple	ADJ
ejpam-5479	17	21	pendulum	pendulum	NOUN
ejpam-5479	17	22	,	,	PUNCT
ejpam-5479	17	23	rolling	rolling	NOUN
ejpam-5479	17	24	wheel	wheel	NOUN
ejpam-5479	17	25	,	,	PUNCT
ejpam-5479	17	26	non	non	ADJ
ejpam-5479	17	27	-	-	ADJ
ejpam-5479	17	28	perturbative	perturbative	ADJ
ejpam-5479	17	29	approach	approach	NOUN
ejpam-5479	17	30	,	,	PUNCT
ejpam-5479	17	31	he	he	PRON
ejpam-5479	17	32	’s	’	VERB
ejpam-5479	17	33	frequency	frequency	NOUN
ejpam-5479	17	34	formula	formula	NOUN
ejpam-5479	17	35	,	,	PUNCT
ejpam-5479	17	36	nonlinear	nonlinear	ADJ
ejpam-5479	17	37	stability	stability	NOUN
ejpam-5479	17	38	analysis	analysis	NOUN
ejpam-5479	17	39	,	,	PUNCT
ejpam-5479	17	40	time	time	NOUN
ejpam-5479	17	41	history	history	NOUN
ejpam-5479	17	42	∗corresponding	∗corresponde	VERB
ejpam-5479	17	43	author	author	NOUN
ejpam-5479	17	44	.	.	PUNCT
ejpam-5479	18	1	doi	doi	NOUN
ejpam-5479	18	2	:	:	PUNCT
ejpam-5479	18	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5479	https://doi.org/10.29020/nybg.ejpam.v17i4.5479	ADP
ejpam-5479	18	4	email	email	NOUN
ejpam-5479	18	5	addresses	address	NOUN
ejpam-5479	18	6	:	:	PUNCT
ejpam-5479	18	7	kalluhydan@ksu.edu.sa	kalluhydan@ksu.edu.sa	PROPN
ejpam-5479	18	8	(	(	PUNCT
ejpam-5479	18	9	k.	k.	PROPN
ejpam-5479	18	10	alluhydan	alluhydan	PROPN
ejpam-5479	18	11	)	)	PUNCT
ejpam-5479	18	12	,	,	PUNCT
ejpam-5479	18	13	gal	gal	ADJ
ejpam-5479	18	14	moa@edu.asu.edu.eg	moa@edu.asu.edu.eg	PROPN
ejpam-5479	18	15	(	(	PUNCT
ejpam-5479	18	16	g.	g.	PROPN
ejpam-5479	18	17	m	m	PROPN
ejpam-5479	18	18	moatimid	moatimid	PROPN
ejpam-5479	18	19	)	)	PUNCT
ejpam-5479	18	20	,	,	PUNCT
ejpam-5479	18	21	tarek.saleh@science.tanta.edu.eg	tarek.saleh@science.tanta.edu.eg	X
ejpam-5479	18	22	(	(	PUNCT
ejpam-5479	18	23	t.	t.	PROPN
ejpam-5479	18	24	s.	s.	PROPN
ejpam-5479	18	25	amer	amer	PROPN
ejpam-5479	18	26	)	)	PUNCT
ejpam-5479	18	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5479	19	1	3185	3185	NUM
ejpam-5479	20	1	copyright	copyright	NOUN
ejpam-5479	20	2	:	:	PUNCT
ejpam-5479	20	3	©	©	PROPN
ejpam-5479	20	4	2024	2024	NUM
ejpam-5479	20	5	the	the	DET
ejpam-5479	20	6	author(s	author(s	NOUN
ejpam-5479	20	7	)	)	PUNCT
ejpam-5479	20	8	.	.	PUNCT
ejpam-5479	21	1	(	(	PUNCT
ejpam-5479	21	2	cc	cc	NOUN
ejpam-5479	21	3	by	by	ADP
ejpam-5479	21	4	-	-	PUNCT
ejpam-5479	21	5	nc	nc	PROPN
ejpam-5479	21	6	4.0	4.0	NUM
ejpam-5479	21	7	)	)	PUNCT
ejpam-5479	21	8	k.	k.	PROPN
ejpam-5479	21	9	alluhydan	alluhydan	PROPN
ejpam-5479	21	10	,	,	PUNCT
ejpam-5479	21	11	g.	g.	PROPN
ejpam-5479	21	12	m	m	PROPN
ejpam-5479	21	13	moatimid	moatimid	PROPN
ejpam-5479	21	14	,	,	PUNCT
ejpam-5479	21	15	t.	t.	PROPN
ejpam-5479	21	16	s.	s.	PROPN
ejpam-5479	21	17	amer	amer	PROPN
ejpam-5479	21	18	/	/	SYM
ejpam-5479	21	19	eur	eur	PROPN
ejpam-5479	21	20	.	.	PUNCT
ejpam-5479	22	1	j.	j.	PROPN
ejpam-5479	22	2	pure	pure	PROPN
ejpam-5479	22	3	appl	appl	PROPN
ejpam-5479	22	4	.	.	PROPN
ejpam-5479	22	5	math	math	PROPN
ejpam-5479	22	6	,	,	PUNCT
ejpam-5479	22	7	17	17	NUM
ejpam-5479	22	8	(	(	PUNCT
ejpam-5479	22	9	4	4	NUM
ejpam-5479	22	10	)	)	PUNCT
ejpam-5479	22	11	(	(	PUNCT
ejpam-5479	22	12	2024	2024	NUM
ejpam-5479	22	13	)	)	PUNCT
ejpam-5479	22	14	,	,	PUNCT
ejpam-5479	22	15	3185	3185	NUM
ejpam-5479	22	16	-	-	SYM
ejpam-5479	22	17	3208	3208	NUM
ejpam-5479	22	18	3186	3186	NUM
ejpam-5479	22	19	abbreviations	abbreviation	NOUN
ejpam-5479	22	20	symbol	symbol	NOUN
ejpam-5479	22	21	meaning	mean	VERB
ejpam-5479	22	22	symbol	symbol	NOUN
ejpam-5479	22	23	meaning	mean	VERB
ejpam-5479	22	24	hff	hff	NOUN
ejpam-5479	22	25	he	he	PRON
ejpam-5479	22	26	’s	’s	PART
ejpam-5479	22	27	frequency	frequency	NOUN
ejpam-5479	22	28	formula	formula	NOUN
ejpam-5479	22	29	ode	ode	ADJ
ejpam-5479	22	30	ordinary	ordinary	ADJ
ejpam-5479	22	31	differential	differential	ADJ
ejpam-5479	22	32	equation	equation	NOUN
ejpam-5479	22	33	npa	npa	PROPN
ejpam-5479	22	34	non	non	ADJ
ejpam-5479	22	35	-	-	ADJ
ejpam-5479	22	36	perturbative	perturbative	ADJ
ejpam-5479	22	37	analysis	analysis	NOUN
ejpam-5479	22	38	do	do	AUX
ejpam-5479	22	39	duffing	duffe	VERB
ejpam-5479	22	40	oscillator	oscillator	NOUN
ejpam-5479	22	41	ms	ms	PROPN
ejpam-5479	22	42	mathematica	mathematica	PROPN
ejpam-5479	22	43	software	software	PROPN
ejpam-5479	22	44	hpm	hpm	PROPN
ejpam-5479	22	45	homotopy	homotopy	VERB
ejpam-5479	22	46	perturbation	perturbation	NOUN
ejpam-5479	22	47	technique	technique	NOUN
ejpam-5479	22	48	i.c	i.c	PROPN
ejpam-5479	22	49	.	.	PROPN
ejpam-5479	22	50	initial	initial	ADJ
ejpam-5479	22	51	conditions	condition	NOUN
ejpam-5479	22	52	sp	sp	ADP
ejpam-5479	22	53	simple	simple	ADJ
ejpam-5479	22	54	pendulum	pendulum	NOUN
ejpam-5479	22	55	1	1	NUM
ejpam-5479	22	56	.	.	PUNCT
ejpam-5479	23	1	introduction	introduction	NOUN
ejpam-5479	23	2	a	a	DET
ejpam-5479	23	3	basic	basic	ADJ
ejpam-5479	23	4	sp	sp	NOUN
ejpam-5479	23	5	,	,	PUNCT
ejpam-5479	23	6	which	which	PRON
ejpam-5479	23	7	is	be	AUX
ejpam-5479	23	8	only	only	ADV
ejpam-5479	23	9	a	a	DET
ejpam-5479	23	10	mass	mass	NOUN
ejpam-5479	23	11	(	(	PUNCT
ejpam-5479	23	12	which	which	PRON
ejpam-5479	23	13	is	be	AUX
ejpam-5479	23	14	defined	define	VERB
ejpam-5479	23	15	as	as	ADP
ejpam-5479	23	16	a	a	DET
ejpam-5479	23	17	bob	bob	NOUN
ejpam-5479	23	18	)	)	PUNCT
ejpam-5479	23	19	hanging	hang	VERB
ejpam-5479	23	20	from	from	ADP
ejpam-5479	23	21	a	a	DET
ejpam-5479	23	22	fixed	fix	VERB
ejpam-5479	23	23	location	location	NOUN
ejpam-5479	23	24	by	by	ADP
ejpam-5479	23	25	a	a	DET
ejpam-5479	23	26	thread	thread	NOUN
ejpam-5479	23	27	or	or	CCONJ
ejpam-5479	23	28	rod	rod	NOUN
ejpam-5479	23	29	that	that	PRON
ejpam-5479	23	30	influences	influence	VERB
ejpam-5479	23	31	in	in	ADP
ejpam-5479	23	32	response	response	NOUN
ejpam-5479	23	33	to	to	ADP
ejpam-5479	23	34	gravity	gravity	NOUN
ejpam-5479	23	35	,	,	PUNCT
ejpam-5479	23	36	can	can	AUX
ejpam-5479	23	37	perform	perform	VERB
ejpam-5479	23	38	a	a	DET
ejpam-5479	23	39	great	great	ADJ
ejpam-5479	23	40	deal	deal	NOUN
ejpam-5479	23	41	of	of	ADP
ejpam-5479	23	42	the	the	DET
ejpam-5479	23	43	current	current	ADJ
ejpam-5479	23	44	work	work	NOUN
ejpam-5479	23	45	.	.	PUNCT
ejpam-5479	24	1	among	among	ADP
ejpam-5479	24	2	sps	sps	PROPN
ejpam-5479	24	3	,	,	PUNCT
ejpam-5479	24	4	pendulum	pendulum	NOUN
ejpam-5479	24	5	clocks	clock	NOUN
ejpam-5479	24	6	are	be	AUX
ejpam-5479	24	7	the	the	DET
ejpam-5479	24	8	most	most	ADV
ejpam-5479	24	9	well	well	ADV
ejpam-5479	24	10	-	-	PUNCT
ejpam-5479	24	11	known	know	VERB
ejpam-5479	24	12	problem	problem	NOUN
ejpam-5479	24	13	.	.	PUNCT
ejpam-5479	25	1	the	the	DET
ejpam-5479	25	2	hands	hand	NOUN
ejpam-5479	25	3	of	of	ADP
ejpam-5479	25	4	the	the	DET
ejpam-5479	25	5	clock	clock	NOUN
ejpam-5479	25	6	are	be	AUX
ejpam-5479	25	7	twisting	twist	VERB
ejpam-5479	25	8	to	to	PART
ejpam-5479	25	9	keep	keep	VERB
ejpam-5479	25	10	precise	precise	ADJ
ejpam-5479	25	11	time	time	NOUN
ejpam-5479	25	12	by	by	ADP
ejpam-5479	25	13	means	mean	NOUN
ejpam-5479	25	14	of	of	ADP
ejpam-5479	25	15	a	a	DET
ejpam-5479	25	16	pendulum	pendulum	NOUN
ejpam-5479	25	17	that	that	PRON
ejpam-5479	25	18	swings	swing	VERB
ejpam-5479	25	19	back	back	ADV
ejpam-5479	25	20	and	and	CCONJ
ejpam-5479	25	21	forth	forth	ADV
ejpam-5479	25	22	at	at	ADP
ejpam-5479	25	23	regular	regular	ADJ
ejpam-5479	25	24	intervals	interval	NOUN
ejpam-5479	25	25	.	.	PUNCT
ejpam-5479	26	1	a	a	DET
ejpam-5479	26	2	sp	sp	NOUN
ejpam-5479	26	3	is	be	AUX
ejpam-5479	26	4	a	a	DET
ejpam-5479	26	5	perfect	perfect	ADJ
ejpam-5479	26	6	watch	watch	NOUN
ejpam-5479	26	7	because	because	SCONJ
ejpam-5479	26	8	its	its	PRON
ejpam-5479	26	9	period	period	NOUN
ejpam-5479	26	10	is	be	AUX
ejpam-5479	26	11	insensitive	insensitive	ADJ
ejpam-5479	26	12	to	to	ADP
ejpam-5479	26	13	changes	change	NOUN
ejpam-5479	26	14	in	in	ADP
ejpam-5479	26	15	amplitude	amplitude	NOUN
ejpam-5479	26	16	.	.	PUNCT
ejpam-5479	27	1	with	with	ADP
ejpam-5479	27	2	the	the	DET
ejpam-5479	27	3	use	use	NOUN
ejpam-5479	27	4	of	of	ADP
ejpam-5479	27	5	a	a	DET
ejpam-5479	27	6	newly	newly	ADV
ejpam-5479	27	7	proposed	propose	VERB
ejpam-5479	27	8	formula	formula	NOUN
ejpam-5479	27	9	,	,	PUNCT
ejpam-5479	27	10	one	one	PRON
ejpam-5479	27	11	can	can	AUX
ejpam-5479	27	12	approximately	approximately	ADV
ejpam-5479	27	13	determine	determine	VERB
ejpam-5479	27	14	the	the	DET
ejpam-5479	27	15	period	period	NOUN
ejpam-5479	27	16	of	of	ADP
ejpam-5479	27	17	a	a	DET
ejpam-5479	27	18	sp	sp	NOUN
ejpam-5479	27	19	[	[	NOUN
ejpam-5479	27	20	2	2	NUM
ejpam-5479	27	21	]	]	PUNCT
ejpam-5479	27	22	.	.	PUNCT
ejpam-5479	28	1	it	it	PRON
ejpam-5479	28	2	was	be	AUX
ejpam-5479	28	3	considered	consider	VERB
ejpam-5479	28	4	both	both	CCONJ
ejpam-5479	28	5	small	small	ADJ
ejpam-5479	28	6	and	and	CCONJ
ejpam-5479	28	7	large	large	ADJ
ejpam-5479	28	8	amplitudes	amplitude	NOUN
ejpam-5479	28	9	of	of	ADP
ejpam-5479	28	10	oscillation	oscillation	NOUN
ejpam-5479	28	11	,	,	PUNCT
ejpam-5479	28	12	while	while	SCONJ
ejpam-5479	28	13	deriving	derive	VERB
ejpam-5479	28	14	the	the	DET
ejpam-5479	28	15	nonlinear	nonlinear	ADJ
ejpam-5479	28	16	ode	ode	NOUN
ejpam-5479	28	17	,	,	PUNCT
ejpam-5479	28	18	which	which	PRON
ejpam-5479	28	19	represents	represent	VERB
ejpam-5479	28	20	and	and	CCONJ
ejpam-5479	28	21	explains	explain	VERB
ejpam-5479	28	22	the	the	DET
ejpam-5479	28	23	swing	swing	NOUN
ejpam-5479	28	24	of	of	ADP
ejpam-5479	28	25	a	a	DET
ejpam-5479	28	26	simple	simple	ADJ
ejpam-5479	28	27	sp	sp	ADP
ejpam-5479	28	28	[	[	X
ejpam-5479	28	29	9	9	NUM
ejpam-5479	28	30	]	]	PUNCT
ejpam-5479	28	31	.	.	PUNCT
ejpam-5479	29	1	the	the	DET
ejpam-5479	29	2	fundamental	fundamental	ADJ
ejpam-5479	29	3	element	element	NOUN
ejpam-5479	29	4	of	of	ADP
ejpam-5479	29	5	a	a	DET
ejpam-5479	29	6	sp	sp	NOUN
ejpam-5479	29	7	experiment	experiment	NOUN
ejpam-5479	29	8	is	be	AUX
ejpam-5479	29	9	a	a	DET
ejpam-5479	29	10	pendulum	pendulum	NOUN
ejpam-5479	29	11	bob	bob	NOUN
ejpam-5479	29	12	,	,	PUNCT
ejpam-5479	29	13	which	which	PRON
ejpam-5479	29	14	is	be	AUX
ejpam-5479	29	15	an	an	DET
ejpam-5479	29	16	item	item	NOUN
ejpam-5479	29	17	with	with	ADP
ejpam-5479	29	18	a	a	DET
ejpam-5479	29	19	slight	slight	ADJ
ejpam-5479	29	20	mass	mass	NOUN
ejpam-5479	29	21	suspended	suspend	VERB
ejpam-5479	29	22	from	from	ADP
ejpam-5479	29	23	a	a	DET
ejpam-5479	29	24	light	light	ADJ
ejpam-5479	29	25	thread	thread	NOUN
ejpam-5479	29	26	cite3	cite3	ADJ
ejpam-5479	29	27	.	.	PUNCT
ejpam-5479	30	1	to	to	PART
ejpam-5479	30	2	solve	solve	VERB
ejpam-5479	30	3	the	the	DET
ejpam-5479	30	4	nonlinear	nonlinear	ADJ
ejpam-5479	30	5	problems	problem	NOUN
ejpam-5479	30	6	of	of	ADP
ejpam-5479	30	7	a	a	DET
ejpam-5479	30	8	mass	mass	ADJ
ejpam-5479	30	9	spring	spring	NOUN
ejpam-5479	30	10	oscillator	oscillator	NOUN
ejpam-5479	30	11	,	,	PUNCT
ejpam-5479	30	12	which	which	PRON
ejpam-5479	30	13	is	be	AUX
ejpam-5479	30	14	the	the	DET
ejpam-5479	30	15	same	same	ADJ
ejpam-5479	30	16	as	as	ADP
ejpam-5479	30	17	the	the	DET
ejpam-5479	30	18	do	do	NOUN
ejpam-5479	31	1	[	[	X
ejpam-5479	31	2	44	44	NUM
ejpam-5479	31	3	]	]	PUNCT
ejpam-5479	31	4	,	,	PUNCT
ejpam-5479	31	5	the	the	DET
ejpam-5479	31	6	vibrational	vibrational	ADJ
ejpam-5479	31	7	iterative	iterative	NOUN
ejpam-5479	31	8	approach	approach	NOUN
ejpam-5479	31	9	and	and	CCONJ
ejpam-5479	31	10	using	use	VERB
ejpam-5479	31	11	the	the	DET
ejpam-5479	31	12	laplace	laplace	NOUN
ejpam-5479	31	13	transform	transform	NOUN
ejpam-5479	31	14	was	be	AUX
ejpam-5479	31	15	used	use	VERB
ejpam-5479	31	16	.	.	PUNCT
ejpam-5479	32	1	discovering	discover	VERB
ejpam-5479	32	2	the	the	DET
ejpam-5479	32	3	lagrange	lagrange	NOUN
ejpam-5479	32	4	multiplier	multiplier	ADV
ejpam-5479	32	5	is	be	AUX
ejpam-5479	32	6	a	a	DET
ejpam-5479	32	7	crucial	crucial	ADJ
ejpam-5479	32	8	part	part	NOUN
ejpam-5479	32	9	of	of	ADP
ejpam-5479	32	10	the	the	DET
ejpam-5479	32	11	variational	variational	ADJ
ejpam-5479	32	12	iterative	iterative	NOUN
ejpam-5479	32	13	method	method	NOUN
ejpam-5479	32	14	,	,	PUNCT
ejpam-5479	32	15	and	and	CCONJ
ejpam-5479	32	16	thus	thus	ADV
ejpam-5479	32	17	is	be	AUX
ejpam-5479	32	18	a	a	DET
ejpam-5479	32	19	common	common	ADJ
ejpam-5479	32	20	application	application	NOUN
ejpam-5479	32	21	of	of	ADP
ejpam-5479	32	22	variational	variational	ADJ
ejpam-5479	32	23	theory	theory	NOUN
ejpam-5479	32	24	.	.	PUNCT
ejpam-5479	33	1	this	this	DET
ejpam-5479	33	2	research	research	NOUN
ejpam-5479	33	3	looked	look	VERB
ejpam-5479	33	4	at	at	ADP
ejpam-5479	33	5	the	the	DET
ejpam-5479	33	6	motion	motion	NOUN
ejpam-5479	33	7	of	of	ADP
ejpam-5479	33	8	a	a	DET
ejpam-5479	33	9	classical	classical	ADJ
ejpam-5479	33	10	point	point	NOUN
ejpam-5479	33	11	particle	particle	NOUN
ejpam-5479	33	12	in	in	ADP
ejpam-5479	33	13	a	a	DET
ejpam-5479	33	14	revolving	revolve	VERB
ejpam-5479	33	15	frame	frame	NOUN
ejpam-5479	33	16	with	with	ADP
ejpam-5479	33	17	a	a	DET
ejpam-5479	33	18	central	central	ADJ
ejpam-5479	33	19	restoring	restore	VERB
ejpam-5479	33	20	force	force	NOUN
ejpam-5479	33	21	[	[	X
ejpam-5479	33	22	8	8	NUM
ejpam-5479	33	23	]	]	PUNCT
ejpam-5479	33	24	.	.	PUNCT
ejpam-5479	34	1	these	these	DET
ejpam-5479	34	2	responses	response	NOUN
ejpam-5479	34	3	were	be	AUX
ejpam-5479	34	4	applied	apply	VERB
ejpam-5479	34	5	to	to	ADP
ejpam-5479	34	6	the	the	DET
ejpam-5479	34	7	problems	problem	NOUN
ejpam-5479	34	8	of	of	ADP
ejpam-5479	34	9	surface	surface	NOUN
ejpam-5479	34	10	-	-	PUNCT
ejpam-5479	34	11	based	base	VERB
ejpam-5479	34	12	pendulums	pendulum	NOUN
ejpam-5479	34	13	,	,	PUNCT
ejpam-5479	34	14	and	and	CCONJ
ejpam-5479	34	15	most	most	ADV
ejpam-5479	34	16	especially	especially	ADV
ejpam-5479	34	17	to	to	ADP
ejpam-5479	34	18	the	the	DET
ejpam-5479	34	19	sp	sp	NOUN
ejpam-5479	34	20	.	.	PUNCT
ejpam-5479	35	1	it	it	PRON
ejpam-5479	35	2	is	be	AUX
ejpam-5479	35	3	possible	possible	ADJ
ejpam-5479	35	4	for	for	SCONJ
ejpam-5479	35	5	a	a	DET
ejpam-5479	35	6	cubic	cubic	ADJ
ejpam-5479	35	7	-	-	PUNCT
ejpam-5479	35	8	quintic	quintic	ADJ
ejpam-5479	35	9	do	do	NOUN
ejpam-5479	35	10	to	to	PART
ejpam-5479	35	11	arise	arise	VERB
ejpam-5479	35	12	,	,	PUNCT
ejpam-5479	35	13	for	for	ADP
ejpam-5479	35	14	instance	instance	NOUN
ejpam-5479	35	15	,	,	PUNCT
ejpam-5479	35	16	in	in	ADP
ejpam-5479	35	17	the	the	DET
ejpam-5479	35	18	case	case	NOUN
ejpam-5479	35	19	of	of	ADP
ejpam-5479	35	20	a	a	DET
ejpam-5479	35	21	magnetic	magnetic	ADJ
ejpam-5479	35	22	spherical	spherical	ADJ
ejpam-5479	35	23	pendulum	pendulum	NOUN
ejpam-5479	35	24	’s	’s	PART
ejpam-5479	35	25	governing	govern	VERB
ejpam-5479	35	26	equation	equation	NOUN
ejpam-5479	35	27	of	of	ADP
ejpam-5479	35	28	motion	motion	NOUN
ejpam-5479	35	29	.	.	PUNCT
ejpam-5479	36	1	the	the	DET
ejpam-5479	36	2	current	current	ADJ
ejpam-5479	36	3	endeavor	endeavor	NOUN
ejpam-5479	36	4	aims	aim	VERB
ejpam-5479	36	5	to	to	PART
ejpam-5479	36	6	solve	solve	VERB
ejpam-5479	36	7	this	this	DET
ejpam-5479	36	8	problem	problem	NOUN
ejpam-5479	36	9	analytically	analytically	ADV
ejpam-5479	36	10	within	within	ADP
ejpam-5479	36	11	certain	certain	ADJ
ejpam-5479	36	12	bounds	bound	NOUN
ejpam-5479	36	13	.	.	PUNCT
ejpam-5479	37	1	the	the	DET
ejpam-5479	37	2	problem	problem	NOUN
ejpam-5479	37	3	was	be	AUX
ejpam-5479	37	4	resolved	resolve	VERB
ejpam-5479	37	5	by	by	ADP
ejpam-5479	37	6	integrating	integrate	VERB
ejpam-5479	37	7	methods	method	NOUN
ejpam-5479	37	8	such	such	ADJ
ejpam-5479	37	9	as	as	ADP
ejpam-5479	37	10	the	the	DET
ejpam-5479	37	11	hpm	hpm	NOUN
ejpam-5479	37	12	,	,	PUNCT
ejpam-5479	37	13	nonlinear	nonlinear	ADJ
ejpam-5479	37	14	expanded	expand	VERB
ejpam-5479	37	15	frequency	frequency	NOUN
ejpam-5479	37	16	,	,	PUNCT
ejpam-5479	37	17	and	and	CCONJ
ejpam-5479	37	18	laplace	laplace	NOUN
ejpam-5479	37	19	transforms	transform	VERB
ejpam-5479	37	20	[	[	X
ejpam-5479	37	21	21	21	NUM
ejpam-5479	37	22	]	]	PUNCT
ejpam-5479	37	23	.	.	PUNCT
ejpam-5479	38	1	keep	keep	VERB
ejpam-5479	38	2	in	in	ADP
ejpam-5479	38	3	mind	mind	NOUN
ejpam-5479	38	4	that	that	SCONJ
ejpam-5479	38	5	this	this	DET
ejpam-5479	38	6	issue	issue	NOUN
ejpam-5479	38	7	covers	cover	VERB
ejpam-5479	38	8	the	the	DET
ejpam-5479	38	9	same	same	ADJ
ejpam-5479	38	10	ground	ground	NOUN
ejpam-5479	38	11	as	as	ADP
ejpam-5479	38	12	the	the	DET
ejpam-5479	38	13	previous	previous	ADJ
ejpam-5479	38	14	one	one	NUM
ejpam-5479	38	15	[	[	X
ejpam-5479	38	16	20	20	NUM
ejpam-5479	38	17	]	]	PUNCT
ejpam-5479	38	18	,	,	PUNCT
ejpam-5479	38	19	but	but	CCONJ
ejpam-5479	38	20	with	with	ADP
ejpam-5479	38	21	certain	certain	ADJ
ejpam-5479	38	22	limitations	limitation	NOUN
ejpam-5479	38	23	:	:	PUNCT
ejpam-5479	38	24	1	1	X
ejpam-5479	38	25	.	.	X
ejpam-5479	38	26	a	a	DET
ejpam-5479	38	27	crucial	crucial	ADJ
ejpam-5479	38	28	component	component	NOUN
ejpam-5479	38	29	of	of	ADP
ejpam-5479	38	30	this	this	DET
ejpam-5479	38	31	inquiry	inquiry	NOUN
ejpam-5479	38	32	is	be	AUX
ejpam-5479	38	33	the	the	DET
ejpam-5479	38	34	time	time	NOUN
ejpam-5479	38	35	-	-	PUNCT
ejpam-5479	38	36	delay	delay	NOUN
ejpam-5479	38	37	.	.	PUNCT
ejpam-5479	39	1	2	2	X
ejpam-5479	39	2	.	.	X
ejpam-5479	39	3	the	the	DET
ejpam-5479	39	4	current	current	ADJ
ejpam-5479	39	5	approach	approach	NOUN
ejpam-5479	39	6	uses	use	VERB
ejpam-5479	39	7	the	the	DET
ejpam-5479	39	8	so	so	ADV
ejpam-5479	39	9	-	-	PUNCT
ejpam-5479	39	10	called	call	VERB
ejpam-5479	39	11	npa	npa	NOUN
ejpam-5479	39	12	rather	rather	ADV
ejpam-5479	39	13	than	than	ADP
ejpam-5479	39	14	the	the	DET
ejpam-5479	39	15	hpm	hpm	NOUN
ejpam-5479	39	16	.	.	PUNCT
ejpam-5479	40	1	3	3	X
ejpam-5479	40	2	.	.	X
ejpam-5479	40	3	neglecting	neglect	VERB
ejpam-5479	40	4	the	the	DET
ejpam-5479	40	5	disadvantages	disadvantage	NOUN
ejpam-5479	40	6	of	of	ADP
ejpam-5479	40	7	increasing	increase	VERB
ejpam-5479	40	8	the	the	DET
ejpam-5479	40	9	restoring	restore	VERB
ejpam-5479	40	10	forces	force	NOUN
ejpam-5479	40	11	through	through	ADP
ejpam-5479	40	12	taylor	taylor	PROPN
ejpam-5479	40	13	expansion	expansion	NOUN
ejpam-5479	40	14	,	,	PUNCT
ejpam-5479	40	15	which	which	PRON
ejpam-5479	40	16	is	be	AUX
ejpam-5479	40	17	an	an	DET
ejpam-5479	40	18	essential	essential	ADJ
ejpam-5479	40	19	part	part	NOUN
ejpam-5479	40	20	of	of	ADP
ejpam-5479	40	21	the	the	DET
ejpam-5479	40	22	equation	equation	NOUN
ejpam-5479	40	23	of	of	ADP
ejpam-5479	40	24	motion	motion	NOUN
ejpam-5479	40	25	,	,	PUNCT
ejpam-5479	40	26	is	be	AUX
ejpam-5479	40	27	considered	consider	VERB
ejpam-5479	40	28	.	.	PUNCT
ejpam-5479	41	1	the	the	DET
ejpam-5479	41	2	odes	ode	NOUN
ejpam-5479	41	3	played	play	VERB
ejpam-5479	41	4	a	a	DET
ejpam-5479	41	5	vital	vital	ADJ
ejpam-5479	41	6	role	role	NOUN
ejpam-5479	41	7	in	in	ADP
ejpam-5479	41	8	many	many	ADJ
ejpam-5479	41	9	branches	branch	NOUN
ejpam-5479	41	10	of	of	ADP
ejpam-5479	41	11	applications	application	NOUN
ejpam-5479	41	12	,	,	PUNCT
ejpam-5479	41	13	including	include	VERB
ejpam-5479	41	14	applied	apply	VERB
ejpam-5479	41	15	mathematics	mathematic	NOUN
ejpam-5479	41	16	,	,	PUNCT
ejpam-5479	41	17	physics	physics	NOUN
ejpam-5479	41	18	,	,	PUNCT
ejpam-5479	41	19	chemistry	chemistry	NOUN
ejpam-5479	41	20	,	,	PUNCT
ejpam-5479	41	21	and	and	CCONJ
ejpam-5479	41	22	biology	biology	NOUN
ejpam-5479	41	23	.	.	PUNCT
ejpam-5479	42	1	the	the	DET
ejpam-5479	42	2	physical	physical	ADJ
ejpam-5479	42	3	significance	significance	NOUN
ejpam-5479	42	4	of	of	ADP
ejpam-5479	42	5	the	the	DET
ejpam-5479	42	6	scenario	scenario	NOUN
ejpam-5479	42	7	is	be	AUX
ejpam-5479	42	8	a	a	DET
ejpam-5479	42	9	qualitative	qualitative	ADJ
ejpam-5479	42	10	factor	factor	NOUN
ejpam-5479	42	11	that	that	PRON
ejpam-5479	42	12	governs	govern	VERB
ejpam-5479	42	13	dynamic	dynamic	ADJ
ejpam-5479	42	14	behaviors	behavior	NOUN
ejpam-5479	42	15	.	.	PUNCT
ejpam-5479	43	1	although	although	SCONJ
ejpam-5479	43	2	establishing	establish	VERB
ejpam-5479	43	3	a	a	DET
ejpam-5479	43	4	significant	significant	ADJ
ejpam-5479	43	5	analysis	analysis	NOUN
ejpam-5479	43	6	of	of	ADP
ejpam-5479	43	7	a	a	DET
ejpam-5479	43	8	nonlinear	nonlinear	NOUN
ejpam-5479	43	9	do	do	AUX
ejpam-5479	43	10	can	can	AUX
ejpam-5479	43	11	often	often	ADV
ejpam-5479	43	12	be	be	AUX
ejpam-5479	43	13	challenging	challenging	ADJ
ejpam-5479	43	14	,	,	PUNCT
ejpam-5479	43	15	the	the	DET
ejpam-5479	43	16	solution	solution	NOUN
ejpam-5479	43	17	to	to	ADP
ejpam-5479	43	18	a	a	DET
ejpam-5479	43	19	linear	linear	ADJ
ejpam-5479	43	20	ode	ode	NOUN
ejpam-5479	43	21	was	be	AUX
ejpam-5479	43	22	k.	k.	PROPN
ejpam-5479	43	23	alluhydan	alluhydan	PROPN
ejpam-5479	43	24	,	,	PUNCT
ejpam-5479	43	25	g.	g.	PROPN
ejpam-5479	43	26	m	m	PROPN
ejpam-5479	43	27	moatimid	moatimid	PROPN
ejpam-5479	43	28	,	,	PUNCT
ejpam-5479	43	29	t.	t.	PROPN
ejpam-5479	43	30	s.	s.	PROPN
ejpam-5479	43	31	amer	amer	PROPN
ejpam-5479	43	32	/	/	SYM
ejpam-5479	43	33	eur	eur	PROPN
ejpam-5479	43	34	.	.	PUNCT
ejpam-5479	44	1	j.	j.	PROPN
ejpam-5479	44	2	pure	pure	PROPN
ejpam-5479	44	3	appl	appl	PROPN
ejpam-5479	44	4	.	.	PROPN
ejpam-5479	44	5	math	math	PROPN
ejpam-5479	44	6	,	,	PUNCT
ejpam-5479	44	7	17	17	NUM
ejpam-5479	44	8	(	(	PUNCT
ejpam-5479	44	9	4	4	NUM
ejpam-5479	44	10	)	)	PUNCT
ejpam-5479	44	11	(	(	PUNCT
ejpam-5479	44	12	2024	2024	NUM
ejpam-5479	44	13	)	)	PUNCT
ejpam-5479	44	14	,	,	PUNCT
ejpam-5479	44	15	3185	3185	NUM
ejpam-5479	44	16	-	-	SYM
ejpam-5479	44	17	3208	3208	NUM
ejpam-5479	44	18	3187	3187	NUM
ejpam-5479	44	19	straightforward	straightforward	NOUN
ejpam-5479	44	20	.	.	PUNCT
ejpam-5479	45	1	evaluating	evaluate	VERB
ejpam-5479	45	2	minuscule	minuscule	ADJ
ejpam-5479	45	3	parameters	parameter	NOUN
ejpam-5479	45	4	posed	pose	VERB
ejpam-5479	45	5	a	a	DET
ejpam-5479	45	6	challenging	challenging	ADJ
ejpam-5479	45	7	endeavor	endeavor	NOUN
ejpam-5479	45	8	,	,	PUNCT
ejpam-5479	45	9	demanding	demand	VERB
ejpam-5479	45	10	the	the	DET
ejpam-5479	45	11	utilization	utilization	NOUN
ejpam-5479	45	12	of	of	ADP
ejpam-5479	45	13	distinct	distinct	ADJ
ejpam-5479	45	14	methodologies	methodology	NOUN
ejpam-5479	45	15	.	.	PUNCT
ejpam-5479	46	1	the	the	DET
ejpam-5479	46	2	semi	semi	ADJ
ejpam-5479	46	3	-	-	ADJ
ejpam-5479	46	4	analytical	analytical	ADJ
ejpam-5479	46	5	hpm	hpm	NOUN
ejpam-5479	46	6	can	can	AUX
ejpam-5479	46	7	be	be	AUX
ejpam-5479	46	8	a	a	DET
ejpam-5479	46	9	helpful	helpful	ADJ
ejpam-5479	46	10	approach	approach	NOUN
ejpam-5479	46	11	to	to	ADP
ejpam-5479	46	12	comprehending	comprehend	VERB
ejpam-5479	46	13	common	common	ADJ
ejpam-5479	46	14	nonlinear	nonlinear	NOUN
ejpam-5479	46	15	do	do	NOUN
ejpam-5479	46	16	.	.	PUNCT
ejpam-5479	47	1	the	the	DET
ejpam-5479	47	2	first	first	ADJ
ejpam-5479	47	3	chinese	chinese	ADJ
ejpam-5479	47	4	mathematician	mathematician	ADJ
ejpam-5479	47	5	prof	prof	NOUN
ejpam-5479	47	6	.	.	PUNCT
ejpam-5479	48	1	he	he	PRON
ejpam-5479	48	2	suggested	suggest	VERB
ejpam-5479	48	3	this	this	DET
ejpam-5479	48	4	approach	approach	NOUN
ejpam-5479	48	5	to	to	PART
ejpam-5479	48	6	analyze	analyze	VERB
ejpam-5479	48	7	the	the	DET
ejpam-5479	48	8	nonlinear	nonlinear	NOUN
ejpam-5479	48	9	do	do	AUX
ejpam-5479	48	10	[	[	X
ejpam-5479	48	11	31	31	NUM
ejpam-5479	48	12	]	]	PUNCT
ejpam-5479	48	13	.	.	PUNCT
ejpam-5479	49	1	except	except	SCONJ
ejpam-5479	49	2	for	for	ADP
ejpam-5479	49	3	the	the	DET
ejpam-5479	49	4	requirement	requirement	NOUN
ejpam-5479	49	5	for	for	ADP
ejpam-5479	49	6	a	a	DET
ejpam-5479	49	7	modest	modest	ADJ
ejpam-5479	49	8	parametric	parametric	ADJ
ejpam-5479	49	9	assumption	assumption	NOUN
ejpam-5479	49	10	,	,	PUNCT
ejpam-5479	49	11	the	the	DET
ejpam-5479	49	12	hpm	hpm	NOUN
ejpam-5479	49	13	has	have	VERB
ejpam-5479	49	14	all	all	DET
ejpam-5479	49	15	the	the	DET
ejpam-5479	49	16	compensations	compensation	NOUN
ejpam-5479	49	17	of	of	ADP
ejpam-5479	49	18	all	all	DET
ejpam-5479	49	19	perturbation	perturbation	NOUN
ejpam-5479	49	20	methodologies	methodology	NOUN
ejpam-5479	49	21	.	.	PUNCT
ejpam-5479	50	1	in	in	ADP
ejpam-5479	50	2	comparison	comparison	NOUN
ejpam-5479	50	3	to	to	ADP
ejpam-5479	50	4	earlier	early	ADJ
ejpam-5479	50	5	approaches	approach	NOUN
ejpam-5479	50	6	,	,	PUNCT
ejpam-5479	50	7	the	the	DET
ejpam-5479	50	8	hpm	hpm	NOUN
ejpam-5479	50	9	was	be	AUX
ejpam-5479	50	10	overcome	overcome	VERB
ejpam-5479	50	11	by	by	ADP
ejpam-5479	50	12	the	the	DET
ejpam-5479	50	13	complexity	complexity	NOUN
ejpam-5479	50	14	of	of	ADP
ejpam-5479	50	15	calculation	calculation	NOUN
ejpam-5479	50	16	,	,	PUNCT
ejpam-5479	50	17	so	so	ADV
ejpam-5479	50	18	using	use	VERB
ejpam-5479	50	19	less	less	ADJ
ejpam-5479	50	20	computer	computer	NOUN
ejpam-5479	50	21	memory	memory	NOUN
ejpam-5479	50	22	,	,	PUNCT
ejpam-5479	50	23	and	and	CCONJ
ejpam-5479	50	24	calculating	calculate	VERB
ejpam-5479	50	25	more	more	ADV
ejpam-5479	50	26	quickly	quickly	ADV
ejpam-5479	50	27	.	.	PUNCT
ejpam-5479	51	1	alluhydan	alluhydan	PROPN
ejpam-5479	51	2	et	et	PROPN
ejpam-5479	51	3	al	al	PROPN
ejpam-5479	51	4	.	.	PUNCT
ejpam-5479	52	1	[	[	X
ejpam-5479	52	2	40	40	NUM
ejpam-5479	52	3	]	]	PUNCT
ejpam-5479	52	4	studied	study	VERB
ejpam-5479	52	5	how	how	SCONJ
ejpam-5479	52	6	a	a	DET
ejpam-5479	52	7	location	location	NOUN
ejpam-5479	52	8	and	and	CCONJ
ejpam-5479	52	9	velocity	velocity	NOUN
ejpam-5479	52	10	time	time	NOUN
ejpam-5479	52	11	-	-	PUNCT
ejpam-5479	52	12	delay	delay	NOUN
ejpam-5479	52	13	could	could	AUX
ejpam-5479	52	14	reduce	reduce	VERB
ejpam-5479	52	15	the	the	DET
ejpam-5479	52	16	excited	excited	ADJ
ejpam-5479	52	17	nonlinear	nonlinear	ADJ
ejpam-5479	52	18	vibration	vibration	NOUN
ejpam-5479	52	19	of	of	ADP
ejpam-5479	52	20	do	do	PROPN
ejpam-5479	52	21	.	.	PUNCT
ejpam-5479	53	1	a	a	DET
ejpam-5479	53	2	modified	modify	VERB
ejpam-5479	53	3	was	be	AUX
ejpam-5479	53	4	employed	employ	VERB
ejpam-5479	53	5	to	to	PART
ejpam-5479	53	6	attain	attain	VERB
ejpam-5479	53	7	an	an	DET
ejpam-5479	53	8	approximate	approximate	ADJ
ejpam-5479	53	9	uniform	uniform	ADJ
ejpam-5479	53	10	solution	solution	NOUN
ejpam-5479	53	11	to	to	ADP
ejpam-5479	53	12	the	the	DET
ejpam-5479	53	13	issue	issue	NOUN
ejpam-5479	53	14	being	be	AUX
ejpam-5479	53	15	addressed	address	VERB
ejpam-5479	53	16	.	.	PUNCT
ejpam-5479	54	1	the	the	DET
ejpam-5479	54	2	linear	linear	ADJ
ejpam-5479	54	3	time	time	NOUN
ejpam-5479	54	4	-	-	PUNCT
ejpam-5479	54	5	delay	delay	NOUN
ejpam-5479	54	6	system	system	NOUN
ejpam-5479	54	7	stability	stability	NOUN
ejpam-5479	54	8	problem	problem	NOUN
ejpam-5479	54	9	was	be	AUX
ejpam-5479	54	10	created	create	VERB
ejpam-5479	54	11	[	[	X
ejpam-5479	54	12	54	54	NUM
ejpam-5479	54	13	]	]	PUNCT
ejpam-5479	54	14	.	.	PUNCT
ejpam-5479	55	1	it	it	PRON
ejpam-5479	55	2	began	begin	VERB
ejpam-5479	55	3	by	by	ADP
ejpam-5479	55	4	describing	describe	VERB
ejpam-5479	55	5	a	a	DET
ejpam-5479	55	6	comprehensive	comprehensive	ADJ
ejpam-5479	55	7	vector	vector	NOUN
ejpam-5479	55	8	of	of	ADP
ejpam-5479	55	9	multiple	multiple	ADJ
ejpam-5479	55	10	integral	integral	ADJ
ejpam-5479	55	11	inequalities	inequality	NOUN
ejpam-5479	55	12	,	,	PUNCT
ejpam-5479	55	13	which	which	PRON
ejpam-5479	55	14	can	can	AUX
ejpam-5479	55	15	understand	understand	VERB
ejpam-5479	55	16	many	many	ADJ
ejpam-5479	55	17	results	result	NOUN
ejpam-5479	55	18	as	as	ADP
ejpam-5479	55	19	unusual	unusual	ADJ
ejpam-5479	55	20	situations	situation	NOUN
ejpam-5479	55	21	.	.	PUNCT
ejpam-5479	56	1	second	second	ADJ
ejpam-5479	56	2	,	,	PUNCT
ejpam-5479	56	3	these	these	DET
ejpam-5479	56	4	multiples	multiple	NOUN
ejpam-5479	56	5	were	be	AUX
ejpam-5479	56	6	used	use	VERB
ejpam-5479	56	7	to	to	PART
ejpam-5479	56	8	build	build	VERB
ejpam-5479	56	9	a	a	DET
ejpam-5479	56	10	delay	delay	NOUN
ejpam-5479	56	11	-	-	PUNCT
ejpam-5479	56	12	dependent	dependent	ADJ
ejpam-5479	56	13	stability	stability	NOUN
ejpam-5479	56	14	standard	standard	NOUN
ejpam-5479	56	15	for	for	ADP
ejpam-5479	56	16	time	time	NOUN
ejpam-5479	56	17	-	-	PUNCT
ejpam-5479	56	18	delay	delay	NOUN
ejpam-5479	56	19	systems	system	NOUN
ejpam-5479	56	20	.	.	PUNCT
ejpam-5479	57	1	for	for	ADP
ejpam-5479	57	2	a	a	DET
ejpam-5479	57	3	time	time	NOUN
ejpam-5479	57	4	-	-	PUNCT
ejpam-5479	57	5	varying	vary	VERB
ejpam-5479	57	6	delay	delay	NOUN
ejpam-5479	57	7	linear	linear	NOUN
ejpam-5479	57	8	system	system	NOUN
ejpam-5479	57	9	,	,	PUNCT
ejpam-5479	57	10	the	the	DET
ejpam-5479	57	11	delay	delay	NOUN
ejpam-5479	57	12	-	-	PUNCT
ejpam-5479	57	13	dependent	dependent	ADJ
ejpam-5479	57	14	stability	stability	NOUN
ejpam-5479	57	15	problem	problem	NOUN
ejpam-5479	57	16	was	be	AUX
ejpam-5479	57	17	suggested	suggest	VERB
ejpam-5479	57	18	[	[	X
ejpam-5479	57	19	55	55	NUM
ejpam-5479	57	20	]	]	PUNCT
ejpam-5479	57	21	.	.	PUNCT
ejpam-5479	58	1	they	they	PRON
ejpam-5479	58	2	provided	provide	VERB
ejpam-5479	58	3	evidence	evidence	NOUN
ejpam-5479	58	4	that	that	SCONJ
ejpam-5479	58	5	their	their	PRON
ejpam-5479	58	6	approach	approach	NOUN
ejpam-5479	58	7	was	be	AUX
ejpam-5479	58	8	more	more	ADV
ejpam-5479	58	9	useful	useful	ADJ
ejpam-5479	58	10	for	for	ADP
ejpam-5479	58	11	handling	handle	VERB
ejpam-5479	58	12	time	time	NOUN
ejpam-5479	58	13	-	-	PUNCT
ejpam-5479	58	14	varying	vary	VERB
ejpam-5479	58	15	delay	delay	NOUN
ejpam-5479	58	16	systems	system	NOUN
ejpam-5479	58	17	.	.	PUNCT
ejpam-5479	59	1	rahman	rahman	PROPN
ejpam-5479	60	1	[	[	X
ejpam-5479	60	2	5	5	NUM
ejpam-5479	60	3	]	]	PUNCT
ejpam-5479	60	4	reviewed	review	VERB
ejpam-5479	60	5	many	many	ADJ
ejpam-5479	60	6	models	model	NOUN
ejpam-5479	60	7	that	that	PRON
ejpam-5479	60	8	incorporate	incorporate	VERB
ejpam-5479	60	9	time	time	NOUN
ejpam-5479	60	10	-	-	PUNCT
ejpam-5479	60	11	delays	delay	NOUN
ejpam-5479	60	12	,	,	PUNCT
ejpam-5479	60	13	including	include	VERB
ejpam-5479	60	14	discrete	discrete	ADJ
ejpam-5479	60	15	,	,	PUNCT
ejpam-5479	60	16	distributed	distribute	VERB
ejpam-5479	60	17	,	,	PUNCT
ejpam-5479	60	18	and	and	CCONJ
ejpam-5479	60	19	hybrid	hybrid	ADJ
ejpam-5479	60	20	approaches	approach	NOUN
ejpam-5479	60	21	that	that	PRON
ejpam-5479	60	22	combine	combine	VERB
ejpam-5479	60	23	the	the	DET
ejpam-5479	60	24	two	two	NUM
ejpam-5479	60	25	,	,	PUNCT
ejpam-5479	60	26	highlighting	highlight	VERB
ejpam-5479	60	27	the	the	DET
ejpam-5479	60	28	rationale	rationale	NOUN
ejpam-5479	60	29	behind	behind	ADP
ejpam-5479	60	30	doing	do	VERB
ejpam-5479	60	31	so	so	ADV
ejpam-5479	60	32	.	.	PUNCT
ejpam-5479	61	1	a	a	DET
ejpam-5479	61	2	time	time	NOUN
ejpam-5479	61	3	-	-	PUNCT
ejpam-5479	61	4	delayed	delay	VERB
ejpam-5479	61	5	nonlinear	nonlinear	ADJ
ejpam-5479	61	6	vibration	vibration	NOUN
ejpam-5479	61	7	absorption	absorption	NOUN
ejpam-5479	61	8	system	system	NOUN
ejpam-5479	61	9	’s	’s	PART
ejpam-5479	61	10	dynamical	dynamical	ADJ
ejpam-5479	61	11	responses	response	NOUN
ejpam-5479	61	12	to	to	PART
ejpam-5479	61	13	harmonic	harmonic	ADJ
ejpam-5479	61	14	excitation	excitation	NOUN
ejpam-5479	61	15	were	be	AUX
ejpam-5479	61	16	documented	document	VERB
ejpam-5479	61	17	in	in	ADP
ejpam-5479	61	18	a	a	DET
ejpam-5479	61	19	previous	previous	ADJ
ejpam-5479	61	20	article	article	NOUN
ejpam-5479	61	21	[	[	X
ejpam-5479	61	22	49	49	NUM
ejpam-5479	61	23	]	]	PUNCT
ejpam-5479	61	24	.	.	PUNCT
ejpam-5479	62	1	a	a	DET
ejpam-5479	62	2	complicated	complicate	VERB
ejpam-5479	62	3	averaging	averaging	NOUN
ejpam-5479	62	4	method	method	NOUN
ejpam-5479	62	5	was	be	AUX
ejpam-5479	62	6	used	use	VERB
ejpam-5479	62	7	to	to	PART
ejpam-5479	62	8	study	study	VERB
ejpam-5479	62	9	the	the	DET
ejpam-5479	62	10	forced	force	VERB
ejpam-5479	62	11	system	system	NOUN
ejpam-5479	62	12	’s	’s	PART
ejpam-5479	62	13	slow	slow	ADJ
ejpam-5479	62	14	and	and	CCONJ
ejpam-5479	62	15	fast	fast	ADJ
ejpam-5479	62	16	dynamics	dynamic	NOUN
ejpam-5479	62	17	.	.	PUNCT
ejpam-5479	63	1	the	the	DET
ejpam-5479	63	2	system	system	NOUN
ejpam-5479	63	3	under	under	ADP
ejpam-5479	63	4	consideration	consideration	NOUN
ejpam-5479	63	5	was	be	AUX
ejpam-5479	63	6	a	a	DET
ejpam-5479	63	7	one	one	NUM
ejpam-5479	63	8	-	-	PUNCT
ejpam-5479	63	9	equation	equation	NOUN
ejpam-5479	63	10	of	of	ADP
ejpam-5479	63	11	motion	motion	NOUN
ejpam-5479	63	12	model	model	NOUN
ejpam-5479	63	13	with	with	ADP
ejpam-5479	63	14	nonlinear	nonlinear	ADJ
ejpam-5479	63	15	restoration	restoration	NOUN
ejpam-5479	63	16	and	and	CCONJ
ejpam-5479	63	17	damping	damp	VERB
ejpam-5479	63	18	functions	function	NOUN
ejpam-5479	63	19	[	[	X
ejpam-5479	63	20	30	30	NUM
ejpam-5479	63	21	]	]	PUNCT
ejpam-5479	63	22	.	.	PUNCT
ejpam-5479	64	1	two	two	NUM
ejpam-5479	64	2	species	specie	NOUN
ejpam-5479	64	3	of	of	ADP
ejpam-5479	64	4	zooplankton	zooplankton	NOUN
ejpam-5479	64	5	and	and	CCONJ
ejpam-5479	64	6	one	one	NUM
ejpam-5479	64	7	phytoplankton	phytoplankton	NOUN
ejpam-5479	64	8	species	specie	NOUN
ejpam-5479	64	9	coexisted	coexist	VERB
ejpam-5479	64	10	under	under	ADP
ejpam-5479	64	11	certain	certain	ADJ
ejpam-5479	64	12	conditions	condition	NOUN
ejpam-5479	64	13	[	[	X
ejpam-5479	64	14	3	3	NUM
ejpam-5479	64	15	]	]	PUNCT
ejpam-5479	64	16	.	.	PUNCT
ejpam-5479	65	1	the	the	DET
ejpam-5479	65	2	exact	exact	ADJ
ejpam-5479	65	3	solutions	solution	NOUN
ejpam-5479	65	4	of	of	ADP
ejpam-5479	65	5	the	the	DET
ejpam-5479	65	6	complicated	complicated	ADJ
ejpam-5479	65	7	nonlinear	nonlinear	ADJ
ejpam-5479	65	8	odes	ode	NOUN
ejpam-5479	65	9	that	that	PRON
ejpam-5479	65	10	govern	govern	VERB
ejpam-5479	65	11	the	the	DET
ejpam-5479	65	12	dynamical	dynamical	ADJ
ejpam-5479	65	13	regulations	regulation	NOUN
ejpam-5479	65	14	generally	generally	ADV
ejpam-5479	65	15	seen	see	VERB
ejpam-5479	65	16	in	in	ADP
ejpam-5479	65	17	engineering	engineering	NOUN
ejpam-5479	65	18	and	and	CCONJ
ejpam-5479	65	19	physics	physics	NOUN
ejpam-5479	65	20	are	be	AUX
ejpam-5479	65	21	often	often	ADV
ejpam-5479	65	22	unknown	unknown	ADJ
ejpam-5479	65	23	.	.	PUNCT
ejpam-5479	66	1	traditional	traditional	ADJ
ejpam-5479	66	2	approaches	approach	NOUN
ejpam-5479	66	3	,	,	PUNCT
ejpam-5479	66	4	such	such	ADJ
ejpam-5479	66	5	as	as	ADP
ejpam-5479	66	6	numerical	numerical	ADJ
ejpam-5479	66	7	methods	method	NOUN
ejpam-5479	66	8	and	and	CCONJ
ejpam-5479	66	9	perturbation	perturbation	NOUN
ejpam-5479	66	10	techniques	technique	NOUN
ejpam-5479	66	11	,	,	PUNCT
ejpam-5479	66	12	are	be	AUX
ejpam-5479	66	13	utilized	utilize	VERB
ejpam-5479	66	14	to	to	PART
ejpam-5479	66	15	establish	establish	VERB
ejpam-5479	66	16	the	the	DET
ejpam-5479	66	17	precise	precise	ADJ
ejpam-5479	66	18	frequency	frequency	NOUN
ejpam-5479	66	19	-	-	PUNCT
ejpam-5479	66	20	amplitude	amplitude	NOUN
ejpam-5479	66	21	connection	connection	NOUN
ejpam-5479	66	22	and	and	CCONJ
ejpam-5479	66	23	predict	predict	VERB
ejpam-5479	66	24	the	the	DET
ejpam-5479	66	25	dynamic	dynamic	ADJ
ejpam-5479	66	26	reactions	reaction	NOUN
ejpam-5479	66	27	.	.	PUNCT
ejpam-5479	67	1	the	the	DET
ejpam-5479	67	2	complex	complex	ADJ
ejpam-5479	67	3	dynamics	dynamic	NOUN
ejpam-5479	67	4	of	of	ADP
ejpam-5479	67	5	systems	system	NOUN
ejpam-5479	67	6	can	can	AUX
ejpam-5479	67	7	be	be	AUX
ejpam-5479	67	8	better	well	ADV
ejpam-5479	67	9	understood	understand	VERB
ejpam-5479	67	10	with	with	ADP
ejpam-5479	67	11	the	the	DET
ejpam-5479	67	12	use	use	NOUN
ejpam-5479	67	13	of	of	ADP
ejpam-5479	67	14	these	these	DET
ejpam-5479	67	15	methods	method	NOUN
ejpam-5479	67	16	,	,	PUNCT
ejpam-5479	67	17	which	which	PRON
ejpam-5479	67	18	allow	allow	VERB
ejpam-5479	67	19	for	for	ADP
ejpam-5479	67	20	a	a	DET
ejpam-5479	67	21	thorough	thorough	ADJ
ejpam-5479	67	22	examination	examination	NOUN
ejpam-5479	67	23	of	of	ADP
ejpam-5479	67	24	quantitative	quantitative	ADJ
ejpam-5479	67	25	and	and	CCONJ
ejpam-5479	67	26	qualitative	qualitative	ADJ
ejpam-5479	67	27	aspects	aspect	NOUN
ejpam-5479	67	28	of	of	ADP
ejpam-5479	67	29	system	system	NOUN
ejpam-5479	67	30	behavior	behavior	NOUN
ejpam-5479	67	31	.	.	PUNCT
ejpam-5479	68	1	an	an	DET
ejpam-5479	68	2	excessive	excessive	ADJ
ejpam-5479	68	3	arrangement	arrangement	NOUN
ejpam-5479	68	4	of	of	ADP
ejpam-5479	68	5	studies	study	NOUN
ejpam-5479	68	6	has	have	AUX
ejpam-5479	68	7	been	be	AUX
ejpam-5479	68	8	conducted	conduct	VERB
ejpam-5479	68	9	on	on	ADP
ejpam-5479	68	10	the	the	DET
ejpam-5479	68	11	efficacy	efficacy	NOUN
ejpam-5479	68	12	and	and	CCONJ
ejpam-5479	68	13	broad	broad	ADJ
ejpam-5479	68	14	applicability	applicability	NOUN
ejpam-5479	68	15	of	of	ADP
ejpam-5479	68	16	this	this	DET
ejpam-5479	68	17	methodology	methodology	NOUN
ejpam-5479	68	18	[	[	X
ejpam-5479	68	19	28	28	NUM
ejpam-5479	68	20	,	,	PUNCT
ejpam-5479	68	21	41	41	NUM
ejpam-5479	68	22	,	,	PUNCT
ejpam-5479	68	23	43	43	NUM
ejpam-5479	68	24	,	,	PUNCT
ejpam-5479	68	25	52	52	NUM
ejpam-5479	68	26	]	]	PUNCT
ejpam-5479	68	27	.	.	PUNCT
ejpam-5479	69	1	as	as	SCONJ
ejpam-5479	69	2	mentioned	mention	VERB
ejpam-5479	69	3	earlier	early	ADV
ejpam-5479	69	4	,	,	PUNCT
ejpam-5479	69	5	the	the	DET
ejpam-5479	69	6	hff	hff	NOUN
ejpam-5479	69	7	was	be	AUX
ejpam-5479	69	8	played	play	VERB
ejpam-5479	69	9	a	a	DET
ejpam-5479	69	10	crucial	crucial	ADJ
ejpam-5479	69	11	role	role	NOUN
ejpam-5479	69	12	in	in	ADP
ejpam-5479	69	13	obtaining	obtain	VERB
ejpam-5479	69	14	closed	closed	ADJ
ejpam-5479	69	15	-	-	PUNCT
ejpam-5479	69	16	form	form	NOUN
ejpam-5479	69	17	analytical	analytical	ADJ
ejpam-5479	69	18	solutions	solution	NOUN
ejpam-5479	69	19	for	for	ADP
ejpam-5479	69	20	oscillators	oscillator	NOUN
ejpam-5479	69	21	,	,	PUNCT
ejpam-5479	69	22	especially	especially	ADV
ejpam-5479	69	23	those	those	PRON
ejpam-5479	69	24	using	use	VERB
ejpam-5479	69	25	the	the	DET
ejpam-5479	69	26	do	do	NOUN
ejpam-5479	69	27	[	[	X
ejpam-5479	69	28	45	45	NUM
ejpam-5479	69	29	]	]	PUNCT
ejpam-5479	69	30	.	.	PUNCT
ejpam-5479	70	1	the	the	DET
ejpam-5479	70	2	hff	hff	NOUN
ejpam-5479	70	3	formula	formula	NOUN
ejpam-5479	70	4	has	have	AUX
ejpam-5479	70	5	evolved	evolve	VERB
ejpam-5479	70	6	into	into	ADP
ejpam-5479	70	7	a	a	DET
ejpam-5479	70	8	powerful	powerful	ADJ
ejpam-5479	70	9	mathematical	mathematical	ADJ
ejpam-5479	70	10	instrument	instrument	NOUN
ejpam-5479	70	11	in	in	ADP
ejpam-5479	70	12	studying	study	VERB
ejpam-5479	70	13	nonlinear	nonlinear	ADJ
ejpam-5479	70	14	oscillators	oscillator	NOUN
ejpam-5479	70	15	with	with	ADP
ejpam-5479	70	16	periodic	periodic	ADJ
ejpam-5479	70	17	solutions	solution	NOUN
ejpam-5479	70	18	.	.	PUNCT
ejpam-5479	71	1	prof	prof	NOUN
ejpam-5479	71	2	.	.	PUNCT
ejpam-5479	72	1	he	he	PRON
ejpam-5479	72	2	gave	give	VERB
ejpam-5479	72	3	an	an	DET
ejpam-5479	72	4	innovative	innovative	ADJ
ejpam-5479	72	5	review	review	NOUN
ejpam-5479	72	6	paper	paper	NOUN
ejpam-5479	72	7	and	and	CCONJ
ejpam-5479	72	8	was	be	AUX
ejpam-5479	72	9	the	the	DET
ejpam-5479	72	10	first	first	ADJ
ejpam-5479	72	11	to	to	PART
ejpam-5479	72	12	present	present	VERB
ejpam-5479	72	13	it	it	PRON
ejpam-5479	72	14	[	[	X
ejpam-5479	72	15	32	32	NUM
ejpam-5479	72	16	]	]	PUNCT
ejpam-5479	72	17	.	.	PUNCT
ejpam-5479	73	1	the	the	DET
ejpam-5479	73	2	clarity	clarity	NOUN
ejpam-5479	73	3	and	and	CCONJ
ejpam-5479	73	4	empirical	empirical	ADJ
ejpam-5479	73	5	confirmation	confirmation	NOUN
ejpam-5479	73	6	of	of	ADP
ejpam-5479	73	7	this	this	DET
ejpam-5479	73	8	frequency	frequency	NOUN
ejpam-5479	73	9	formula	formula	NOUN
ejpam-5479	73	10	made	make	VERB
ejpam-5479	73	11	it	it	PRON
ejpam-5479	73	12	a	a	DET
ejpam-5479	73	13	fast	fast	ADJ
ejpam-5479	73	14	favorite	favorite	ADJ
ejpam-5479	73	15	among	among	ADP
ejpam-5479	73	16	engineers	engineer	NOUN
ejpam-5479	73	17	[	[	X
ejpam-5479	73	18	29	29	NUM
ejpam-5479	73	19	,	,	PUNCT
ejpam-5479	73	20	33	33	NUM
ejpam-5479	73	21	,	,	PUNCT
ejpam-5479	73	22	34	34	NUM
ejpam-5479	73	23	,	,	PUNCT
ejpam-5479	73	24	42	42	NUM
ejpam-5479	73	25	,	,	PUNCT
ejpam-5479	73	26	50	50	NUM
ejpam-5479	73	27	,	,	PUNCT
ejpam-5479	73	28	51	51	NUM
ejpam-5479	73	29	,	,	PUNCT
ejpam-5479	73	30	56	56	NUM
ejpam-5479	73	31	,	,	PUNCT
ejpam-5479	73	32	57	57	NUM
ejpam-5479	73	33	]	]	PUNCT
ejpam-5479	73	34	.	.	PUNCT
ejpam-5479	74	1	hff	hff	PROPN
ejpam-5479	74	2	has	have	AUX
ejpam-5479	74	3	been	be	AUX
ejpam-5479	74	4	fine	fine	ADV
ejpam-5479	74	5	-	-	PUNCT
ejpam-5479	74	6	tuned	tune	VERB
ejpam-5479	74	7	through	through	ADP
ejpam-5479	74	8	the	the	DET
ejpam-5479	74	9	years	year	NOUN
ejpam-5479	74	10	,	,	PUNCT
ejpam-5479	74	11	leading	lead	VERB
ejpam-5479	74	12	to	to	ADP
ejpam-5479	74	13	even	even	ADV
ejpam-5479	74	14	greater	great	ADJ
ejpam-5479	74	15	accuracy	accuracy	NOUN
ejpam-5479	74	16	,	,	PUNCT
ejpam-5479	74	17	as	as	SCONJ
ejpam-5479	74	18	was	be	AUX
ejpam-5479	74	19	previously	previously	ADV
ejpam-5479	74	20	seen	see	VERB
ejpam-5479	74	21	[	[	X
ejpam-5479	74	22	12	12	NUM
ejpam-5479	74	23	,	,	PUNCT
ejpam-5479	74	24	35	35	NUM
ejpam-5479	74	25	,	,	PUNCT
ejpam-5479	74	26	38	38	NUM
ejpam-5479	74	27	]	]	PUNCT
ejpam-5479	74	28	.	.	PUNCT
ejpam-5479	75	1	furthermore	furthermore	ADV
ejpam-5479	75	2	,	,	PUNCT
ejpam-5479	75	3	as	as	SCONJ
ejpam-5479	75	4	mentioned	mention	VERB
ejpam-5479	75	5	earlier	early	ADV
ejpam-5479	75	6	,	,	PUNCT
ejpam-5479	75	7	the	the	DET
ejpam-5479	75	8	scope	scope	NOUN
ejpam-5479	75	9	of	of	ADP
ejpam-5479	75	10	this	this	DET
ejpam-5479	75	11	frequency	frequency	NOUN
ejpam-5479	75	12	method	method	NOUN
ejpam-5479	75	13	’s	’s	PART
ejpam-5479	75	14	utility	utility	NOUN
ejpam-5479	75	15	has	have	AUX
ejpam-5479	75	16	expanded	expand	VERB
ejpam-5479	75	17	to	to	PART
ejpam-5479	75	18	include	include	VERB
ejpam-5479	75	19	fractal	fractal	ADJ
ejpam-5479	75	20	oscillators	oscillator	NOUN
ejpam-5479	75	21	[	[	X
ejpam-5479	75	22	53	53	NUM
ejpam-5479	75	23	]	]	PUNCT
ejpam-5479	75	24	.	.	PUNCT
ejpam-5479	76	1	in	in	ADP
ejpam-5479	76	2	the	the	DET
ejpam-5479	76	3	study	study	NOUN
ejpam-5479	76	4	of	of	ADP
ejpam-5479	76	5	nonlinear	nonlinear	ADJ
ejpam-5479	76	6	oscillatory	oscillatory	ADJ
ejpam-5479	76	7	systems	system	NOUN
ejpam-5479	76	8	,	,	PUNCT
ejpam-5479	76	9	the	the	DET
ejpam-5479	76	10	npa	npa	NOUN
ejpam-5479	76	11	stands	stand	VERB
ejpam-5479	76	12	in	in	ADP
ejpam-5479	76	13	unambiguous	unambiguous	ADJ
ejpam-5479	76	14	contrast	contrast	NOUN
ejpam-5479	76	15	to	to	ADP
ejpam-5479	76	16	traditional	traditional	ADJ
ejpam-5479	76	17	perturbative	perturbative	ADJ
ejpam-5479	76	18	approaches	approach	NOUN
ejpam-5479	76	19	.	.	PUNCT
ejpam-5479	77	1	this	this	DET
ejpam-5479	77	2	method	method	NOUN
ejpam-5479	77	3	is	be	AUX
ejpam-5479	77	4	a	a	DET
ejpam-5479	77	5	strong	strong	ADJ
ejpam-5479	77	6	mathematical	mathematical	ADJ
ejpam-5479	77	7	instrument	instrument	NOUN
ejpam-5479	77	8	that	that	PRON
ejpam-5479	77	9	can	can	AUX
ejpam-5479	77	10	deal	deal	VERB
ejpam-5479	77	11	with	with	ADP
ejpam-5479	77	12	many	many	ADJ
ejpam-5479	77	13	parameter	parameter	NOUN
ejpam-5479	77	14	regimes	regime	NOUN
ejpam-5479	77	15	,	,	PUNCT
ejpam-5479	77	16	particularly	particularly	ADV
ejpam-5479	77	17	those	those	PRON
ejpam-5479	77	18	with	with	ADP
ejpam-5479	77	19	strong	strong	ADJ
ejpam-5479	77	20	nonlinearity	nonlinearity	NOUN
ejpam-5479	77	21	.	.	PUNCT
ejpam-5479	78	1	an	an	DET
ejpam-5479	78	2	important	important	ADJ
ejpam-5479	78	3	method	method	NOUN
ejpam-5479	78	4	for	for	ADP
ejpam-5479	78	5	obtaining	obtain	VERB
ejpam-5479	78	6	analytical	analytical	ADJ
ejpam-5479	78	7	approximations	approximation	NOUN
ejpam-5479	78	8	in	in	ADP
ejpam-5479	78	9	research	research	NOUN
ejpam-5479	78	10	on	on	ADP
ejpam-5479	78	11	nonlinear	nonlinear	PROPN
ejpam-5479	78	12	k.	k.	PROPN
ejpam-5479	78	13	alluhydan	alluhydan	PROPN
ejpam-5479	78	14	,	,	PUNCT
ejpam-5479	78	15	g.	g.	PROPN
ejpam-5479	78	16	m	m	PROPN
ejpam-5479	78	17	moatimid	moatimid	PROPN
ejpam-5479	78	18	,	,	PUNCT
ejpam-5479	78	19	t.	t.	PROPN
ejpam-5479	78	20	s.	s.	PROPN
ejpam-5479	78	21	amer	amer	PROPN
ejpam-5479	78	22	/	/	SYM
ejpam-5479	78	23	eur	eur	PROPN
ejpam-5479	78	24	.	.	PUNCT
ejpam-5479	79	1	j.	j.	PROPN
ejpam-5479	79	2	pure	pure	PROPN
ejpam-5479	79	3	appl	appl	PROPN
ejpam-5479	79	4	.	.	PROPN
ejpam-5479	79	5	math	math	PROPN
ejpam-5479	79	6	,	,	PUNCT
ejpam-5479	79	7	17	17	NUM
ejpam-5479	79	8	(	(	PUNCT
ejpam-5479	79	9	4	4	NUM
ejpam-5479	79	10	)	)	PUNCT
ejpam-5479	79	11	(	(	PUNCT
ejpam-5479	79	12	2024	2024	NUM
ejpam-5479	79	13	)	)	PUNCT
ejpam-5479	79	14	,	,	PUNCT
ejpam-5479	79	15	3185	3185	NUM
ejpam-5479	79	16	-	-	SYM
ejpam-5479	79	17	3208	3208	NUM
ejpam-5479	79	18	3188	3188	NUM
ejpam-5479	79	19	oscillators	oscillator	NOUN
ejpam-5479	79	20	was	be	AUX
ejpam-5479	79	21	employed	employ	VERB
ejpam-5479	79	22	.	.	PUNCT
ejpam-5479	80	1	the	the	DET
ejpam-5479	80	2	primary	primary	ADJ
ejpam-5479	80	3	goal	goal	NOUN
ejpam-5479	80	4	of	of	ADP
ejpam-5479	80	5	the	the	DET
ejpam-5479	80	6	npa	npa	NOUN
ejpam-5479	80	7	is	be	AUX
ejpam-5479	80	8	to	to	PART
ejpam-5479	80	9	reduce	reduce	VERB
ejpam-5479	80	10	the	the	DET
ejpam-5479	80	11	complexity	complexity	NOUN
ejpam-5479	80	12	of	of	ADP
ejpam-5479	80	13	the	the	DET
ejpam-5479	80	14	nonlinear	nonlinear	ADJ
ejpam-5479	80	15	model	model	NOUN
ejpam-5479	80	16	to	to	ADP
ejpam-5479	80	17	a	a	DET
ejpam-5479	80	18	more	more	ADV
ejpam-5479	80	19	manageable	manageable	ADJ
ejpam-5479	80	20	level	level	NOUN
ejpam-5479	80	21	so	so	SCONJ
ejpam-5479	80	22	that	that	SCONJ
ejpam-5479	80	23	the	the	DET
ejpam-5479	80	24	solutions	solution	NOUN
ejpam-5479	80	25	can	can	AUX
ejpam-5479	80	26	be	be	AUX
ejpam-5479	80	27	clearly	clearly	ADV
ejpam-5479	80	28	specified	specify	VERB
ejpam-5479	80	29	.	.	PUNCT
ejpam-5479	81	1	this	this	PRON
ejpam-5479	81	2	will	will	AUX
ejpam-5479	81	3	allow	allow	VERB
ejpam-5479	81	4	for	for	ADP
ejpam-5479	81	5	a	a	DET
ejpam-5479	81	6	more	more	ADV
ejpam-5479	81	7	accurate	accurate	ADJ
ejpam-5479	81	8	approximation	approximation	NOUN
ejpam-5479	81	9	of	of	ADP
ejpam-5479	81	10	the	the	DET
ejpam-5479	81	11	original	original	ADJ
ejpam-5479	81	12	system	system	NOUN
ejpam-5479	81	13	’s	’s	PART
ejpam-5479	81	14	behavior	behavior	NOUN
ejpam-5479	81	15	[	[	X
ejpam-5479	81	16	10	10	NUM
ejpam-5479	81	17	,	,	PUNCT
ejpam-5479	81	18	11	11	NUM
ejpam-5479	81	19	,	,	PUNCT
ejpam-5479	81	20	13–19	13–19	NUM
ejpam-5479	81	21	,	,	PUNCT
ejpam-5479	81	22	22–27	22–27	NUM
ejpam-5479	81	23	]	]	PUNCT
ejpam-5479	81	24	.	.	PUNCT
ejpam-5479	82	1	the	the	DET
ejpam-5479	82	2	goal	goal	NOUN
ejpam-5479	82	3	of	of	ADP
ejpam-5479	82	4	this	this	DET
ejpam-5479	82	5	simplification	simplification	NOUN
ejpam-5479	82	6	is	be	AUX
ejpam-5479	82	7	to	to	PART
ejpam-5479	82	8	reduce	reduce	VERB
ejpam-5479	82	9	the	the	DET
ejpam-5479	82	10	average	average	ADJ
ejpam-5479	82	11	difference	difference	NOUN
ejpam-5479	82	12	between	between	ADP
ejpam-5479	82	13	the	the	DET
ejpam-5479	82	14	two	two	NUM
ejpam-5479	82	15	systems	system	NOUN
ejpam-5479	82	16	by	by	ADP
ejpam-5479	82	17	making	make	VERB
ejpam-5479	82	18	the	the	DET
ejpam-5479	82	19	transformation	transformation	NOUN
ejpam-5479	82	20	from	from	ADP
ejpam-5479	82	21	a	a	DET
ejpam-5479	82	22	nonlinear	nonlinear	NOUN
ejpam-5479	82	23	to	to	ADP
ejpam-5479	82	24	a	a	DET
ejpam-5479	82	25	linear	linear	ADJ
ejpam-5479	82	26	form	form	NOUN
ejpam-5479	82	27	of	of	ADP
ejpam-5479	82	28	the	the	DET
ejpam-5479	82	29	equation	equation	NOUN
ejpam-5479	82	30	.	.	PUNCT
ejpam-5479	83	1	accordingly	accordingly	ADV
ejpam-5479	83	2	,	,	PUNCT
ejpam-5479	83	3	departing	depart	VERB
ejpam-5479	83	4	from	from	ADP
ejpam-5479	83	5	perturbation	perturbation	NOUN
ejpam-5479	83	6	techniques	technique	NOUN
ejpam-5479	83	7	’	'	PUNCT
ejpam-5479	83	8	repetitive	repetitive	ADJ
ejpam-5479	83	9	refining	refining	NOUN
ejpam-5479	83	10	,	,	PUNCT
ejpam-5479	83	11	the	the	DET
ejpam-5479	83	12	npa	npa	NOUN
ejpam-5479	83	13	offered	offer	VERB
ejpam-5479	83	14	a	a	DET
ejpam-5479	83	15	fresh	fresh	ADJ
ejpam-5479	83	16	viewpoint	viewpoint	NOUN
ejpam-5479	83	17	.	.	PUNCT
ejpam-5479	84	1	the	the	DET
ejpam-5479	84	2	goal	goal	NOUN
ejpam-5479	84	3	of	of	ADP
ejpam-5479	84	4	the	the	DET
ejpam-5479	84	5	npa	npa	NOUN
ejpam-5479	84	6	is	be	AUX
ejpam-5479	84	7	to	to	PART
ejpam-5479	84	8	understand	understand	VERB
ejpam-5479	84	9	the	the	DET
ejpam-5479	84	10	details	detail	NOUN
ejpam-5479	84	11	of	of	ADP
ejpam-5479	84	12	nonlinear	nonlinear	ADJ
ejpam-5479	84	13	systems	system	NOUN
ejpam-5479	84	14	on	on	ADP
ejpam-5479	84	15	their	their	PRON
ejpam-5479	84	16	own	own	ADJ
ejpam-5479	84	17	,	,	PUNCT
ejpam-5479	84	18	without	without	ADP
ejpam-5479	84	19	relying	rely	VERB
ejpam-5479	84	20	on	on	ADP
ejpam-5479	84	21	small	small	ADJ
ejpam-5479	84	22	changes	change	NOUN
ejpam-5479	84	23	from	from	ADP
ejpam-5479	84	24	a	a	DET
ejpam-5479	84	25	known	know	VERB
ejpam-5479	84	26	solution	solution	NOUN
ejpam-5479	84	27	.	.	PUNCT
ejpam-5479	85	1	this	this	DET
ejpam-5479	85	2	method	method	NOUN
ejpam-5479	85	3	can	can	AUX
ejpam-5479	85	4	reveal	reveal	VERB
ejpam-5479	85	5	insights	insight	NOUN
ejpam-5479	85	6	into	into	ADP
ejpam-5479	85	7	a	a	DET
ejpam-5479	85	8	broader	broad	ADJ
ejpam-5479	85	9	range	range	NOUN
ejpam-5479	85	10	of	of	ADP
ejpam-5479	85	11	system	system	NOUN
ejpam-5479	85	12	behavior	behavior	NOUN
ejpam-5479	85	13	,	,	PUNCT
ejpam-5479	85	14	unconstrained	unconstraine	VERB
ejpam-5479	85	15	by	by	ADP
ejpam-5479	85	16	the	the	DET
ejpam-5479	85	17	constraints	constraint	NOUN
ejpam-5479	85	18	of	of	ADP
ejpam-5479	85	19	minor	minor	ADJ
ejpam-5479	85	20	disturbances	disturbance	NOUN
ejpam-5479	85	21	.	.	PUNCT
ejpam-5479	86	1	the	the	DET
ejpam-5479	86	2	ability	ability	NOUN
ejpam-5479	86	3	to	to	PART
ejpam-5479	86	4	probe	probe	VERB
ejpam-5479	86	5	dynamics	dynamic	NOUN
ejpam-5479	86	6	that	that	PRON
ejpam-5479	86	7	may	may	AUX
ejpam-5479	86	8	be	be	AUX
ejpam-5479	86	9	inaccessible	inaccessible	ADJ
ejpam-5479	86	10	or	or	CCONJ
ejpam-5479	86	11	concealed	conceal	VERB
ejpam-5479	86	12	by	by	ADP
ejpam-5479	86	13	more	more	ADJ
ejpam-5479	86	14	traditional	traditional	ADJ
ejpam-5479	86	15	perturbation	perturbation	NOUN
ejpam-5479	86	16	approaches	approach	NOUN
ejpam-5479	86	17	makes	make	VERB
ejpam-5479	86	18	this	this	DET
ejpam-5479	86	19	breadth	breadth	NOUN
ejpam-5479	86	20	all	all	DET
ejpam-5479	86	21	the	the	DET
ejpam-5479	86	22	more	more	ADV
ejpam-5479	86	23	important	important	ADJ
ejpam-5479	86	24	.	.	PUNCT
ejpam-5479	87	1	a	a	DET
ejpam-5479	87	2	two	two	NUM
ejpam-5479	87	3	-	-	PUNCT
ejpam-5479	87	4	dimensional	dimensional	ADJ
ejpam-5479	87	5	asymmetric	asymmetric	ADJ
ejpam-5479	87	6	system	system	NOUN
ejpam-5479	87	7	was	be	AUX
ejpam-5479	87	8	examined	examine	VERB
ejpam-5479	87	9	[	[	PUNCT
ejpam-5479	87	10	6	6	NUM
ejpam-5479	87	11	]	]	PUNCT
ejpam-5479	87	12	.	.	PUNCT
ejpam-5479	88	1	the	the	DET
ejpam-5479	88	2	system	system	NOUN
ejpam-5479	88	3	’s	’s	PART
ejpam-5479	88	4	equations	equation	NOUN
ejpam-5479	88	5	of	of	ADP
ejpam-5479	88	6	motion	motion	NOUN
ejpam-5479	88	7	were	be	AUX
ejpam-5479	88	8	generated	generate	VERB
ejpam-5479	88	9	and	and	CCONJ
ejpam-5479	88	10	solved	solve	VERB
ejpam-5479	88	11	analytically	analytically	ADV
ejpam-5479	88	12	.	.	PUNCT
ejpam-5479	89	1	a	a	DET
ejpam-5479	89	2	nonlinear	nonlinear	ADJ
ejpam-5479	89	3	oscillator	oscillator	NOUN
ejpam-5479	89	4	equation	equation	NOUN
ejpam-5479	89	5	featuring	feature	VERB
ejpam-5479	89	6	two	two	NUM
ejpam-5479	89	7	dominant	dominant	ADJ
ejpam-5479	89	8	linear	linear	PROPN
ejpam-5479	89	9	terms	term	NOUN
ejpam-5479	89	10	was	be	AUX
ejpam-5479	89	11	analyzed	analyze	VERB
ejpam-5479	89	12	[	[	X
ejpam-5479	89	13	1	1	NUM
ejpam-5479	89	14	]	]	PUNCT
ejpam-5479	89	15	.	.	PUNCT
ejpam-5479	90	1	an	an	DET
ejpam-5479	90	2	approximate	approximate	ADJ
ejpam-5479	90	3	solution	solution	NOUN
ejpam-5479	90	4	was	be	AUX
ejpam-5479	90	5	derived	derive	VERB
ejpam-5479	90	6	with	with	ADP
ejpam-5479	90	7	the	the	DET
ejpam-5479	90	8	power	power	NOUN
ejpam-5479	90	9	series	series	PROPN
ejpam-5479	90	10	method	method	PROPN
ejpam-5479	90	11	.	.	PUNCT
ejpam-5479	91	1	additionally	additionally	ADV
ejpam-5479	91	2	,	,	PUNCT
ejpam-5479	91	3	by	by	ADP
ejpam-5479	91	4	including	include	VERB
ejpam-5479	91	5	a	a	DET
ejpam-5479	91	6	parameter	parameter	NOUN
ejpam-5479	91	7	into	into	ADP
ejpam-5479	91	8	the	the	DET
ejpam-5479	91	9	original	original	ADJ
ejpam-5479	91	10	equation	equation	NOUN
ejpam-5479	91	11	,	,	PUNCT
ejpam-5479	91	12	we	we	PRON
ejpam-5479	91	13	identify	identify	VERB
ejpam-5479	91	14	the	the	DET
ejpam-5479	91	15	fixed	fix	VERB
ejpam-5479	91	16	points	point	NOUN
ejpam-5479	91	17	of	of	ADP
ejpam-5479	91	18	the	the	DET
ejpam-5479	91	19	altered	alter	VERB
ejpam-5479	91	20	nonlinear	nonlinear	PROPN
ejpam-5479	91	21	oscillator	oscillator	NOUN
ejpam-5479	91	22	equation	equation	NOUN
ejpam-5479	91	23	and	and	CCONJ
ejpam-5479	91	24	conduct	conduct	VERB
ejpam-5479	91	25	a	a	DET
ejpam-5479	91	26	stability	stability	NOUN
ejpam-5479	91	27	analysis	analysis	NOUN
ejpam-5479	91	28	of	of	ADP
ejpam-5479	91	29	these	these	DET
ejpam-5479	91	30	fixed	fix	VERB
ejpam-5479	91	31	points	point	NOUN
ejpam-5479	91	32	.	.	PUNCT
ejpam-5479	92	1	the	the	DET
ejpam-5479	92	2	periodic	periodic	ADJ
ejpam-5479	92	3	motion	motion	NOUN
ejpam-5479	92	4	of	of	ADP
ejpam-5479	92	5	the	the	DET
ejpam-5479	92	6	micro	micro	ADJ
ejpam-5479	92	7	-	-	ADJ
ejpam-5479	92	8	electro	electro	ADJ
ejpam-5479	92	9	-	-	PUNCT
ejpam-5479	92	10	mechanical	mechanical	ADJ
ejpam-5479	92	11	system	system	NOUN
ejpam-5479	92	12	(	(	PUNCT
ejpam-5479	92	13	mems	mem	NOUN
ejpam-5479	92	14	)	)	PUNCT
ejpam-5479	92	15	was	be	AUX
ejpam-5479	92	16	analyzed	analyze	VERB
ejpam-5479	92	17	[	[	X
ejpam-5479	92	18	37	37	NUM
ejpam-5479	92	19	]	]	PUNCT
ejpam-5479	92	20	.	.	PUNCT
ejpam-5479	93	1	a	a	DET
ejpam-5479	93	2	novel	novel	ADJ
ejpam-5479	93	3	approach	approach	NOUN
ejpam-5479	93	4	using	use	VERB
ejpam-5479	93	5	polyvinylidene	polyvinylidene	NOUN
ejpam-5479	93	6	fluoride	fluoride	NOUN
ejpam-5479	93	7	unsmooth	unsmooth	ADJ
ejpam-5479	93	8	nanofibers	nanofiber	NOUN
ejpam-5479	93	9	to	to	PART
ejpam-5479	93	10	transfer	transfer	VERB
ejpam-5479	93	11	electronic	electronic	ADJ
ejpam-5479	93	12	current	current	NOUN
ejpam-5479	93	13	was	be	AUX
ejpam-5479	93	14	provided	provide	VERB
ejpam-5479	93	15	[	[	X
ejpam-5479	93	16	39	39	NUM
ejpam-5479	93	17	]	]	PUNCT
ejpam-5479	93	18	.	.	PUNCT
ejpam-5479	94	1	the	the	DET
ejpam-5479	94	2	unique	unique	ADJ
ejpam-5479	94	3	unsmooth	unsmooth	ADJ
ejpam-5479	94	4	surface	surface	NOUN
ejpam-5479	94	5	of	of	ADP
ejpam-5479	94	6	these	these	DET
ejpam-5479	94	7	nanofibers	nanofiber	NOUN
ejpam-5479	94	8	provides	provide	VERB
ejpam-5479	94	9	a	a	DET
ejpam-5479	94	10	high	high	ADJ
ejpam-5479	94	11	surface	surface	NOUN
ejpam-5479	94	12	energy	energy	NOUN
ejpam-5479	94	13	(	(	PUNCT
ejpam-5479	94	14	geometrical	geometrical	ADJ
ejpam-5479	94	15	potential	potential	NOUN
ejpam-5479	94	16	)	)	PUNCT
ejpam-5479	94	17	,	,	PUNCT
ejpam-5479	94	18	making	make	VERB
ejpam-5479	94	19	them	they	PRON
ejpam-5479	94	20	highly	highly	ADV
ejpam-5479	94	21	sensitive	sensitive	ADJ
ejpam-5479	94	22	to	to	ADP
ejpam-5479	94	23	microorganisms	microorganism	NOUN
ejpam-5479	94	24	(	(	PUNCT
ejpam-5479	94	25	e.g.	e.g.	ADV
ejpam-5479	94	26	,	,	PUNCT
ejpam-5479	94	27	viruses	virus	NOUN
ejpam-5479	94	28	)	)	PUNCT
ejpam-5479	94	29	absorbed	absorb	VERB
ejpam-5479	94	30	on	on	ADP
ejpam-5479	94	31	their	their	PRON
ejpam-5479	94	32	surface	surface	NOUN
ejpam-5479	94	33	.	.	PUNCT
ejpam-5479	95	1	in	in	ADP
ejpam-5479	95	2	light	light	NOUN
ejpam-5479	95	3	of	of	ADP
ejpam-5479	95	4	the	the	DET
ejpam-5479	95	5	significance	significance	NOUN
ejpam-5479	95	6	of	of	ADP
ejpam-5479	95	7	the	the	DET
ejpam-5479	95	8	aforementioned	aforementioned	ADJ
ejpam-5479	95	9	aspects	aspect	NOUN
ejpam-5479	95	10	,	,	PUNCT
ejpam-5479	95	11	the	the	DET
ejpam-5479	95	12	present	present	ADJ
ejpam-5479	95	13	work	work	NOUN
ejpam-5479	95	14	emphasizes	emphasize	VERB
ejpam-5479	95	15	analyzing	analyze	VERB
ejpam-5479	95	16	the	the	DET
ejpam-5479	95	17	movement	movement	NOUN
ejpam-5479	95	18	of	of	ADP
ejpam-5479	95	19	an	an	DET
ejpam-5479	95	20	sp	sp	NOUN
ejpam-5479	95	21	that	that	PRON
ejpam-5479	95	22	is	be	AUX
ejpam-5479	95	23	connected	connect	VERB
ejpam-5479	95	24	to	to	ADP
ejpam-5479	95	25	a	a	DET
ejpam-5479	95	26	rolling	rolling	ADJ
ejpam-5479	95	27	wheel	wheel	NOUN
ejpam-5479	95	28	and	and	CCONJ
ejpam-5479	95	29	linked	link	VERB
ejpam-5479	95	30	by	by	ADP
ejpam-5479	95	31	a	a	DET
ejpam-5479	95	32	light	light	ADJ
ejpam-5479	95	33	spring	spring	NOUN
ejpam-5479	95	34	.	.	PUNCT
ejpam-5479	96	1	this	this	DET
ejpam-5479	96	2	topic	topic	NOUN
ejpam-5479	96	3	is	be	AUX
ejpam-5479	96	4	motivated	motivate	VERB
ejpam-5479	96	5	due	due	ADP
ejpam-5479	96	6	to	to	ADP
ejpam-5479	96	7	the	the	DET
ejpam-5479	96	8	prospective	prospective	ADJ
ejpam-5479	96	9	implementations	implementation	NOUN
ejpam-5479	96	10	of	of	ADP
ejpam-5479	96	11	the	the	DET
ejpam-5479	96	12	sp	sp	NOUN
ejpam-5479	96	13	in	in	ADP
ejpam-5479	96	14	physics	physics	NOUN
ejpam-5479	96	15	,	,	PUNCT
ejpam-5479	96	16	manufacturing	manufacturing	NOUN
ejpam-5479	96	17	,	,	PUNCT
ejpam-5479	96	18	and	and	CCONJ
ejpam-5479	96	19	practical	practical	ADJ
ejpam-5479	96	20	mechanisms	mechanism	NOUN
ejpam-5479	96	21	.	.	PUNCT
ejpam-5479	97	1	a	a	DET
ejpam-5479	97	2	classic	classic	ADJ
ejpam-5479	97	3	experiment	experiment	NOUN
ejpam-5479	97	4	involving	involve	VERB
ejpam-5479	97	5	a	a	DET
ejpam-5479	97	6	light	light	ADJ
ejpam-5479	97	7	spring	spring	NOUN
ejpam-5479	97	8	attached	attach	VERB
ejpam-5479	97	9	to	to	ADP
ejpam-5479	97	10	a	a	DET
ejpam-5479	97	11	rolling	rolling	ADJ
ejpam-5479	97	12	wheel	wheel	NOUN
ejpam-5479	97	13	,	,	PUNCT
ejpam-5479	97	14	followed	follow	VERB
ejpam-5479	97	15	by	by	ADP
ejpam-5479	97	16	a	a	DET
ejpam-5479	97	17	sp	sp	NOUN
ejpam-5479	97	18	,	,	PUNCT
ejpam-5479	97	19	can	can	AUX
ejpam-5479	97	20	be	be	AUX
ejpam-5479	97	21	used	use	VERB
ejpam-5479	97	22	to	to	PART
ejpam-5479	97	23	investigate	investigate	VERB
ejpam-5479	97	24	various	various	ADJ
ejpam-5479	97	25	physical	physical	ADJ
ejpam-5479	97	26	phenomena	phenomenon	NOUN
ejpam-5479	97	27	.	.	PUNCT
ejpam-5479	98	1	here	here	ADV
ejpam-5479	98	2	are	be	AUX
ejpam-5479	98	3	some	some	DET
ejpam-5479	98	4	specific	specific	ADJ
ejpam-5479	98	5	examples	example	NOUN
ejpam-5479	98	6	:	:	PUNCT
ejpam-5479	99	1	1	1	X
ejpam-5479	99	2	.	.	X
ejpam-5479	99	3	this	this	DET
ejpam-5479	99	4	model	model	NOUN
ejpam-5479	99	5	is	be	AUX
ejpam-5479	99	6	useful	useful	ADJ
ejpam-5479	99	7	for	for	ADP
ejpam-5479	99	8	studying	study	VERB
ejpam-5479	99	9	oscillations	oscillation	NOUN
ejpam-5479	99	10	that	that	PRON
ejpam-5479	99	11	involve	involve	VERB
ejpam-5479	99	12	both	both	DET
ejpam-5479	99	13	a	a	DET
ejpam-5479	99	14	spring	spring	NOUN
ejpam-5479	99	15	’s	’s	NOUN
ejpam-5479	99	16	restoring	restore	VERB
ejpam-5479	99	17	force	force	NOUN
ejpam-5479	99	18	and	and	CCONJ
ejpam-5479	99	19	the	the	DET
ejpam-5479	99	20	rotational	rotational	ADJ
ejpam-5479	99	21	dynamics	dynamic	NOUN
ejpam-5479	99	22	introduced	introduce	VERB
ejpam-5479	99	23	by	by	ADP
ejpam-5479	99	24	a	a	DET
ejpam-5479	99	25	rolling	rolling	ADJ
ejpam-5479	99	26	wheel	wheel	NOUN
ejpam-5479	99	27	.	.	PUNCT
ejpam-5479	100	1	the	the	DET
ejpam-5479	100	2	sp	sp	NOUN
ejpam-5479	100	3	adds	add	VERB
ejpam-5479	100	4	an	an	DET
ejpam-5479	100	5	additional	additional	ADJ
ejpam-5479	100	6	degree	degree	NOUN
ejpam-5479	100	7	of	of	ADP
ejpam-5479	100	8	freedom	freedom	NOUN
ejpam-5479	100	9	,	,	PUNCT
ejpam-5479	100	10	making	make	VERB
ejpam-5479	100	11	the	the	DET
ejpam-5479	100	12	system	system	NOUN
ejpam-5479	100	13	more	more	ADV
ejpam-5479	100	14	complex	complex	ADJ
ejpam-5479	100	15	and	and	CCONJ
ejpam-5479	100	16	enhancing	enhance	VERB
ejpam-5479	100	17	its	its	PRON
ejpam-5479	100	18	usefulness	usefulness	NOUN
ejpam-5479	100	19	for	for	ADP
ejpam-5479	100	20	studying	study	VERB
ejpam-5479	100	21	multi	multi	ADJ
ejpam-5479	100	22	-	-	ADJ
ejpam-5479	100	23	mode	mode	ADJ
ejpam-5479	100	24	oscillations	oscillation	NOUN
ejpam-5479	100	25	.	.	PUNCT
ejpam-5479	101	1	2	2	X
ejpam-5479	101	2	.	.	X
ejpam-5479	101	3	by	by	ADP
ejpam-5479	101	4	carefully	carefully	ADV
ejpam-5479	101	5	examining	examine	VERB
ejpam-5479	101	6	the	the	DET
ejpam-5479	101	7	system	system	NOUN
ejpam-5479	101	8	,	,	PUNCT
ejpam-5479	101	9	investigators	investigator	NOUN
ejpam-5479	101	10	can	can	AUX
ejpam-5479	101	11	investigate	investigate	VERB
ejpam-5479	101	12	into	into	ADP
ejpam-5479	101	13	the	the	DET
ejpam-5479	101	14	preservation	preservation	NOUN
ejpam-5479	101	15	of	of	ADP
ejpam-5479	101	16	energy	energy	NOUN
ejpam-5479	101	17	in	in	ADP
ejpam-5479	101	18	a	a	DET
ejpam-5479	101	19	system	system	NOUN
ejpam-5479	101	20	that	that	PRON
ejpam-5479	101	21	involves	involve	VERB
ejpam-5479	101	22	both	both	CCONJ
ejpam-5479	101	23	rotational	rotational	ADJ
ejpam-5479	101	24	and	and	CCONJ
ejpam-5479	101	25	translational	translational	ADJ
ejpam-5479	101	26	motion	motion	NOUN
ejpam-5479	101	27	.	.	PUNCT
ejpam-5479	102	1	the	the	DET
ejpam-5479	102	2	sp	sp	ADP
ejpam-5479	102	3	and	and	CCONJ
ejpam-5479	102	4	wheel	wheel	NOUN
ejpam-5479	102	5	enable	enable	VERB
ejpam-5479	102	6	the	the	DET
ejpam-5479	102	7	exploration	exploration	NOUN
ejpam-5479	102	8	of	of	ADP
ejpam-5479	102	9	how	how	SCONJ
ejpam-5479	102	10	potential	potential	ADJ
ejpam-5479	102	11	and	and	CCONJ
ejpam-5479	102	12	kinetic	kinetic	ADJ
ejpam-5479	102	13	energy	energy	NOUN
ejpam-5479	102	14	are	be	AUX
ejpam-5479	102	15	exchanged	exchange	VERB
ejpam-5479	102	16	within	within	ADP
ejpam-5479	102	17	the	the	DET
ejpam-5479	102	18	system	system	NOUN
ejpam-5479	102	19	.	.	PUNCT
ejpam-5479	103	1	3	3	X
ejpam-5479	103	2	.	.	PUNCT
ejpam-5479	103	3	this	this	DET
ejpam-5479	103	4	circumstance	circumstance	NOUN
ejpam-5479	103	5	can	can	AUX
ejpam-5479	103	6	be	be	AUX
ejpam-5479	103	7	expanded	expand	VERB
ejpam-5479	103	8	to	to	PART
ejpam-5479	103	9	encompass	encompass	VERB
ejpam-5479	103	10	damping	damp	VERB
ejpam-5479	103	11	forces	force	NOUN
ejpam-5479	103	12	or	or	CCONJ
ejpam-5479	103	13	external	external	ADJ
ejpam-5479	103	14	driving	drive	VERB
ejpam-5479	103	15	forces	force	NOUN
ejpam-5479	103	16	to	to	PART
ejpam-5479	103	17	examine	examine	VERB
ejpam-5479	103	18	more	more	ADV
ejpam-5479	103	19	intricate	intricate	ADJ
ejpam-5479	103	20	phenomena	phenomenon	NOUN
ejpam-5479	103	21	such	such	ADJ
ejpam-5479	103	22	as	as	ADP
ejpam-5479	103	23	resonance	resonance	NOUN
ejpam-5479	103	24	,	,	PUNCT
ejpam-5479	103	25	damping	damp	VERB
ejpam-5479	103	26	,	,	PUNCT
ejpam-5479	103	27	and	and	CCONJ
ejpam-5479	103	28	stability	stability	NOUN
ejpam-5479	103	29	in	in	ADP
ejpam-5479	103	30	oscillatory	oscillatory	ADJ
ejpam-5479	103	31	systems	system	NOUN
ejpam-5479	103	32	.	.	PUNCT
ejpam-5479	104	1	4	4	X
ejpam-5479	104	2	.	.	X
ejpam-5479	104	3	when	when	SCONJ
ejpam-5479	104	4	the	the	DET
ejpam-5479	104	5	oscillations	oscillation	NOUN
ejpam-5479	104	6	reach	reach	VERB
ejpam-5479	104	7	a	a	DET
ejpam-5479	104	8	large	large	ADJ
ejpam-5479	104	9	magnitude	magnitude	NOUN
ejpam-5479	104	10	,	,	PUNCT
ejpam-5479	104	11	the	the	DET
ejpam-5479	104	12	system	system	NOUN
ejpam-5479	104	13	may	may	AUX
ejpam-5479	104	14	exhibit	exhibit	VERB
ejpam-5479	104	15	nonlinear	nonlinear	PROPN
ejpam-5479	104	16	k.	k.	PROPN
ejpam-5479	104	17	alluhydan	alluhydan	PROPN
ejpam-5479	104	18	,	,	PUNCT
ejpam-5479	104	19	g.	g.	PROPN
ejpam-5479	104	20	m	m	PROPN
ejpam-5479	104	21	moatimid	moatimid	PROPN
ejpam-5479	104	22	,	,	PUNCT
ejpam-5479	104	23	t.	t.	PROPN
ejpam-5479	104	24	s.	s.	PROPN
ejpam-5479	104	25	amer	amer	PROPN
ejpam-5479	104	26	/	/	SYM
ejpam-5479	104	27	eur	eur	PROPN
ejpam-5479	104	28	.	.	PUNCT
ejpam-5479	105	1	j.	j.	PROPN
ejpam-5479	105	2	pure	pure	PROPN
ejpam-5479	105	3	appl	appl	PROPN
ejpam-5479	105	4	.	.	PROPN
ejpam-5479	105	5	math	math	PROPN
ejpam-5479	105	6	,	,	PUNCT
ejpam-5479	105	7	17	17	NUM
ejpam-5479	105	8	(	(	PUNCT
ejpam-5479	105	9	4	4	NUM
ejpam-5479	105	10	)	)	PUNCT
ejpam-5479	105	11	(	(	PUNCT
ejpam-5479	105	12	2024	2024	NUM
ejpam-5479	105	13	)	)	PUNCT
ejpam-5479	105	14	,	,	PUNCT
ejpam-5479	105	15	3185	3185	NUM
ejpam-5479	105	16	-	-	SYM
ejpam-5479	105	17	3208	3208	NUM
ejpam-5479	105	18	3189	3189	NUM
ejpam-5479	105	19	behavior	behavior	NOUN
ejpam-5479	105	20	,	,	PUNCT
ejpam-5479	105	21	which	which	PRON
ejpam-5479	105	22	can	can	AUX
ejpam-5479	105	23	be	be	AUX
ejpam-5479	105	24	determined	determine	VERB
ejpam-5479	105	25	using	use	VERB
ejpam-5479	105	26	this	this	DET
ejpam-5479	105	27	prototype	prototype	NOUN
ejpam-5479	105	28	.	.	PUNCT
ejpam-5479	106	1	nonlinear	nonlinear	ADJ
ejpam-5479	106	2	dynamics	dynamic	NOUN
ejpam-5479	106	3	is	be	AUX
ejpam-5479	106	4	an	an	DET
ejpam-5479	106	5	attractive	attractive	ADJ
ejpam-5479	106	6	area	area	NOUN
ejpam-5479	106	7	of	of	ADP
ejpam-5479	106	8	focus	focus	NOUN
ejpam-5479	106	9	in	in	ADP
ejpam-5479	106	10	physics	physics	NOUN
ejpam-5479	106	11	,	,	PUNCT
ejpam-5479	106	12	particularly	particularly	ADV
ejpam-5479	106	13	when	when	SCONJ
ejpam-5479	106	14	studying	study	VERB
ejpam-5479	106	15	chaotic	chaotic	ADJ
ejpam-5479	106	16	systems	system	NOUN
ejpam-5479	106	17	.	.	PUNCT
ejpam-5479	107	1	5	5	X
ejpam-5479	107	2	.	.	X
ejpam-5479	107	3	this	this	DET
ejpam-5479	107	4	prototype	prototype	NOUN
ejpam-5479	107	5	serves	serve	VERB
ejpam-5479	107	6	as	as	ADP
ejpam-5479	107	7	an	an	DET
ejpam-5479	107	8	educational	educational	ADJ
ejpam-5479	107	9	tool	tool	NOUN
ejpam-5479	107	10	for	for	ADP
ejpam-5479	107	11	teaching	teach	VERB
ejpam-5479	107	12	fundamental	fundamental	ADJ
ejpam-5479	107	13	concepts	concept	NOUN
ejpam-5479	107	14	in	in	ADP
ejpam-5479	107	15	classical	classical	ADJ
ejpam-5479	107	16	mechanics	mechanic	NOUN
ejpam-5479	107	17	,	,	PUNCT
ejpam-5479	107	18	including	include	VERB
ejpam-5479	107	19	rotational	rotational	ADJ
ejpam-5479	107	20	dynamics	dynamic	NOUN
ejpam-5479	107	21	,	,	PUNCT
ejpam-5479	107	22	harmonic	harmonic	ADJ
ejpam-5479	107	23	motion	motion	NOUN
ejpam-5479	107	24	,	,	PUNCT
ejpam-5479	107	25	and	and	CCONJ
ejpam-5479	107	26	the	the	DET
ejpam-5479	107	27	interaction	interaction	NOUN
ejpam-5479	107	28	between	between	ADP
ejpam-5479	107	29	different	different	ADJ
ejpam-5479	107	30	types	type	NOUN
ejpam-5479	107	31	of	of	ADP
ejpam-5479	107	32	motion	motion	NOUN
ejpam-5479	107	33	.	.	PUNCT
ejpam-5479	108	1	6	6	X
ejpam-5479	108	2	.	.	X
ejpam-5479	108	3	in	in	ADP
ejpam-5479	108	4	manufacturing	manufacturing	NOUN
ejpam-5479	108	5	,	,	PUNCT
ejpam-5479	108	6	prototypes	prototype	NOUN
ejpam-5479	108	7	have	have	VERB
ejpam-5479	108	8	the	the	DET
ejpam-5479	108	9	ability	ability	NOUN
ejpam-5479	108	10	to	to	PART
ejpam-5479	108	11	mimic	mimic	VERB
ejpam-5479	108	12	real	real	ADJ
ejpam-5479	108	13	-	-	PUNCT
ejpam-5479	108	14	world	world	NOUN
ejpam-5479	108	15	systems	system	NOUN
ejpam-5479	108	16	found	find	VERB
ejpam-5479	108	17	in	in	ADP
ejpam-5479	108	18	automobiles	automobile	NOUN
ejpam-5479	108	19	,	,	PUNCT
ejpam-5479	108	20	such	such	ADJ
ejpam-5479	108	21	as	as	ADP
ejpam-5479	108	22	suspension	suspension	NOUN
ejpam-5479	108	23	systems	system	NOUN
ejpam-5479	108	24	that	that	PRON
ejpam-5479	108	25	involve	involve	VERB
ejpam-5479	108	26	springs	spring	NOUN
ejpam-5479	108	27	,	,	PUNCT
ejpam-5479	108	28	wheels	wheel	NOUN
ejpam-5479	108	29	,	,	PUNCT
ejpam-5479	108	30	and	and	CCONJ
ejpam-5479	108	31	rotating	rotate	VERB
ejpam-5479	108	32	components	component	NOUN
ejpam-5479	108	33	working	work	VERB
ejpam-5479	108	34	together	together	ADV
ejpam-5479	108	35	.	.	PUNCT
ejpam-5479	109	1	gaining	gain	VERB
ejpam-5479	109	2	insight	insight	NOUN
ejpam-5479	109	3	into	into	ADP
ejpam-5479	109	4	these	these	DET
ejpam-5479	109	5	interactions	interaction	NOUN
ejpam-5479	109	6	is	be	AUX
ejpam-5479	109	7	crucial	crucial	ADJ
ejpam-5479	109	8	for	for	ADP
ejpam-5479	109	9	developing	develop	VERB
ejpam-5479	109	10	highly	highly	ADV
ejpam-5479	109	11	efficient	efficient	ADJ
ejpam-5479	109	12	mechanical	mechanical	ADJ
ejpam-5479	109	13	systems	system	NOUN
ejpam-5479	109	14	.	.	PUNCT
ejpam-5479	110	1	this	this	DET
ejpam-5479	110	2	model	model	NOUN
ejpam-5479	110	3	offers	offer	VERB
ejpam-5479	110	4	a	a	DET
ejpam-5479	110	5	diverse	diverse	ADJ
ejpam-5479	110	6	framework	framework	NOUN
ejpam-5479	110	7	for	for	ADP
ejpam-5479	110	8	exploring	explore	VERB
ejpam-5479	110	9	different	different	ADJ
ejpam-5479	110	10	mechanical	mechanical	ADJ
ejpam-5479	110	11	principles	principle	NOUN
ejpam-5479	110	12	,	,	PUNCT
ejpam-5479	110	13	incorporating	incorporate	VERB
ejpam-5479	110	14	rotational	rotational	ADJ
ejpam-5479	110	15	motion	motion	NOUN
ejpam-5479	110	16	,	,	PUNCT
ejpam-5479	110	17	spring	spring	NOUN
ejpam-5479	110	18	dynamics	dynamic	NOUN
ejpam-5479	110	19	,	,	PUNCT
ejpam-5479	110	20	and	and	CCONJ
ejpam-5479	110	21	sp	sp	ADP
ejpam-5479	110	22	oscillation	oscillation	NOUN
ejpam-5479	110	23	.	.	PUNCT
ejpam-5479	111	1	several	several	ADJ
ejpam-5479	111	2	quires	quire	NOUN
ejpam-5479	111	3	are	be	AUX
ejpam-5479	111	4	answered	answer	VERB
ejpam-5479	111	5	at	at	ADP
ejpam-5479	111	6	the	the	DET
ejpam-5479	111	7	end	end	NOUN
ejpam-5479	111	8	of	of	ADP
ejpam-5479	111	9	the	the	DET
ejpam-5479	111	10	current	current	ADJ
ejpam-5479	111	11	work	work	NOUN
ejpam-5479	111	12	such	such	ADJ
ejpam-5479	111	13	as	as	ADP
ejpam-5479	111	14	:	:	PUNCT
ejpam-5479	111	15	i.	i.	NOUN
ejpam-5479	111	16	what	what	PRON
ejpam-5479	111	17	about	about	ADP
ejpam-5479	111	18	the	the	DET
ejpam-5479	111	19	governing	govern	VERB
ejpam-5479	111	20	equation	equation	NOUN
ejpam-5479	111	21	of	of	ADP
ejpam-5479	111	22	motion	motion	NOUN
ejpam-5479	111	23	of	of	ADP
ejpam-5479	111	24	the	the	DET
ejpam-5479	111	25	model	model	NOUN
ejpam-5479	111	26	?	?	PUNCT
ejpam-5479	112	1	ii	ii	PROPN
ejpam-5479	112	2	.	.	PUNCT
ejpam-5479	113	1	how	how	SCONJ
ejpam-5479	113	2	does	do	AUX
ejpam-5479	113	3	the	the	DET
ejpam-5479	113	4	npa	npa	NOUN
ejpam-5479	113	5	convert	convert	VERB
ejpam-5479	113	6	the	the	DET
ejpam-5479	113	7	original	original	ADJ
ejpam-5479	113	8	nonlinear	nonlinear	NOUN
ejpam-5479	113	9	ode	ode	NOUN
ejpam-5479	113	10	into	into	ADP
ejpam-5479	113	11	a	a	DET
ejpam-5479	113	12	linear	linear	ADJ
ejpam-5479	113	13	one	one	NUM
ejpam-5479	113	14	?	?	PUNCT
ejpam-5479	113	15	iii	iii	X
ejpam-5479	113	16	.	.	PUNCT
ejpam-5479	114	1	what	what	PRON
ejpam-5479	114	2	is	be	AUX
ejpam-5479	114	3	the	the	DET
ejpam-5479	114	4	influence	influence	NOUN
ejpam-5479	114	5	of	of	ADP
ejpam-5479	114	6	the	the	DET
ejpam-5479	114	7	time	time	NOUN
ejpam-5479	114	8	-	-	PUNCT
ejpam-5479	114	9	delay	delay	NOUN
ejpam-5479	114	10	parameter	parameter	NOUN
ejpam-5479	114	11	?	?	PUNCT
ejpam-5479	115	1	iv	iv	X
ejpam-5479	115	2	.	.	PUNCT
ejpam-5479	116	1	what	what	PRON
ejpam-5479	116	2	about	about	ADP
ejpam-5479	116	3	the	the	DET
ejpam-5479	116	4	time	time	NOUN
ejpam-5479	116	5	history	history	NOUN
ejpam-5479	116	6	as	as	ADV
ejpam-5479	116	7	well	well	ADV
ejpam-5479	116	8	as	as	ADP
ejpam-5479	116	9	stability	stability	NOUN
ejpam-5479	116	10	analysis	analysis	NOUN
ejpam-5479	116	11	of	of	ADP
ejpam-5479	116	12	the	the	DET
ejpam-5479	116	13	system	system	NOUN
ejpam-5479	116	14	?	?	PUNCT
ejpam-5479	117	1	to	to	PART
ejpam-5479	117	2	crystallize	crystallize	VERB
ejpam-5479	117	3	the	the	DET
ejpam-5479	117	4	presentation	presentation	NOUN
ejpam-5479	117	5	of	of	ADP
ejpam-5479	117	6	the	the	DET
ejpam-5479	117	7	problem	problem	NOUN
ejpam-5479	117	8	,	,	PUNCT
ejpam-5479	117	9	the	the	DET
ejpam-5479	117	10	subsequent	subsequent	ADJ
ejpam-5479	117	11	sections	section	NOUN
ejpam-5479	117	12	of	of	ADP
ejpam-5479	117	13	the	the	DET
ejpam-5479	117	14	article	article	NOUN
ejpam-5479	117	15	will	will	AUX
ejpam-5479	117	16	be	be	AUX
ejpam-5479	117	17	organized	organize	VERB
ejpam-5479	117	18	as	as	SCONJ
ejpam-5479	117	19	follows	follow	VERB
ejpam-5479	117	20	:	:	PUNCT
ejpam-5479	117	21	a	a	DET
ejpam-5479	117	22	brief	brief	ADJ
ejpam-5479	117	23	explanation	explanation	NOUN
ejpam-5479	117	24	of	of	ADP
ejpam-5479	117	25	the	the	DET
ejpam-5479	117	26	npa	npa	NOUN
ejpam-5479	117	27	is	be	AUX
ejpam-5479	117	28	presented	present	VERB
ejpam-5479	117	29	in	in	ADP
ejpam-5479	117	30	§	§	PROPN
ejpam-5479	117	31	2	2	NUM
ejpam-5479	117	32	.	.	PUNCT
ejpam-5479	118	1	the	the	DET
ejpam-5479	118	2	methodology	methodology	NOUN
ejpam-5479	118	3	of	of	ADP
ejpam-5479	118	4	the	the	DET
ejpam-5479	118	5	problem	problem	NOUN
ejpam-5479	118	6	is	be	AUX
ejpam-5479	118	7	presented	present	VERB
ejpam-5479	118	8	in	in	ADP
ejpam-5479	118	9	§	§	PROPN
ejpam-5479	118	10	3	3	NUM
ejpam-5479	118	11	.	.	PUNCT
ejpam-5479	118	12	two	two	NUM
ejpam-5479	118	13	scenarios	scenario	NOUN
ejpam-5479	118	14	involving	involve	VERB
ejpam-5479	118	15	the	the	DET
ejpam-5479	118	16	presence	presence	NOUN
ejpam-5479	118	17	/	/	SYM
ejpam-5479	118	18	absence	absence	NOUN
ejpam-5479	118	19	of	of	ADP
ejpam-5479	118	20	the	the	DET
ejpam-5479	118	21	time	time	NOUN
ejpam-5479	118	22	-	-	PUNCT
ejpam-5479	118	23	delay	delay	NOUN
ejpam-5479	118	24	factor	factor	NOUN
ejpam-5479	118	25	are	be	AUX
ejpam-5479	118	26	discussed	discuss	VERB
ejpam-5479	118	27	.	.	PUNCT
ejpam-5479	119	1	furthermore	furthermore	ADV
ejpam-5479	119	2	,	,	PUNCT
ejpam-5479	119	3	the	the	DET
ejpam-5479	119	4	estimated	estimate	VERB
ejpam-5479	119	5	solution	solution	NOUN
ejpam-5479	119	6	is	be	AUX
ejpam-5479	119	7	contrasted	contrast	VERB
ejpam-5479	119	8	with	with	ADP
ejpam-5479	119	9	numerical	numerical	ADJ
ejpam-5479	119	10	calculations	calculation	NOUN
ejpam-5479	119	11	to	to	PART
ejpam-5479	119	12	authenticate	authenticate	VERB
ejpam-5479	119	13	the	the	DET
ejpam-5479	119	14	prototype	prototype	NOUN
ejpam-5479	119	15	link	link	NOUN
ejpam-5479	119	16	.	.	PUNCT
ejpam-5479	120	1	the	the	DET
ejpam-5479	120	2	results	result	NOUN
ejpam-5479	120	3	of	of	ADP
ejpam-5479	120	4	the	the	DET
ejpam-5479	120	5	main	main	ADJ
ejpam-5479	120	6	outcomes	outcome	NOUN
ejpam-5479	120	7	are	be	AUX
ejpam-5479	120	8	presented	present	VERB
ejpam-5479	120	9	in	in	ADP
ejpam-5479	120	10	§	§	PROPN
ejpam-5479	120	11	4	4	NUM
ejpam-5479	120	12	.	.	PUNCT
ejpam-5479	121	1	a	a	DET
ejpam-5479	121	2	summary	summary	NOUN
ejpam-5479	121	3	of	of	ADP
ejpam-5479	121	4	the	the	DET
ejpam-5479	121	5	principal	principal	ADJ
ejpam-5479	121	6	conclusions	conclusion	NOUN
ejpam-5479	121	7	is	be	AUX
ejpam-5479	121	8	provided	provide	VERB
ejpam-5479	121	9	in	in	ADP
ejpam-5479	121	10	which	which	PRON
ejpam-5479	121	11	the	the	DET
ejpam-5479	121	12	solution	solution	NOUN
ejpam-5479	121	13	attained	attain	VERB
ejpam-5479	121	14	is	be	AUX
ejpam-5479	121	15	graphed	graph	VERB
ejpam-5479	121	16	over	over	ADP
ejpam-5479	121	17	time	time	NOUN
ejpam-5479	121	18	to	to	PART
ejpam-5479	121	19	illustrate	illustrate	VERB
ejpam-5479	121	20	the	the	DET
ejpam-5479	121	21	effects	effect	NOUN
ejpam-5479	121	22	of	of	ADP
ejpam-5479	121	23	the	the	DET
ejpam-5479	121	24	operated	operate	VERB
ejpam-5479	121	25	parameters	parameter	NOUN
ejpam-5479	121	26	.	.	PUNCT
ejpam-5479	122	1	additionally	additionally	ADV
ejpam-5479	122	2	,	,	PUNCT
ejpam-5479	122	3	the	the	DET
ejpam-5479	122	4	phase	phase	NOUN
ejpam-5479	122	5	plane	plane	NOUN
ejpam-5479	122	6	curves	curve	NOUN
ejpam-5479	122	7	corresponding	correspond	VERB
ejpam-5479	122	8	to	to	ADP
ejpam-5479	122	9	the	the	DET
ejpam-5479	122	10	depicted	depict	VERB
ejpam-5479	122	11	solution	solution	NOUN
ejpam-5479	122	12	are	be	AUX
ejpam-5479	122	13	showcased	showcase	VERB
ejpam-5479	122	14	and	and	CCONJ
ejpam-5479	122	15	scrutinized	scrutinize	VERB
ejpam-5479	122	16	.	.	PUNCT
ejpam-5479	123	1	stability	stability	NOUN
ejpam-5479	123	2	criteria	criterion	NOUN
ejpam-5479	123	3	are	be	AUX
ejpam-5479	123	4	furnished	furnish	VERB
ejpam-5479	123	5	and	and	CCONJ
ejpam-5479	123	6	depicted	depict	VERB
ejpam-5479	123	7	to	to	PART
ejpam-5479	123	8	delve	delve	VERB
ejpam-5479	123	9	into	into	ADP
ejpam-5479	123	10	regions	region	NOUN
ejpam-5479	123	11	of	of	ADP
ejpam-5479	123	12	both	both	DET
ejpam-5479	123	13	stability	stability	NOUN
ejpam-5479	123	14	and	and	CCONJ
ejpam-5479	123	15	instability	instability	NOUN
ejpam-5479	123	16	.	.	PUNCT
ejpam-5479	124	1	lastly	lastly	ADV
ejpam-5479	124	2	,	,	PUNCT
ejpam-5479	124	3	§	§	PROPN
ejpam-5479	124	4	5	5	NUM
ejpam-5479	124	5	contains	contain	VERB
ejpam-5479	124	6	the	the	DET
ejpam-5479	124	7	concluding	concluding	NOUN
ejpam-5479	124	8	remakes	remake	NOUN
ejpam-5479	124	9	of	of	ADP
ejpam-5479	124	10	the	the	DET
ejpam-5479	124	11	obtained	obtain	VERB
ejpam-5479	124	12	results	result	NOUN
ejpam-5479	124	13	are	be	AUX
ejpam-5479	124	14	provided	provide	VERB
ejpam-5479	124	15	.	.	PUNCT
ejpam-5479	125	1	2	2	X
ejpam-5479	125	2	.	.	X
ejpam-5479	125	3	a	a	DET
ejpam-5479	125	4	brief	brief	ADJ
ejpam-5479	125	5	clarification	clarification	NOUN
ejpam-5479	125	6	of	of	ADP
ejpam-5479	125	7	the	the	DET
ejpam-5479	125	8	npa	npa	NOUN
ejpam-5479	125	9	the	the	DET
ejpam-5479	125	10	aim	aim	NOUN
ejpam-5479	125	11	of	of	ADP
ejpam-5479	125	12	this	this	DET
ejpam-5479	125	13	section	section	NOUN
ejpam-5479	125	14	is	be	AUX
ejpam-5479	125	15	to	to	PART
ejpam-5479	125	16	create	create	VERB
ejpam-5479	125	17	specific	specific	ADJ
ejpam-5479	125	18	structures	structure	NOUN
ejpam-5479	125	19	in	in	ADP
ejpam-5479	125	20	converting	convert	VERB
ejpam-5479	125	21	the	the	DET
ejpam-5479	125	22	nonlinear	nonlinear	ADJ
ejpam-5479	125	23	configuration	configuration	NOUN
ejpam-5479	125	24	to	to	ADP
ejpam-5479	125	25	a	a	DET
ejpam-5479	125	26	linear	linear	ADJ
ejpam-5479	125	27	one	one	NOUN
ejpam-5479	125	28	that	that	PRON
ejpam-5479	125	29	has	have	AUX
ejpam-5479	125	30	documented	document	VERB
ejpam-5479	125	31	solutions	solution	NOUN
ejpam-5479	125	32	and	and	CCONJ
ejpam-5479	125	33	can	can	AUX
ejpam-5479	125	34	be	be	AUX
ejpam-5479	125	35	rationally	rationally	ADV
ejpam-5479	125	36	approached	approach	VERB
ejpam-5479	125	37	by	by	ADP
ejpam-5479	125	38	the	the	DET
ejpam-5479	125	39	inventive	inventive	ADJ
ejpam-5479	125	40	organization	organization	NOUN
ejpam-5479	125	41	[	[	X
ejpam-5479	125	42	48	48	NUM
ejpam-5479	125	43	]	]	PUNCT
ejpam-5479	125	44	.	.	PUNCT
ejpam-5479	126	1	in	in	ADP
ejpam-5479	126	2	a	a	DET
ejpam-5479	126	3	few	few	ADJ
ejpam-5479	126	4	opinions	opinion	NOUN
ejpam-5479	126	5	,	,	PUNCT
ejpam-5479	126	6	it	it	PRON
ejpam-5479	126	7	is	be	AUX
ejpam-5479	126	8	possible	possible	ADJ
ejpam-5479	126	9	to	to	PART
ejpam-5479	126	10	interpret	interpret	VERB
ejpam-5479	126	11	a	a	DET
ejpam-5479	126	12	nonlinear	nonlinear	ADJ
ejpam-5479	126	13	ode	ode	NOUN
ejpam-5479	126	14	into	into	ADP
ejpam-5479	126	15	a	a	DET
ejpam-5479	126	16	linear	linear	ADJ
ejpam-5479	126	17	one	one	NUM
ejpam-5479	126	18	in	in	ADP
ejpam-5479	126	19	a	a	DET
ejpam-5479	126	20	way	way	NOUN
ejpam-5479	126	21	that	that	PRON
ejpam-5479	126	22	reduces	reduce	VERB
ejpam-5479	126	23	the	the	DET
ejpam-5479	126	24	consistency	consistency	NOUN
ejpam-5479	126	25	of	of	ADP
ejpam-5479	126	26	the	the	DET
ejpam-5479	126	27	two	two	NUM
ejpam-5479	126	28	systems	system	NOUN
ejpam-5479	126	29	’	'	PUNCT
ejpam-5479	126	30	alterations	alteration	NOUN
ejpam-5479	126	31	.	.	PUNCT
ejpam-5479	127	1	it	it	PRON
ejpam-5479	127	2	is	be	AUX
ejpam-5479	127	3	exemplified	exemplify	VERB
ejpam-5479	127	4	that	that	SCONJ
ejpam-5479	127	5	this	this	DET
ejpam-5479	127	6	additional	additional	ADJ
ejpam-5479	127	7	can	can	AUX
ejpam-5479	127	8	be	be	AUX
ejpam-5479	127	9	simply	simply	ADV
ejpam-5479	127	10	skillful	skillful	ADJ
ejpam-5479	127	11	.	.	PUNCT
ejpam-5479	128	1	the	the	DET
ejpam-5479	128	2	basic	basic	ADJ
ejpam-5479	128	3	idea	idea	NOUN
ejpam-5479	128	4	of	of	ADP
ejpam-5479	128	5	hff	hff	PROPN
ejpam-5479	128	6	is	be	AUX
ejpam-5479	128	7	now	now	ADV
ejpam-5479	128	8	utilized	utilize	VERB
ejpam-5479	128	9	to	to	PART
ejpam-5479	128	10	linearize	linearize	VERB
ejpam-5479	128	11	a	a	DET
ejpam-5479	128	12	nonlinear	nonlinear	ADJ
ejpam-5479	128	13	oscillator	oscillator	NOUN
ejpam-5479	128	14	,	,	PUNCT
ejpam-5479	128	15	resulting	result	VERB
ejpam-5479	128	16	in	in	ADP
ejpam-5479	128	17	a	a	DET
ejpam-5479	128	18	linear	linear	ADJ
ejpam-5479	128	19	oscillator	oscillator	NOUN
ejpam-5479	128	20	generating	generating	PROPN
ejpam-5479	128	21	k.	k.	PROPN
ejpam-5479	128	22	alluhydan	alluhydan	PROPN
ejpam-5479	128	23	,	,	PUNCT
ejpam-5479	128	24	g.	g.	PROPN
ejpam-5479	128	25	m	m	PROPN
ejpam-5479	128	26	moatimid	moatimid	PROPN
ejpam-5479	128	27	,	,	PUNCT
ejpam-5479	128	28	t.	t.	PROPN
ejpam-5479	128	29	s.	s.	PROPN
ejpam-5479	128	30	amer	amer	PROPN
ejpam-5479	128	31	/	/	SYM
ejpam-5479	128	32	eur	eur	PROPN
ejpam-5479	128	33	.	.	PUNCT
ejpam-5479	129	1	j.	j.	PROPN
ejpam-5479	129	2	pure	pure	PROPN
ejpam-5479	129	3	appl	appl	PROPN
ejpam-5479	129	4	.	.	PROPN
ejpam-5479	129	5	math	math	PROPN
ejpam-5479	129	6	,	,	PUNCT
ejpam-5479	129	7	17	17	NUM
ejpam-5479	129	8	(	(	PUNCT
ejpam-5479	129	9	4	4	NUM
ejpam-5479	129	10	)	)	PUNCT
ejpam-5479	129	11	(	(	PUNCT
ejpam-5479	129	12	2024	2024	NUM
ejpam-5479	129	13	)	)	PUNCT
ejpam-5479	129	14	,	,	PUNCT
ejpam-5479	129	15	3185	3185	NUM
ejpam-5479	129	16	-	-	SYM
ejpam-5479	129	17	3208	3208	NUM
ejpam-5479	129	18	3190	3190	NUM
ejpam-5479	129	19	a	a	DET
ejpam-5479	129	20	solution	solution	NOUN
ejpam-5479	129	21	that	that	PRON
ejpam-5479	129	22	covers	cover	VERB
ejpam-5479	129	23	the	the	DET
ejpam-5479	129	24	complete	complete	ADJ
ejpam-5479	129	25	time	time	NOUN
ejpam-5479	129	26	period	period	NOUN
ejpam-5479	129	27	of	of	ADP
ejpam-5479	129	28	the	the	DET
ejpam-5479	129	29	oscillation	oscillation	NOUN
ejpam-5479	129	30	history	history	NOUN
ejpam-5479	130	1	[	[	X
ejpam-5479	130	2	47	47	NUM
ejpam-5479	130	3	]	]	PUNCT
ejpam-5479	130	4	.	.	PUNCT
ejpam-5479	131	1	the	the	DET
ejpam-5479	131	2	reality	reality	NOUN
ejpam-5479	131	3	and	and	CCONJ
ejpam-5479	131	4	uniqueness	uniqueness	NOUN
ejpam-5479	131	5	of	of	ADP
ejpam-5479	131	6	a	a	DET
ejpam-5479	131	7	comprehensive	comprehensive	ADJ
ejpam-5479	131	8	corresponding	corresponding	ADJ
ejpam-5479	131	9	linear	linear	NOUN
ejpam-5479	131	10	system	system	NOUN
ejpam-5479	131	11	have	have	AUX
ejpam-5479	131	12	previously	previously	ADV
ejpam-5479	131	13	been	be	AUX
ejpam-5479	131	14	thoroughly	thoroughly	ADV
ejpam-5479	131	15	examined	examine	VERB
ejpam-5479	131	16	[	[	X
ejpam-5479	131	17	36	36	NUM
ejpam-5479	131	18	]	]	PUNCT
ejpam-5479	131	19	.	.	PUNCT
ejpam-5479	132	1	the	the	DET
ejpam-5479	132	2	npa	npa	NOUN
ejpam-5479	132	3	can	can	AUX
ejpam-5479	132	4	now	now	ADV
ejpam-5479	132	5	designated	designate	VERB
ejpam-5479	132	6	as	as	SCONJ
ejpam-5479	132	7	follows	follow	VERB
ejpam-5479	132	8	:	:	PUNCT
ejpam-5479	132	9	given	give	VERB
ejpam-5479	132	10	a	a	DET
ejpam-5479	132	11	nonlinear	nonlinear	ADJ
ejpam-5479	132	12	ode	ode	NOUN
ejpam-5479	132	13	,	,	PUNCT
ejpam-5479	132	14	the	the	DET
ejpam-5479	132	15	nonlinear	nonlinear	ADJ
ejpam-5479	132	16	forces	force	NOUN
ejpam-5479	132	17	may	may	AUX
ejpam-5479	132	18	be	be	AUX
ejpam-5479	132	19	abstracted	abstract	VERB
ejpam-5479	132	20	as	as	ADP
ejpam-5479	132	21	three	three	NUM
ejpam-5479	132	22	different	different	ADJ
ejpam-5479	132	23	features	feature	NOUN
ejpam-5479	132	24	as	as	SCONJ
ejpam-5479	132	25	follows	follow	VERB
ejpam-5479	132	26	:	:	PUNCT
ejpam-5479	132	27	quadratic	quadratic	ADJ
ejpam-5479	132	28	nonlinear	nonlinear	ADJ
ejpam-5479	132	29	forces	force	NOUN
ejpam-5479	132	30	(	(	PUNCT
ejpam-5479	132	31	do	do	AUX
ejpam-5479	132	32	not	not	PART
ejpam-5479	132	33	produce	produce	VERB
ejpam-5479	132	34	secular	secular	ADJ
ejpam-5479	132	35	terms	term	NOUN
ejpam-5479	132	36	)	)	PUNCT
ejpam-5479	132	37	,	,	PUNCT
ejpam-5479	132	38	odd	odd	ADJ
ejpam-5479	132	39	nonlinear	nonlinear	ADJ
ejpam-5479	132	40	damping	damp	VERB
ejpam-5479	132	41	forces	force	NOUN
ejpam-5479	132	42	(	(	PUNCT
ejpam-5479	132	43	yield	yield	VERB
ejpam-5479	132	44	secular	secular	ADJ
ejpam-5479	132	45	terms	term	NOUN
ejpam-5479	132	46	)	)	PUNCT
ejpam-5479	132	47	,	,	PUNCT
ejpam-5479	132	48	and	and	CCONJ
ejpam-5479	132	49	lastly	lastly	ADV
ejpam-5479	132	50	the	the	DET
ejpam-5479	132	51	restoring	restore	VERB
ejpam-5479	132	52	nonlinear	nonlinear	ADJ
ejpam-5479	132	53	odd	odd	ADJ
ejpam-5479	132	54	force	force	NOUN
ejpam-5479	132	55	(	(	PUNCT
ejpam-5479	132	56	yield	yield	VERB
ejpam-5479	132	57	secular	secular	ADJ
ejpam-5479	132	58	terms	term	NOUN
ejpam-5479	132	59	)	)	PUNCT
ejpam-5479	133	1	[	[	X
ejpam-5479	133	2	4	4	NUM
ejpam-5479	133	3	]	]	PUNCT
ejpam-5479	133	4	.	.	PUNCT
ejpam-5479	134	1	this	this	PRON
ejpam-5479	134	2	means	mean	VERB
ejpam-5479	134	3	that	that	SCONJ
ejpam-5479	134	4	any	any	DET
ejpam-5479	134	5	nonlinear	nonlinear	ADJ
ejpam-5479	134	6	ode	ode	NOUN
ejpam-5479	134	7	may	may	AUX
ejpam-5479	134	8	be	be	AUX
ejpam-5479	134	9	reorganized	reorganize	VERB
ejpam-5479	134	10	using	use	VERB
ejpam-5479	134	11	these	these	DET
ejpam-5479	134	12	modules	module	NOUN
ejpam-5479	134	13	,	,	PUNCT
ejpam-5479	134	14	which	which	PRON
ejpam-5479	134	15	leads	lead	VERB
ejpam-5479	134	16	to	to	ADP
ejpam-5479	134	17	the	the	DET
ejpam-5479	134	18	subsequent	subsequent	ADJ
ejpam-5479	134	19	example	example	NOUN
ejpam-5479	134	20	:	:	PUNCT
ejpam-5479	134	21	ξ̈	ξ̈	X
ejpam-5479	135	1	+	+	CCONJ
ejpam-5479	135	2	f1(ζ	f1(ζ	PROPN
ejpam-5479	135	3	,	,	PUNCT
ejpam-5479	135	4	ζ̇	ζ̇	NOUN
ejpam-5479	135	5	,	,	PUNCT
ejpam-5479	135	6	ζ̈	ζ̈	NOUN
ejpam-5479	135	7	)	)	PUNCT
ejpam-5479	135	8	+	+	CCONJ
ejpam-5479	135	9	f2(ζ	f2(ζ	NOUN
ejpam-5479	135	10	,	,	PUNCT
ejpam-5479	135	11	ζ̇	ζ̇	NOUN
ejpam-5479	135	12	,	,	PUNCT
ejpam-5479	135	13	ζ̈	ζ̈	NOUN
ejpam-5479	135	14	)	)	PUNCT
ejpam-5479	135	15	+	+	CCONJ
ejpam-5479	135	16	f3(ζ	f3(ζ	PROPN
ejpam-5479	135	17	,	,	PUNCT
ejpam-5479	135	18	ζ̇	ζ̇	PROPN
ejpam-5479	135	19	,	,	PUNCT
ejpam-5479	135	20	ζ̈	ζ̈	NOUN
ejpam-5479	135	21	)	)	PUNCT
ejpam-5479	135	22	=	=	SYM
ejpam-5479	135	23	0	0	NUM
ejpam-5479	135	24	,	,	PUNCT
ejpam-5479	135	25	(	(	PUNCT
ejpam-5479	135	26	1	1	X
ejpam-5479	135	27	)	)	PUNCT
ejpam-5479	135	28	where	where	SCONJ
ejpam-5479	135	29	f1(ζ	f1(ζ	PROPN
ejpam-5479	135	30	,	,	PUNCT
ejpam-5479	135	31	ζ̇	ζ̇	NOUN
ejpam-5479	135	32	,	,	PUNCT
ejpam-5479	135	33	ζ̈	ζ̈	NOUN
ejpam-5479	135	34	)	)	PUNCT
ejpam-5479	135	35	,	,	PUNCT
ejpam-5479	135	36	f2(ζ	f2(ζ	X
ejpam-5479	135	37	,	,	PUNCT
ejpam-5479	135	38	ζ̇	ζ̇	NOUN
ejpam-5479	135	39	,	,	PUNCT
ejpam-5479	135	40	ζ̈	ζ̈	NOUN
ejpam-5479	135	41	)	)	PUNCT
ejpam-5479	135	42	and	and	CCONJ
ejpam-5479	135	43	f3(ζ	f3(ζ	PROPN
ejpam-5479	135	44	,	,	PUNCT
ejpam-5479	135	45	ζ̇	ζ̇	PROPN
ejpam-5479	135	46	,	,	PUNCT
ejpam-5479	135	47	ζ̈	ζ̈	NOUN
ejpam-5479	135	48	)	)	PUNCT
ejpam-5479	135	49	are	be	AUX
ejpam-5479	135	50	the	the	DET
ejpam-5479	135	51	odd	odd	ADJ
ejpam-5479	135	52	damping	damp	VERB
ejpam-5479	135	53	secular	secular	ADJ
ejpam-5479	135	54	terms	term	NOUN
ejpam-5479	135	55	,	,	PUNCT
ejpam-5479	135	56	even	even	ADV
ejpam-5479	135	57	nonsecular	nonsecular	ADJ
ejpam-5479	135	58	terms	term	NOUN
ejpam-5479	135	59	,	,	PUNCT
ejpam-5479	135	60	and	and	CCONJ
ejpam-5479	135	61	odd	odd	ADJ
ejpam-5479	135	62	secular	secular	ADJ
ejpam-5479	135	63	terms	term	NOUN
ejpam-5479	135	64	respectively	respectively	ADV
ejpam-5479	135	65	,	,	PUNCT
ejpam-5479	135	66	in	in	ADP
ejpam-5479	135	67	which	which	PRON
ejpam-5479	135	68	they	they	PRON
ejpam-5479	135	69	are	be	AUX
ejpam-5479	135	70	defined	define	VERB
ejpam-5479	135	71	as	as	ADP
ejpam-5479	135	72	:	:	PUNCT
ejpam-5479	135	73	f1(ζ	f1(ζ	PROPN
ejpam-5479	135	74	,	,	PUNCT
ejpam-5479	135	75	ζ̇	ζ̇	NOUN
ejpam-5479	135	76	,	,	PUNCT
ejpam-5479	135	77	ζ̈	ζ̈	NOUN
ejpam-5479	135	78	)	)	PUNCT
ejpam-5479	135	79	=	=	SYM
ejpam-5479	135	80	a1ζ̇	a1ζ̇	NOUN
ejpam-5479	135	81	+	+	CCONJ
ejpam-5479	135	82	b1ζ	b1ζ	X
ejpam-5479	135	83	2ζ̇	2ζ̇	PROPN
ejpam-5479	135	84	+	+	CCONJ
ejpam-5479	135	85	c1ζζ̇	c1ζζ̇	SYM
ejpam-5479	135	86	2	2	NUM
ejpam-5479	135	87	+	+	CCONJ
ejpam-5479	135	88	d1ζ̇	d1ζ̇	PROPN
ejpam-5479	135	89	3	3	NUM
ejpam-5479	135	90	+	+	CCONJ
ejpam-5479	135	91	e1ζ̈	e1ζ̈	PRON
ejpam-5479	135	92	ζ̇	ζ̇	NOUN
ejpam-5479	135	93	2	2	NUM
ejpam-5479	135	94	f2(ζ	f2(ζ	NOUN
ejpam-5479	135	95	,	,	PUNCT
ejpam-5479	135	96	ζ̇	ζ̇	NOUN
ejpam-5479	135	97	,	,	PUNCT
ejpam-5479	135	98	ζ̈	ζ̈	NOUN
ejpam-5479	135	99	)	)	PUNCT
ejpam-5479	135	100	=	=	PUNCT
ejpam-5479	136	1	a2ζ̇ζ	a2ζ̇ζ	NOUN
ejpam-5479	136	2	+	+	CCONJ
ejpam-5479	136	3	b2ζ̇	b2ζ̇	DET
ejpam-5479	136	4	2	2	NUM
ejpam-5479	136	5	+	+	NUM
ejpam-5479	136	6	c2ζ	c2ζ	NOUN
ejpam-5479	136	7	2	2	NUM
ejpam-5479	136	8	+	+	NUM
ejpam-5479	136	9	d2ζ̇	d2ζ̇	NOUN
ejpam-5479	136	10	ζ̈	ζ̈	NOUN
ejpam-5479	136	11	f3(ζ	f3(ζ	PROPN
ejpam-5479	136	12	,	,	PUNCT
ejpam-5479	136	13	ζ̇	ζ̇	PROPN
ejpam-5479	136	14	,	,	PUNCT
ejpam-5479	136	15	ζ̈	ζ̈	NOUN
ejpam-5479	136	16	)	)	PUNCT
ejpam-5479	136	17	=	=	PUNCT
ejpam-5479	136	18	ω2ζ	ω2ζ	PROPN
ejpam-5479	137	1	+	+	PUNCT
ejpam-5479	137	2	b3ζζ̇ζ̈	b3ζζ̇ζ̈	NOUN
ejpam-5479	137	3	+	+	CCONJ
ejpam-5479	137	4	c3ζ	c3ζ	NOUN
ejpam-5479	137	5	2ζ̈	2ζ̈	NUM
ejpam-5479	137	6	+	+	CCONJ
ejpam-5479	137	7	d3ζ	d3ζ	X
ejpam-5479	137	8	3	3	NUM
ejpam-5479	137	9	+	+	NUM
ejpam-5479	137	10	e3ζ̈ζ	e3ζ̈ζ	NOUN
ejpam-5479	137	11	2	2	NUM
ejpam-5479	137	12			NOUN
ejpam-5479	137	13	,	,	PUNCT
ejpam-5479	137	14	(	(	PUNCT
ejpam-5479	137	15	2	2	X
ejpam-5479	137	16	)	)	PUNCT
ejpam-5479	137	17	where	where	SCONJ
ejpam-5479	137	18	ω	ω	PROPN
ejpam-5479	137	19	is	be	AUX
ejpam-5479	137	20	the	the	DET
ejpam-5479	137	21	natural	natural	ADJ
ejpam-5479	137	22	frequency	frequency	NOUN
ejpam-5479	137	23	,	,	PUNCT
ejpam-5479	137	24	aj	aj	PROPN
ejpam-5479	137	25	,	,	PUNCT
ejpam-5479	137	26	bj	bj	VERB
ejpam-5479	137	27	,	,	PUNCT
ejpam-5479	137	28	cj	cj	NOUN
ejpam-5479	137	29	,	,	PUNCT
ejpam-5479	137	30	dj	dj	X
ejpam-5479	137	31	,	,	PUNCT
ejpam-5479	137	32	and	and	CCONJ
ejpam-5479	137	33	ej	ej	X
ejpam-5479	137	34	(	(	PUNCT
ejpam-5479	137	35	j	j	NOUN
ejpam-5479	137	36	=	=	SYM
ejpam-5479	137	37	1	1	NUM
ejpam-5479	137	38	,	,	PUNCT
ejpam-5479	137	39	2	2	NUM
ejpam-5479	137	40	,	,	PUNCT
ejpam-5479	137	41	3	3	NUM
ejpam-5479	137	42	)	)	PUNCT
ejpam-5479	137	43	are	be	AUX
ejpam-5479	137	44	the	the	DET
ejpam-5479	137	45	constant	constant	ADJ
ejpam-5479	137	46	physical	physical	ADJ
ejpam-5479	137	47	coefficients	coefficient	NOUN
ejpam-5479	137	48	.	.	PUNCT
ejpam-5479	138	1	the	the	DET
ejpam-5479	138	2	hff	hff	NOUN
ejpam-5479	138	3	aims	aim	VERB
ejpam-5479	138	4	to	to	PART
ejpam-5479	138	5	convert	convert	VERB
ejpam-5479	138	6	the	the	DET
ejpam-5479	138	7	nonlinear	nonlinear	ADJ
ejpam-5479	138	8	ode	ode	NOUN
ejpam-5479	138	9	as	as	SCONJ
ejpam-5479	138	10	given	give	VERB
ejpam-5479	138	11	in	in	ADP
ejpam-5479	138	12	eq	eq	ADP
ejpam-5479	138	13	.	.	PUNCT
ejpam-5479	139	1	(	(	PUNCT
ejpam-5479	139	2	1	1	NUM
ejpam-5479	139	3	)	)	PUNCT
ejpam-5479	139	4	into	into	ADP
ejpam-5479	139	5	the	the	DET
ejpam-5479	139	6	following	follow	VERB
ejpam-5479	139	7	linear	linear	PROPN
ejpam-5479	139	8	differential	differential	NOUN
ejpam-5479	139	9	equation	equation	NOUN
ejpam-5479	139	10	,	,	PUNCT
ejpam-5479	139	11	following	follow	VERB
ejpam-5479	139	12	moatimid	moatimid	PROPN
ejpam-5479	139	13	et	et	PROPN
ejpam-5479	139	14	al	al	PROPN
ejpam-5479	139	15	.	.	PUNCT
ejpam-5479	140	1	[	[	X
ejpam-5479	140	2	10	10	NUM
ejpam-5479	140	3	,	,	PUNCT
ejpam-5479	140	4	11	11	NUM
ejpam-5479	140	5	,	,	PUNCT
ejpam-5479	140	6	13–19	13–19	NUM
ejpam-5479	140	7	,	,	PUNCT
ejpam-5479	140	8	22–27	22–27	NUM
ejpam-5479	140	9	]	]	PUNCT
ejpam-5479	140	10	,	,	PUNCT
ejpam-5479	140	11	one	one	PRON
ejpam-5479	140	12	gets	get	VERB
ejpam-5479	140	13	v̈	v̈	PRON
ejpam-5479	140	14	+	+	CCONJ
ejpam-5479	140	15	σeqvv̇	σeqvv̇	NOUN
ejpam-5479	140	16	+	+	CCONJ
ejpam-5479	140	17	ω2	ω2	ADJ
ejpam-5479	140	18	eqvv	eqvv	NOUN
ejpam-5479	140	19	=	=	SYM
ejpam-5479	140	20	λ	λ	PROPN
ejpam-5479	140	21	.	.	PROPN
ejpam-5479	141	1	(	(	PUNCT
ejpam-5479	141	2	3	3	NUM
ejpam-5479	141	3	)	)	PUNCT
ejpam-5479	141	4	eq	eq	NOUN
ejpam-5479	141	5	.	.	PUNCT
ejpam-5479	142	1	(	(	PUNCT
ejpam-5479	142	2	3	3	X
ejpam-5479	142	3	)	)	PUNCT
ejpam-5479	142	4	is	be	AUX
ejpam-5479	142	5	a	a	DET
ejpam-5479	142	6	linear	linear	ADJ
ejpam-5479	142	7	equation	equation	NOUN
ejpam-5479	142	8	that	that	PRON
ejpam-5479	142	9	can	can	AUX
ejpam-5479	142	10	be	be	AUX
ejpam-5479	142	11	determined	determine	VERB
ejpam-5479	142	12	using	use	VERB
ejpam-5479	142	13	conventional	conventional	ADJ
ejpam-5479	142	14	techniques	technique	NOUN
ejpam-5479	142	15	.	.	PUNCT
ejpam-5479	143	1	the	the	DET
ejpam-5479	143	2	aim	aim	NOUN
ejpam-5479	143	3	is	be	AUX
ejpam-5479	143	4	to	to	PART
ejpam-5479	143	5	calculate	calculate	VERB
ejpam-5479	143	6	the	the	DET
ejpam-5479	143	7	three	three	NUM
ejpam-5479	143	8	coefficients	coefficient	NOUN
ejpam-5479	143	9	that	that	PRON
ejpam-5479	143	10	contained	contain	VERB
ejpam-5479	143	11	in	in	ADP
ejpam-5479	143	12	eq	eq	ADP
ejpam-5479	143	13	.	.	PUNCT
ejpam-5479	144	1	(	(	PUNCT
ejpam-5479	144	2	3	3	NUM
ejpam-5479	144	3	)	)	PUNCT
ejpam-5479	144	4	.	.	PUNCT
ejpam-5479	145	1	this	this	DET
ejpam-5479	145	2	equation	equation	NOUN
ejpam-5479	145	3	contains	contain	VERB
ejpam-5479	145	4	the	the	DET
ejpam-5479	145	5	damping	damp	VERB
ejpam-5479	145	6	constant	constant	ADJ
ejpam-5479	145	7	σeqv	σeqv	NOUN
ejpam-5479	145	8	(	(	PUNCT
ejpam-5479	145	9	equivalent	equivalent	ADJ
ejpam-5479	145	10	damping	damping	NOUN
ejpam-5479	145	11	)	)	PUNCT
ejpam-5479	145	12	,	,	PUNCT
ejpam-5479	145	13	ω2	ω2	ADJ
ejpam-5479	145	14	eqv	eqv	NOUN
ejpam-5479	145	15	(	(	PUNCT
ejpam-5479	145	16	equivalent	equivalent	ADJ
ejpam-5479	145	17	frequency	frequency	NOUN
ejpam-5479	145	18	)	)	PUNCT
ejpam-5479	145	19	and	and	CCONJ
ejpam-5479	145	20	the	the	DET
ejpam-5479	145	21	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5479	145	22	part	part	NOUN
ejpam-5479	145	23	λ	λ	PROPN
ejpam-5479	145	24	.	.	PUNCT
ejpam-5479	146	1	the	the	DET
ejpam-5479	146	2	total	total	ADJ
ejpam-5479	146	3	frequency	frequency	NOUN
ejpam-5479	146	4	is	be	AUX
ejpam-5479	146	5	shortened	shorten	VERB
ejpam-5479	146	6	to	to	ADP
ejpam-5479	146	7	∆2	∆2	X
ejpam-5479	146	8	,	,	PUNCT
ejpam-5479	146	9	which	which	PRON
ejpam-5479	146	10	will	will	AUX
ejpam-5479	146	11	be	be	AUX
ejpam-5479	146	12	determined	determine	VERB
ejpam-5479	146	13	later	later	ADV
ejpam-5479	146	14	.	.	PUNCT
ejpam-5479	147	1	this	this	DET
ejpam-5479	147	2	frequency	frequency	NOUN
ejpam-5479	147	3	comes	come	VERB
ejpam-5479	147	4	simply	simply	ADV
ejpam-5479	147	5	from	from	ADP
ejpam-5479	147	6	the	the	DET
ejpam-5479	147	7	standard	standard	ADJ
ejpam-5479	147	8	normal	normal	ADJ
ejpam-5479	147	9	form	form	NOUN
ejpam-5479	147	10	approach	approach	NOUN
ejpam-5479	147	11	.	.	PUNCT
ejpam-5479	148	1	this	this	DET
ejpam-5479	148	2	concept	concept	NOUN
ejpam-5479	148	3	may	may	AUX
ejpam-5479	148	4	simply	simply	ADV
ejpam-5479	148	5	be	be	AUX
ejpam-5479	148	6	introduced	introduce	VERB
ejpam-5479	148	7	as	as	ADP
ejpam-5479	148	8	:	:	PUNCT
ejpam-5479	148	9	v(t	v(t	NUM
ejpam-5479	148	10	)	)	PUNCT
ejpam-5479	148	11	=	=	SYM
ejpam-5479	148	12	ψ(t)exp(−σeqvt/2	ψ(t)exp(−σeqvt/2	NOUN
ejpam-5479	148	13	)	)	PUNCT
ejpam-5479	148	14	,	,	PUNCT
ejpam-5479	148	15	where	where	SCONJ
ejpam-5479	148	16	ψ(t	ψ(t	PROPN
ejpam-5479	148	17	)	)	PUNCT
ejpam-5479	148	18	is	be	AUX
ejpam-5479	148	19	an	an	DET
ejpam-5479	148	20	unknown	unknown	ADJ
ejpam-5479	148	21	function	function	NOUN
ejpam-5479	148	22	to	to	PART
ejpam-5479	148	23	be	be	AUX
ejpam-5479	148	24	determined	determine	VERB
ejpam-5479	148	25	.	.	PUNCT
ejpam-5479	149	1	therefore	therefore	ADV
ejpam-5479	149	2	,	,	PUNCT
ejpam-5479	149	3	eq	eq	ADJ
ejpam-5479	149	4	.	.	PUNCT
ejpam-5479	150	1	(	(	PUNCT
ejpam-5479	150	2	3	3	X
ejpam-5479	150	3	)	)	PUNCT
ejpam-5479	150	4	is	be	AUX
ejpam-5479	150	5	then	then	ADV
ejpam-5479	150	6	used	use	VERB
ejpam-5479	150	7	to	to	PART
ejpam-5479	150	8	produce	produce	VERB
ejpam-5479	150	9	the	the	DET
ejpam-5479	150	10	harmonic	harmonic	ADJ
ejpam-5479	150	11	equation	equation	NOUN
ejpam-5479	150	12	as	as	SCONJ
ejpam-5479	150	13	shown	show	VERB
ejpam-5479	150	14	below	below	ADV
ejpam-5479	150	15	.	.	PUNCT
ejpam-5479	151	1	ψ̈	ψ̈	CCONJ
ejpam-5479	152	1	+	+	VERB
ejpam-5479	152	2	∆2ψ	∆2ψ	NOUN
ejpam-5479	152	3	=	=	SYM
ejpam-5479	152	4	λexp(σeqvt/2	λexp(σeqvt/2	NOUN
ejpam-5479	152	5	)	)	PUNCT
ejpam-5479	152	6	,	,	PUNCT
ejpam-5479	152	7	(	(	PUNCT
ejpam-5479	152	8	4	4	X
ejpam-5479	152	9	)	)	PUNCT
ejpam-5479	152	10	where	where	SCONJ
ejpam-5479	152	11	∆2	∆2	PROPN
ejpam-5479	152	12	=	=	SYM
ejpam-5479	152	13	ω2	ω2	ADJ
ejpam-5479	152	14	eqv	eqv	NOUN
ejpam-5479	152	15	−	−	PROPN
ejpam-5479	152	16	1	1	NUM
ejpam-5479	152	17	4σ	4σ	NUM
ejpam-5479	152	18	2	2	NUM
ejpam-5479	152	19	eqv	eqv	NOUN
ejpam-5479	152	20	represents	represent	VERB
ejpam-5479	152	21	the	the	DET
ejpam-5479	152	22	total	total	ADJ
ejpam-5479	152	23	frequency	frequency	NOUN
ejpam-5479	152	24	of	of	ADP
ejpam-5479	152	25	the	the	DET
ejpam-5479	152	26	system	system	NOUN
ejpam-5479	152	27	.	.	PUNCT
ejpam-5479	153	1	the	the	DET
ejpam-5479	153	2	linear	linear	ADJ
ejpam-5479	153	3	version	version	NOUN
ejpam-5479	153	4	of	of	ADP
ejpam-5479	153	5	the	the	DET
ejpam-5479	153	6	modest	modest	ADJ
ejpam-5479	153	7	harmonic	harmonic	ADJ
ejpam-5479	153	8	oscillator	oscillator	NOUN
ejpam-5479	153	9	is	be	AUX
ejpam-5479	153	10	represented	represent	VERB
ejpam-5479	153	11	by	by	ADP
ejpam-5479	153	12	eq	eq	PROPN
ejpam-5479	153	13	.	.	PUNCT
ejpam-5479	154	1	(	(	PUNCT
ejpam-5479	154	2	3	3	NUM
ejpam-5479	154	3	)	)	PUNCT
ejpam-5479	154	4	.	.	PUNCT
ejpam-5479	155	1	prof	prof	PROPN
ejpam-5479	155	2	.	.	PUNCT
ejpam-5479	156	1	he	he	PRON
ejpam-5479	156	2	recently	recently	ADV
ejpam-5479	156	3	investigated	investigate	VERB
ejpam-5479	156	4	this	this	DET
ejpam-5479	156	5	topic	topic	NOUN
ejpam-5479	156	6	by	by	ADP
ejpam-5479	156	7	leveraging	leverage	VERB
ejpam-5479	156	8	the	the	DET
ejpam-5479	156	9	peculiarities	peculiarity	NOUN
ejpam-5479	156	10	of	of	ADP
ejpam-5479	156	11	specific	specific	ADJ
ejpam-5479	156	12	functions	function	NOUN
ejpam-5479	156	13	[	[	X
ejpam-5479	156	14	36	36	NUM
ejpam-5479	156	15	]	]	PUNCT
ejpam-5479	156	16	.	.	PUNCT
ejpam-5479	157	1	it	it	PRON
ejpam-5479	157	2	was	be	AUX
ejpam-5479	157	3	provided	provide	VERB
ejpam-5479	157	4	the	the	DET
ejpam-5479	157	5	subsequent	subsequent	ADJ
ejpam-5479	157	6	guessing	guess	VERB
ejpam-5479	157	7	solution	solution	NOUN
ejpam-5479	157	8	:	:	PUNCT
ejpam-5479	157	9	u	u	NOUN
ejpam-5479	157	10	=	=	PUNCT
ejpam-5479	157	11	a	a	DET
ejpam-5479	157	12	cos∆t	cos∆t	PROPN
ejpam-5479	157	13	,	,	PUNCT
ejpam-5479	157	14	u(0	u(0	NOUN
ejpam-5479	157	15	)	)	PUNCT
ejpam-5479	157	16	=	=	SYM
ejpam-5479	157	17	a	a	PRON
ejpam-5479	157	18	,	,	PUNCT
ejpam-5479	157	19	u̇(0	u̇(0	NOUN
ejpam-5479	157	20	)	)	PUNCT
ejpam-5479	157	21	=	=	SYM
ejpam-5479	158	1	0	0	X
ejpam-5479	158	2	.	.	PUNCT
ejpam-5479	159	1	(	(	PUNCT
ejpam-5479	159	2	5	5	NUM
ejpam-5479	159	3	)	)	PUNCT
ejpam-5479	159	4	according	accord	VERB
ejpam-5479	159	5	to	to	ADP
ejpam-5479	159	6	moatimid	moatimid	PROPN
ejpam-5479	159	7	et	et	PROPN
ejpam-5479	159	8	al	al	PROPN
ejpam-5479	159	9	.	.	PUNCT
ejpam-5479	160	1	[	[	X
ejpam-5479	160	2	10	10	NUM
ejpam-5479	160	3	,	,	PUNCT
ejpam-5479	160	4	11	11	NUM
ejpam-5479	160	5	,	,	PUNCT
ejpam-5479	160	6	13–19	13–19	NUM
ejpam-5479	160	7	,	,	PUNCT
ejpam-5479	160	8	22–27	22–27	NUM
ejpam-5479	160	9	]	]	PUNCT
ejpam-5479	160	10	,	,	PUNCT
ejpam-5479	160	11	the	the	DET
ejpam-5479	160	12	three	three	NUM
ejpam-5479	160	13	factors	factor	NOUN
ejpam-5479	160	14	that	that	PRON
ejpam-5479	160	15	have	have	AUX
ejpam-5479	160	16	emerged	emerge	VERB
ejpam-5479	160	17	from	from	ADP
ejpam-5479	160	18	eq	eq	ADP
ejpam-5479	160	19	.	.	PUNCT
ejpam-5479	161	1	(	(	PUNCT
ejpam-5479	161	2	3	3	X
ejpam-5479	161	3	)	)	PUNCT
ejpam-5479	161	4	can	can	AUX
ejpam-5479	161	5	be	be	AUX
ejpam-5479	161	6	written	write	VERB
ejpam-5479	161	7	as	as	SCONJ
ejpam-5479	161	8	follows	follow	VERB
ejpam-5479	161	9	:	:	PUNCT
ejpam-5479	161	10	(	(	PUNCT
ejpam-5479	161	11	1	1	X
ejpam-5479	161	12	)	)	PUNCT
ejpam-5479	161	13	frequency	frequency	NOUN
ejpam-5479	161	14	formula	formula	NOUN
ejpam-5479	161	15	k.	k.	PROPN
ejpam-5479	161	16	alluhydan	alluhydan	PROPN
ejpam-5479	161	17	,	,	PUNCT
ejpam-5479	161	18	g.	g.	PROPN
ejpam-5479	161	19	m	m	PROPN
ejpam-5479	161	20	moatimid	moatimid	PROPN
ejpam-5479	161	21	,	,	PUNCT
ejpam-5479	161	22	t.	t.	PROPN
ejpam-5479	161	23	s.	s.	PROPN
ejpam-5479	161	24	amer	amer	PROPN
ejpam-5479	161	25	/	/	SYM
ejpam-5479	161	26	eur	eur	PROPN
ejpam-5479	161	27	.	.	PUNCT
ejpam-5479	162	1	j.	j.	PROPN
ejpam-5479	162	2	pure	pure	PROPN
ejpam-5479	162	3	appl	appl	PROPN
ejpam-5479	162	4	.	.	PROPN
ejpam-5479	162	5	math	math	PROPN
ejpam-5479	162	6	,	,	PUNCT
ejpam-5479	162	7	17	17	NUM
ejpam-5479	162	8	(	(	PUNCT
ejpam-5479	162	9	4	4	NUM
ejpam-5479	162	10	)	)	PUNCT
ejpam-5479	162	11	(	(	PUNCT
ejpam-5479	162	12	2024	2024	NUM
ejpam-5479	162	13	)	)	PUNCT
ejpam-5479	162	14	,	,	PUNCT
ejpam-5479	162	15	3185	3185	NUM
ejpam-5479	162	16	-	-	SYM
ejpam-5479	162	17	3208	3208	NUM
ejpam-5479	162	18	3191	3191	NUM
ejpam-5479	162	19	employing	employ	VERB
ejpam-5479	162	20	the	the	DET
ejpam-5479	162	21	hff	hff	NOUN
ejpam-5479	162	22	to	to	PART
ejpam-5479	162	23	show	show	VERB
ejpam-5479	162	24	a	a	DET
ejpam-5479	162	25	benefit	benefit	NOUN
ejpam-5479	162	26	in	in	ADP
ejpam-5479	162	27	scheming	scheme	VERB
ejpam-5479	162	28	frequencies	frequency	NOUN
ejpam-5479	162	29	for	for	ADP
ejpam-5479	162	30	the	the	DET
ejpam-5479	162	31	developed	develop	VERB
ejpam-5479	162	32	generalized	generalized	ADJ
ejpam-5479	162	33	f3(ζ	f3(ζ	PROPN
ejpam-5479	162	34	,	,	PUNCT
ejpam-5479	162	35	ζ̇	ζ̇	PROPN
ejpam-5479	162	36	,	,	PUNCT
ejpam-5479	162	37	ζ̈	ζ̈	NOUN
ejpam-5479	162	38	)	)	PUNCT
ejpam-5479	162	39	.	.	PUNCT
ejpam-5479	163	1	according	accord	VERB
ejpam-5479	163	2	to	to	ADP
ejpam-5479	163	3	moatimid	moatimid	PROPN
ejpam-5479	163	4	et	et	PROPN
ejpam-5479	163	5	al	al	PROPN
ejpam-5479	163	6	.	.	PUNCT
ejpam-5479	164	1	[	[	X
ejpam-5479	164	2	10	10	NUM
ejpam-5479	164	3	,	,	PUNCT
ejpam-5479	164	4	11	11	NUM
ejpam-5479	164	5	,	,	PUNCT
ejpam-5479	164	6	13–19	13–19	NUM
ejpam-5479	164	7	,	,	PUNCT
ejpam-5479	164	8	22–27	22–27	NUM
ejpam-5479	164	9	]	]	PUNCT
ejpam-5479	164	10	,	,	PUNCT
ejpam-5479	164	11	eĺıas	eĺıas	PROPN
ejpam-5479	164	12	-	-	PROPN
ejpam-5479	164	13	zúñiga	zúñiga	NUM
ejpam-5479	164	14	et	et	NOUN
ejpam-5479	164	15	al	al	PROPN
ejpam-5479	164	16	.	.	PUNCT
ejpam-5479	165	1	[	[	X
ejpam-5479	165	2	46	46	NUM
ejpam-5479	165	3	]	]	PUNCT
ejpam-5479	165	4	,	,	PUNCT
ejpam-5479	165	5	he	he	PRON
ejpam-5479	165	6	,	,	PUNCT
ejpam-5479	165	7	and	and	CCONJ
ejpam-5479	165	8	liu	liu	PROPN
ejpam-5479	166	1	[	[	X
ejpam-5479	166	2	7	7	NUM
ejpam-5479	166	3	]	]	PUNCT
ejpam-5479	166	4	,	,	PUNCT
ejpam-5479	166	5	the	the	DET
ejpam-5479	166	6	corresponding	corresponding	ADJ
ejpam-5479	166	7	parameter	parameter	NOUN
ejpam-5479	166	8	may	may	AUX
ejpam-5479	166	9	be	be	AUX
ejpam-5479	166	10	determined	determine	VERB
ejpam-5479	166	11	as	as	ADP
ejpam-5479	166	12	:	:	PUNCT
ejpam-5479	166	13	ω2	ω2	ADJ
ejpam-5479	166	14	eqv	eqv	NOUN
ejpam-5479	166	15	=	=	SYM
ejpam-5479	166	16	∫	∫	PROPN
ejpam-5479	167	1	2π/∆	2π/∆	NUM
ejpam-5479	167	2	0	0	NUM
ejpam-5479	167	3	ζ	ζ	PROPN
ejpam-5479	167	4	f3(ζ	f3(ζ	PROPN
ejpam-5479	167	5	,	,	PUNCT
ejpam-5479	167	6	ζ̇	ζ̇	PROPN
ejpam-5479	167	7	,	,	PUNCT
ejpam-5479	167	8	ζ̈)dt/	ζ̈)dt/	VERB
ejpam-5479	167	9	∫	∫	PROPN
ejpam-5479	168	1	2π/∆	2π/∆	NUM
ejpam-5479	168	2	0	0	NUM
ejpam-5479	168	3	ζ2dt	ζ2dt	X
ejpam-5479	168	4	.	.	PUNCT
ejpam-5479	169	1	(	(	PUNCT
ejpam-5479	169	2	6	6	NUM
ejpam-5479	169	3	)	)	PUNCT
ejpam-5479	169	4	(	(	PUNCT
ejpam-5479	169	5	2	2	X
ejpam-5479	169	6	)	)	PUNCT
ejpam-5479	169	7	damping	damp	VERB
ejpam-5479	169	8	formula	formula	NOUN
ejpam-5479	169	9	one	one	PRON
ejpam-5479	169	10	may	may	AUX
ejpam-5479	169	11	estimate	estimate	VERB
ejpam-5479	169	12	the	the	DET
ejpam-5479	169	13	frequency	frequency	NOUN
ejpam-5479	169	14	of	of	ADP
ejpam-5479	169	15	a	a	DET
ejpam-5479	169	16	particular	particular	ADJ
ejpam-5479	169	17	function	function	NOUN
ejpam-5479	169	18	f1(ζ	f1(ζ	PROPN
ejpam-5479	169	19	,	,	PUNCT
ejpam-5479	169	20	ζ̇	ζ̇	NOUN
ejpam-5479	169	21	,	,	PUNCT
ejpam-5479	169	22	ζ̈	ζ̈	NOUN
ejpam-5479	169	23	)	)	PUNCT
ejpam-5479	169	24	using	use	VERB
ejpam-5479	169	25	the	the	DET
ejpam-5479	169	26	hff	hff	NOUN
ejpam-5479	169	27	.	.	PUNCT
ejpam-5479	170	1	as	as	ADV
ejpam-5479	170	2	well	well	ADV
ejpam-5479	170	3	as	as	ADP
ejpam-5479	170	4	the	the	DET
ejpam-5479	170	5	procedure	procedure	NOUN
ejpam-5479	170	6	of	of	ADP
ejpam-5479	170	7	moatimid	moatimid	PROPN
ejpam-5479	170	8	et	et	PROPN
ejpam-5479	170	9	al	al	PROPN
ejpam-5479	170	10	.	.	PUNCT
ejpam-5479	171	1	[	[	X
ejpam-5479	171	2	10	10	NUM
ejpam-5479	171	3	,	,	PUNCT
ejpam-5479	171	4	11	11	NUM
ejpam-5479	171	5	,	,	PUNCT
ejpam-5479	171	6	13–19	13–19	NUM
ejpam-5479	171	7	,	,	PUNCT
ejpam-5479	171	8	22–27	22–27	NUM
ejpam-5479	171	9	]	]	PUNCT
ejpam-5479	171	10	to	to	PART
ejpam-5479	171	11	achieve	achieve	VERB
ejpam-5479	171	12	the	the	DET
ejpam-5479	171	13	corresponding	corresponding	ADJ
ejpam-5479	171	14	damping	damp	VERB
ejpam-5479	171	15	term	term	NOUN
ejpam-5479	171	16	:	:	PUNCT
ejpam-5479	171	17	σeqv	σeqv	NOUN
ejpam-5479	171	18	=	=	SYM
ejpam-5479	171	19	∫	∫	NOUN
ejpam-5479	171	20	2π	2π	NOUN
ejpam-5479	171	21	/	/	SYM
ejpam-5479	171	22	ω	ω	NUM
ejpam-5479	171	23	0	0	NUM
ejpam-5479	171	24	ζ̇f1(ζ	ζ̇f1(ζ	PROPN
ejpam-5479	171	25	,	,	PUNCT
ejpam-5479	171	26	ζ̇	ζ̇	PROPN
ejpam-5479	171	27	,	,	PUNCT
ejpam-5479	171	28	ζ̈)dt/	ζ̈)dt/	VERB
ejpam-5479	171	29	∫	∫	PROPN
ejpam-5479	171	30	2π	2π	NOUN
ejpam-5479	171	31	/	/	SYM
ejpam-5479	172	1	ω	ω	NOUN
ejpam-5479	172	2	0	0	NUM
ejpam-5479	172	3	ζ̇2dt	ζ̇2dt	NUM
ejpam-5479	172	4	.	.	PUNCT
ejpam-5479	173	1	(	(	PUNCT
ejpam-5479	173	2	7	7	NUM
ejpam-5479	173	3	)	)	PUNCT
ejpam-5479	173	4	(	(	PUNCT
ejpam-5479	173	5	3	3	X
ejpam-5479	173	6	)	)	PUNCT
ejpam-5479	173	7	non	non	ADJ
ejpam-5479	173	8	-	-	ADJ
ejpam-5479	173	9	secular	secular	ADJ
ejpam-5479	173	10	part	part	NOUN
ejpam-5479	173	11	it	it	PRON
ejpam-5479	173	12	must	must	AUX
ejpam-5479	173	13	be	be	AUX
ejpam-5479	173	14	noted	note	VERB
ejpam-5479	173	15	that	that	SCONJ
ejpam-5479	173	16	the	the	DET
ejpam-5479	173	17	quadratic	quadratic	ADJ
ejpam-5479	173	18	formula	formula	NOUN
ejpam-5479	173	19	applies	apply	VERB
ejpam-5479	173	20	to	to	ADP
ejpam-5479	173	21	the	the	DET
ejpam-5479	173	22	non	non	ADJ
ejpam-5479	173	23	-	-	ADJ
ejpam-5479	173	24	secular	secular	ADJ
ejpam-5479	173	25	component	component	NOUN
ejpam-5479	173	26	.	.	PUNCT
ejpam-5479	174	1	accordingly	accordingly	ADV
ejpam-5479	174	2	,	,	PUNCT
ejpam-5479	174	3	the	the	DET
ejpam-5479	174	4	inhomogeneity	inhomogeneity	NOUN
ejpam-5479	174	5	will	will	AUX
ejpam-5479	174	6	be	be	AUX
ejpam-5479	174	7	calculated	calculate	VERB
ejpam-5479	174	8	by	by	ADP
ejpam-5479	174	9	substituting	substitute	VERB
ejpam-5479	174	10	:	:	PUNCT
ejpam-5479	174	11	u→	u→	PROPN
ejpam-5479	174	12	ka	ka	PROPN
ejpam-5479	174	13	,	,	PUNCT
ejpam-5479	174	14	u̇→	u̇→	PROPN
ejpam-5479	174	15	kaω	kaω	PROPN
ejpam-5479	174	16	,	,	PUNCT
ejpam-5479	174	17	and	and	CCONJ
ejpam-5479	174	18	ü→	ü→	NUM
ejpam-5479	174	19	kaω2	kaω2	NOUN
ejpam-5479	174	20	in	in	ADP
ejpam-5479	174	21	the	the	DET
ejpam-5479	174	22	even	even	ADJ
ejpam-5479	174	23	non	non	ADJ
ejpam-5479	174	24	-	-	ADJ
ejpam-5479	174	25	secular	secular	ADJ
ejpam-5479	174	26	function	function	NOUN
ejpam-5479	174	27	g(u	g(u	PROPN
ejpam-5479	174	28	,	,	PUNCT
ejpam-5479	174	29	u̇	u̇	PROPN
ejpam-5479	174	30	,	,	PUNCT
ejpam-5479	174	31	ü	ü	NUM
ejpam-5479	174	32	)	)	PUNCT
ejpam-5479	174	33	.	.	PUNCT
ejpam-5479	175	1	as	as	SCONJ
ejpam-5479	175	2	shown	show	VERB
ejpam-5479	175	3	by	by	ADP
ejpam-5479	175	4	moatimid	moatimid	PROPN
ejpam-5479	175	5	et	et	PROPN
ejpam-5479	175	6	al	al	PROPN
ejpam-5479	175	7	.	.	PUNCT
ejpam-5479	176	1	[	[	X
ejpam-5479	176	2	10	10	NUM
ejpam-5479	176	3	,	,	PUNCT
ejpam-5479	176	4	11	11	NUM
ejpam-5479	176	5	,	,	PUNCT
ejpam-5479	176	6	13	13	NUM
ejpam-5479	176	7	–	–	SYM
ejpam-5479	176	8	19	19	NUM
ejpam-5479	176	9	,	,	PUNCT
ejpam-5479	176	10	22–27	22–27	NUM
ejpam-5479	176	11	]	]	PUNCT
ejpam-5479	176	12	,	,	PUNCT
ejpam-5479	176	13	the	the	DET
ejpam-5479	176	14	factor	factor	NOUN
ejpam-5479	176	15	k	k	PROPN
ejpam-5479	176	16	is	be	AUX
ejpam-5479	176	17	defined	define	VERB
ejpam-5479	176	18	as	as	ADP
ejpam-5479	176	19	k	k	PROPN
ejpam-5479	176	20	=	=	PROPN
ejpam-5479	176	21	1/2	1/2	NUM
ejpam-5479	176	22	√	√	NUM
ejpam-5479	176	23	n−	n−	PROPN
ejpam-5479	176	24	r	r	NOUN
ejpam-5479	176	25	,	,	PUNCT
ejpam-5479	176	26	where	where	SCONJ
ejpam-5479	176	27	n	n	PRON
ejpam-5479	176	28	indicates	indicate	VERB
ejpam-5479	176	29	the	the	DET
ejpam-5479	176	30	order	order	NOUN
ejpam-5479	176	31	of	of	ADP
ejpam-5479	176	32	the	the	DET
ejpam-5479	176	33	system	system	NOUN
ejpam-5479	176	34	and	and	CCONJ
ejpam-5479	176	35	r	r	NOUN
ejpam-5479	176	36	signifies	signify	VERB
ejpam-5479	176	37	the	the	DET
ejpam-5479	176	38	degree	degree	NOUN
ejpam-5479	176	39	of	of	ADP
ejpam-5479	176	40	freedom	freedom	NOUN
ejpam-5479	176	41	of	of	ADP
ejpam-5479	176	42	the	the	DET
ejpam-5479	176	43	system	system	NOUN
ejpam-5479	176	44	.	.	PUNCT
ejpam-5479	177	1	therefore	therefore	ADV
ejpam-5479	177	2	,	,	PUNCT
ejpam-5479	177	3	in	in	ADP
ejpam-5479	177	4	the	the	DET
ejpam-5479	177	5	present	present	ADJ
ejpam-5479	177	6	case	case	NOUN
ejpam-5479	177	7	:	:	PUNCT
ejpam-5479	177	8	n	n	PROPN
ejpam-5479	177	9	=	=	SYM
ejpam-5479	177	10	2	2	NUM
ejpam-5479	177	11	and	and	CCONJ
ejpam-5479	177	12	r	r	NOUN
ejpam-5479	177	13	=	=	SYM
ejpam-5479	177	14	1	1	NUM
ejpam-5479	177	15	,	,	PUNCT
ejpam-5479	177	16	then	then	ADV
ejpam-5479	177	17	the	the	DET
ejpam-5479	177	18	significance	significance	NOUN
ejpam-5479	177	19	of	of	ADP
ejpam-5479	177	20	k	k	PROPN
ejpam-5479	177	21	becomes	become	VERB
ejpam-5479	177	22	k	k	NOUN
ejpam-5479	177	23	=	=	SYM
ejpam-5479	177	24	1/2	1/2	NUM
ejpam-5479	177	25	.	.	PUNCT
ejpam-5479	178	1	to	to	PART
ejpam-5479	178	2	do	do	VERB
ejpam-5479	178	3	this	this	PRON
ejpam-5479	178	4	,	,	PUNCT
ejpam-5479	178	5	the	the	DET
ejpam-5479	178	6	nonlinear	nonlinear	NOUN
ejpam-5479	178	7	eq	eq	NOUN
ejpam-5479	178	8	.	.	PUNCT
ejpam-5479	179	1	(	(	PUNCT
ejpam-5479	179	2	1	1	X
ejpam-5479	179	3	)	)	PUNCT
ejpam-5479	179	4	is	be	AUX
ejpam-5479	179	5	converted	convert	VERB
ejpam-5479	179	6	into	into	ADP
ejpam-5479	179	7	the	the	DET
ejpam-5479	179	8	linear	linear	NOUN
ejpam-5479	179	9	eq	eq	NOUN
ejpam-5479	179	10	.	.	PUNCT
ejpam-5479	180	1	(	(	PUNCT
ejpam-5479	180	2	3	3	NUM
ejpam-5479	180	3	)	)	PUNCT
ejpam-5479	180	4	.	.	PUNCT
ejpam-5479	181	1	the	the	DET
ejpam-5479	181	2	standard	standard	ADJ
ejpam-5479	181	3	normal	normal	ADJ
ejpam-5479	181	4	form	form	NOUN
ejpam-5479	181	5	of	of	ADP
ejpam-5479	181	6	eq	eq	PROPN
ejpam-5479	181	7	.	.	PUNCT
ejpam-5479	182	1	(	(	PUNCT
ejpam-5479	182	2	3	3	X
ejpam-5479	182	3	)	)	PUNCT
ejpam-5479	182	4	may	may	AUX
ejpam-5479	182	5	be	be	AUX
ejpam-5479	182	6	used	use	VERB
ejpam-5479	182	7	to	to	PART
ejpam-5479	182	8	guess	guess	VERB
ejpam-5479	182	9	the	the	DET
ejpam-5479	182	10	stability	stability	NOUN
ejpam-5479	182	11	requirements	requirement	NOUN
ejpam-5479	182	12	in	in	ADP
ejpam-5479	182	13	a	a	DET
ejpam-5479	182	14	humbler	humble	ADJ
ejpam-5479	182	15	procedure	procedure	NOUN
ejpam-5479	182	16	,	,	PUNCT
ejpam-5479	182	17	where	where	SCONJ
ejpam-5479	182	18	the	the	DET
ejpam-5479	182	19	total	total	ADJ
ejpam-5479	182	20	frequency	frequency	NOUN
ejpam-5479	182	21	is	be	AUX
ejpam-5479	182	22	defined	define	VERB
ejpam-5479	182	23	by	by	ADP
ejpam-5479	182	24	the	the	DET
ejpam-5479	182	25	formulation	formulation	NOUN
ejpam-5479	182	26	:	:	PUNCT
ejpam-5479	183	1	∆2	∆2	PROPN
ejpam-5479	183	2	=	=	SYM
ejpam-5479	183	3	ω2	ω2	ADJ
ejpam-5479	183	4	eqv	eqv	NOUN
ejpam-5479	183	5	−	−	PROPN
ejpam-5479	183	6	σ2eqv/4	σ2eqv/4	NOUN
ejpam-5479	183	7	.	.	PUNCT
ejpam-5479	184	1	the	the	DET
ejpam-5479	184	2	stability	stability	NOUN
ejpam-5479	184	3	requirements	requirement	NOUN
ejpam-5479	184	4	need	need	VERB
ejpam-5479	184	5	:	:	PUNCT
ejpam-5479	184	6	∆2	∆2	X
ejpam-5479	184	7	>	>	PUNCT
ejpam-5479	184	8	0	0	PUNCT
ejpam-5479	184	9	and	and	CCONJ
ejpam-5479	184	10	σeqv	σeqv	NOUN
ejpam-5479	184	11	>	>	X
ejpam-5479	184	12	0	0	NUM
ejpam-5479	184	13	.	.	NOUN
ejpam-5479	185	1	3	3	X
ejpam-5479	185	2	.	.	X
ejpam-5479	185	3	structure	structure	NOUN
ejpam-5479	185	4	of	of	ADP
ejpam-5479	185	5	the	the	DET
ejpam-5479	185	6	model	model	NOUN
ejpam-5479	185	7	in	in	ADP
ejpam-5479	185	8	our	our	PRON
ejpam-5479	185	9	earlier	early	ADJ
ejpam-5479	185	10	work	work	NOUN
ejpam-5479	185	11	[	[	X
ejpam-5479	185	12	20	20	NUM
ejpam-5479	185	13	]	]	PUNCT
ejpam-5479	186	1	,	,	PUNCT
ejpam-5479	186	2	we	we	PRON
ejpam-5479	186	3	deduced	deduce	VERB
ejpam-5479	186	4	the	the	DET
ejpam-5479	186	5	controlling	control	VERB
ejpam-5479	186	6	governing	govern	VERB
ejpam-5479	186	7	equation	equation	NOUN
ejpam-5479	186	8	of	of	ADP
ejpam-5479	186	9	the	the	DET
ejpam-5479	186	10	sp	sp	NOUN
ejpam-5479	186	11	linked	link	VERB
ejpam-5479	186	12	with	with	ADP
ejpam-5479	186	13	a	a	DET
ejpam-5479	186	14	rotating	rotate	VERB
ejpam-5479	186	15	wheel	wheel	NOUN
ejpam-5479	186	16	and	and	CCONJ
ejpam-5479	186	17	constrained	constrain	VERB
ejpam-5479	186	18	by	by	ADP
ejpam-5479	186	19	a	a	DET
ejpam-5479	186	20	light	light	ADJ
ejpam-5479	186	21	spring	spring	NOUN
ejpam-5479	186	22	.	.	PUNCT
ejpam-5479	187	1	the	the	DET
ejpam-5479	187	2	fundamental	fundamental	ADJ
ejpam-5479	187	3	controlling	control	VERB
ejpam-5479	187	4	equation	equation	NOUN
ejpam-5479	187	5	for	for	ADP
ejpam-5479	187	6	motion	motion	NOUN
ejpam-5479	187	7	is	be	AUX
ejpam-5479	187	8	given	give	VERB
ejpam-5479	187	9	as	as	ADP
ejpam-5479	187	10	:(	:(	PROPN
ejpam-5479	187	11	r2	r2	PROPN
ejpam-5479	187	12	+	+	CCONJ
ejpam-5479	187	13	1	1	NUM
ejpam-5479	187	14	+	+	SYM
ejpam-5479	187	15	2r	2r	NUM
ejpam-5479	187	16	cos	cos	PROPN
ejpam-5479	187	17	θ	θ	PROPN
ejpam-5479	187	18	)	)	PUNCT
ejpam-5479	188	1	θ̈	θ̈	ADP
ejpam-5479	188	2	−	−	NOUN
ejpam-5479	188	3	rθ̇2	rθ̇2	ADJ
ejpam-5479	188	4	sin	sin	NOUN
ejpam-5479	188	5	θ	θ	PROPN
ejpam-5479	188	6	+	+	CCONJ
ejpam-5479	188	7	kr2θ	kr2θ	PROPN
ejpam-5479	188	8	=	=	SYM
ejpam-5479	188	9	0	0	NUM
ejpam-5479	188	10	,	,	PUNCT
ejpam-5479	188	11	(	(	PUNCT
ejpam-5479	188	12	8)	8)	NUM
ejpam-5479	188	13	where	where	SCONJ
ejpam-5479	188	14	r	r	NOUN
ejpam-5479	188	15	is	be	AUX
ejpam-5479	188	16	the	the	DET
ejpam-5479	188	17	radius	radius	NOUN
ejpam-5479	188	18	of	of	ADP
ejpam-5479	188	19	the	the	DET
ejpam-5479	188	20	rolling	rolling	ADJ
ejpam-5479	188	21	wheel	wheel	NOUN
ejpam-5479	188	22	,	,	PUNCT
ejpam-5479	188	23	and	and	CCONJ
ejpam-5479	188	24	k	k	PROPN
ejpam-5479	188	25	is	be	AUX
ejpam-5479	188	26	the	the	DET
ejpam-5479	188	27	stiffness	stiffness	NOUN
ejpam-5479	188	28	of	of	ADP
ejpam-5479	188	29	the	the	DET
ejpam-5479	188	30	light	light	ADJ
ejpam-5479	188	31	spring	spring	NOUN
ejpam-5479	188	32	.	.	PUNCT
ejpam-5479	189	1	it	it	PRON
ejpam-5479	189	2	should	should	AUX
ejpam-5479	189	3	be	be	AUX
ejpam-5479	189	4	noted	note	VERB
ejpam-5479	189	5	that	that	SCONJ
ejpam-5479	189	6	the	the	DET
ejpam-5479	189	7	stiffness	stiffness	NOUN
ejpam-5479	189	8	of	of	ADP
ejpam-5479	189	9	the	the	DET
ejpam-5479	189	10	light	light	ADJ
ejpam-5479	189	11	spring	spring	NOUN
ejpam-5479	189	12	is	be	AUX
ejpam-5479	189	13	a	a	DET
ejpam-5479	189	14	critical	critical	ADJ
ejpam-5479	189	15	factor	factor	NOUN
ejpam-5479	189	16	in	in	ADP
ejpam-5479	189	17	determining	determine	VERB
ejpam-5479	189	18	the	the	DET
ejpam-5479	189	19	dynamic	dynamic	ADJ
ejpam-5479	189	20	properties	property	NOUN
ejpam-5479	189	21	of	of	ADP
ejpam-5479	189	22	the	the	DET
ejpam-5479	189	23	system	system	NOUN
ejpam-5479	189	24	,	,	PUNCT
ejpam-5479	189	25	such	such	ADJ
ejpam-5479	189	26	as	as	ADP
ejpam-5479	189	27	stability	stability	NOUN
ejpam-5479	189	28	,	,	PUNCT
ejpam-5479	189	29	frequency	frequency	NOUN
ejpam-5479	189	30	,	,	PUNCT
ejpam-5479	189	31	and	and	CCONJ
ejpam-5479	189	32	energy	energy	NOUN
ejpam-5479	189	33	characteristics	characteristic	NOUN
ejpam-5479	189	34	.	.	PUNCT
ejpam-5479	190	1	moreover	moreover	ADV
ejpam-5479	190	2	,	,	PUNCT
ejpam-5479	190	3	the	the	DET
ejpam-5479	190	4	radius	radius	NOUN
ejpam-5479	190	5	of	of	ADP
ejpam-5479	190	6	a	a	DET
ejpam-5479	190	7	rolling	rolling	ADJ
ejpam-5479	190	8	wheel	wheel	NOUN
ejpam-5479	190	9	significantly	significantly	ADV
ejpam-5479	190	10	influences	influence	VERB
ejpam-5479	190	11	its	its	PRON
ejpam-5479	190	12	efficiency	efficiency	NOUN
ejpam-5479	190	13	,	,	PUNCT
ejpam-5479	190	14	performance	performance	NOUN
ejpam-5479	190	15	,	,	PUNCT
ejpam-5479	190	16	and	and	CCONJ
ejpam-5479	190	17	applicability	applicability	NOUN
ejpam-5479	190	18	for	for	ADP
ejpam-5479	190	19	particular	particular	ADJ
ejpam-5479	190	20	applications	application	NOUN
ejpam-5479	190	21	.	.	PUNCT
ejpam-5479	191	1	the	the	DET
ejpam-5479	191	2	sketch	sketch	NOUN
ejpam-5479	191	3	of	of	ADP
ejpam-5479	191	4	the	the	DET
ejpam-5479	191	5	physical	physical	ADJ
ejpam-5479	191	6	model	model	NOUN
ejpam-5479	191	7	is	be	AUX
ejpam-5479	191	8	shown	show	VERB
ejpam-5479	191	9	in	in	ADP
ejpam-5479	191	10	fig	fig	NOUN
ejpam-5479	191	11	.	.	PUNCT
ejpam-5479	192	1	(	(	PUNCT
ejpam-5479	192	2	1	1	NUM
ejpam-5479	192	3	)	)	PUNCT
ejpam-5479	192	4	.	.	PUNCT
ejpam-5479	193	1	as	as	SCONJ
ejpam-5479	193	2	previously	previously	ADV
ejpam-5479	193	3	stated	state	VERB
ejpam-5479	193	4	,	,	PUNCT
ejpam-5479	193	5	the	the	DET
ejpam-5479	193	6	current	current	ADJ
ejpam-5479	193	7	calculations	calculation	NOUN
ejpam-5479	193	8	are	be	AUX
ejpam-5479	193	9	a	a	DET
ejpam-5479	193	10	complete	complete	ADJ
ejpam-5479	193	11	departure	departure	NOUN
ejpam-5479	193	12	from	from	ADP
ejpam-5479	193	13	the	the	DET
ejpam-5479	193	14	earlier	early	ADJ
ejpam-5479	193	15	investigation	investigation	NOUN
ejpam-5479	193	16	[	[	X
ejpam-5479	193	17	54	54	NUM
ejpam-5479	193	18	]	]	PUNCT
ejpam-5479	193	19	.	.	PUNCT
ejpam-5479	194	1	k.	k.	PROPN
ejpam-5479	194	2	alluhydan	alluhydan	PROPN
ejpam-5479	194	3	,	,	PUNCT
ejpam-5479	194	4	g.	g.	PROPN
ejpam-5479	194	5	m	m	PROPN
ejpam-5479	194	6	moatimid	moatimid	PROPN
ejpam-5479	194	7	,	,	PUNCT
ejpam-5479	194	8	t.	t.	PROPN
ejpam-5479	194	9	s.	s.	PROPN
ejpam-5479	194	10	amer	amer	PROPN
ejpam-5479	194	11	/	/	SYM
ejpam-5479	194	12	eur	eur	PROPN
ejpam-5479	194	13	.	.	PUNCT
ejpam-5479	195	1	j.	j.	PROPN
ejpam-5479	195	2	pure	pure	PROPN
ejpam-5479	195	3	appl	appl	PROPN
ejpam-5479	195	4	.	.	PROPN
ejpam-5479	195	5	math	math	PROPN
ejpam-5479	195	6	,	,	PUNCT
ejpam-5479	195	7	17	17	NUM
ejpam-5479	195	8	(	(	PUNCT
ejpam-5479	195	9	4	4	NUM
ejpam-5479	195	10	)	)	PUNCT
ejpam-5479	195	11	(	(	PUNCT
ejpam-5479	195	12	2024	2024	NUM
ejpam-5479	195	13	)	)	PUNCT
ejpam-5479	195	14	,	,	PUNCT
ejpam-5479	195	15	3185	3185	NUM
ejpam-5479	195	16	-	-	SYM
ejpam-5479	195	17	3208	3208	NUM
ejpam-5479	195	18	3192	3192	NUM
ejpam-5479	195	19	figure	figure	NOUN
ejpam-5479	195	20	1	1	NUM
ejpam-5479	195	21	:	:	PUNCT
ejpam-5479	195	22	displays	display	VERB
ejpam-5479	195	23	the	the	DET
ejpam-5479	195	24	physical	physical	ADJ
ejpam-5479	195	25	configuration	configuration	NOUN
ejpam-5479	195	26	of	of	ADP
ejpam-5479	195	27	the	the	DET
ejpam-5479	195	28	prototype	prototype	NOUN
ejpam-5479	195	29	.	.	PUNCT
ejpam-5479	196	1	to	to	PART
ejpam-5479	196	2	repair	repair	VERB
ejpam-5479	196	3	the	the	DET
ejpam-5479	196	4	weakness	weakness	NOUN
ejpam-5479	196	5	in	in	ADP
ejpam-5479	196	6	utilizing	utilize	VERB
ejpam-5479	196	7	the	the	DET
ejpam-5479	196	8	taylor	taylor	PROPN
ejpam-5479	196	9	expansion	expansion	NOUN
ejpam-5479	196	10	in	in	ADP
ejpam-5479	196	11	expanding	expand	VERB
ejpam-5479	196	12	the	the	DET
ejpam-5479	196	13	restorative	restorative	ADJ
ejpam-5479	196	14	forces	force	NOUN
ejpam-5479	196	15	,	,	PUNCT
ejpam-5479	196	16	the	the	DET
ejpam-5479	196	17	npa	npa	NOUN
ejpam-5479	196	18	as	as	ADP
ejpam-5479	196	19	a	a	DET
ejpam-5479	196	20	novel	novel	ADJ
ejpam-5479	196	21	approach	approach	NOUN
ejpam-5479	196	22	is	be	AUX
ejpam-5479	196	23	employed	employ	VERB
ejpam-5479	196	24	.	.	PUNCT
ejpam-5479	197	1	eq	eq	X
ejpam-5479	197	2	.	.	PUNCT
ejpam-5479	198	1	(	(	PUNCT
ejpam-5479	198	2	1	1	X
ejpam-5479	198	3	)	)	PUNCT
ejpam-5479	198	4	may	may	AUX
ejpam-5479	198	5	be	be	AUX
ejpam-5479	198	6	formulated	formulate	VERB
ejpam-5479	198	7	as	as	SCONJ
ejpam-5479	198	8	follows	follow	VERB
ejpam-5479	198	9	:	:	PUNCT
ejpam-5479	198	10	θ̈	θ̈	X
ejpam-5479	199	1	+	+	SYM
ejpam-5479	199	2	2r	2r	NUM
ejpam-5479	199	3	1	1	NUM
ejpam-5479	199	4	+	+	NUM
ejpam-5479	199	5	r2	r2	PROPN
ejpam-5479	199	6	cos	cos	ADP
ejpam-5479	199	7	θ	θ	PROPN
ejpam-5479	199	8	θ̈	θ̈	CCONJ
ejpam-5479	199	9	−	−	NUM
ejpam-5479	199	10	1	1	NUM
ejpam-5479	199	11	1	1	NUM
ejpam-5479	199	12	+	+	NUM
ejpam-5479	199	13	r2	r2	PROPN
ejpam-5479	199	14	sin	sin	NOUN
ejpam-5479	199	15	θ	θ	X
ejpam-5479	199	16	θ̇2	θ̇2	PROPN
ejpam-5479	199	17	+	+	CCONJ
ejpam-5479	199	18	kr2	kr2	PROPN
ejpam-5479	199	19	1	1	NUM
ejpam-5479	199	20	+	+	CCONJ
ejpam-5479	199	21	r2	r2	PROPN
ejpam-5479	199	22	θ	θ	PROPN
ejpam-5479	199	23	=	=	SYM
ejpam-5479	199	24	0	0	X
ejpam-5479	199	25	.	.	PUNCT
ejpam-5479	200	1	(	(	PUNCT
ejpam-5479	200	2	9	9	X
ejpam-5479	200	3	)	)	PUNCT
ejpam-5479	200	4	the	the	DET
ejpam-5479	200	5	following	follow	VERB
ejpam-5479	200	6	analysis	analysis	NOUN
ejpam-5479	200	7	tackles	tackle	NOUN
ejpam-5479	200	8	both	both	CCONJ
ejpam-5479	200	9	the	the	DET
ejpam-5479	200	10	presence	presence	NOUN
ejpam-5479	200	11	and	and	CCONJ
ejpam-5479	200	12	absence	absence	NOUN
ejpam-5479	200	13	of	of	ADP
ejpam-5479	200	14	the	the	DET
ejpam-5479	200	15	time	time	NOUN
ejpam-5479	200	16	delay	delay	NOUN
ejpam-5479	200	17	.	.	PUNCT
ejpam-5479	201	1	3.1	3.1	NUM
ejpam-5479	201	2	.	.	PUNCT
ejpam-5479	202	1	the	the	DET
ejpam-5479	202	2	presence	presence	NOUN
ejpam-5479	202	3	of	of	ADP
ejpam-5479	202	4	a	a	DET
ejpam-5479	202	5	time	time	NOUN
ejpam-5479	202	6	-	-	PUNCT
ejpam-5479	202	7	delay	delay	NOUN
ejpam-5479	202	8	as	as	SCONJ
ejpam-5479	202	9	shown	show	VERB
ejpam-5479	202	10	in	in	ADP
ejpam-5479	202	11	the	the	DET
ejpam-5479	202	12	introduction	introduction	NOUN
ejpam-5479	202	13	,	,	PUNCT
ejpam-5479	202	14	the	the	DET
ejpam-5479	202	15	time	time	NOUN
ejpam-5479	202	16	delay	delay	NOUN
ejpam-5479	202	17	has	have	VERB
ejpam-5479	202	18	much	much	ADJ
ejpam-5479	202	19	significance	significance	NOUN
ejpam-5479	202	20	in	in	ADP
ejpam-5479	202	21	diverse	diverse	ADJ
ejpam-5479	202	22	fields	field	NOUN
ejpam-5479	202	23	.	.	PUNCT
ejpam-5479	203	1	timedelay	timedelay	VERB
ejpam-5479	203	2	in	in	ADP
ejpam-5479	203	3	a	a	DET
ejpam-5479	203	4	dynamical	dynamical	ADJ
ejpam-5479	203	5	system	system	NOUN
ejpam-5479	203	6	is	be	AUX
ejpam-5479	203	7	the	the	DET
ejpam-5479	203	8	period	period	NOUN
ejpam-5479	203	9	of	of	ADP
ejpam-5479	203	10	time	time	NOUN
ejpam-5479	203	11	that	that	PRON
ejpam-5479	203	12	elapses	elapse	VERB
ejpam-5479	203	13	between	between	ADP
ejpam-5479	203	14	the	the	DET
ejpam-5479	203	15	input	input	NOUN
ejpam-5479	203	16	and	and	CCONJ
ejpam-5479	203	17	a	a	DET
ejpam-5479	203	18	modification	modification	NOUN
ejpam-5479	203	19	in	in	ADP
ejpam-5479	203	20	the	the	DET
ejpam-5479	203	21	system	system	NOUN
ejpam-5479	203	22	and	and	CCONJ
ejpam-5479	203	23	the	the	DET
ejpam-5479	203	24	corresponding	corresponding	ADJ
ejpam-5479	203	25	reaction	reaction	NOUN
ejpam-5479	203	26	.	.	PUNCT
ejpam-5479	204	1	1	1	X
ejpam-5479	204	2	.	.	X
ejpam-5479	204	3	stability	stability	NOUN
ejpam-5479	204	4	:	:	PUNCT
ejpam-5479	204	5	the	the	DET
ejpam-5479	204	6	presence	presence	NOUN
ejpam-5479	204	7	of	of	ADP
ejpam-5479	204	8	a	a	DET
ejpam-5479	204	9	time	time	NOUN
ejpam-5479	204	10	-	-	PUNCT
ejpam-5479	204	11	delay	delay	NOUN
ejpam-5479	204	12	can	can	AUX
ejpam-5479	204	13	have	have	VERB
ejpam-5479	204	14	an	an	DET
ejpam-5479	204	15	impact	impact	NOUN
ejpam-5479	204	16	on	on	ADP
ejpam-5479	204	17	the	the	DET
ejpam-5479	204	18	stability	stability	NOUN
ejpam-5479	204	19	of	of	ADP
ejpam-5479	204	20	a	a	DET
ejpam-5479	204	21	system	system	NOUN
ejpam-5479	204	22	.	.	PUNCT
ejpam-5479	205	1	introducing	introduce	VERB
ejpam-5479	205	2	a	a	DET
ejpam-5479	205	3	delay	delay	NOUN
ejpam-5479	205	4	to	to	ADP
ejpam-5479	205	5	a	a	DET
ejpam-5479	205	6	system	system	NOUN
ejpam-5479	205	7	that	that	PRON
ejpam-5479	205	8	is	be	AUX
ejpam-5479	205	9	initially	initially	ADV
ejpam-5479	205	10	stable	stable	ADJ
ejpam-5479	205	11	can	can	AUX
ejpam-5479	205	12	cause	cause	VERB
ejpam-5479	205	13	it	it	PRON
ejpam-5479	205	14	to	to	PART
ejpam-5479	205	15	become	become	VERB
ejpam-5479	205	16	unstable	unstable	ADJ
ejpam-5479	205	17	,	,	PUNCT
ejpam-5479	205	18	as	as	SCONJ
ejpam-5479	205	19	the	the	DET
ejpam-5479	205	20	system	system	NOUN
ejpam-5479	205	21	’s	’s	PART
ejpam-5479	205	22	reaction	reaction	NOUN
ejpam-5479	205	23	may	may	AUX
ejpam-5479	205	24	no	no	ADV
ejpam-5479	205	25	longer	long	ADV
ejpam-5479	205	26	be	be	AUX
ejpam-5479	205	27	synchronized	synchronize	VERB
ejpam-5479	205	28	with	with	ADP
ejpam-5479	205	29	the	the	DET
ejpam-5479	205	30	inputs	input	NOUN
ejpam-5479	205	31	.	.	PUNCT
ejpam-5479	206	1	2	2	X
ejpam-5479	206	2	.	.	X
ejpam-5479	206	3	oscillations	oscillation	NOUN
ejpam-5479	206	4	:	:	PUNCT
ejpam-5479	206	5	time	time	NOUN
ejpam-5479	206	6	-	-	PUNCT
ejpam-5479	206	7	delays	delay	NOUN
ejpam-5479	206	8	have	have	VERB
ejpam-5479	206	9	the	the	DET
ejpam-5479	206	10	ability	ability	NOUN
ejpam-5479	206	11	to	to	PART
ejpam-5479	206	12	cause	cause	VERB
ejpam-5479	206	13	systems	system	NOUN
ejpam-5479	206	14	that	that	PRON
ejpam-5479	206	15	would	would	AUX
ejpam-5479	206	16	otherwise	otherwise	ADV
ejpam-5479	206	17	have	have	VERB
ejpam-5479	206	18	a	a	DET
ejpam-5479	206	19	stable	stable	ADJ
ejpam-5479	206	20	state	state	NOUN
ejpam-5479	206	21	to	to	PART
ejpam-5479	206	22	exhibit	exhibit	VERB
ejpam-5479	206	23	oscillating	oscillate	VERB
ejpam-5479	206	24	behavior	behavior	NOUN
ejpam-5479	206	25	.	.	PUNCT
ejpam-5479	207	1	this	this	DET
ejpam-5479	207	2	phenomenon	phenomenon	NOUN
ejpam-5479	207	3	might	might	AUX
ejpam-5479	207	4	result	result	VERB
ejpam-5479	207	5	in	in	ADP
ejpam-5479	207	6	prolonged	prolonged	ADJ
ejpam-5479	207	7	or	or	CCONJ
ejpam-5479	207	8	even	even	ADV
ejpam-5479	207	9	escalating	escalate	VERB
ejpam-5479	207	10	oscillations	oscillation	NOUN
ejpam-5479	207	11	,	,	PUNCT
ejpam-5479	207	12	which	which	PRON
ejpam-5479	207	13	may	may	AUX
ejpam-5479	207	14	be	be	AUX
ejpam-5479	207	15	undesirable	undesirable	ADJ
ejpam-5479	207	16	in	in	ADP
ejpam-5479	207	17	some	some	DET
ejpam-5479	207	18	applications	application	NOUN
ejpam-5479	207	19	.	.	PUNCT
ejpam-5479	208	1	2	2	X
ejpam-5479	208	2	.	.	X
ejpam-5479	208	3	control	control	NOUN
ejpam-5479	208	4	challenges	challenge	NOUN
ejpam-5479	208	5	:	:	PUNCT
ejpam-5479	208	6	when	when	SCONJ
ejpam-5479	208	7	dealing	deal	VERB
ejpam-5479	208	8	with	with	ADP
ejpam-5479	208	9	time	time	NOUN
ejpam-5479	208	10	-	-	PUNCT
ejpam-5479	208	11	delay	delay	NOUN
ejpam-5479	208	12	,	,	PUNCT
ejpam-5479	208	13	as	as	SCONJ
ejpam-5479	208	14	it	it	PRON
ejpam-5479	208	15	adds	add	VERB
ejpam-5479	208	16	complexity	complexity	NOUN
ejpam-5479	208	17	to	to	ADP
ejpam-5479	208	18	the	the	DET
ejpam-5479	208	19	controller	controller	NOUN
ejpam-5479	208	20	design	design	NOUN
ejpam-5479	208	21	and	and	CCONJ
ejpam-5479	208	22	makes	make	VERB
ejpam-5479	208	23	it	it	PRON
ejpam-5479	208	24	harder	hard	ADJ
ejpam-5479	208	25	to	to	PART
ejpam-5479	208	26	forecast	forecast	VERB
ejpam-5479	208	27	the	the	DET
ejpam-5479	208	28	future	future	ADJ
ejpam-5479	208	29	state	state	NOUN
ejpam-5479	208	30	of	of	ADP
ejpam-5479	208	31	the	the	DET
ejpam-5479	208	32	system	system	NOUN
ejpam-5479	208	33	.	.	PUNCT
ejpam-5479	209	1	it	it	PRON
ejpam-5479	209	2	is	be	AUX
ejpam-5479	209	3	necessary	necessary	ADJ
ejpam-5479	209	4	to	to	PART
ejpam-5479	209	5	implement	implement	VERB
ejpam-5479	209	6	more	more	ADV
ejpam-5479	209	7	advanced	advanced	ADJ
ejpam-5479	209	8	control	control	NOUN
ejpam-5479	209	9	mechanisms	mechanism	NOUN
ejpam-5479	209	10	in	in	ADP
ejpam-5479	209	11	order	order	NOUN
ejpam-5479	209	12	to	to	PART
ejpam-5479	209	13	guarantee	guarantee	VERB
ejpam-5479	209	14	the	the	DET
ejpam-5479	209	15	appropriate	appropriate	ADJ
ejpam-5479	209	16	level	level	NOUN
ejpam-5479	209	17	of	of	ADP
ejpam-5479	209	18	performance	performance	NOUN
ejpam-5479	209	19	.	.	PUNCT
ejpam-5479	210	1	k.	k.	PROPN
ejpam-5479	210	2	alluhydan	alluhydan	PROPN
ejpam-5479	210	3	,	,	PUNCT
ejpam-5479	210	4	g.	g.	PROPN
ejpam-5479	210	5	m	m	PROPN
ejpam-5479	210	6	moatimid	moatimid	PROPN
ejpam-5479	210	7	,	,	PUNCT
ejpam-5479	210	8	t.	t.	PROPN
ejpam-5479	210	9	s.	s.	PROPN
ejpam-5479	210	10	amer	amer	PROPN
ejpam-5479	210	11	/	/	SYM
ejpam-5479	210	12	eur	eur	PROPN
ejpam-5479	210	13	.	.	PUNCT
ejpam-5479	211	1	j.	j.	PROPN
ejpam-5479	211	2	pure	pure	PROPN
ejpam-5479	211	3	appl	appl	PROPN
ejpam-5479	211	4	.	.	PROPN
ejpam-5479	211	5	math	math	PROPN
ejpam-5479	211	6	,	,	PUNCT
ejpam-5479	211	7	17	17	NUM
ejpam-5479	211	8	(	(	PUNCT
ejpam-5479	211	9	4	4	NUM
ejpam-5479	211	10	)	)	PUNCT
ejpam-5479	211	11	(	(	PUNCT
ejpam-5479	211	12	2024	2024	NUM
ejpam-5479	211	13	)	)	PUNCT
ejpam-5479	211	14	,	,	PUNCT
ejpam-5479	211	15	3185	3185	NUM
ejpam-5479	211	16	-	-	SYM
ejpam-5479	211	17	3208	3208	NUM
ejpam-5479	211	18	3193	3193	NUM
ejpam-5479	211	19	4	4	NUM
ejpam-5479	211	20	.	.	PUNCT
ejpam-5479	211	21	precision	precision	NOUN
ejpam-5479	211	22	:	:	PUNCT
ejpam-5479	212	1	delays	delay	NOUN
ejpam-5479	212	2	can	can	AUX
ejpam-5479	212	3	lessen	lessen	VERB
ejpam-5479	212	4	the	the	DET
ejpam-5479	212	5	accuracy	accuracy	NOUN
ejpam-5479	212	6	of	of	ADP
ejpam-5479	212	7	the	the	DET
ejpam-5479	212	8	system	system	NOUN
ejpam-5479	212	9	’s	’s	PART
ejpam-5479	212	10	reaction	reaction	NOUN
ejpam-5479	212	11	,	,	PUNCT
ejpam-5479	212	12	principally	principally	ADV
ejpam-5479	212	13	in	in	ADP
ejpam-5479	212	14	systems	system	NOUN
ejpam-5479	212	15	that	that	PRON
ejpam-5479	212	16	necessitate	necessitate	ADJ
ejpam-5479	212	17	instantaneous	instantaneous	ADJ
ejpam-5479	212	18	processing	processing	NOUN
ejpam-5479	212	19	,	,	PUNCT
ejpam-5479	212	20	such	such	ADJ
ejpam-5479	212	21	as	as	ADP
ejpam-5479	212	22	communication	communication	NOUN
ejpam-5479	212	23	systems	system	NOUN
ejpam-5479	212	24	or	or	CCONJ
ejpam-5479	212	25	robots	robot	NOUN
ejpam-5479	212	26	.	.	PUNCT
ejpam-5479	213	1	in	in	ADP
ejpam-5479	213	2	the	the	DET
ejpam-5479	213	3	design	design	NOUN
ejpam-5479	213	4	and	and	CCONJ
ejpam-5479	213	5	analysis	analysis	NOUN
ejpam-5479	213	6	of	of	ADP
ejpam-5479	213	7	dynamical	dynamical	ADJ
ejpam-5479	213	8	systems	system	NOUN
ejpam-5479	213	9	,	,	PUNCT
ejpam-5479	213	10	it	it	PRON
ejpam-5479	213	11	is	be	AUX
ejpam-5479	213	12	crucial	crucial	ADJ
ejpam-5479	213	13	to	to	PART
ejpam-5479	213	14	properly	properly	ADV
ejpam-5479	213	15	take	take	VERB
ejpam-5479	213	16	into	into	ADP
ejpam-5479	213	17	account	account	NOUN
ejpam-5479	213	18	time	time	NOUN
ejpam-5479	213	19	-	-	PUNCT
ejpam-5479	213	20	delays	delay	NOUN
ejpam-5479	213	21	to	to	PART
ejpam-5479	213	22	guarantee	guarantee	VERB
ejpam-5479	213	23	appropriate	appropriate	ADJ
ejpam-5479	213	24	functioning	functioning	NOUN
ejpam-5479	213	25	and	and	CCONJ
ejpam-5479	213	26	stability	stability	NOUN
ejpam-5479	213	27	.	.	PUNCT
ejpam-5479	214	1	therefore	therefore	ADV
ejpam-5479	214	2	,	,	PUNCT
ejpam-5479	214	3	the	the	DET
ejpam-5479	214	4	upcoming	upcoming	ADJ
ejpam-5479	214	5	analysis	analysis	NOUN
ejpam-5479	214	6	is	be	AUX
ejpam-5479	214	7	based	base	VERB
ejpam-5479	214	8	on	on	ADP
ejpam-5479	214	9	the	the	DET
ejpam-5479	214	10	time	time	NOUN
ejpam-5479	214	11	-	-	PUNCT
ejpam-5479	214	12	delay	delay	NOUN
ejpam-5479	214	13	of	of	ADP
ejpam-5479	214	14	the	the	DET
ejpam-5479	214	15	position	position	NOUN
ejpam-5479	214	16	,	,	PUNCT
ejpam-5479	214	17	i.e.	i.e.	X
ejpam-5479	214	18	,	,	PUNCT
ejpam-5479	214	19	in	in	ADP
ejpam-5479	214	20	the	the	DET
ejpam-5479	214	21	last	last	ADJ
ejpam-5479	214	22	term	term	NOUN
ejpam-5479	214	23	in	in	ADP
ejpam-5479	214	24	eq	eq	ADP
ejpam-5479	214	25	.	.	PUNCT
ejpam-5479	215	1	(	(	PUNCT
ejpam-5479	215	2	9	9	NUM
ejpam-5479	215	3	)	)	PUNCT
ejpam-5479	215	4	.	.	PUNCT
ejpam-5479	216	1	accordingly	accordingly	ADV
ejpam-5479	216	2	,	,	PUNCT
ejpam-5479	216	3	one	one	PRON
ejpam-5479	216	4	gets	get	VERB
ejpam-5479	216	5	:	:	PUNCT
ejpam-5479	216	6	θ̈	θ̈	NOUN
ejpam-5479	217	1	+	+	SYM
ejpam-5479	217	2	2r	2r	NUM
ejpam-5479	217	3	1	1	NUM
ejpam-5479	217	4	+	+	NUM
ejpam-5479	217	5	r2	r2	PROPN
ejpam-5479	217	6	cos	cos	ADP
ejpam-5479	217	7	θ	θ	PROPN
ejpam-5479	217	8	θ̈	θ̈	CCONJ
ejpam-5479	217	9	−	−	NUM
ejpam-5479	217	10	1	1	NUM
ejpam-5479	217	11	1	1	NUM
ejpam-5479	217	12	+	+	NUM
ejpam-5479	217	13	r2	r2	PROPN
ejpam-5479	217	14	sin	sin	NOUN
ejpam-5479	217	15	θ	θ	X
ejpam-5479	217	16	θ̇2	θ̇2	PROPN
ejpam-5479	217	17	+	+	CCONJ
ejpam-5479	217	18	kr2	kr2	PROPN
ejpam-5479	217	19	1	1	NUM
ejpam-5479	217	20	+	+	CCONJ
ejpam-5479	217	21	r2	r2	PROPN
ejpam-5479	217	22	θ(t−	θ(t−	PROPN
ejpam-5479	217	23	τ	τ	NOUN
ejpam-5479	217	24	)	)	PUNCT
ejpam-5479	217	25	=	=	SYM
ejpam-5479	217	26	0	0	X
ejpam-5479	217	27	.	.	PUNCT
ejpam-5479	218	1	(	(	PUNCT
ejpam-5479	218	2	10	10	NUM
ejpam-5479	218	3	)	)	PUNCT
ejpam-5479	218	4	the	the	DET
ejpam-5479	218	5	time	time	NOUN
ejpam-5479	218	6	-	-	PUNCT
ejpam-5479	218	7	delay	delay	NOUN
ejpam-5479	218	8	in	in	ADP
ejpam-5479	218	9	position	position	NOUN
ejpam-5479	218	10	denotes	denote	VERB
ejpam-5479	218	11	the	the	DET
ejpam-5479	218	12	interval	interval	NOUN
ejpam-5479	218	13	between	between	ADP
ejpam-5479	218	14	the	the	DET
ejpam-5479	218	15	implementation	implementation	NOUN
ejpam-5479	218	16	of	of	ADP
ejpam-5479	218	17	a	a	DET
ejpam-5479	218	18	modification	modification	NOUN
ejpam-5479	218	19	in	in	ADP
ejpam-5479	218	20	a	a	DET
ejpam-5479	218	21	system	system	NOUN
ejpam-5479	218	22	and	and	CCONJ
ejpam-5479	218	23	the	the	DET
ejpam-5479	218	24	subsequent	subsequent	ADJ
ejpam-5479	218	25	observation	observation	NOUN
ejpam-5479	218	26	of	of	ADP
ejpam-5479	218	27	its	its	PRON
ejpam-5479	218	28	influence	influence	NOUN
ejpam-5479	218	29	on	on	ADP
ejpam-5479	218	30	the	the	DET
ejpam-5479	218	31	system	system	NOUN
ejpam-5479	218	32	’s	’s	PART
ejpam-5479	218	33	position	position	NOUN
ejpam-5479	218	34	.	.	PUNCT
ejpam-5479	219	1	this	this	DET
ejpam-5479	219	2	postponement	postponement	NOUN
ejpam-5479	219	3	may	may	AUX
ejpam-5479	219	4	arise	arise	VERB
ejpam-5479	219	5	from	from	ADP
ejpam-5479	219	6	various	various	ADJ
ejpam-5479	219	7	factors	factor	NOUN
ejpam-5479	219	8	:	:	PUNCT
ejpam-5479	219	9	1	1	X
ejpam-5479	219	10	.	.	X
ejpam-5479	219	11	massive	massive	ADJ
ejpam-5479	219	12	objects	object	NOUN
ejpam-5479	219	13	oppose	oppose	VERB
ejpam-5479	219	14	alterations	alteration	NOUN
ejpam-5479	219	15	in	in	ADP
ejpam-5479	219	16	their	their	PRON
ejpam-5479	219	17	motion	motion	NOUN
ejpam-5479	219	18	because	because	SCONJ
ejpam-5479	219	19	of	of	ADP
ejpam-5479	219	20	inertia	inertia	NOUN
ejpam-5479	219	21	.	.	PUNCT
ejpam-5479	220	1	upon	upon	SCONJ
ejpam-5479	220	2	the	the	DET
ejpam-5479	220	3	application	application	NOUN
ejpam-5479	220	4	of	of	ADP
ejpam-5479	220	5	a	a	DET
ejpam-5479	220	6	force	force	NOUN
ejpam-5479	220	7	,	,	PUNCT
ejpam-5479	220	8	there	there	PRON
ejpam-5479	220	9	is	be	VERB
ejpam-5479	220	10	a	a	DET
ejpam-5479	220	11	time	time	NOUN
ejpam-5479	220	12	-	-	PUNCT
ejpam-5479	220	13	delay	delay	NOUN
ejpam-5479	220	14	before	before	SCONJ
ejpam-5479	220	15	the	the	DET
ejpam-5479	220	16	item	item	NOUN
ejpam-5479	220	17	accelerates	accelerate	VERB
ejpam-5479	220	18	and	and	CCONJ
ejpam-5479	220	19	its	its	PRON
ejpam-5479	220	20	position	position	NOUN
ejpam-5479	220	21	alters	alter	VERB
ejpam-5479	220	22	,	,	PUNCT
ejpam-5479	220	23	correspondingly	correspondingly	ADV
ejpam-5479	220	24	.	.	PUNCT
ejpam-5479	221	1	2	2	X
ejpam-5479	221	2	.	.	X
ejpam-5479	221	3	in	in	ADP
ejpam-5479	221	4	several	several	ADJ
ejpam-5479	221	5	systems	system	NOUN
ejpam-5479	221	6	,	,	PUNCT
ejpam-5479	221	7	the	the	DET
ejpam-5479	221	8	command	command	NOUN
ejpam-5479	221	9	or	or	CCONJ
ejpam-5479	221	10	signal	signal	VERB
ejpam-5479	221	11	for	for	ADP
ejpam-5479	221	12	positional	positional	ADJ
ejpam-5479	221	13	alteration	alteration	NOUN
ejpam-5479	221	14	requires	require	VERB
ejpam-5479	221	15	time	time	NOUN
ejpam-5479	221	16	to	to	PART
ejpam-5479	221	17	propagate	propagate	VERB
ejpam-5479	221	18	through	through	ADP
ejpam-5479	221	19	the	the	DET
ejpam-5479	221	20	system	system	NOUN
ejpam-5479	221	21	.	.	PUNCT
ejpam-5479	222	1	in	in	ADP
ejpam-5479	222	2	mechanical	mechanical	ADJ
ejpam-5479	222	3	systems	system	NOUN
ejpam-5479	222	4	,	,	PUNCT
ejpam-5479	222	5	signals	signal	NOUN
ejpam-5479	222	6	must	must	AUX
ejpam-5479	222	7	traverse	traverse	VERB
ejpam-5479	222	8	gears	gear	NOUN
ejpam-5479	222	9	or	or	CCONJ
ejpam-5479	222	10	linkages	linkage	NOUN
ejpam-5479	222	11	,	,	PUNCT
ejpam-5479	222	12	but	but	CCONJ
ejpam-5479	222	13	in	in	ADP
ejpam-5479	222	14	electronic	electronic	ADJ
ejpam-5479	222	15	systems	system	NOUN
ejpam-5479	222	16	,	,	PUNCT
ejpam-5479	222	17	signals	signal	NOUN
ejpam-5479	222	18	propagate	propagate	VERB
ejpam-5479	222	19	at	at	ADP
ejpam-5479	222	20	finite	finite	ADJ
ejpam-5479	222	21	velocities	velocity	NOUN
ejpam-5479	222	22	.	.	PUNCT
ejpam-5479	223	1	3	3	X
ejpam-5479	223	2	.	.	X
ejpam-5479	223	3	frictional	frictional	ADJ
ejpam-5479	223	4	forces	force	NOUN
ejpam-5479	223	5	and	and	CCONJ
ejpam-5479	223	6	damping	damp	VERB
ejpam-5479	223	7	mechanisms	mechanism	NOUN
ejpam-5479	223	8	,	,	PUNCT
ejpam-5479	223	9	such	such	ADJ
ejpam-5479	223	10	as	as	ADP
ejpam-5479	223	11	air	air	NOUN
ejpam-5479	223	12	resistance	resistance	NOUN
ejpam-5479	223	13	or	or	CCONJ
ejpam-5479	223	14	internal	internal	ADJ
ejpam-5479	223	15	system	system	NOUN
ejpam-5479	223	16	damping	damp	VERB
ejpam-5479	223	17	,	,	PUNCT
ejpam-5479	223	18	can	can	AUX
ejpam-5479	223	19	induce	induce	VERB
ejpam-5479	223	20	a	a	DET
ejpam-5479	223	21	delay	delay	NOUN
ejpam-5479	223	22	in	in	ADP
ejpam-5479	223	23	response	response	NOUN
ejpam-5479	223	24	,	,	PUNCT
ejpam-5479	223	25	impeding	impede	VERB
ejpam-5479	223	26	positional	positional	ADJ
ejpam-5479	223	27	changes	change	NOUN
ejpam-5479	223	28	.	.	PUNCT
ejpam-5479	224	1	4	4	X
ejpam-5479	224	2	.	.	X
ejpam-5479	224	3	frictional	frictional	ADJ
ejpam-5479	224	4	forces	force	NOUN
ejpam-5479	224	5	and	and	CCONJ
ejpam-5479	224	6	damping	damp	VERB
ejpam-5479	224	7	components	component	NOUN
ejpam-5479	224	8	,	,	PUNCT
ejpam-5479	224	9	such	such	ADJ
ejpam-5479	224	10	as	as	ADP
ejpam-5479	224	11	air	air	NOUN
ejpam-5479	224	12	resistance	resistance	NOUN
ejpam-5479	224	13	or	or	CCONJ
ejpam-5479	224	14	internal	internal	ADJ
ejpam-5479	224	15	system	system	NOUN
ejpam-5479	224	16	damping	damp	VERB
ejpam-5479	224	17	,	,	PUNCT
ejpam-5479	224	18	can	can	AUX
ejpam-5479	224	19	induce	induce	VERB
ejpam-5479	224	20	a	a	DET
ejpam-5479	224	21	delay	delay	NOUN
ejpam-5479	224	22	in	in	ADP
ejpam-5479	224	23	response	response	NOUN
ejpam-5479	224	24	,	,	PUNCT
ejpam-5479	224	25	impeding	impede	VERB
ejpam-5479	224	26	positional	positional	ADJ
ejpam-5479	224	27	changes	change	NOUN
ejpam-5479	224	28	.	.	PUNCT
ejpam-5479	225	1	5	5	X
ejpam-5479	225	2	.	.	X
ejpam-5479	225	3	in	in	ADP
ejpam-5479	225	4	systems	system	NOUN
ejpam-5479	225	5	regulated	regulate	VERB
ejpam-5479	225	6	by	by	ADP
ejpam-5479	225	7	control	control	NOUN
ejpam-5479	225	8	loops	loop	NOUN
ejpam-5479	225	9	(	(	PUNCT
ejpam-5479	225	10	e.g.	e.g.	ADV
ejpam-5479	225	11	,	,	PUNCT
ejpam-5479	225	12	robotic	robotic	ADJ
ejpam-5479	225	13	arms	arm	NOUN
ejpam-5479	225	14	,	,	PUNCT
ejpam-5479	225	15	motors	motor	NOUN
ejpam-5479	225	16	)	)	PUNCT
ejpam-5479	225	17	,	,	PUNCT
ejpam-5479	225	18	intrinsic	intrinsic	ADJ
ejpam-5479	225	19	timedelays	timedelay	NOUN
ejpam-5479	225	20	arise	arise	VERB
ejpam-5479	225	21	from	from	ADP
ejpam-5479	225	22	feedback	feedback	NOUN
ejpam-5479	225	23	processing	processing	NOUN
ejpam-5479	225	24	,	,	PUNCT
ejpam-5479	225	25	decision	decision	NOUN
ejpam-5479	225	26	-	-	PUNCT
ejpam-5479	225	27	making	making	NOUN
ejpam-5479	225	28	within	within	ADP
ejpam-5479	225	29	control	control	NOUN
ejpam-5479	225	30	algorithms	algorithm	NOUN
ejpam-5479	225	31	,	,	PUNCT
ejpam-5479	225	32	and	and	CCONJ
ejpam-5479	225	33	actuator	actuator	NOUN
ejpam-5479	225	34	reaction	reaction	PROPN
ejpam-5479	225	35	times	time	NOUN
ejpam-5479	225	36	.	.	PUNCT
ejpam-5479	226	1	6	6	NUM
ejpam-5479	226	2	.	.	X
ejpam-5479	226	3	in	in	ADP
ejpam-5479	226	4	structures	structure	NOUN
ejpam-5479	226	5	,	,	PUNCT
ejpam-5479	226	6	material	material	NOUN
ejpam-5479	226	7	elasticity	elasticity	NOUN
ejpam-5479	226	8	can	can	AUX
ejpam-5479	226	9	induce	induce	VERB
ejpam-5479	226	10	a	a	DET
ejpam-5479	226	11	lagged	lag	VERB
ejpam-5479	226	12	response	response	NOUN
ejpam-5479	226	13	,	,	PUNCT
ejpam-5479	226	14	since	since	SCONJ
ejpam-5479	226	15	applied	apply	VERB
ejpam-5479	226	16	forces	force	NOUN
ejpam-5479	226	17	lead	lead	VERB
ejpam-5479	226	18	to	to	ADP
ejpam-5479	226	19	progressive	progressive	ADJ
ejpam-5479	226	20	deformations	deformation	NOUN
ejpam-5479	226	21	that	that	PRON
ejpam-5479	226	22	influence	influence	NOUN
ejpam-5479	226	23	positioning	positioning	NOUN
ejpam-5479	226	24	.	.	PUNCT
ejpam-5479	227	1	these	these	DET
ejpam-5479	227	2	variables	variable	NOUN
ejpam-5479	227	3	accumulatively	accumulatively	ADV
ejpam-5479	227	4	result	result	VERB
ejpam-5479	227	5	in	in	ADP
ejpam-5479	227	6	a	a	DET
ejpam-5479	227	7	delayed	delay	VERB
ejpam-5479	227	8	response	response	NOUN
ejpam-5479	227	9	of	of	ADP
ejpam-5479	227	10	an	an	DET
ejpam-5479	227	11	object	object	NOUN
ejpam-5479	227	12	’s	’s	PART
ejpam-5479	227	13	or	or	CCONJ
ejpam-5479	227	14	system	system	NOUN
ejpam-5479	227	15	’s	’s	PART
ejpam-5479	227	16	position	position	NOUN
ejpam-5479	227	17	to	to	ADP
ejpam-5479	227	18	an	an	DET
ejpam-5479	227	19	input	input	NOUN
ejpam-5479	227	20	change	change	NOUN
ejpam-5479	227	21	,	,	PUNCT
ejpam-5479	227	22	referred	refer	VERB
ejpam-5479	227	23	to	to	ADP
ejpam-5479	227	24	as	as	ADP
ejpam-5479	227	25	”	"	PUNCT
ejpam-5479	227	26	time	time	NOUN
ejpam-5479	227	27	delay	delay	NOUN
ejpam-5479	227	28	in	in	ADP
ejpam-5479	227	29	position	position	NOUN
ejpam-5479	227	30	”	"	PUNCT
ejpam-5479	227	31	.	.	PUNCT
ejpam-5479	228	1	the	the	DET
ejpam-5479	228	2	i.c	i.c	PROPN
ejpam-5479	228	3	.	.	PROPN
ejpam-5479	228	4	should	should	AUX
ejpam-5479	228	5	ideally	ideally	ADV
ejpam-5479	228	6	be	be	AUX
ejpam-5479	228	7	visualized	visualize	VERB
ejpam-5479	228	8	as	as	ADP
ejpam-5479	228	9	in	in	ADP
ejpam-5479	228	10	the	the	DET
ejpam-5479	228	11	following	follow	VERB
ejpam-5479	228	12	manner	manner	NOUN
ejpam-5479	228	13	θ(0	θ(0	PROPN
ejpam-5479	228	14	)	)	PUNCT
ejpam-5479	228	15	=	=	SYM
ejpam-5479	228	16	a	a	PRON
ejpam-5479	228	17	,	,	PUNCT
ejpam-5479	228	18	θ̇(0	θ̇(0	NOUN
ejpam-5479	228	19	)	)	PUNCT
ejpam-5479	228	20	=	=	SYM
ejpam-5479	229	1	0	0	X
ejpam-5479	229	2	.	.	PUNCT
ejpam-5479	230	1	(	(	PUNCT
ejpam-5479	230	2	11	11	NUM
ejpam-5479	230	3	)	)	PUNCT
ejpam-5479	230	4	where	where	SCONJ
ejpam-5479	230	5	a	a	PRON
ejpam-5479	230	6	is	be	AUX
ejpam-5479	230	7	the	the	DET
ejpam-5479	230	8	initial	initial	ADJ
ejpam-5479	230	9	oscillation	oscillation	NOUN
ejpam-5479	230	10	amplitude	amplitude	NOUN
ejpam-5479	230	11	.	.	PUNCT
ejpam-5479	231	1	now	now	ADV
ejpam-5479	231	2	,	,	PUNCT
ejpam-5479	231	3	returning	return	VERB
ejpam-5479	231	4	again	again	ADV
ejpam-5479	231	5	to	to	ADP
ejpam-5479	231	6	the	the	DET
ejpam-5479	231	7	fundamental	fundamental	ADJ
ejpam-5479	231	8	time	time	NOUN
ejpam-5479	231	9	delay	delay	NOUN
ejpam-5479	231	10	as	as	ADP
ejpam-5479	231	11	in	in	ADP
ejpam-5479	231	12	eq	eq	NOUN
ejpam-5479	231	13	.	.	PUNCT
ejpam-5479	232	1	(	(	PUNCT
ejpam-5479	232	2	10	10	NUM
ejpam-5479	232	3	)	)	PUNCT
ejpam-5479	232	4	,	,	PUNCT
ejpam-5479	232	5	the	the	DET
ejpam-5479	232	6	npa	npa	NOUN
ejpam-5479	232	7	enables	enable	VERB
ejpam-5479	232	8	us	we	PRON
ejpam-5479	232	9	to	to	PART
ejpam-5479	232	10	transform	transform	VERB
ejpam-5479	232	11	the	the	DET
ejpam-5479	232	12	nonlinear	nonlinear	ADJ
ejpam-5479	232	13	ode	ode	NOUN
ejpam-5479	232	14	as	as	SCONJ
ejpam-5479	232	15	given	give	VERB
ejpam-5479	232	16	in	in	ADP
ejpam-5479	232	17	eq	eq	ADP
ejpam-5479	232	18	.	.	PUNCT
ejpam-5479	233	1	(	(	PUNCT
ejpam-5479	233	2	10	10	NUM
ejpam-5479	233	3	)	)	PUNCT
ejpam-5479	233	4	into	into	ADP
ejpam-5479	233	5	an	an	DET
ejpam-5479	233	6	equivalent	equivalent	ADJ
ejpam-5479	233	7	linear	linear	NOUN
ejpam-5479	233	8	one	one	NUM
ejpam-5479	233	9	like	like	ADP
ejpam-5479	233	10	k.	k.	PROPN
ejpam-5479	233	11	alluhydan	alluhydan	PROPN
ejpam-5479	233	12	,	,	PUNCT
ejpam-5479	233	13	g.	g.	PROPN
ejpam-5479	233	14	m	m	PROPN
ejpam-5479	234	1	moatimid	moatimid	PROPN
ejpam-5479	234	2	,	,	PUNCT
ejpam-5479	234	3	t.	t.	PROPN
ejpam-5479	234	4	s.	s.	PROPN
ejpam-5479	234	5	amer	amer	PROPN
ejpam-5479	234	6	/	/	SYM
ejpam-5479	234	7	eur	eur	PROPN
ejpam-5479	234	8	.	.	PUNCT
ejpam-5479	235	1	j.	j.	PROPN
ejpam-5479	235	2	pure	pure	PROPN
ejpam-5479	235	3	appl	appl	PROPN
ejpam-5479	235	4	.	.	PROPN
ejpam-5479	235	5	math	math	PROPN
ejpam-5479	235	6	,	,	PUNCT
ejpam-5479	235	7	17	17	NUM
ejpam-5479	235	8	(	(	PUNCT
ejpam-5479	235	9	4	4	NUM
ejpam-5479	235	10	)	)	PUNCT
ejpam-5479	235	11	(	(	PUNCT
ejpam-5479	235	12	2024	2024	NUM
ejpam-5479	235	13	)	)	PUNCT
ejpam-5479	235	14	,	,	PUNCT
ejpam-5479	235	15	3185	3185	NUM
ejpam-5479	235	16	-	-	SYM
ejpam-5479	235	17	3208	3208	NUM
ejpam-5479	235	18	3194	3194	NUM
ejpam-5479	235	19	the	the	DET
ejpam-5479	235	20	simple	simple	ADJ
ejpam-5479	235	21	harmonic	harmonic	ADJ
ejpam-5479	235	22	motion	motion	NOUN
ejpam-5479	235	23	under	under	ADP
ejpam-5479	235	24	the	the	DET
ejpam-5479	235	25	same	same	ADJ
ejpam-5479	235	26	i.c	i.c	PROPN
ejpam-5479	235	27	.	.	PUNCT
ejpam-5479	236	1	as	as	SCONJ
ejpam-5479	236	2	given	give	VERB
ejpam-5479	236	3	in	in	ADP
ejpam-5479	236	4	eq	eq	ADP
ejpam-5479	236	5	.	.	PUNCT
ejpam-5479	237	1	(	(	PUNCT
ejpam-5479	237	2	11	11	NUM
ejpam-5479	237	3	)	)	PUNCT
ejpam-5479	237	4	.	.	PUNCT
ejpam-5479	238	1	therefore	therefore	ADV
ejpam-5479	238	2	,	,	PUNCT
ejpam-5479	238	3	the	the	DET
ejpam-5479	238	4	formulation	formulation	NOUN
ejpam-5479	238	5	of	of	ADP
ejpam-5479	238	6	the	the	DET
ejpam-5479	238	7	guessing	guess	VERB
ejpam-5479	238	8	solution	solution	NOUN
ejpam-5479	238	9	may	may	AUX
ejpam-5479	238	10	proceed	proceed	VERB
ejpam-5479	238	11	as	as	SCONJ
ejpam-5479	238	12	follows	follow	VERB
ejpam-5479	238	13	:	:	PUNCT
ejpam-5479	238	14	u	u	NOUN
ejpam-5479	238	15	=	=	PUNCT
ejpam-5479	238	16	a	a	DET
ejpam-5479	238	17	cosωt	cosωt	NOUN
ejpam-5479	238	18	,	,	PUNCT
ejpam-5479	238	19	u̇	u̇	PROPN
ejpam-5479	238	20	=	=	PUNCT
ejpam-5479	238	21	−aωsinωt	−aωsinωt	PROPN
ejpam-5479	238	22	,	,	PUNCT
ejpam-5479	238	23	and	and	CCONJ
ejpam-5479	238	24	ü	ü	X
ejpam-5479	238	25	=	=	SYM
ejpam-5479	238	26	−ω2u	−ω2u	NUM
ejpam-5479	238	27	,	,	PUNCT
ejpam-5479	238	28	(	(	PUNCT
ejpam-5479	238	29	12	12	NUM
ejpam-5479	238	30	)	)	PUNCT
ejpam-5479	238	31	where	where	SCONJ
ejpam-5479	238	32	ω	ω	NOUN
ejpam-5479	238	33	is	be	AUX
ejpam-5479	238	34	known	know	VERB
ejpam-5479	238	35	as	as	ADP
ejpam-5479	238	36	the	the	DET
ejpam-5479	238	37	total	total	ADJ
ejpam-5479	238	38	frequency	frequency	NOUN
ejpam-5479	238	39	that	that	PRON
ejpam-5479	238	40	depends	depend	VERB
ejpam-5479	238	41	on	on	ADP
ejpam-5479	238	42	all	all	DET
ejpam-5479	238	43	parameters	parameter	NOUN
ejpam-5479	238	44	of	of	ADP
ejpam-5479	238	45	the	the	DET
ejpam-5479	238	46	original	original	ADJ
ejpam-5479	238	47	system	system	NOUN
ejpam-5479	238	48	.	.	PUNCT
ejpam-5479	239	1	it	it	PRON
ejpam-5479	239	2	will	will	AUX
ejpam-5479	239	3	be	be	AUX
ejpam-5479	239	4	determined	determine	VERB
ejpam-5479	239	5	later	later	ADV
ejpam-5479	239	6	.	.	PUNCT
ejpam-5479	240	1	appropriately	appropriately	ADV
ejpam-5479	240	2	,	,	PUNCT
ejpam-5479	240	3	the	the	DET
ejpam-5479	240	4	shift	shift	NOUN
ejpam-5479	240	5	of	of	ADP
ejpam-5479	240	6	the	the	DET
ejpam-5479	240	7	independent	independent	ADJ
ejpam-5479	240	8	time	time	NOUN
ejpam-5479	240	9	delay	delay	NOUN
ejpam-5479	240	10	may	may	AUX
ejpam-5479	240	11	be	be	AUX
ejpam-5479	240	12	expressed	express	VERB
ejpam-5479	240	13	as	as	ADP
ejpam-5479	240	14	:	:	PUNCT
ejpam-5479	240	15	u(t−	u(t−	PROPN
ejpam-5479	240	16	τ	τ	PROPN
ejpam-5479	240	17	)	)	PUNCT
ejpam-5479	240	18	=	=	PUNCT
ejpam-5479	241	1	a	a	DET
ejpam-5479	241	2	cosω(t−	cosω(t−	NOUN
ejpam-5479	241	3	τ	τ	X
ejpam-5479	241	4	)	)	PUNCT
ejpam-5479	241	5	=	=	SYM
ejpam-5479	241	6	a(cosωt	a(cosωt	NOUN
ejpam-5479	241	7	cosωτ	cosωτ	NOUN
ejpam-5479	241	8	+	+	CCONJ
ejpam-5479	241	9	sinωt	sinωt	NOUN
ejpam-5479	241	10	sinωτ	sinωτ	NOUN
ejpam-5479	241	11	)	)	PUNCT
ejpam-5479	241	12	=	=	SYM
ejpam-5479	241	13	u(t	u(t	NOUN
ejpam-5479	241	14	)	)	PUNCT
ejpam-5479	241	15	cosωτ	cosωτ	NOUN
ejpam-5479	241	16	−	−	NOUN
ejpam-5479	241	17	1	1	NUM
ejpam-5479	241	18	ω	ω	NUM
ejpam-5479	241	19	u̇(t	u̇(t	NOUN
ejpam-5479	241	20	)	)	PUNCT
ejpam-5479	241	21	sinωτ	sinωτ	NOUN
ejpam-5479	241	22	.	.	PUNCT
ejpam-5479	242	1	(	(	PUNCT
ejpam-5479	242	2	13	13	NUM
ejpam-5479	242	3	)	)	PUNCT
ejpam-5479	242	4	at	at	ADP
ejpam-5479	242	5	this	this	DET
ejpam-5479	242	6	stage	stage	NOUN
ejpam-5479	242	7	,	,	PUNCT
ejpam-5479	242	8	eq	eq	NOUN
ejpam-5479	242	9	.	.	PUNCT
ejpam-5479	243	1	(	(	PUNCT
ejpam-5479	243	2	3	3	X
ejpam-5479	243	3	)	)	PUNCT
ejpam-5479	243	4	can	can	AUX
ejpam-5479	243	5	be	be	AUX
ejpam-5479	243	6	expressed	express	VERB
ejpam-5479	243	7	as	as	SCONJ
ejpam-5479	243	8	follows	follow	VERB
ejpam-5479	243	9	:	:	PUNCT
ejpam-5479	243	10	θ̈	θ̈	X
ejpam-5479	243	11	+	+	CCONJ
ejpam-5479	243	12	f1(θ̇	f1(θ̇	ADJ
ejpam-5479	243	13	)	)	PUNCT
ejpam-5479	243	14	+	+	X
ejpam-5479	243	15	f2(θ	f2(θ	ADJ
ejpam-5479	243	16	,	,	PUNCT
ejpam-5479	243	17	θ̇	θ̇	ADJ
ejpam-5479	243	18	,	,	PUNCT
ejpam-5479	243	19	θ̈	θ̈	NOUN
ejpam-5479	243	20	)	)	PUNCT
ejpam-5479	243	21	=	=	SYM
ejpam-5479	243	22	0	0	NUM
ejpam-5479	243	23	,	,	PUNCT
ejpam-5479	243	24	(	(	PUNCT
ejpam-5479	243	25	14	14	NUM
ejpam-5479	243	26	)	)	PUNCT
ejpam-5479	243	27	where	where	SCONJ
ejpam-5479	243	28	f1(θ̇	f1(θ̇	NOUN
ejpam-5479	243	29	)	)	PUNCT
ejpam-5479	243	30	=	=	SYM
ejpam-5479	243	31	−	−	PROPN
ejpam-5479	243	32	kr2	kr2	NUM
ejpam-5479	243	33	ω(1+r2	ω(1+r2	PROPN
ejpam-5479	243	34	)	)	PUNCT
ejpam-5479	243	35	θ̇	θ̇	PRON
ejpam-5479	243	36	sinωτ	sinωτ	NOUN
ejpam-5479	243	37	f2(θ	f2(θ	PROPN
ejpam-5479	243	38	,	,	PUNCT
ejpam-5479	243	39	θ̇	θ̇	ADJ
ejpam-5479	243	40	,	,	PUNCT
ejpam-5479	243	41	θ̈	θ̈	NOUN
ejpam-5479	243	42	)	)	PUNCT
ejpam-5479	243	43	=	=	SYM
ejpam-5479	244	1	2r	2r	NUM
ejpam-5479	244	2	1+r2	1+r2	NUM
ejpam-5479	244	3	cos	cos	ADP
ejpam-5479	244	4	θ	θ	PROPN
ejpam-5479	244	5	θ̈	θ̈	NOUN
ejpam-5479	244	6	−	−	NUM
ejpam-5479	244	7	r	r	NOUN
ejpam-5479	244	8	1+r2	1+r2	NUM
ejpam-5479	244	9	θ̇2	θ̇2	PROPN
ejpam-5479	244	10	sin	sin	VERB
ejpam-5479	244	11	θ	θ	PROPN
ejpam-5479	244	12	+	+	CCONJ
ejpam-5479	245	1	kr2	kr2	PROPN
ejpam-5479	245	2	1+r2	1+r2	NUM
ejpam-5479	245	3	θ	θ	NOUN
ejpam-5479	245	4	cosωτ	cosωτ	NOUN
ejpam-5479	245	5	}	}	PUNCT
ejpam-5479	245	6	.	.	PUNCT
ejpam-5479	246	1	(	(	PUNCT
ejpam-5479	246	2	15	15	NUM
ejpam-5479	246	3	)	)	PUNCT
ejpam-5479	246	4	currently	currently	ADV
ejpam-5479	246	5	,	,	PUNCT
ejpam-5479	246	6	an	an	DET
ejpam-5479	246	7	equivalent	equivalent	ADJ
ejpam-5479	246	8	frequency	frequency	NOUN
ejpam-5479	246	9	ϖ2	ϖ2	NOUN
ejpam-5479	246	10	can	can	AUX
ejpam-5479	246	11	be	be	AUX
ejpam-5479	246	12	evaluated	evaluate	VERB
ejpam-5479	246	13	as	as	SCONJ
ejpam-5479	246	14	shown	show	VERB
ejpam-5479	246	15	previously	previously	ADV
ejpam-5479	246	16	by	by	ADP
ejpam-5479	246	17	moatimid	moatimid	PROPN
ejpam-5479	246	18	et	et	PROPN
ejpam-5479	246	19	al	al	PROPN
ejpam-5479	246	20	.	.	PUNCT
ejpam-5479	247	1	[	[	X
ejpam-5479	247	2	10	10	NUM
ejpam-5479	247	3	,	,	PUNCT
ejpam-5479	247	4	11	11	NUM
ejpam-5479	247	5	,	,	PUNCT
ejpam-5479	247	6	13–19	13–19	NUM
ejpam-5479	247	7	,	,	PUNCT
ejpam-5479	247	8	22–27	22–27	NUM
ejpam-5479	247	9	]	]	PUNCT
ejpam-5479	247	10	in	in	ADP
ejpam-5479	247	11	the	the	DET
ejpam-5479	247	12	following	following	ADJ
ejpam-5479	247	13	manner	manner	NOUN
ejpam-5479	247	14	:	:	PUNCT
ejpam-5479	247	15	ϖ2	ϖ2	NOUN
ejpam-5479	247	16	eqv	eqv	NOUN
ejpam-5479	247	17	=	=	SYM
ejpam-5479	247	18	∫	∫	PROPN
ejpam-5479	247	19	2π	2π	NOUN
ejpam-5479	247	20	/	/	SYM
ejpam-5479	248	1	ω	ω	NUM
ejpam-5479	248	2	0	0	NUM
ejpam-5479	248	3	uf2(u	uf2(u	PROPN
ejpam-5479	248	4	,	,	PUNCT
ejpam-5479	248	5	u̇	u̇	PROPN
ejpam-5479	248	6	,	,	PUNCT
ejpam-5479	248	7	ü)dt/	ü)dt/	PROPN
ejpam-5479	248	8	∫	∫	PROPN
ejpam-5479	248	9	2π	2π	NOUN
ejpam-5479	248	10	/	/	SYM
ejpam-5479	248	11	ω	ω	NUM
ejpam-5479	248	12	0	0	PUNCT
ejpam-5479	248	13	u2dt	u2dt	PUNCT
ejpam-5479	248	14	=	=	SYM
ejpam-5479	248	15	r	r	NOUN
ejpam-5479	248	16	1	1	NUM
ejpam-5479	248	17	+	+	NUM
ejpam-5479	248	18	r2	r2	PROPN
ejpam-5479	248	19	(	(	PUNCT
ejpam-5479	248	20	−2ω2j0(a	−2ω2j0(a	PROPN
ejpam-5479	248	21	)	)	PUNCT
ejpam-5479	248	22	+	+	CCONJ
ejpam-5479	248	23	kr	kr	PROPN
ejpam-5479	248	24	cosωτ	cosωτ	PROPN
ejpam-5479	248	25	)	)	PUNCT
ejpam-5479	248	26	,	,	PUNCT
ejpam-5479	248	27	(	(	PUNCT
ejpam-5479	248	28	16	16	NUM
ejpam-5479	248	29	)	)	PUNCT
ejpam-5479	248	30	where	where	SCONJ
ejpam-5479	248	31	j0(a	j0(a	X
ejpam-5479	248	32	)	)	PUNCT
ejpam-5479	248	33	is	be	AUX
ejpam-5479	248	34	the	the	DET
ejpam-5479	248	35	bessel	bessel	ADJ
ejpam-5479	248	36	function	function	NOUN
ejpam-5479	248	37	of	of	ADP
ejpam-5479	248	38	the	the	DET
ejpam-5479	248	39	first	first	ADJ
ejpam-5479	248	40	kind	kind	NOUN
ejpam-5479	248	41	of	of	ADP
ejpam-5479	248	42	argument	argument	NOUN
ejpam-5479	248	43	a	a	PRON
ejpam-5479	248	44	of	of	ADP
ejpam-5479	248	45	order	order	NOUN
ejpam-5479	248	46	zero	zero	NUM
ejpam-5479	248	47	.	.	PUNCT
ejpam-5479	249	1	additionally	additionally	ADV
ejpam-5479	249	2	,	,	PUNCT
ejpam-5479	249	3	following	follow	VERB
ejpam-5479	249	4	moatimid	moatimid	PROPN
ejpam-5479	249	5	et	et	PROPN
ejpam-5479	249	6	al	al	PROPN
ejpam-5479	249	7	.	.	PUNCT
ejpam-5479	250	1	[	[	X
ejpam-5479	250	2	10	10	NUM
ejpam-5479	250	3	,	,	PUNCT
ejpam-5479	250	4	11	11	NUM
ejpam-5479	250	5	,	,	PUNCT
ejpam-5479	250	6	13–19	13–19	NUM
ejpam-5479	250	7	,	,	PUNCT
ejpam-5479	250	8	22–27	22–27	NUM
ejpam-5479	250	9	]	]	PUNCT
ejpam-5479	250	10	,	,	PUNCT
ejpam-5479	250	11	eĺıas	eĺıas	PROPN
ejpam-5479	250	12	-	-	PROPN
ejpam-5479	250	13	zúñiga	zúñiga	NUM
ejpam-5479	250	14	et	et	NOUN
ejpam-5479	250	15	al	al	PROPN
ejpam-5479	250	16	.	.	PUNCT
ejpam-5479	251	1	[	[	X
ejpam-5479	251	2	46	46	NUM
ejpam-5479	251	3	]	]	PUNCT
ejpam-5479	251	4	,	,	PUNCT
ejpam-5479	251	5	he	he	PRON
ejpam-5479	251	6	,	,	PUNCT
ejpam-5479	251	7	and	and	CCONJ
ejpam-5479	251	8	liu	liu	PROPN
ejpam-5479	252	1	[	[	X
ejpam-5479	252	2	7	7	NUM
ejpam-5479	252	3	]	]	PUNCT
ejpam-5479	252	4	,	,	PUNCT
ejpam-5479	252	5	the	the	DET
ejpam-5479	252	6	assessment	assessment	NOUN
ejpam-5479	252	7	of	of	ADP
ejpam-5479	252	8	the	the	DET
ejpam-5479	252	9	equivalent	equivalent	ADJ
ejpam-5479	252	10	damping	damp	VERB
ejpam-5479	252	11	term	term	NOUN
ejpam-5479	252	12	can	can	AUX
ejpam-5479	252	13	be	be	AUX
ejpam-5479	252	14	carried	carry	VERB
ejpam-5479	252	15	out	out	ADP
ejpam-5479	252	16	as	as	SCONJ
ejpam-5479	252	17	follows	follow	VERB
ejpam-5479	252	18	:	:	PUNCT
ejpam-5479	252	19	γeqv	γeqv	NOUN
ejpam-5479	252	20	=	=	SYM
ejpam-5479	252	21	∫	∫	PROPN
ejpam-5479	252	22	2π	2π	NOUN
ejpam-5479	252	23	/	/	SYM
ejpam-5479	253	1	ω	ω	NOUN
ejpam-5479	253	2	0	0	PUNCT
ejpam-5479	254	1	u̇f1(u̇)dt/	u̇f1(u̇)dt/	NUM
ejpam-5479	254	2	∫	∫	PROPN
ejpam-5479	254	3	2π	2π	NOUN
ejpam-5479	254	4	/	/	SYM
ejpam-5479	254	5	ω	ω	NOUN
ejpam-5479	254	6	0	0	X
ejpam-5479	254	7	u̇2dt	u̇2dt	NUM
ejpam-5479	254	8	=	=	SYM
ejpam-5479	254	9	−	−	PROPN
ejpam-5479	254	10	kr2	kr2	PROPN
ejpam-5479	254	11	ω(1	ω(1	PROPN
ejpam-5479	254	12	+	+	CCONJ
ejpam-5479	254	13	r2	r2	PROPN
ejpam-5479	254	14	)	)	PUNCT
ejpam-5479	254	15	sinωτ	sinωτ	NOUN
ejpam-5479	254	16	.	.	PUNCT
ejpam-5479	255	1	(	(	PUNCT
ejpam-5479	255	2	17	17	NUM
ejpam-5479	255	3	)	)	PUNCT
ejpam-5479	255	4	the	the	DET
ejpam-5479	255	5	equivalent	equivalent	ADJ
ejpam-5479	255	6	linear	linear	PROPN
ejpam-5479	255	7	ode	ode	PROPN
ejpam-5479	255	8	,	,	PUNCT
ejpam-5479	255	9	as	as	SCONJ
ejpam-5479	255	10	given	give	VERB
ejpam-5479	255	11	in	in	ADP
ejpam-5479	255	12	the	the	DET
ejpam-5479	255	13	simple	simple	ADJ
ejpam-5479	255	14	harmonic	harmonic	ADJ
ejpam-5479	255	15	motion	motion	NOUN
ejpam-5479	255	16	,	,	PUNCT
ejpam-5479	255	17	can	can	AUX
ejpam-5479	255	18	now	now	ADV
ejpam-5479	255	19	be	be	AUX
ejpam-5479	255	20	constructed	construct	VERB
ejpam-5479	255	21	as	as	SCONJ
ejpam-5479	255	22	follows	follow	VERB
ejpam-5479	255	23	:	:	PUNCT
ejpam-5479	255	24	ü+	ü+	VERB
ejpam-5479	255	25	γeqv	γeqv	NOUN
ejpam-5479	255	26	u̇+ϖ2	u̇+ϖ2	NOUN
ejpam-5479	255	27	eqvu	eqvu	NOUN
ejpam-5479	255	28	=	=	SYM
ejpam-5479	255	29	0	0	NUM
ejpam-5479	255	30	.	.	PUNCT
ejpam-5479	256	1	(	(	PUNCT
ejpam-5479	256	2	18	18	NUM
ejpam-5479	256	3	)	)	PUNCT
ejpam-5479	256	4	furthermore	furthermore	ADV
ejpam-5479	256	5	,	,	PUNCT
ejpam-5479	256	6	the	the	DET
ejpam-5479	256	7	standard	standard	ADJ
ejpam-5479	256	8	normal	normal	ADJ
ejpam-5479	256	9	form	form	NOUN
ejpam-5479	256	10	can	can	AUX
ejpam-5479	256	11	be	be	AUX
ejpam-5479	256	12	attained	attain	VERB
ejpam-5479	256	13	along	along	ADP
ejpam-5479	256	14	with	with	ADP
ejpam-5479	256	15	the	the	DET
ejpam-5479	256	16	transformation	transformation	NOUN
ejpam-5479	256	17	u(t	u(t	NOUN
ejpam-5479	256	18	)	)	PUNCT
ejpam-5479	256	19	=	=	SYM
ejpam-5479	256	20	f(t)exp(−γeqv	f(t)exp(−γeqv	NOUN
ejpam-5479	256	21	t/2	t/2	NUM
ejpam-5479	256	22	)	)	PUNCT
ejpam-5479	256	23	.	.	PUNCT
ejpam-5479	257	1	elementary	elementary	PROPN
ejpam-5479	257	2	,	,	PUNCT
ejpam-5479	257	3	the	the	DET
ejpam-5479	257	4	unknown	unknown	ADJ
ejpam-5479	257	5	function	function	NOUN
ejpam-5479	257	6	satisfies	satisfy	VERB
ejpam-5479	257	7	the	the	DET
ejpam-5479	257	8	following	follow	VERB
ejpam-5479	257	9	simple	simple	ADJ
ejpam-5479	257	10	harmonic	harmonic	ADJ
ejpam-5479	257	11	differential	differential	NOUN
ejpam-5479	257	12	equation	equation	NOUN
ejpam-5479	257	13	:	:	PUNCT
ejpam-5479	257	14	f̈	f̈	X
ejpam-5479	257	15	+	+	PROPN
ejpam-5479	257	16	ω2f	ω2f	PROPN
ejpam-5479	257	17	=	=	SYM
ejpam-5479	257	18	0	0	NUM
ejpam-5479	257	19	,	,	PUNCT
ejpam-5479	257	20	(	(	PUNCT
ejpam-5479	257	21	19	19	NUM
ejpam-5479	257	22	)	)	PUNCT
ejpam-5479	258	1	where	where	SCONJ
ejpam-5479	258	2	ω2	ω2	NOUN
ejpam-5479	258	3	=	=	SYM
ejpam-5479	258	4	ϖ2	ϖ2	NOUN
ejpam-5479	258	5	eqv	eqv	NOUN
ejpam-5479	258	6	−	−	PROPN
ejpam-5479	258	7	γ2	γ2	PROPN
ejpam-5479	258	8	eqv/4	eqv/4	PROPN
ejpam-5479	258	9	.	.	PUNCT
ejpam-5479	259	1	k.	k.	PROPN
ejpam-5479	259	2	alluhydan	alluhydan	PROPN
ejpam-5479	259	3	,	,	PUNCT
ejpam-5479	259	4	g.	g.	PROPN
ejpam-5479	259	5	m	m	PROPN
ejpam-5479	259	6	moatimid	moatimid	PROPN
ejpam-5479	259	7	,	,	PUNCT
ejpam-5479	259	8	t.	t.	PROPN
ejpam-5479	259	9	s.	s.	PROPN
ejpam-5479	259	10	amer	amer	PROPN
ejpam-5479	259	11	/	/	SYM
ejpam-5479	259	12	eur	eur	PROPN
ejpam-5479	259	13	.	.	PUNCT
ejpam-5479	260	1	j.	j.	PROPN
ejpam-5479	260	2	pure	pure	PROPN
ejpam-5479	260	3	appl	appl	PROPN
ejpam-5479	260	4	.	.	PROPN
ejpam-5479	260	5	math	math	PROPN
ejpam-5479	260	6	,	,	PUNCT
ejpam-5479	260	7	17	17	NUM
ejpam-5479	260	8	(	(	PUNCT
ejpam-5479	260	9	4	4	NUM
ejpam-5479	260	10	)	)	PUNCT
ejpam-5479	260	11	(	(	PUNCT
ejpam-5479	260	12	2024	2024	NUM
ejpam-5479	260	13	)	)	PUNCT
ejpam-5479	260	14	,	,	PUNCT
ejpam-5479	260	15	3185	3185	NUM
ejpam-5479	260	16	-	-	SYM
ejpam-5479	260	17	3208	3208	NUM
ejpam-5479	260	18	3195	3195	NUM
ejpam-5479	260	19	in	in	ADP
ejpam-5479	260	20	other	other	ADJ
ejpam-5479	260	21	words	word	NOUN
ejpam-5479	260	22	,	,	PUNCT
ejpam-5479	260	23	the	the	DET
ejpam-5479	260	24	total	total	ADJ
ejpam-5479	260	25	frequency	frequency	NOUN
ejpam-5479	260	26	can	can	AUX
ejpam-5479	260	27	be	be	AUX
ejpam-5479	260	28	obtained	obtain	VERB
ejpam-5479	260	29	by	by	ADP
ejpam-5479	260	30	combining	combine	VERB
ejpam-5479	260	31	the	the	DET
ejpam-5479	260	32	results	result	NOUN
ejpam-5479	260	33	in	in	ADP
ejpam-5479	260	34	eqs	eqs	PROPN
ejpam-5479	260	35	.	.	PUNCT
ejpam-5479	261	1	(	(	PUNCT
ejpam-5479	261	2	10	10	NUM
ejpam-5479	261	3	)	)	PUNCT
ejpam-5479	261	4	and	and	CCONJ
ejpam-5479	261	5	(	(	PUNCT
ejpam-5479	261	6	11	11	NUM
ejpam-5479	261	7	)	)	PUNCT
ejpam-5479	261	8	with	with	ADP
ejpam-5479	261	9	the	the	DET
ejpam-5479	261	10	previous	previous	ADJ
ejpam-5479	261	11	relation	relation	NOUN
ejpam-5479	261	12	to	to	PART
ejpam-5479	261	13	produce	produce	VERB
ejpam-5479	261	14	:	:	PUNCT
ejpam-5479	261	15	ω2	ω2	ADJ
ejpam-5479	261	16	=	=	SYM
ejpam-5479	261	17	r	r	NOUN
ejpam-5479	261	18	1	1	NUM
ejpam-5479	261	19	+	+	NUM
ejpam-5479	261	20	r2	r2	PROPN
ejpam-5479	261	21	(	(	PUNCT
ejpam-5479	261	22	−2ω2j0(a	−2ω2j0(a	PROPN
ejpam-5479	261	23	)	)	PUNCT
ejpam-5479	261	24	+	+	CCONJ
ejpam-5479	261	25	kr	kr	PROPN
ejpam-5479	261	26	cosωτ	cosωτ	NOUN
ejpam-5479	261	27	)	)	PUNCT
ejpam-5479	262	1	+	+	CCONJ
ejpam-5479	262	2	λ	λ	NOUN
ejpam-5479	262	3	cosωτ	cosωτ	NOUN
ejpam-5479	262	4	−	−	ADP
ejpam-5479	262	5	1	1	NUM
ejpam-5479	262	6	4	4	NUM
ejpam-5479	262	7	(	(	PUNCT
ejpam-5479	262	8	−	−	PROPN
ejpam-5479	262	9	kr2	kr2	PROPN
ejpam-5479	262	10	1	1	NUM
ejpam-5479	262	11	+	+	NUM
ejpam-5479	262	12	r2	r2	PROPN
ejpam-5479	262	13	sinωτ	sinωτ	NOUN
ejpam-5479	262	14	)	)	PUNCT
ejpam-5479	262	15	2	2	X
ejpam-5479	262	16	.	.	PUNCT
ejpam-5479	263	1	(	(	PUNCT
ejpam-5479	263	2	20	20	NUM
ejpam-5479	263	3	)	)	PUNCT
ejpam-5479	263	4	as	as	SCONJ
ejpam-5479	263	5	seen	see	VERB
ejpam-5479	263	6	,	,	PUNCT
ejpam-5479	263	7	eq	eq	ADJ
ejpam-5479	263	8	.	.	PUNCT
ejpam-5479	264	1	(	(	PUNCT
ejpam-5479	264	2	20	20	NUM
ejpam-5479	264	3	)	)	PUNCT
ejpam-5479	264	4	is	be	AUX
ejpam-5479	264	5	a	a	DET
ejpam-5479	264	6	transcendental	transcendental	ADJ
ejpam-5479	264	7	equation	equation	NOUN
ejpam-5479	264	8	in	in	ADP
ejpam-5479	264	9	ω	ω	PROPN
ejpam-5479	264	10	.	.	PUNCT
ejpam-5479	265	1	for	for	ADP
ejpam-5479	265	2	simplicity	simplicity	NOUN
ejpam-5479	265	3	,	,	PUNCT
ejpam-5479	265	4	taylor	taylor	PROPN
ejpam-5479	265	5	expansion	expansion	NOUN
ejpam-5479	265	6	may	may	AUX
ejpam-5479	265	7	be	be	AUX
ejpam-5479	265	8	employed	employ	VERB
ejpam-5479	265	9	to	to	PART
ejpam-5479	265	10	approximate	approximate	VERB
ejpam-5479	265	11	the	the	DET
ejpam-5479	265	12	values	value	NOUN
ejpam-5479	265	13	of	of	ADP
ejpam-5479	265	14	the	the	DET
ejpam-5479	265	15	trigonometric	trigonometric	ADJ
ejpam-5479	265	16	functions	function	NOUN
ejpam-5479	265	17	in	in	ADP
ejpam-5479	265	18	ω	ω	PROPN
ejpam-5479	265	19	as	as	ADP
ejpam-5479	265	20	sin	sin	NOUN
ejpam-5479	265	21	ε	ε	PROPN
ejpam-5479	265	22	∼=	∼=	PROPN
ejpam-5479	265	23	ε	ε	PROPN
ejpam-5479	265	24	,	,	PUNCT
ejpam-5479	265	25	and	and	CCONJ
ejpam-5479	265	26	cos	cos	ADP
ejpam-5479	265	27	ε	ε	PROPN
ejpam-5479	265	28	∼=	∼=	PROPN
ejpam-5479	265	29	1	1	NUM
ejpam-5479	265	30	.	.	PUNCT
ejpam-5479	266	1	in	in	ADP
ejpam-5479	266	2	this	this	DET
ejpam-5479	266	3	simplification	simplification	NOUN
ejpam-5479	266	4	,	,	PUNCT
ejpam-5479	266	5	the	the	DET
ejpam-5479	266	6	total	total	ADJ
ejpam-5479	266	7	frequency	frequency	NOUN
ejpam-5479	266	8	can	can	AUX
ejpam-5479	266	9	be	be	AUX
ejpam-5479	266	10	written	write	VERB
ejpam-5479	266	11	as	as	SCONJ
ejpam-5479	266	12	follows	follow	VERB
ejpam-5479	266	13	:	:	PUNCT
ejpam-5479	266	14	ω	ω	NUM
ejpam-5479	266	15	=	=	PUNCT
ejpam-5479	266	16	r	r	NOUN
ejpam-5479	266	17	√	√	NUM
ejpam-5479	266	18	4k	4k	NUM
ejpam-5479	266	19	+	+	CCONJ
ejpam-5479	266	20	4kr2	4kr2	NUM
ejpam-5479	266	21	−	−	NOUN
ejpam-5479	266	22	k2r2τ2	k2r2τ2	NOUN
ejpam-5479	266	23	2	2	NUM
ejpam-5479	266	24	√	√	NUM
ejpam-5479	266	25	(	(	PUNCT
ejpam-5479	266	26	1	1	NUM
ejpam-5479	266	27	+	+	NUM
ejpam-5479	266	28	r2	r2	NOUN
ejpam-5479	266	29	)	)	PUNCT
ejpam-5479	266	30	(	(	PUNCT
ejpam-5479	266	31	1	1	NUM
ejpam-5479	266	32	+	+	NUM
ejpam-5479	266	33	r2	r2	PROPN
ejpam-5479	266	34	+	+	CCONJ
ejpam-5479	266	35	2rj0(a	2rj0(a	NUM
ejpam-5479	266	36	)	)	PUNCT
ejpam-5479	266	37	)	)	PUNCT
ejpam-5479	266	38	.	.	PUNCT
ejpam-5479	267	1	(	(	PUNCT
ejpam-5479	267	2	21	21	NUM
ejpam-5479	267	3	)	)	PUNCT
ejpam-5479	267	4	to	to	PART
ejpam-5479	267	5	determine	determine	VERB
ejpam-5479	267	6	the	the	DET
ejpam-5479	267	7	value	value	NOUN
ejpam-5479	267	8	of	of	ADP
ejpam-5479	267	9	the	the	DET
ejpam-5479	267	10	equivalent	equivalent	ADJ
ejpam-5479	267	11	frequency	frequency	NOUN
ejpam-5479	267	12	,	,	PUNCT
ejpam-5479	267	13	consider	consider	VERB
ejpam-5479	267	14	the	the	DET
ejpam-5479	267	15	following	follow	VERB
ejpam-5479	267	16	dataset	dataset	NOUN
ejpam-5479	267	17	:	:	PUNCT
ejpam-5479	267	18	r	r	NOUN
ejpam-5479	267	19	=	=	SYM
ejpam-5479	267	20	3.0	3.0	NUM
ejpam-5479	267	21	,	,	PUNCT
ejpam-5479	267	22	k	k	PROPN
ejpam-5479	267	23	=	=	SYM
ejpam-5479	267	24	0.5	0.5	NUM
ejpam-5479	267	25	,	,	PUNCT
ejpam-5479	267	26	τ	τ	PROPN
ejpam-5479	267	27	=	=	SYM
ejpam-5479	267	28	0.001	0.001	NUM
ejpam-5479	267	29	and	and	CCONJ
ejpam-5479	267	30	a	a	DET
ejpam-5479	267	31	=	=	SYM
ejpam-5479	267	32	0.5	0.5	NUM
ejpam-5479	267	33	.	.	PUNCT
ejpam-5479	268	1	the	the	DET
ejpam-5479	268	2	stability	stability	NOUN
ejpam-5479	268	3	standard	standard	NOUN
ejpam-5479	268	4	requires	require	VERB
ejpam-5479	268	5	ω2	ω2	ADV
ejpam-5479	268	6	>	>	X
ejpam-5479	268	7	0	0	NUM
ejpam-5479	268	8	,	,	PUNCT
ejpam-5479	268	9	and	and	CCONJ
ejpam-5479	268	10	γeqv	γeqv	NOUN
ejpam-5479	268	11	>	>	X
ejpam-5479	268	12	0	0	NUM
ejpam-5479	268	13	.	.	PUNCT
ejpam-5479	269	1	(	(	PUNCT
ejpam-5479	269	2	22	22	NUM
ejpam-5479	269	3	)	)	PUNCT
ejpam-5479	269	4	for	for	ADP
ejpam-5479	269	5	more	more	ADJ
ejpam-5479	269	6	convenience	convenience	NOUN
ejpam-5479	269	7	,	,	PUNCT
ejpam-5479	269	8	along	along	ADP
ejpam-5479	269	9	with	with	ADP
ejpam-5479	269	10	the	the	DET
ejpam-5479	269	11	mathematic	mathematic	ADJ
ejpam-5479	269	12	software	software	NOUN
ejpam-5479	269	13	with	with	ADP
ejpam-5479	269	14	the	the	DET
ejpam-5479	269	15	commend	commend	NOUN
ejpam-5479	269	16	ndsolve	ndsolve	NOUN
ejpam-5479	269	17	,	,	PUNCT
ejpam-5479	269	18	the	the	DET
ejpam-5479	269	19	graph	graph	NOUN
ejpam-5479	269	20	of	of	ADP
ejpam-5479	269	21	the	the	DET
ejpam-5479	269	22	nonlinear	nonlinear	ADJ
ejpam-5479	269	23	ode	ode	NOUN
ejpam-5479	269	24	as	as	ADP
ejpam-5479	269	25	in	in	ADP
ejpam-5479	269	26	eq	eq	NOUN
ejpam-5479	269	27	.	.	PUNCT
ejpam-5479	270	1	(	(	PUNCT
ejpam-5479	270	2	10	10	NUM
ejpam-5479	270	3	)	)	PUNCT
ejpam-5479	270	4	is	be	AUX
ejpam-5479	270	5	graphed	graph	VERB
ejpam-5479	270	6	with	with	ADP
ejpam-5479	270	7	the	the	DET
ejpam-5479	270	8	linear	linear	ADJ
ejpam-5479	270	9	ode	ode	NOUN
ejpam-5479	270	10	as	as	SCONJ
ejpam-5479	270	11	given	give	VERB
ejpam-5479	270	12	in	in	ADP
ejpam-5479	270	13	eq	eq	ADP
ejpam-5479	270	14	.	.	PUNCT
ejpam-5479	271	1	(	(	PUNCT
ejpam-5479	271	2	18	18	NUM
ejpam-5479	271	3	)	)	PUNCT
ejpam-5479	271	4	.	.	PUNCT
ejpam-5479	272	1	returning	return	VERB
ejpam-5479	272	2	to	to	ADP
ejpam-5479	272	3	the	the	DET
ejpam-5479	272	4	foundational	foundational	ADJ
ejpam-5479	272	5	time	time	NOUN
ejpam-5479	272	6	delay	delay	NOUN
ejpam-5479	272	7	as	as	SCONJ
ejpam-5479	272	8	given	give	VERB
ejpam-5479	272	9	in	in	ADP
ejpam-5479	272	10	eq	eq	ADP
ejpam-5479	272	11	.	.	PUNCT
ejpam-5479	273	1	(	(	PUNCT
ejpam-5479	273	2	10	10	NUM
ejpam-5479	273	3	)	)	PUNCT
ejpam-5479	273	4	,	,	PUNCT
ejpam-5479	273	5	the	the	DET
ejpam-5479	273	6	npa	npa	NOUN
ejpam-5479	273	7	enables	enable	VERB
ejpam-5479	273	8	us	we	PRON
ejpam-5479	273	9	to	to	PART
ejpam-5479	273	10	create	create	VERB
ejpam-5479	273	11	a	a	DET
ejpam-5479	273	12	comparable	comparable	ADJ
ejpam-5479	273	13	linear	linear	ADJ
ejpam-5479	273	14	ode	ode	PROPN
ejpam-5479	273	15	.	.	PUNCT
ejpam-5479	274	1	the	the	DET
ejpam-5479	274	2	i.c	i.c	PROPN
ejpam-5479	274	3	.	.	PROPN
ejpam-5479	274	4	are	be	AUX
ejpam-5479	274	5	given	give	VERB
ejpam-5479	274	6	in	in	ADP
ejpam-5479	274	7	eq	eq	ADP
ejpam-5479	274	8	.	.	PUNCT
ejpam-5479	275	1	(	(	PUNCT
ejpam-5479	275	2	11	11	NUM
ejpam-5479	275	3	)	)	PUNCT
ejpam-5479	275	4	.	.	PUNCT
ejpam-5479	276	1	they	they	PRON
ejpam-5479	276	2	are	be	AUX
ejpam-5479	276	3	identical	identical	ADJ
ejpam-5479	276	4	to	to	ADP
ejpam-5479	276	5	those	those	PRON
ejpam-5479	276	6	used	use	VERB
ejpam-5479	276	7	by	by	ADP
ejpam-5479	276	8	the	the	DET
ejpam-5479	276	9	resulting	result	VERB
ejpam-5479	276	10	linear	linear	ADJ
ejpam-5479	276	11	equation	equation	NOUN
ejpam-5479	276	12	as	as	SCONJ
ejpam-5479	276	13	displayed	display	VERB
ejpam-5479	276	14	in	in	ADP
ejpam-5479	276	15	eq	eq	PROPN
ejpam-5479	276	16	.	.	PUNCT
ejpam-5479	277	1	(	(	PUNCT
ejpam-5479	277	2	18	18	NUM
ejpam-5479	277	3	)	)	PUNCT
ejpam-5479	277	4	to	to	PART
ejpam-5479	277	5	obtain	obtain	VERB
ejpam-5479	277	6	the	the	DET
ejpam-5479	277	7	non	non	ADJ
ejpam-5479	277	8	-	-	ADJ
ejpam-5479	277	9	perturbative	perturbative	ADJ
ejpam-5479	277	10	solution	solution	NOUN
ejpam-5479	277	11	(	(	PUNCT
ejpam-5479	277	12	nps	nps	PROPN
ejpam-5479	277	13	)	)	PUNCT
ejpam-5479	277	14	.	.	PUNCT
ejpam-5479	278	1	as	as	SCONJ
ejpam-5479	278	2	stated	state	VERB
ejpam-5479	278	3	earlier	early	ADV
ejpam-5479	278	4	,	,	PUNCT
ejpam-5479	278	5	the	the	DET
ejpam-5479	278	6	corresponding	corresponding	ADJ
ejpam-5479	278	7	frequency	frequency	NOUN
ejpam-5479	278	8	is	be	AUX
ejpam-5479	278	9	influenced	influence	VERB
ejpam-5479	278	10	by	by	ADP
ejpam-5479	278	11	each	each	PRON
ejpam-5479	278	12	of	of	ADP
ejpam-5479	278	13	the	the	DET
ejpam-5479	278	14	original	original	ADJ
ejpam-5479	278	15	characteristics	characteristic	NOUN
ejpam-5479	278	16	(	(	PUNCT
ejpam-5479	278	17	15	15	NUM
ejpam-5479	278	18	)	)	PUNCT
ejpam-5479	278	19	.	.	PUNCT
ejpam-5479	279	1	it	it	PRON
ejpam-5479	279	2	is	be	AUX
ejpam-5479	279	3	also	also	ADV
ejpam-5479	279	4	useful	useful	ADJ
ejpam-5479	279	5	to	to	PART
ejpam-5479	279	6	contrast	contrast	VERB
ejpam-5479	279	7	the	the	DET
ejpam-5479	279	8	equivalent	equivalent	ADJ
ejpam-5479	279	9	linear	linear	ADJ
ejpam-5479	279	10	ode	ode	ADJ
ejpam-5479	279	11	solution	solution	NOUN
ejpam-5479	279	12	with	with	ADP
ejpam-5479	279	13	the	the	DET
ejpam-5479	279	14	numerical	numerical	ADJ
ejpam-5479	279	15	solution	solution	NOUN
ejpam-5479	279	16	(	(	PUNCT
ejpam-5479	279	17	ns	ns	NUM
ejpam-5479	279	18	)	)	PUNCT
ejpam-5479	279	19	of	of	ADP
ejpam-5479	279	20	eq	eq	PROPN
ejpam-5479	279	21	.	.	PUNCT
ejpam-5479	280	1	(	(	PUNCT
ejpam-5479	280	2	10	10	NUM
ejpam-5479	280	3	)	)	PUNCT
ejpam-5479	280	4	.	.	PUNCT
ejpam-5479	281	1	the	the	DET
ejpam-5479	281	2	equivalent	equivalent	ADJ
ejpam-5479	281	3	linear	linear	ADJ
ejpam-5479	281	4	damping	damp	VERB
ejpam-5479	281	5	parameter	parameter	NOUN
ejpam-5479	281	6	is	be	AUX
ejpam-5479	281	7	provided	provide	VERB
ejpam-5479	281	8	in	in	ADP
ejpam-5479	281	9	eq	eq	ADP
ejpam-5479	281	10	.	.	PUNCT
ejpam-5479	282	1	(	(	PUNCT
ejpam-5479	282	2	19	19	NUM
ejpam-5479	282	3	)	)	PUNCT
ejpam-5479	282	4	.	.	PUNCT
ejpam-5479	283	1	the	the	DET
ejpam-5479	283	2	two	two	NUM
ejpam-5479	283	3	responses	response	NOUN
ejpam-5479	283	4	are	be	AUX
ejpam-5479	283	5	shown	show	VERB
ejpam-5479	283	6	in	in	ADP
ejpam-5479	283	7	this	this	DET
ejpam-5479	283	8	comparison	comparison	NOUN
ejpam-5479	283	9	,	,	PUNCT
ejpam-5479	283	10	as	as	SCONJ
ejpam-5479	283	11	shown	show	VERB
ejpam-5479	283	12	in	in	ADP
ejpam-5479	283	13	fig	fig	NOUN
ejpam-5479	283	14	.	.	PUNCT
ejpam-5479	284	1	(	(	PUNCT
ejpam-5479	284	2	2	2	NUM
ejpam-5479	284	3	)	)	PUNCT
ejpam-5479	284	4	.	.	PUNCT
ejpam-5479	285	1	the	the	DET
ejpam-5479	285	2	two	two	NUM
ejpam-5479	285	3	curves	curve	NOUN
ejpam-5479	285	4	are	be	AUX
ejpam-5479	285	5	plotted	plot	VERB
ejpam-5479	285	6	with	with	ADP
ejpam-5479	285	7	the	the	DET
ejpam-5479	285	8	previous	previous	ADJ
ejpam-5479	285	9	data	datum	NOUN
ejpam-5479	285	10	.	.	PUNCT
ejpam-5479	286	1	as	as	SCONJ
ejpam-5479	286	2	observed	observe	VERB
ejpam-5479	286	3	,	,	PUNCT
ejpam-5479	286	4	the	the	DET
ejpam-5479	286	5	results	result	NOUN
ejpam-5479	286	6	are	be	AUX
ejpam-5479	286	7	quite	quite	ADV
ejpam-5479	286	8	consistent	consistent	ADJ
ejpam-5479	286	9	with	with	ADP
ejpam-5479	286	10	each	each	DET
ejpam-5479	286	11	other	other	ADJ
ejpam-5479	286	12	.	.	PUNCT
ejpam-5479	287	1	moreover	moreover	ADV
ejpam-5479	287	2	,	,	PUNCT
ejpam-5479	287	3	the	the	DET
ejpam-5479	287	4	mathematical	mathematical	ADJ
ejpam-5479	287	5	software	software	NOUN
ejpam-5479	287	6	indicates	indicate	VERB
ejpam-5479	287	7	that	that	SCONJ
ejpam-5479	287	8	within	within	ADP
ejpam-5479	287	9	a	a	DET
ejpam-5479	287	10	time	time	NOUN
ejpam-5479	287	11	span	span	NOUN
ejpam-5479	287	12	of	of	ADP
ejpam-5479	287	13	100	100	NUM
ejpam-5479	287	14	units	unit	NOUN
ejpam-5479	287	15	,	,	PUNCT
ejpam-5479	287	16	the	the	DET
ejpam-5479	287	17	absolute	absolute	ADJ
ejpam-5479	287	18	error	error	NOUN
ejpam-5479	287	19	between	between	ADP
ejpam-5479	287	20	the	the	DET
ejpam-5479	287	21	theoretical	theoretical	ADJ
ejpam-5479	287	22	and	and	CCONJ
ejpam-5479	287	23	computed	computed	ADJ
ejpam-5479	287	24	solutions	solution	NOUN
ejpam-5479	287	25	is	be	AUX
ejpam-5479	287	26	0.00284	0.00284	NUM
ejpam-5479	287	27	.	.	PUNCT
ejpam-5479	288	1	when	when	SCONJ
ejpam-5479	288	2	the	the	DET
ejpam-5479	288	3	linear	linear	ADJ
ejpam-5479	288	4	and	and	CCONJ
ejpam-5479	288	5	nonlinear	nonlinear	ADJ
ejpam-5479	288	6	solutions	solution	NOUN
ejpam-5479	288	7	are	be	AUX
ejpam-5479	288	8	coinciding	coincide	VERB
ejpam-5479	288	9	,	,	PUNCT
ejpam-5479	288	10	it	it	PRON
ejpam-5479	288	11	indicates	indicate	VERB
ejpam-5479	288	12	that	that	SCONJ
ejpam-5479	288	13	,	,	PUNCT
ejpam-5479	288	14	despite	despite	SCONJ
ejpam-5479	288	15	differing	differ	VERB
ejpam-5479	288	16	definitions	definition	NOUN
ejpam-5479	288	17	,	,	PUNCT
ejpam-5479	288	18	they	they	PRON
ejpam-5479	288	19	share	share	VERB
ejpam-5479	288	20	the	the	DET
ejpam-5479	288	21	same	same	ADJ
ejpam-5479	288	22	spatial	spatial	ADJ
ejpam-5479	288	23	positions	position	NOUN
ejpam-5479	288	24	.	.	PUNCT
ejpam-5479	289	1	this	this	PRON
ejpam-5479	289	2	indicates	indicate	VERB
ejpam-5479	289	3	that	that	SCONJ
ejpam-5479	289	4	the	the	DET
ejpam-5479	289	5	two	two	NUM
ejpam-5479	289	6	curves	curve	NOUN
ejpam-5479	289	7	embody	embody	VERB
ejpam-5479	289	8	the	the	DET
ejpam-5479	289	9	same	same	ADJ
ejpam-5479	289	10	geometric	geometric	ADJ
ejpam-5479	289	11	form	form	NOUN
ejpam-5479	289	12	or	or	CCONJ
ejpam-5479	289	13	trajectory	trajectory	NOUN
ejpam-5479	289	14	.	.	PUNCT
ejpam-5479	290	1	it	it	PRON
ejpam-5479	290	2	frequently	frequently	ADV
ejpam-5479	290	3	implies	imply	VERB
ejpam-5479	290	4	that	that	SCONJ
ejpam-5479	290	5	the	the	DET
ejpam-5479	290	6	fundamental	fundamental	ADJ
ejpam-5479	290	7	physical	physical	ADJ
ejpam-5479	290	8	processes	process	NOUN
ejpam-5479	290	9	,	,	PUNCT
ejpam-5479	290	10	restrictions	restriction	NOUN
ejpam-5479	290	11	,	,	PUNCT
ejpam-5479	290	12	or	or	CCONJ
ejpam-5479	290	13	relationships	relationship	NOUN
ejpam-5479	290	14	governing	govern	VERB
ejpam-5479	290	15	the	the	DET
ejpam-5479	290	16	curves	curve	NOUN
ejpam-5479	290	17	are	be	AUX
ejpam-5479	290	18	analogous	analogous	ADJ
ejpam-5479	290	19	,	,	PUNCT
ejpam-5479	290	20	or	or	CCONJ
ejpam-5479	290	21	that	that	SCONJ
ejpam-5479	290	22	one	one	NUM
ejpam-5479	290	23	curve	curve	NOUN
ejpam-5479	290	24	represents	represent	VERB
ejpam-5479	290	25	a	a	DET
ejpam-5479	290	26	transformation	transformation	NOUN
ejpam-5479	290	27	or	or	CCONJ
ejpam-5479	290	28	particular	particular	ADJ
ejpam-5479	290	29	instance	instance	NOUN
ejpam-5479	290	30	of	of	ADP
ejpam-5479	290	31	the	the	DET
ejpam-5479	290	32	other	other	ADJ
ejpam-5479	290	33	.	.	PUNCT
ejpam-5479	291	1	k.	k.	PROPN
ejpam-5479	291	2	alluhydan	alluhydan	PROPN
ejpam-5479	291	3	,	,	PUNCT
ejpam-5479	291	4	g.	g.	PROPN
ejpam-5479	291	5	m	m	PROPN
ejpam-5479	291	6	moatimid	moatimid	PROPN
ejpam-5479	291	7	,	,	PUNCT
ejpam-5479	291	8	t.	t.	PROPN
ejpam-5479	291	9	s.	s.	PROPN
ejpam-5479	291	10	amer	amer	PROPN
ejpam-5479	291	11	/	/	SYM
ejpam-5479	291	12	eur	eur	PROPN
ejpam-5479	291	13	.	.	PUNCT
ejpam-5479	292	1	j.	j.	PROPN
ejpam-5479	292	2	pure	pure	PROPN
ejpam-5479	292	3	appl	appl	PROPN
ejpam-5479	292	4	.	.	PROPN
ejpam-5479	292	5	math	math	PROPN
ejpam-5479	292	6	,	,	PUNCT
ejpam-5479	292	7	17	17	NUM
ejpam-5479	292	8	(	(	PUNCT
ejpam-5479	292	9	4	4	NUM
ejpam-5479	292	10	)	)	PUNCT
ejpam-5479	292	11	(	(	PUNCT
ejpam-5479	292	12	2024	2024	NUM
ejpam-5479	292	13	)	)	PUNCT
ejpam-5479	292	14	,	,	PUNCT
ejpam-5479	292	15	3185	3185	NUM
ejpam-5479	292	16	-	-	SYM
ejpam-5479	292	17	3208	3208	NUM
ejpam-5479	292	18	3196	3196	NUM
ejpam-5479	292	19	figure	figure	NOUN
ejpam-5479	292	20	2	2	NUM
ejpam-5479	292	21	:	:	PUNCT
ejpam-5479	292	22	demonstrates	demonstrate	VERB
ejpam-5479	292	23	a	a	DET
ejpam-5479	292	24	strong	strong	ADJ
ejpam-5479	292	25	correspondence	correspondence	NOUN
ejpam-5479	292	26	between	between	ADP
ejpam-5479	292	27	the	the	DET
ejpam-5479	292	28	ns	ns	NOUN
ejpam-5479	292	29	of	of	ADP
ejpam-5479	292	30	eq	eq	NOUN
ejpam-5479	292	31	.	.	PUNCT
ejpam-5479	293	1	(	(	PUNCT
ejpam-5479	293	2	10	10	NUM
ejpam-5479	293	3	)	)	PUNCT
ejpam-5479	293	4	and	and	CCONJ
ejpam-5479	293	5	the	the	DET
ejpam-5479	293	6	nps	nps	PROPN
ejpam-5479	293	7	of	of	ADP
ejpam-5479	293	8	eq	eq	PROPN
ejpam-5479	293	9	.	.	PUNCT
ejpam-5479	294	1	(	(	PUNCT
ejpam-5479	294	2	19	19	NUM
ejpam-5479	294	3	)	)	PUNCT
ejpam-5479	294	4	.	.	PUNCT
ejpam-5479	295	1	for	for	ADP
ejpam-5479	295	2	more	more	ADJ
ejpam-5479	295	3	convenience	convenience	NOUN
ejpam-5479	295	4	,	,	PUNCT
ejpam-5479	295	5	with	with	ADP
ejpam-5479	295	6	the	the	DET
ejpam-5479	295	7	aid	aid	NOUN
ejpam-5479	295	8	of	of	ADP
ejpam-5479	295	9	ms	ms	PROPN
ejpam-5479	295	10	,	,	PUNCT
ejpam-5479	295	11	table	table	NOUN
ejpam-5479	295	12	(	(	PUNCT
ejpam-5479	295	13	1	1	NUM
ejpam-5479	295	14	)	)	PUNCT
ejpam-5479	295	15	is	be	AUX
ejpam-5479	295	16	presented	present	VERB
ejpam-5479	295	17	to	to	PART
ejpam-5479	295	18	indicate	indicate	VERB
ejpam-5479	295	19	the	the	DET
ejpam-5479	295	20	relation	relation	NOUN
ejpam-5479	295	21	between	between	ADP
ejpam-5479	295	22	the	the	DET
ejpam-5479	295	23	numerical	numerical	ADJ
ejpam-5479	295	24	as	as	ADV
ejpam-5479	295	25	well	well	ADV
ejpam-5479	295	26	as	as	ADP
ejpam-5479	295	27	the	the	DET
ejpam-5479	295	28	actual	actual	ADJ
ejpam-5479	295	29	values	value	NOUN
ejpam-5479	295	30	.	.	PUNCT
ejpam-5479	296	1	table	table	NOUN
ejpam-5479	296	2	(	(	PUNCT
ejpam-5479	296	3	1	1	NUM
ejpam-5479	296	4	):	):	PUNCT
ejpam-5479	296	5	points	point	VERB
ejpam-5479	296	6	out	out	ADP
ejpam-5479	296	7	the	the	DET
ejpam-5479	296	8	rapprochement	rapprochement	NOUN
ejpam-5479	296	9	between	between	ADP
ejpam-5479	296	10	the	the	DET
ejpam-5479	296	11	numerical	numerical	ADJ
ejpam-5479	296	12	ns	ns	ADJ
ejpam-5479	296	13	and	and	CCONJ
ejpam-5479	296	14	npa	npa	NOUN
ejpam-5479	296	15	outcomes	outcome	NOUN
ejpam-5479	296	16	t	t	PROPN
ejpam-5479	296	17	numerical	numerical	PROPN
ejpam-5479	296	18	equivalent	equivalent	ADJ
ejpam-5479	296	19	absolute	absolute	ADJ
ejpam-5479	296	20	error	error	NOUN
ejpam-5479	296	21	0	0	NUM
ejpam-5479	296	22	0.5	0.5	NUM
ejpam-5479	296	23	0.5	0.5	NUM
ejpam-5479	296	24	0	0	NUM
ejpam-5479	296	25	.	.	PUNCT
ejpam-5479	297	1	10	10	NUM
ejpam-5479	297	2	0.304706739041348	0.304706739041348	NUM
ejpam-5479	297	3	0.30224373475524535	0.30224373475524535	NUM
ejpam-5479	297	4	0.0024630042861026324	0.0024630042861026324	NUM
ejpam-5479	297	5	20	20	NUM
ejpam-5479	297	6	−0.13107368871285635	−0.13107368871285635	NOUN
ejpam-5479	297	7	−0.1291550605636387	−0.1291550605636387	PUNCT
ejpam-5479	297	8	0.0019186281492176438	0.0019186281492176438	NUM
ejpam-5479	297	9	30	30	NUM
ejpam-5479	297	10	−0.4657496564370769	−0.4657496564370769	NUM
ejpam-5479	297	11	−0.4635706663352717	−0.4635706663352717	NOUN
ejpam-5479	297	12	0.002178990101805167	0.002178990101805167	NUM
ejpam-5479	297	13	40	40	NUM
ejpam-5479	297	14	−0.4356924771688938	−0.4356924771688938	NOUN
ejpam-5479	297	15	−0.4334637584494958	−0.4334637584494958	NUM
ejpam-5479	297	16	0.002228718719398004	0.002228718719398004	NUM
ejpam-5479	297	17	50	50	NUM
ejpam-5479	297	18	−0.06289263814986465	−0.06289263814986465	ADP
ejpam-5479	297	19	−0.06340077978309462	−0.06340077978309462	NOUN
ejpam-5479	297	20	0.0005081416332299721	0.0005081416332299721	NUM
ejpam-5479	297	21	60	60	NUM
ejpam-5479	297	22	0.3610442523582828	0.3610442523582828	NUM
ejpam-5479	297	23	0.35565425149696445	0.35565425149696445	NUM
ejpam-5479	297	24	0.005390000861318356	0.005390000861318356	NUM
ejpam-5479	297	25	70	70	NUM
ejpam-5479	297	26	0.5029857461263576	0.5029857461263576	NUM
ejpam-5479	297	27	0.500386739396239	0.500386739396239	NUM
ejpam-5479	297	28	0.0025990067301185915	0.0025990067301185915	NUM
ejpam-5479	297	29	80	80	NUM
ejpam-5479	297	30	0.2500442070772532	0.2500442070772532	NUM
ejpam-5479	297	31	0.2492719030498598	0.2492719030498598	NUM
ejpam-5479	297	32	0.0007723040273934223	0.0007723040273934223	NUM
ejpam-5479	297	33	90	90	NUM
ejpam-5479	297	34	−0.20066057864782982	−0.20066057864782982	NOUN
ejpam-5479	297	35	−0.19307043080206004	−0.19307043080206004	X
ejpam-5479	297	36	0.007590147845769779	0.007590147845769779	NUM
ejpam-5479	297	37	100	100	NUM
ejpam-5479	297	38	−0.4956085135621511	−0.4956085135621511	NOUN
ejpam-5479	297	39	−0.48979923333890363	−0.48979923333890363	NOUN
ejpam-5479	297	40	0.005809280223247448	0.005809280223247448	NUM
ejpam-5479	297	41	for	for	ADP
ejpam-5479	297	42	more	more	ADJ
ejpam-5479	297	43	clarification	clarification	NOUN
ejpam-5479	297	44	,	,	PUNCT
ejpam-5479	297	45	the	the	DET
ejpam-5479	297	46	stability	stability	NOUN
ejpam-5479	297	47	diagrams	diagram	NOUN
ejpam-5479	297	48	are	be	AUX
ejpam-5479	297	49	plotted	plot	VERB
ejpam-5479	297	50	to	to	PART
ejpam-5479	297	51	display	display	VERB
ejpam-5479	297	52	the	the	DET
ejpam-5479	297	53	stability	stability	NOUN
ejpam-5479	297	54	configuration	configuration	NOUN
ejpam-5479	297	55	due	due	ADP
ejpam-5479	297	56	to	to	ADP
ejpam-5479	297	57	the	the	DET
ejpam-5479	297	58	influence	influence	NOUN
ejpam-5479	297	59	of	of	ADP
ejpam-5479	297	60	the	the	DET
ejpam-5479	297	61	variation	variation	NOUN
ejpam-5479	297	62	of	of	ADP
ejpam-5479	297	63	the	the	DET
ejpam-5479	297	64	various	various	ADJ
ejpam-5479	297	65	physical	physical	ADJ
ejpam-5479	297	66	parameters	parameter	NOUN
ejpam-5479	297	67	.	.	PUNCT
ejpam-5479	298	1	therefore	therefore	ADV
ejpam-5479	298	2	,	,	PUNCT
ejpam-5479	298	3	the	the	DET
ejpam-5479	298	4	stability	stability	NOUN
ejpam-5479	298	5	configurations	configuration	NOUN
ejpam-5479	298	6	are	be	AUX
ejpam-5479	298	7	plotted	plot	VERB
ejpam-5479	298	8	to	to	PART
ejpam-5479	298	9	show	show	VERB
ejpam-5479	298	10	the	the	DET
ejpam-5479	298	11	impacts	impact	NOUN
ejpam-5479	298	12	of	of	ADP
ejpam-5479	298	13	the	the	DET
ejpam-5479	298	14	parameters	parameter	NOUN
ejpam-5479	298	15	;	;	PUNCT
ejpam-5479	298	16	r	r	X
ejpam-5479	298	17	,	,	PUNCT
ejpam-5479	298	18	k	k	NOUN
ejpam-5479	298	19	,	,	PUNCT
ejpam-5479	298	20	and	and	CCONJ
ejpam-5479	298	21	τ	τ	PROPN
ejpam-5479	298	22	in	in	ADP
ejpam-5479	298	23	figs	fig	NOUN
ejpam-5479	298	24	.	.	PUNCT
ejpam-5479	299	1	(	(	PUNCT
ejpam-5479	299	2	3	3	NUM
ejpam-5479	299	3	)	)	PUNCT
ejpam-5479	299	4	,	,	PUNCT
ejpam-5479	299	5	(	(	PUNCT
ejpam-5479	299	6	4	4	NUM
ejpam-5479	299	7	)	)	PUNCT
ejpam-5479	299	8	,	,	PUNCT
ejpam-5479	299	9	and	and	CCONJ
ejpam-5479	299	10	(	(	PUNCT
ejpam-5479	299	11	5	5	NUM
ejpam-5479	299	12	)	)	PUNCT
ejpam-5479	299	13	.	.	PUNCT
ejpam-5479	300	1	in	in	ADP
ejpam-5479	300	2	this	this	DET
ejpam-5479	300	3	regard	regard	NOUN
ejpam-5479	300	4	,	,	PUNCT
ejpam-5479	300	5	fig	fig	NOUN
ejpam-5479	300	6	.	.	PUNCT
ejpam-5479	301	1	(	(	PUNCT
ejpam-5479	301	2	3	3	X
ejpam-5479	301	3	)	)	PUNCT
ejpam-5479	301	4	is	be	AUX
ejpam-5479	301	5	sketched	sketch	VERB
ejpam-5479	301	6	to	to	PART
ejpam-5479	301	7	illustrate	illustrate	VERB
ejpam-5479	301	8	the	the	DET
ejpam-5479	301	9	influence	influence	NOUN
ejpam-5479	301	10	of	of	ADP
ejpam-5479	301	11	the	the	DET
ejpam-5479	301	12	radius	radius	NOUN
ejpam-5479	301	13	of	of	ADP
ejpam-5479	301	14	the	the	DET
ejpam-5479	301	15	rolling	rolling	ADJ
ejpam-5479	301	16	wheel	wheel	NOUN
ejpam-5479	301	17	.	.	PUNCT
ejpam-5479	302	1	as	as	SCONJ
ejpam-5479	302	2	seen	see	VERB
ejpam-5479	302	3	this	this	DET
ejpam-5479	302	4	parameter	parameter	NOUN
ejpam-5479	302	5	has	have	VERB
ejpam-5479	302	6	a	a	DET
ejpam-5479	302	7	destabilizing	destabilizing	ADJ
ejpam-5479	302	8	influence	influence	NOUN
ejpam-5479	302	9	.	.	PUNCT
ejpam-5479	303	1	the	the	DET
ejpam-5479	303	2	destabilizing	destabilizing	ADJ
ejpam-5479	303	3	impact	impact	NOUN
ejpam-5479	303	4	of	of	ADP
ejpam-5479	303	5	a	a	DET
ejpam-5479	303	6	rotating	rotate	VERB
ejpam-5479	303	7	wheel	wheel	NOUN
ejpam-5479	303	8	,	,	PUNCT
ejpam-5479	303	9	especially	especially	ADV
ejpam-5479	303	10	in	in	ADP
ejpam-5479	303	11	the	the	DET
ejpam-5479	303	12	context	context	NOUN
ejpam-5479	303	13	of	of	ADP
ejpam-5479	303	14	automobiles	automobile	NOUN
ejpam-5479	303	15	,	,	PUNCT
ejpam-5479	303	16	is	be	AUX
ejpam-5479	303	17	caused	cause	VERB
ejpam-5479	303	18	by	by	ADP
ejpam-5479	303	19	a	a	DET
ejpam-5479	303	20	phenomenon	phenomenon	NOUN
ejpam-5479	303	21	known	know	VERB
ejpam-5479	303	22	as	as	ADP
ejpam-5479	303	23	gyroscopic	gyroscopic	NOUN
ejpam-5479	303	24	effect	effect	NOUN
ejpam-5479	303	25	or	or	CCONJ
ejpam-5479	303	26	gyroscopic	gyroscopic	NOUN
ejpam-5479	303	27	precession	precession	NOUN
ejpam-5479	303	28	.	.	PUNCT
ejpam-5479	304	1	when	when	SCONJ
ejpam-5479	304	2	a	a	DET
ejpam-5479	304	3	wheel	wheel	NOUN
ejpam-5479	304	4	is	be	AUX
ejpam-5479	304	5	in	in	ADP
ejpam-5479	304	6	motion	motion	NOUN
ejpam-5479	304	7	,	,	PUNCT
ejpam-5479	304	8	it	it	PRON
ejpam-5479	304	9	produces	produce	VERB
ejpam-5479	304	10	angular	angular	ADJ
ejpam-5479	304	11	momentum	momentum	NOUN
ejpam-5479	304	12	,	,	PUNCT
ejpam-5479	304	13	which	which	PRON
ejpam-5479	304	14	enhances	enhance	VERB
ejpam-5479	304	15	stability	stability	NOUN
ejpam-5479	304	16	within	within	ADP
ejpam-5479	304	17	the	the	DET
ejpam-5479	304	18	rotational	rotational	ADJ
ejpam-5479	304	19	plane	plane	NOUN
ejpam-5479	304	20	.	.	PUNCT
ejpam-5479	305	1	however	however	ADV
ejpam-5479	305	2	,	,	PUNCT
ejpam-5479	305	3	if	if	SCONJ
ejpam-5479	305	4	not	not	PART
ejpam-5479	305	5	adequately	adequately	ADV
ejpam-5479	305	6	balanced	balanced	ADJ
ejpam-5479	305	7	,	,	PUNCT
ejpam-5479	305	8	this	this	PRON
ejpam-5479	305	9	can	can	AUX
ejpam-5479	305	10	also	also	ADV
ejpam-5479	305	11	increase	increase	VERB
ejpam-5479	305	12	the	the	DET
ejpam-5479	305	13	likelihood	likelihood	NOUN
ejpam-5479	305	14	of	of	ADP
ejpam-5479	305	15	tipping	tip	VERB
ejpam-5479	305	16	over	over	ADP
ejpam-5479	305	17	for	for	ADP
ejpam-5479	305	18	systems	system	NOUN
ejpam-5479	305	19	such	such	ADJ
ejpam-5479	305	20	as	as	ADP
ejpam-5479	305	21	bicycles	bicycle	NOUN
ejpam-5479	305	22	or	or	CCONJ
ejpam-5479	305	23	motorcycles	motorcycle	NOUN
ejpam-5479	305	24	.	.	PUNCT
ejpam-5479	306	1	the	the	DET
ejpam-5479	306	2	gyroscopic	gyroscopic	NOUN
ejpam-5479	306	3	effect	effect	NOUN
ejpam-5479	306	4	serves	serve	VERB
ejpam-5479	306	5	to	to	PART
ejpam-5479	306	6	stabilise	stabilise	VERB
ejpam-5479	306	7	k.	k.	PROPN
ejpam-5479	306	8	alluhydan	alluhydan	PROPN
ejpam-5479	306	9	,	,	PUNCT
ejpam-5479	306	10	g.	g.	PROPN
ejpam-5479	306	11	m	m	PROPN
ejpam-5479	306	12	moatimid	moatimid	PROPN
ejpam-5479	306	13	,	,	PUNCT
ejpam-5479	306	14	t.	t.	PROPN
ejpam-5479	306	15	s.	s.	PROPN
ejpam-5479	306	16	amer	amer	PROPN
ejpam-5479	306	17	/	/	SYM
ejpam-5479	306	18	eur	eur	PROPN
ejpam-5479	306	19	.	.	PUNCT
ejpam-5479	307	1	j.	j.	PROPN
ejpam-5479	307	2	pure	pure	PROPN
ejpam-5479	307	3	appl	appl	PROPN
ejpam-5479	307	4	.	.	PROPN
ejpam-5479	307	5	math	math	PROPN
ejpam-5479	307	6	,	,	PUNCT
ejpam-5479	307	7	17	17	NUM
ejpam-5479	307	8	(	(	PUNCT
ejpam-5479	307	9	4	4	NUM
ejpam-5479	307	10	)	)	PUNCT
ejpam-5479	307	11	(	(	PUNCT
ejpam-5479	307	12	2024	2024	NUM
ejpam-5479	307	13	)	)	PUNCT
ejpam-5479	307	14	,	,	PUNCT
ejpam-5479	307	15	3185	3185	NUM
ejpam-5479	307	16	-	-	SYM
ejpam-5479	307	17	3208	3208	NUM
ejpam-5479	307	18	3197	3197	NUM
ejpam-5479	307	19	the	the	DET
ejpam-5479	307	20	wheel	wheel	NOUN
ejpam-5479	307	21	against	against	ADP
ejpam-5479	307	22	minor	minor	ADJ
ejpam-5479	307	23	disturbances	disturbance	NOUN
ejpam-5479	307	24	,	,	PUNCT
ejpam-5479	307	25	but	but	CCONJ
ejpam-5479	307	26	it	it	PRON
ejpam-5479	307	27	can	can	AUX
ejpam-5479	307	28	also	also	ADV
ejpam-5479	307	29	present	present	VERB
ejpam-5479	307	30	difficulties	difficulty	NOUN
ejpam-5479	307	31	in	in	ADP
ejpam-5479	307	32	maintaining	maintain	VERB
ejpam-5479	307	33	balance	balance	NOUN
ejpam-5479	307	34	when	when	SCONJ
ejpam-5479	307	35	steering	steering	NOUN
ejpam-5479	307	36	or	or	CCONJ
ejpam-5479	307	37	when	when	SCONJ
ejpam-5479	307	38	external	external	ADJ
ejpam-5479	307	39	forces	force	NOUN
ejpam-5479	307	40	,	,	PUNCT
ejpam-5479	307	41	such	such	ADJ
ejpam-5479	307	42	as	as	ADP
ejpam-5479	307	43	bumps	bump	NOUN
ejpam-5479	307	44	or	or	CCONJ
ejpam-5479	307	45	side	side	NOUN
ejpam-5479	307	46	winds	wind	NOUN
ejpam-5479	307	47	,	,	PUNCT
ejpam-5479	307	48	impact	impact	VERB
ejpam-5479	307	49	the	the	DET
ejpam-5479	307	50	wheel	wheel	NOUN
ejpam-5479	307	51	.	.	PUNCT
ejpam-5479	308	1	the	the	DET
ejpam-5479	308	2	interplay	interplay	NOUN
ejpam-5479	308	3	between	between	ADP
ejpam-5479	308	4	the	the	DET
ejpam-5479	308	5	steering	steering	NOUN
ejpam-5479	308	6	forces	force	NOUN
ejpam-5479	308	7	and	and	CCONJ
ejpam-5479	308	8	the	the	DET
ejpam-5479	308	9	wheel	wheel	NOUN
ejpam-5479	308	10	’s	’s	PART
ejpam-5479	308	11	angular	angular	ADJ
ejpam-5479	308	12	momentum	momentum	NOUN
ejpam-5479	308	13	can	can	AUX
ejpam-5479	308	14	result	result	VERB
ejpam-5479	308	15	in	in	ADP
ejpam-5479	308	16	a	a	DET
ejpam-5479	308	17	phenomenon	phenomenon	NOUN
ejpam-5479	308	18	called	call	VERB
ejpam-5479	308	19	”	"	PUNCT
ejpam-5479	308	20	speed	speed	NOUN
ejpam-5479	308	21	vibrate	vibrate	NOUN
ejpam-5479	308	22	,	,	PUNCT
ejpam-5479	308	23	”	"	PUNCT
ejpam-5479	308	24	characterized	characterize	VERB
ejpam-5479	308	25	by	by	ADP
ejpam-5479	308	26	wobbling	wobble	VERB
ejpam-5479	308	27	or	or	CCONJ
ejpam-5479	308	28	oscillation	oscillation	NOUN
ejpam-5479	308	29	.	.	PUNCT
ejpam-5479	309	1	if	if	SCONJ
ejpam-5479	309	2	left	leave	VERB
ejpam-5479	309	3	uncontrolled	uncontrolled	ADJ
ejpam-5479	309	4	,	,	PUNCT
ejpam-5479	309	5	this	this	PRON
ejpam-5479	309	6	can	can	AUX
ejpam-5479	309	7	have	have	VERB
ejpam-5479	309	8	a	a	DET
ejpam-5479	309	9	destabilizing	destabilizing	ADJ
ejpam-5479	309	10	effect	effect	NOUN
ejpam-5479	309	11	.	.	PUNCT
ejpam-5479	310	1	furthermore	furthermore	ADV
ejpam-5479	310	2	,	,	PUNCT
ejpam-5479	310	3	the	the	DET
ejpam-5479	310	4	area	area	NOUN
ejpam-5479	310	5	of	of	ADP
ejpam-5479	310	6	contact	contact	NOUN
ejpam-5479	310	7	between	between	ADP
ejpam-5479	310	8	the	the	DET
ejpam-5479	310	9	wheel	wheel	NOUN
ejpam-5479	310	10	and	and	CCONJ
ejpam-5479	310	11	the	the	DET
ejpam-5479	310	12	ground	ground	NOUN
ejpam-5479	310	13	might	might	AUX
ejpam-5479	310	14	move	move	VERB
ejpam-5479	310	15	as	as	SCONJ
ejpam-5479	310	16	the	the	DET
ejpam-5479	310	17	wheel	wheel	NOUN
ejpam-5479	310	18	is	be	AUX
ejpam-5479	310	19	rolling	roll	VERB
ejpam-5479	310	20	,	,	PUNCT
ejpam-5479	310	21	causing	cause	VERB
ejpam-5479	310	22	alterations	alteration	NOUN
ejpam-5479	310	23	in	in	ADP
ejpam-5479	310	24	the	the	DET
ejpam-5479	310	25	direction	direction	NOUN
ejpam-5479	310	26	of	of	ADP
ejpam-5479	310	27	the	the	DET
ejpam-5479	310	28	frictional	frictional	ADJ
ejpam-5479	310	29	force	force	NOUN
ejpam-5479	310	30	.	.	PUNCT
ejpam-5479	311	1	if	if	SCONJ
ejpam-5479	311	2	these	these	DET
ejpam-5479	311	3	variations	variation	NOUN
ejpam-5479	311	4	are	be	AUX
ejpam-5479	311	5	not	not	PART
ejpam-5479	311	6	accounted	account	VERB
ejpam-5479	311	7	for	for	ADP
ejpam-5479	311	8	by	by	ADP
ejpam-5479	311	9	the	the	DET
ejpam-5479	311	10	rider	rider	NOUN
ejpam-5479	311	11	or	or	CCONJ
ejpam-5479	311	12	the	the	DET
ejpam-5479	311	13	design	design	NOUN
ejpam-5479	311	14	of	of	ADP
ejpam-5479	311	15	the	the	DET
ejpam-5479	311	16	vehicle	vehicle	NOUN
ejpam-5479	311	17	,	,	PUNCT
ejpam-5479	311	18	they	they	PRON
ejpam-5479	311	19	can	can	AUX
ejpam-5479	311	20	potentially	potentially	ADV
ejpam-5479	311	21	disrupt	disrupt	VERB
ejpam-5479	311	22	the	the	DET
ejpam-5479	311	23	motion	motion	NOUN
ejpam-5479	311	24	and	and	CCONJ
ejpam-5479	311	25	make	make	VERB
ejpam-5479	311	26	it	it	PRON
ejpam-5479	311	27	less	less	ADV
ejpam-5479	311	28	stable	stable	ADJ
ejpam-5479	311	29	.	.	PUNCT
ejpam-5479	312	1	similarly	similarly	ADV
ejpam-5479	312	2	,	,	PUNCT
ejpam-5479	312	3	the	the	DET
ejpam-5479	312	4	stiffness	stiffness	NOUN
ejpam-5479	312	5	of	of	ADP
ejpam-5479	312	6	the	the	DET
ejpam-5479	312	7	light	light	ADJ
ejpam-5479	312	8	spring	spring	NOUN
ejpam-5479	312	9	has	have	VERB
ejpam-5479	312	10	a	a	DET
ejpam-5479	312	11	destabilizing	destabilizing	ADJ
ejpam-5479	312	12	impact	impact	NOUN
ejpam-5479	312	13	as	as	SCONJ
ejpam-5479	312	14	seen	see	VERB
ejpam-5479	312	15	in	in	ADP
ejpam-5479	312	16	fig	fig	NOUN
ejpam-5479	312	17	.	.	PUNCT
ejpam-5479	313	1	(	(	PUNCT
ejpam-5479	313	2	4	4	NUM
ejpam-5479	313	3	)	)	PUNCT
ejpam-5479	313	4	.	.	PUNCT
ejpam-5479	314	1	the	the	DET
ejpam-5479	314	2	destabilizing	destabilizing	ADJ
ejpam-5479	314	3	effect	effect	NOUN
ejpam-5479	314	4	of	of	ADP
ejpam-5479	314	5	the	the	DET
ejpam-5479	314	6	rigidity	rigidity	NOUN
ejpam-5479	314	7	of	of	ADP
ejpam-5479	314	8	a	a	DET
ejpam-5479	314	9	lightweight	lightweight	ADJ
ejpam-5479	314	10	spring	spring	NOUN
ejpam-5479	314	11	generally	generally	ADV
ejpam-5479	314	12	pertains	pertain	VERB
ejpam-5479	314	13	to	to	ADP
ejpam-5479	314	14	the	the	DET
ejpam-5479	314	15	inclination	inclination	NOUN
ejpam-5479	314	16	of	of	ADP
ejpam-5479	314	17	a	a	DET
ejpam-5479	314	18	system	system	NOUN
ejpam-5479	314	19	with	with	ADP
ejpam-5479	314	20	a	a	DET
ejpam-5479	314	21	stiff	stiff	ADJ
ejpam-5479	314	22	(	(	PUNCT
ejpam-5479	314	23	high	high	ADJ
ejpam-5479	314	24	spring	spring	NOUN
ejpam-5479	314	25	constant	constant	ADJ
ejpam-5479	314	26	)	)	PUNCT
ejpam-5479	314	27	spring	spring	NOUN
ejpam-5479	314	28	to	to	PART
ejpam-5479	314	29	become	become	VERB
ejpam-5479	314	30	less	less	ADV
ejpam-5479	314	31	stable	stable	ADJ
ejpam-5479	314	32	under	under	ADP
ejpam-5479	314	33	specific	specific	ADJ
ejpam-5479	314	34	circumstances	circumstance	NOUN
ejpam-5479	314	35	.	.	PUNCT
ejpam-5479	315	1	within	within	ADP
ejpam-5479	315	2	mechanical	mechanical	ADJ
ejpam-5479	315	3	systems	system	NOUN
ejpam-5479	315	4	,	,	PUNCT
ejpam-5479	315	5	a	a	DET
ejpam-5479	315	6	spring	spring	NOUN
ejpam-5479	315	7	with	with	ADP
ejpam-5479	315	8	higher	high	ADJ
ejpam-5479	315	9	stiffness	stiffness	NOUN
ejpam-5479	315	10	applies	apply	VERB
ejpam-5479	315	11	a	a	DET
ejpam-5479	315	12	larger	large	ADJ
ejpam-5479	315	13	force	force	NOUN
ejpam-5479	315	14	when	when	SCONJ
ejpam-5479	315	15	subjected	subject	VERB
ejpam-5479	315	16	to	to	ADP
ejpam-5479	315	17	a	a	DET
ejpam-5479	315	18	specific	specific	ADJ
ejpam-5479	315	19	displacement	displacement	NOUN
ejpam-5479	315	20	,	,	PUNCT
ejpam-5479	315	21	resulting	result	VERB
ejpam-5479	315	22	in	in	ADP
ejpam-5479	315	23	more	more	ADV
ejpam-5479	315	24	prominent	prominent	ADJ
ejpam-5479	315	25	oscillations	oscillation	NOUN
ejpam-5479	315	26	or	or	CCONJ
ejpam-5479	315	27	vibrations	vibration	NOUN
ejpam-5479	315	28	.	.	PUNCT
ejpam-5479	316	1	if	if	SCONJ
ejpam-5479	316	2	these	these	DET
ejpam-5479	316	3	oscillations	oscillation	NOUN
ejpam-5479	316	4	are	be	AUX
ejpam-5479	316	5	not	not	PART
ejpam-5479	316	6	adequately	adequately	ADV
ejpam-5479	316	7	attenuated	attenuate	VERB
ejpam-5479	316	8	,	,	PUNCT
ejpam-5479	316	9	they	they	PRON
ejpam-5479	316	10	can	can	AUX
ejpam-5479	316	11	amplify	amplify	VERB
ejpam-5479	316	12	in	in	ADP
ejpam-5479	316	13	magnitude	magnitude	NOUN
ejpam-5479	316	14	,	,	PUNCT
ejpam-5479	316	15	potentially	potentially	ADV
ejpam-5479	316	16	resulting	result	VERB
ejpam-5479	316	17	in	in	ADP
ejpam-5479	316	18	instability	instability	NOUN
ejpam-5479	316	19	.	.	PUNCT
ejpam-5479	317	1	stiff	stiff	ADJ
ejpam-5479	317	2	springs	spring	NOUN
ejpam-5479	317	3	,	,	PUNCT
ejpam-5479	317	4	whether	whether	SCONJ
ejpam-5479	317	5	used	use	VERB
ejpam-5479	317	6	in	in	ADP
ejpam-5479	317	7	control	control	NOUN
ejpam-5479	317	8	systems	system	NOUN
ejpam-5479	317	9	or	or	CCONJ
ejpam-5479	317	10	structural	structural	ADJ
ejpam-5479	317	11	dynamics	dynamic	NOUN
ejpam-5479	317	12	,	,	PUNCT
ejpam-5479	317	13	can	can	AUX
ejpam-5479	317	14	enhance	enhance	VERB
ejpam-5479	317	15	the	the	DET
ejpam-5479	317	16	sensitivity	sensitivity	NOUN
ejpam-5479	317	17	of	of	ADP
ejpam-5479	317	18	a	a	DET
ejpam-5479	317	19	system	system	NOUN
ejpam-5479	317	20	to	to	ADP
ejpam-5479	317	21	external	external	ADJ
ejpam-5479	317	22	forces	force	NOUN
ejpam-5479	317	23	or	or	CCONJ
ejpam-5479	317	24	disturbances	disturbance	NOUN
ejpam-5479	317	25	.	.	PUNCT
ejpam-5479	318	1	the	the	DET
ejpam-5479	318	2	heightened	heighten	VERB
ejpam-5479	318	3	sensitivity	sensitivity	NOUN
ejpam-5479	318	4	might	might	AUX
ejpam-5479	318	5	result	result	VERB
ejpam-5479	318	6	in	in	ADP
ejpam-5479	318	7	a	a	DET
ejpam-5479	318	8	more	more	ADV
ejpam-5479	318	9	intense	intense	ADJ
ejpam-5479	318	10	response	response	NOUN
ejpam-5479	318	11	of	of	ADP
ejpam-5479	318	12	the	the	DET
ejpam-5479	318	13	system	system	NOUN
ejpam-5479	318	14	to	to	ADP
ejpam-5479	318	15	perturbations	perturbation	NOUN
ejpam-5479	318	16	,	,	PUNCT
ejpam-5479	318	17	so	so	ADV
ejpam-5479	318	18	making	make	VERB
ejpam-5479	318	19	it	it	PRON
ejpam-5479	318	20	more	more	ADV
ejpam-5479	318	21	challenging	challenging	ADJ
ejpam-5479	318	22	to	to	PART
ejpam-5479	318	23	maintain	maintain	VERB
ejpam-5479	318	24	balance	balance	NOUN
ejpam-5479	318	25	and	and	CCONJ
ejpam-5479	318	26	perhaps	perhaps	ADV
ejpam-5479	318	27	leading	lead	VERB
ejpam-5479	318	28	to	to	ADP
ejpam-5479	318	29	instability	instability	NOUN
ejpam-5479	318	30	.	.	PUNCT
ejpam-5479	319	1	in	in	ADP
ejpam-5479	319	2	contrast	contrast	NOUN
ejpam-5479	319	3	,	,	PUNCT
ejpam-5479	319	4	the	the	DET
ejpam-5479	319	5	time	time	NOUN
ejpam-5479	319	6	-	-	PUNCT
ejpam-5479	319	7	delay	delay	NOUN
ejpam-5479	319	8	parameter	parameter	NOUN
ejpam-5479	319	9	has	have	VERB
ejpam-5479	319	10	a	a	DET
ejpam-5479	319	11	stabilizing	stabilizing	NOUN
ejpam-5479	319	12	influence	influence	NOUN
ejpam-5479	319	13	as	as	SCONJ
ejpam-5479	319	14	seen	see	VERB
ejpam-5479	319	15	in	in	ADP
ejpam-5479	319	16	fig	fig	NOUN
ejpam-5479	319	17	.	.	PUNCT
ejpam-5479	320	1	(	(	PUNCT
ejpam-5479	320	2	5	5	NUM
ejpam-5479	320	3	)	)	PUNCT
ejpam-5479	320	4	.	.	PUNCT
ejpam-5479	321	1	the	the	DET
ejpam-5479	321	2	stabilizing	stabilize	VERB
ejpam-5479	321	3	effect	effect	NOUN
ejpam-5479	321	4	of	of	ADP
ejpam-5479	321	5	time	time	NOUN
ejpam-5479	321	6	delay	delay	NOUN
ejpam-5479	321	7	pertains	pertain	VERB
ejpam-5479	321	8	to	to	ADP
ejpam-5479	321	9	the	the	DET
ejpam-5479	321	10	occurrence	occurrence	NOUN
ejpam-5479	321	11	where	where	SCONJ
ejpam-5479	321	12	the	the	DET
ejpam-5479	321	13	introduction	introduction	NOUN
ejpam-5479	321	14	of	of	ADP
ejpam-5479	321	15	a	a	DET
ejpam-5479	321	16	delay	delay	NOUN
ejpam-5479	321	17	in	in	ADP
ejpam-5479	321	18	the	the	DET
ejpam-5479	321	19	feedback	feedback	NOUN
ejpam-5479	321	20	loop	loop	NOUN
ejpam-5479	321	21	of	of	ADP
ejpam-5479	321	22	a	a	DET
ejpam-5479	321	23	system	system	NOUN
ejpam-5479	321	24	can	can	AUX
ejpam-5479	321	25	result	result	VERB
ejpam-5479	321	26	in	in	ADP
ejpam-5479	321	27	enhanced	enhanced	ADJ
ejpam-5479	321	28	stability	stability	NOUN
ejpam-5479	321	29	under	under	ADP
ejpam-5479	321	30	specific	specific	ADJ
ejpam-5479	321	31	circumstances	circumstance	NOUN
ejpam-5479	321	32	.	.	PUNCT
ejpam-5479	322	1	although	although	SCONJ
ejpam-5479	322	2	delays	delay	NOUN
ejpam-5479	322	3	are	be	AUX
ejpam-5479	322	4	commonly	commonly	ADV
ejpam-5479	322	5	linked	link	VERB
ejpam-5479	322	6	to	to	ADP
ejpam-5479	322	7	destabilizing	destabilizing	ADJ
ejpam-5479	322	8	effects	effect	NOUN
ejpam-5479	322	9	,	,	PUNCT
ejpam-5479	322	10	this	this	PRON
ejpam-5479	322	11	may	may	AUX
ejpam-5479	322	12	appear	appear	VERB
ejpam-5479	322	13	counterintuitive	counterintuitive	ADJ
ejpam-5479	322	14	.	.	PUNCT
ejpam-5479	323	1	however	however	ADV
ejpam-5479	323	2	,	,	PUNCT
ejpam-5479	323	3	in	in	ADP
ejpam-5479	323	4	certain	certain	ADJ
ejpam-5479	323	5	systems	system	NOUN
ejpam-5479	323	6	,	,	PUNCT
ejpam-5479	323	7	especially	especially	ADV
ejpam-5479	323	8	in	in	ADP
ejpam-5479	323	9	control	control	NOUN
ejpam-5479	323	10	systems	system	NOUN
ejpam-5479	323	11	or	or	CCONJ
ejpam-5479	323	12	in	in	ADP
ejpam-5479	323	13	models	model	NOUN
ejpam-5479	323	14	of	of	ADP
ejpam-5479	323	15	population	population	NOUN
ejpam-5479	323	16	dynamics	dynamic	NOUN
ejpam-5479	323	17	,	,	PUNCT
ejpam-5479	323	18	the	the	DET
ejpam-5479	323	19	introduction	introduction	NOUN
ejpam-5479	323	20	of	of	ADP
ejpam-5479	323	21	a	a	DET
ejpam-5479	323	22	time	time	NOUN
ejpam-5479	323	23	delay	delay	NOUN
ejpam-5479	323	24	can	can	AUX
ejpam-5479	323	25	mitigate	mitigate	VERB
ejpam-5479	323	26	oscillations	oscillation	NOUN
ejpam-5479	323	27	or	or	CCONJ
ejpam-5479	323	28	decrease	decrease	VERB
ejpam-5479	323	29	the	the	DET
ejpam-5479	323	30	magnitude	magnitude	NOUN
ejpam-5479	323	31	of	of	ADP
ejpam-5479	323	32	fluctuations	fluctuation	NOUN
ejpam-5479	323	33	,	,	PUNCT
ejpam-5479	323	34	thus	thus	ADV
ejpam-5479	323	35	leading	lead	VERB
ejpam-5479	323	36	to	to	ADP
ejpam-5479	323	37	the	the	DET
ejpam-5479	323	38	stabilization	stabilization	NOUN
ejpam-5479	323	39	of	of	ADP
ejpam-5479	323	40	the	the	DET
ejpam-5479	323	41	system	system	NOUN
ejpam-5479	323	42	.	.	PUNCT
ejpam-5479	324	1	the	the	DET
ejpam-5479	324	2	stabilization	stabilization	NOUN
ejpam-5479	324	3	is	be	AUX
ejpam-5479	324	4	a	a	DET
ejpam-5479	324	5	result	result	NOUN
ejpam-5479	324	6	of	of	ADP
ejpam-5479	324	7	the	the	DET
ejpam-5479	324	8	delay	delay	NOUN
ejpam-5479	324	9	’s	’s	PART
ejpam-5479	324	10	ability	ability	NOUN
ejpam-5479	324	11	to	to	PART
ejpam-5479	324	12	efficiently	efficiently	ADV
ejpam-5479	324	13	mitigate	mitigate	VERB
ejpam-5479	324	14	abrupt	abrupt	ADJ
ejpam-5479	324	15	fluctuations	fluctuation	NOUN
ejpam-5479	324	16	in	in	ADP
ejpam-5479	324	17	the	the	DET
ejpam-5479	324	18	system	system	NOUN
ejpam-5479	324	19	’s	’s	PART
ejpam-5479	324	20	condition	condition	NOUN
ejpam-5479	324	21	,	,	PUNCT
ejpam-5479	324	22	hence	hence	ADV
ejpam-5479	324	23	limiting	limit	VERB
ejpam-5479	324	24	excessive	excessive	ADJ
ejpam-5479	324	25	responses	response	NOUN
ejpam-5479	324	26	to	to	ADP
ejpam-5479	324	27	disruptions	disruption	NOUN
ejpam-5479	324	28	.	.	PUNCT
ejpam-5479	325	1	by	by	ADP
ejpam-5479	325	2	reducing	reduce	VERB
ejpam-5479	325	3	the	the	DET
ejpam-5479	325	4	speed	speed	NOUN
ejpam-5479	325	5	of	of	ADP
ejpam-5479	325	6	the	the	DET
ejpam-5479	325	7	feedback	feedback	NOUN
ejpam-5479	325	8	,	,	PUNCT
ejpam-5479	325	9	the	the	DET
ejpam-5479	325	10	system	system	NOUN
ejpam-5479	325	11	is	be	AUX
ejpam-5479	325	12	less	less	ADV
ejpam-5479	325	13	prone	prone	ADJ
ejpam-5479	325	14	to	to	ADP
ejpam-5479	325	15	quick	quick	ADJ
ejpam-5479	325	16	oscillations	oscillation	NOUN
ejpam-5479	325	17	or	or	CCONJ
ejpam-5479	325	18	chaotic	chaotic	ADJ
ejpam-5479	325	19	behavior	behavior	NOUN
ejpam-5479	325	20	that	that	PRON
ejpam-5479	325	21	could	could	AUX
ejpam-5479	325	22	arise	arise	VERB
ejpam-5479	325	23	from	from	ADP
ejpam-5479	325	24	immediate	immediate	ADJ
ejpam-5479	325	25	feedback	feedback	NOUN
ejpam-5479	325	26	,	,	PUNCT
ejpam-5479	325	27	thereby	thereby	ADV
ejpam-5479	325	28	improving	improve	VERB
ejpam-5479	325	29	overall	overall	ADJ
ejpam-5479	325	30	stability	stability	NOUN
ejpam-5479	325	31	.	.	PUNCT
ejpam-5479	326	1	k.	k.	PROPN
ejpam-5479	326	2	alluhydan	alluhydan	PROPN
ejpam-5479	326	3	,	,	PUNCT
ejpam-5479	326	4	g.	g.	PROPN
ejpam-5479	326	5	m	m	PROPN
ejpam-5479	326	6	moatimid	moatimid	PROPN
ejpam-5479	326	7	,	,	PUNCT
ejpam-5479	326	8	t.	t.	PROPN
ejpam-5479	326	9	s.	s.	PROPN
ejpam-5479	326	10	amer	amer	PROPN
ejpam-5479	326	11	/	/	SYM
ejpam-5479	326	12	eur	eur	PROPN
ejpam-5479	326	13	.	.	PUNCT
ejpam-5479	327	1	j.	j.	PROPN
ejpam-5479	327	2	pure	pure	PROPN
ejpam-5479	327	3	appl	appl	PROPN
ejpam-5479	327	4	.	.	PROPN
ejpam-5479	327	5	math	math	PROPN
ejpam-5479	327	6	,	,	PUNCT
ejpam-5479	327	7	17	17	NUM
ejpam-5479	327	8	(	(	PUNCT
ejpam-5479	327	9	4	4	NUM
ejpam-5479	327	10	)	)	PUNCT
ejpam-5479	327	11	(	(	PUNCT
ejpam-5479	327	12	2024	2024	NUM
ejpam-5479	327	13	)	)	PUNCT
ejpam-5479	327	14	,	,	PUNCT
ejpam-5479	327	15	3185	3185	NUM
ejpam-5479	327	16	-	-	SYM
ejpam-5479	327	17	3208	3208	NUM
ejpam-5479	327	18	3198	3198	NUM
ejpam-5479	327	19	figure	figure	NOUN
ejpam-5479	327	20	3	3	NUM
ejpam-5479	327	21	:	:	PUNCT
ejpam-5479	327	22	displays	display	VERB
ejpam-5479	327	23	the	the	DET
ejpam-5479	327	24	influence	influence	NOUN
ejpam-5479	327	25	of	of	ADP
ejpam-5479	327	26	the	the	DET
ejpam-5479	327	27	radius	radius	NOUN
ejpam-5479	327	28	of	of	ADP
ejpam-5479	327	29	the	the	DET
ejpam-5479	327	30	rolling	rolling	ADJ
ejpam-5479	327	31	wheel	wheel	NOUN
ejpam-5479	327	32	in	in	ADP
ejpam-5479	327	33	the	the	DET
ejpam-5479	327	34	stability	stability	NOUN
ejpam-5479	327	35	profile	profile	NOUN
ejpam-5479	327	36	.	.	PUNCT
ejpam-5479	328	1	figure	figure	VERB
ejpam-5479	328	2	4	4	NUM
ejpam-5479	328	3	:	:	PUNCT
ejpam-5479	328	4	illustrates	illustrate	VERB
ejpam-5479	328	5	how	how	SCONJ
ejpam-5479	328	6	the	the	DET
ejpam-5479	328	7	spring	spring	NOUN
ejpam-5479	328	8	’s	’s	PART
ejpam-5479	328	9	stiffness	stiffness	NOUN
ejpam-5479	328	10	affects	affect	VERB
ejpam-5479	328	11	the	the	DET
ejpam-5479	328	12	stability	stability	NOUN
ejpam-5479	328	13	profile	profile	NOUN
ejpam-5479	328	14	.	.	PUNCT
ejpam-5479	329	1	k.	k.	PROPN
ejpam-5479	329	2	alluhydan	alluhydan	PROPN
ejpam-5479	329	3	,	,	PUNCT
ejpam-5479	329	4	g.	g.	PROPN
ejpam-5479	329	5	m	m	PROPN
ejpam-5479	329	6	moatimid	moatimid	PROPN
ejpam-5479	329	7	,	,	PUNCT
ejpam-5479	329	8	t.	t.	PROPN
ejpam-5479	329	9	s.	s.	PROPN
ejpam-5479	329	10	amer	amer	PROPN
ejpam-5479	329	11	/	/	SYM
ejpam-5479	329	12	eur	eur	PROPN
ejpam-5479	329	13	.	.	PUNCT
ejpam-5479	330	1	j.	j.	PROPN
ejpam-5479	330	2	pure	pure	PROPN
ejpam-5479	330	3	appl	appl	PROPN
ejpam-5479	330	4	.	.	PROPN
ejpam-5479	330	5	math	math	PROPN
ejpam-5479	330	6	,	,	PUNCT
ejpam-5479	330	7	17	17	NUM
ejpam-5479	330	8	(	(	PUNCT
ejpam-5479	330	9	4	4	NUM
ejpam-5479	330	10	)	)	PUNCT
ejpam-5479	330	11	(	(	PUNCT
ejpam-5479	330	12	2024	2024	NUM
ejpam-5479	330	13	)	)	PUNCT
ejpam-5479	330	14	,	,	PUNCT
ejpam-5479	330	15	3185	3185	NUM
ejpam-5479	330	16	-	-	SYM
ejpam-5479	330	17	3208	3208	NUM
ejpam-5479	330	18	3199	3199	NUM
ejpam-5479	330	19	figure	figure	NOUN
ejpam-5479	330	20	5	5	NUM
ejpam-5479	330	21	:	:	PUNCT
ejpam-5479	330	22	demonstrates	demonstrate	VERB
ejpam-5479	330	23	the	the	DET
ejpam-5479	330	24	impact	impact	NOUN
ejpam-5479	330	25	of	of	ADP
ejpam-5479	330	26	the	the	DET
ejpam-5479	330	27	time	time	NOUN
ejpam-5479	330	28	-	-	PUNCT
ejpam-5479	330	29	delay	delay	NOUN
ejpam-5479	330	30	parameter	parameter	NOUN
ejpam-5479	330	31	on	on	ADP
ejpam-5479	330	32	the	the	DET
ejpam-5479	330	33	stability	stability	NOUN
ejpam-5479	330	34	profile	profile	NOUN
ejpam-5479	330	35	.	.	PUNCT
ejpam-5479	331	1	3.2	3.2	NUM
ejpam-5479	331	2	.	.	PUNCT
ejpam-5479	332	1	the	the	DET
ejpam-5479	332	2	non	non	NOUN
ejpam-5479	332	3	-	-	NOUN
ejpam-5479	332	4	existence	existence	NOUN
ejpam-5479	332	5	of	of	ADP
ejpam-5479	332	6	a	a	DET
ejpam-5479	332	7	time	time	NOUN
ejpam-5479	332	8	-	-	PUNCT
ejpam-5479	332	9	delay	delay	NOUN
ejpam-5479	332	10	simply	simply	ADV
ejpam-5479	332	11	setting	set	VERB
ejpam-5479	332	12	τ	τ	X
ejpam-5479	332	13	=	=	SYM
ejpam-5479	332	14	0	0	PUNCT
ejpam-5479	332	15	and	and	CCONJ
ejpam-5479	332	16	using	use	VERB
ejpam-5479	332	17	the	the	DET
ejpam-5479	332	18	same	same	ADJ
ejpam-5479	332	19	justifications	justification	NOUN
ejpam-5479	332	20	as	as	ADP
ejpam-5479	332	21	in	in	ADP
ejpam-5479	332	22	the	the	DET
ejpam-5479	332	23	preceding	precede	VERB
ejpam-5479	332	24	subsection	subsection	NOUN
ejpam-5479	332	25	,	,	PUNCT
ejpam-5479	332	26	one	one	PRON
ejpam-5479	332	27	finds	find	VERB
ejpam-5479	332	28	that	that	SCONJ
ejpam-5479	332	29	the	the	DET
ejpam-5479	332	30	damping	damp	VERB
ejpam-5479	332	31	term	term	NOUN
ejpam-5479	332	32	disappears	disappear	VERB
ejpam-5479	332	33	.	.	PUNCT
ejpam-5479	333	1	additionally	additionally	ADV
ejpam-5479	333	2	,	,	PUNCT
ejpam-5479	333	3	some	some	DET
ejpam-5479	333	4	modification	modification	NOUN
ejpam-5479	333	5	is	be	AUX
ejpam-5479	333	6	found	find	VERB
ejpam-5479	333	7	in	in	ADP
ejpam-5479	333	8	the	the	DET
ejpam-5479	333	9	equivalent	equivalent	ADJ
ejpam-5479	333	10	frequency	frequency	NOUN
ejpam-5479	333	11	.	.	PUNCT
ejpam-5479	334	1	in	in	ADP
ejpam-5479	334	2	this	this	DET
ejpam-5479	334	3	scenario	scenario	NOUN
ejpam-5479	334	4	,	,	PUNCT
ejpam-5479	334	5	the	the	DET
ejpam-5479	334	6	total	total	ADJ
ejpam-5479	334	7	frequency	frequency	NOUN
ejpam-5479	334	8	has	have	VERB
ejpam-5479	334	9	the	the	DET
ejpam-5479	334	10	same	same	ADJ
ejpam-5479	334	11	form	form	NOUN
ejpam-5479	334	12	as	as	ADP
ejpam-5479	334	13	the	the	DET
ejpam-5479	334	14	equivalent	equivalent	ADJ
ejpam-5479	334	15	frequency	frequency	NOUN
ejpam-5479	334	16	.	.	PUNCT
ejpam-5479	335	1	therefore	therefore	ADV
ejpam-5479	335	2	,	,	PUNCT
ejpam-5479	335	3	it	it	PRON
ejpam-5479	335	4	is	be	AUX
ejpam-5479	335	5	given	give	VERB
ejpam-5479	335	6	as	as	ADP
ejpam-5479	335	7	:	:	PUNCT
ejpam-5479	335	8	ω	ω	NUM
ejpam-5479	335	9	=	=	SYM
ejpam-5479	335	10	r	r	NOUN
ejpam-5479	335	11	√	√	ADJ
ejpam-5479	335	12	k√	k√	NOUN
ejpam-5479	335	13	1+r2	1+r2	NUM
ejpam-5479	335	14	√	√	NOUN
ejpam-5479	335	15	1	1	NUM
ejpam-5479	335	16	+	+	NOUN
ejpam-5479	335	17	2rj0(a)/(1+r2	2rj0(a)/(1+r2	NUM
ejpam-5479	335	18	)	)	PUNCT
ejpam-5479	335	19	.	.	PUNCT
ejpam-5479	336	1	the	the	DET
ejpam-5479	336	2	same	same	ADJ
ejpam-5479	336	3	information	information	NOUN
ejpam-5479	336	4	from	from	ADP
ejpam-5479	336	5	fig	fig	NOUN
ejpam-5479	336	6	.	.	PUNCT
ejpam-5479	337	1	(	(	PUNCT
ejpam-5479	337	2	2	2	X
ejpam-5479	337	3	)	)	PUNCT
ejpam-5479	337	4	is	be	AUX
ejpam-5479	337	5	presented	present	VERB
ejpam-5479	337	6	in	in	ADP
ejpam-5479	337	7	fig	fig	NOUN
ejpam-5479	337	8	.	.	PUNCT
ejpam-5479	338	1	(	(	PUNCT
ejpam-5479	338	2	6	6	NUM
ejpam-5479	338	3	)	)	PUNCT
ejpam-5479	338	4	but	but	CCONJ
ejpam-5479	338	5	without	without	ADP
ejpam-5479	338	6	the	the	DET
ejpam-5479	338	7	time	time	NOUN
ejpam-5479	338	8	-	-	PUNCT
ejpam-5479	338	9	delay	delay	NOUN
ejpam-5479	338	10	aspect	aspect	NOUN
ejpam-5479	338	11	.	.	PUNCT
ejpam-5479	339	1	the	the	DET
ejpam-5479	339	2	mathematica	mathematica	PROPN
ejpam-5479	339	3	software	software	PROPN
ejpam-5479	339	4	12.0.0.0	12.0.0.0	NUM
ejpam-5479	339	5	additionally	additionally	ADV
ejpam-5479	339	6	established	establish	VERB
ejpam-5479	339	7	that	that	SCONJ
ejpam-5479	339	8	the	the	DET
ejpam-5479	339	9	absolute	absolute	ADJ
ejpam-5479	339	10	error	error	NOUN
ejpam-5479	339	11	concerning	concern	VERB
ejpam-5479	339	12	the	the	DET
ejpam-5479	339	13	theoretical	theoretical	ADJ
ejpam-5479	339	14	and	and	CCONJ
ejpam-5479	339	15	computational	computational	ADJ
ejpam-5479	339	16	solutions	solution	NOUN
ejpam-5479	339	17	is	be	AUX
ejpam-5479	339	18	0.00130537	0.00130537	NUM
ejpam-5479	339	19	up	up	ADP
ejpam-5479	339	20	to	to	ADP
ejpam-5479	339	21	a	a	DET
ejpam-5479	339	22	temporal	temporal	ADJ
ejpam-5479	339	23	interval	interval	NOUN
ejpam-5479	339	24	of	of	ADP
ejpam-5479	339	25	100	100	NUM
ejpam-5479	339	26	units	unit	NOUN
ejpam-5479	339	27	.	.	PUNCT
ejpam-5479	340	1	the	the	DET
ejpam-5479	340	2	convergence	convergence	NOUN
ejpam-5479	340	3	of	of	ADP
ejpam-5479	340	4	linear	linear	ADJ
ejpam-5479	340	5	and	and	CCONJ
ejpam-5479	340	6	nonlinear	nonlinear	ADJ
ejpam-5479	340	7	solutions	solution	NOUN
ejpam-5479	340	8	signifies	signify	VERB
ejpam-5479	340	9	that	that	SCONJ
ejpam-5479	340	10	,	,	PUNCT
ejpam-5479	340	11	despite	despite	SCONJ
ejpam-5479	340	12	their	their	PRON
ejpam-5479	340	13	distinct	distinct	ADJ
ejpam-5479	340	14	definitions	definition	NOUN
ejpam-5479	340	15	,	,	PUNCT
ejpam-5479	340	16	they	they	PRON
ejpam-5479	340	17	occupy	occupy	VERB
ejpam-5479	340	18	identical	identical	ADJ
ejpam-5479	340	19	spatial	spatial	ADJ
ejpam-5479	340	20	places	place	NOUN
ejpam-5479	340	21	.	.	PUNCT
ejpam-5479	341	1	this	this	PRON
ejpam-5479	341	2	signifies	signify	VERB
ejpam-5479	341	3	that	that	SCONJ
ejpam-5479	341	4	the	the	DET
ejpam-5479	341	5	two	two	NUM
ejpam-5479	341	6	curves	curve	NOUN
ejpam-5479	341	7	represent	represent	VERB
ejpam-5479	341	8	the	the	DET
ejpam-5479	341	9	same	same	ADJ
ejpam-5479	341	10	geometric	geometric	ADJ
ejpam-5479	341	11	shape	shape	NOUN
ejpam-5479	341	12	or	or	CCONJ
ejpam-5479	341	13	path	path	NOUN
ejpam-5479	341	14	.	.	PUNCT
ejpam-5479	342	1	it	it	PRON
ejpam-5479	342	2	often	often	ADV
ejpam-5479	342	3	suggests	suggest	VERB
ejpam-5479	342	4	that	that	SCONJ
ejpam-5479	342	5	the	the	DET
ejpam-5479	342	6	underlying	underlying	ADJ
ejpam-5479	342	7	physical	physical	ADJ
ejpam-5479	342	8	processes	process	NOUN
ejpam-5479	342	9	,	,	PUNCT
ejpam-5479	342	10	constraints	constraint	NOUN
ejpam-5479	342	11	,	,	PUNCT
ejpam-5479	342	12	or	or	CCONJ
ejpam-5479	342	13	relationships	relationship	NOUN
ejpam-5479	342	14	driving	drive	VERB
ejpam-5479	342	15	the	the	DET
ejpam-5479	342	16	curves	curve	NOUN
ejpam-5479	342	17	are	be	AUX
ejpam-5479	342	18	similar	similar	ADJ
ejpam-5479	342	19	,	,	PUNCT
ejpam-5479	342	20	or	or	CCONJ
ejpam-5479	342	21	that	that	SCONJ
ejpam-5479	342	22	one	one	NUM
ejpam-5479	342	23	curve	curve	NOUN
ejpam-5479	342	24	signifies	signify	VERB
ejpam-5479	342	25	a	a	DET
ejpam-5479	342	26	transition	transition	NOUN
ejpam-5479	342	27	or	or	CCONJ
ejpam-5479	342	28	specific	specific	ADJ
ejpam-5479	342	29	case	case	NOUN
ejpam-5479	342	30	of	of	ADP
ejpam-5479	342	31	the	the	DET
ejpam-5479	342	32	other	other	ADJ
ejpam-5479	342	33	.	.	PUNCT
ejpam-5479	343	1	4	4	X
ejpam-5479	343	2	.	.	X
ejpam-5479	343	3	discussion	discussion	NOUN
ejpam-5479	343	4	of	of	ADP
ejpam-5479	343	5	the	the	DET
ejpam-5479	343	6	results	result	NOUN
ejpam-5479	343	7	the	the	DET
ejpam-5479	343	8	current	current	ADJ
ejpam-5479	343	9	section	section	NOUN
ejpam-5479	343	10	presents	present	VERB
ejpam-5479	343	11	a	a	DET
ejpam-5479	343	12	discussion	discussion	NOUN
ejpam-5479	343	13	of	of	ADP
ejpam-5479	343	14	the	the	DET
ejpam-5479	343	15	achieved	achieve	VERB
ejpam-5479	343	16	results	result	NOUN
ejpam-5479	343	17	which	which	PRON
ejpam-5479	343	18	are	be	AUX
ejpam-5479	343	19	drawn	draw	VERB
ejpam-5479	343	20	in	in	ADP
ejpam-5479	343	21	figs	fig	NOUN
ejpam-5479	343	22	.	.	PUNCT
ejpam-5479	344	1	(	(	PUNCT
ejpam-5479	344	2	7	7	NUM
ejpam-5479	344	3	)	)	PUNCT
ejpam-5479	344	4	,	,	PUNCT
ejpam-5479	344	5	(	(	PUNCT
ejpam-5479	344	6	8)	8)	NUM
ejpam-5479	344	7	,	,	PUNCT
ejpam-5479	344	8	and	and	CCONJ
ejpam-5479	344	9	(	(	PUNCT
ejpam-5479	344	10	9	9	NUM
ejpam-5479	344	11	)	)	PUNCT
ejpam-5479	344	12	.	.	PUNCT
ejpam-5479	345	1	the	the	DET
ejpam-5479	345	2	graphed	graph	VERB
ejpam-5479	345	3	curves	curve	NOUN
ejpam-5479	345	4	in	in	ADP
ejpam-5479	345	5	fig	fig	NOUN
ejpam-5479	345	6	.	.	PUNCT
ejpam-5479	346	1	(	(	PUNCT
ejpam-5479	346	2	7	7	X
ejpam-5479	346	3	)	)	PUNCT
ejpam-5479	346	4	are	be	AUX
ejpam-5479	346	5	calculated	calculate	VERB
ejpam-5479	346	6	when	when	SCONJ
ejpam-5479	346	7	k	k	PROPN
ejpam-5479	346	8	=	=	SYM
ejpam-5479	346	9	0.5	0.5	NUM
ejpam-5479	346	10	,	,	PUNCT
ejpam-5479	346	11	a	a	DET
ejpam-5479	346	12	=	=	SYM
ejpam-5479	346	13	0.5	0.5	NUM
ejpam-5479	346	14	,	,	PUNCT
ejpam-5479	346	15	and	and	CCONJ
ejpam-5479	346	16	τ	τ	PROPN
ejpam-5479	346	17	=	=	NOUN
ejpam-5479	346	18	0.01	0.01	NUM
ejpam-5479	346	19	at	at	ADP
ejpam-5479	346	20	various	various	ADJ
ejpam-5479	346	21	values	value	NOUN
ejpam-5479	346	22	of	of	ADP
ejpam-5479	346	23	r(=	r(=	ADJ
ejpam-5479	346	24	0.5	0.5	NUM
ejpam-5479	346	25	,	,	PUNCT
ejpam-5479	346	26	0.7	0.7	NUM
ejpam-5479	346	27	,	,	PUNCT
ejpam-5479	346	28	0.9	0.9	NUM
ejpam-5479	346	29	)	)	PUNCT
ejpam-5479	346	30	,	,	PUNCT
ejpam-5479	346	31	whereas	whereas	SCONJ
ejpam-5479	346	32	the	the	DET
ejpam-5479	346	33	drawn	draw	VERB
ejpam-5479	346	34	ones	one	NOUN
ejpam-5479	346	35	in	in	ADP
ejpam-5479	346	36	fig	fig	NOUN
ejpam-5479	346	37	.	.	PUNCT
ejpam-5479	347	1	(	(	PUNCT
ejpam-5479	347	2	8)	8)	NUM
ejpam-5479	347	3	are	be	AUX
ejpam-5479	347	4	plotted	plot	VERB
ejpam-5479	347	5	when	when	SCONJ
ejpam-5479	347	6	the	the	DET
ejpam-5479	347	7	values	value	NOUN
ejpam-5479	347	8	r	r	NOUN
ejpam-5479	347	9	=	=	SYM
ejpam-5479	347	10	0.5	0.5	NUM
ejpam-5479	347	11	,	,	PUNCT
ejpam-5479	347	12	a	a	DET
ejpam-5479	347	13	=	=	SYM
ejpam-5479	347	14	0.5	0.5	NUM
ejpam-5479	347	15	,	,	PUNCT
ejpam-5479	347	16	τ	τ	X
ejpam-5479	347	17	=	=	NOUN
ejpam-5479	347	18	0.01	0.01	NUM
ejpam-5479	347	19	,	,	PUNCT
ejpam-5479	347	20	and	and	CCONJ
ejpam-5479	347	21	k(=	k(=	PROPN
ejpam-5479	347	22	0.5	0.5	NUM
ejpam-5479	347	23	,	,	PUNCT
ejpam-5479	347	24	0.7	0.7	NUM
ejpam-5479	347	25	,	,	PUNCT
ejpam-5479	347	26	1	1	NUM
ejpam-5479	347	27	)	)	PUNCT
ejpam-5479	347	28	are	be	AUX
ejpam-5479	347	29	considered	consider	VERB
ejpam-5479	347	30	.	.	PUNCT
ejpam-5479	348	1	furthermore	furthermore	ADV
ejpam-5479	348	2	,	,	PUNCT
ejpam-5479	348	3	the	the	DET
ejpam-5479	348	4	inspection	inspection	NOUN
ejpam-5479	348	5	on	on	ADP
ejpam-5479	348	6	the	the	DET
ejpam-5479	348	7	graphed	graph	VERB
ejpam-5479	348	8	curves	curve	NOUN
ejpam-5479	348	9	in	in	ADP
ejpam-5479	348	10	fig	fig	NOUN
ejpam-5479	348	11	.	.	PUNCT
ejpam-5479	349	1	(	(	PUNCT
ejpam-5479	349	2	9	9	X
ejpam-5479	349	3	)	)	PUNCT
ejpam-5479	349	4	are	be	AUX
ejpam-5479	349	5	explored	explore	VERB
ejpam-5479	349	6	when	when	SCONJ
ejpam-5479	349	7	r	r	NOUN
ejpam-5479	349	8	=	=	PUNCT
ejpam-5479	349	9	a	a	NOUN
ejpam-5479	349	10	=	=	X
ejpam-5479	349	11	k	k	NOUN
ejpam-5479	349	12	=	=	SYM
ejpam-5479	349	13	0.5	0.5	NUM
ejpam-5479	349	14	and	and	CCONJ
ejpam-5479	349	15	τ(=	τ(=	NOUN
ejpam-5479	349	16	0.001	0.001	NUM
ejpam-5479	349	17	,	,	PUNCT
ejpam-5479	349	18	0.01	0.01	NUM
ejpam-5479	349	19	,	,	PUNCT
ejpam-5479	349	20	0.05	0.05	NUM
ejpam-5479	349	21	)	)	PUNCT
ejpam-5479	349	22	.	.	PUNCT
ejpam-5479	350	1	the	the	DET
ejpam-5479	350	2	figures	figure	NOUN
ejpam-5479	350	3	show	show	VERB
ejpam-5479	350	4	the	the	DET
ejpam-5479	350	5	time	time	NOUN
ejpam-5479	350	6	histories	history	NOUN
ejpam-5479	350	7	of	of	ADP
ejpam-5479	350	8	the	the	DET
ejpam-5479	350	9	solution	solution	NOUN
ejpam-5479	350	10	of	of	ADP
ejpam-5479	350	11	eq	eq	PROPN
ejpam-5479	350	12	.	.	PUNCT
ejpam-5479	351	1	(	(	PUNCT
ejpam-5479	351	2	18	18	NUM
ejpam-5479	351	3	)	)	PUNCT
ejpam-5479	351	4	and	and	CCONJ
ejpam-5479	351	5	the	the	DET
ejpam-5479	351	6	corresponding	corresponding	ADJ
ejpam-5479	351	7	phase	phase	NOUN
ejpam-5479	351	8	plane	plane	NOUN
ejpam-5479	351	9	diagrams	diagram	NOUN
ejpam-5479	351	10	as	as	SCONJ
ejpam-5479	351	11	indicated	indicate	VERB
ejpam-5479	351	12	,	,	PUNCT
ejpam-5479	351	13	respectively	respectively	ADV
ejpam-5479	351	14	,	,	PUNCT
ejpam-5479	351	15	k.	k.	PROPN
ejpam-5479	351	16	alluhydan	alluhydan	PROPN
ejpam-5479	351	17	,	,	PUNCT
ejpam-5479	351	18	g.	g.	PROPN
ejpam-5479	351	19	m	m	PROPN
ejpam-5479	351	20	moatimid	moatimid	PROPN
ejpam-5479	351	21	,	,	PUNCT
ejpam-5479	351	22	t.	t.	PROPN
ejpam-5479	351	23	s.	s.	PROPN
ejpam-5479	351	24	amer	amer	PROPN
ejpam-5479	351	25	/	/	SYM
ejpam-5479	351	26	eur	eur	PROPN
ejpam-5479	351	27	.	.	PUNCT
ejpam-5479	352	1	j.	j.	PROPN
ejpam-5479	352	2	pure	pure	PROPN
ejpam-5479	352	3	appl	appl	PROPN
ejpam-5479	352	4	.	.	PROPN
ejpam-5479	352	5	math	math	PROPN
ejpam-5479	352	6	,	,	PUNCT
ejpam-5479	352	7	17	17	NUM
ejpam-5479	352	8	(	(	PUNCT
ejpam-5479	352	9	4	4	NUM
ejpam-5479	352	10	)	)	PUNCT
ejpam-5479	352	11	(	(	PUNCT
ejpam-5479	352	12	2024	2024	NUM
ejpam-5479	352	13	)	)	PUNCT
ejpam-5479	352	14	,	,	PUNCT
ejpam-5479	352	15	3185	3185	NUM
ejpam-5479	352	16	-	-	SYM
ejpam-5479	352	17	3208	3208	NUM
ejpam-5479	352	18	3200	3200	NUM
ejpam-5479	352	19	figure	figure	NOUN
ejpam-5479	352	20	6	6	NUM
ejpam-5479	352	21	:	:	PUNCT
ejpam-5479	352	22	sketches	sketch	VERB
ejpam-5479	352	23	a	a	DET
ejpam-5479	352	24	comparison	comparison	NOUN
ejpam-5479	352	25	between	between	ADP
ejpam-5479	352	26	the	the	DET
ejpam-5479	352	27	ns	ns	NOUN
ejpam-5479	352	28	of	of	ADP
ejpam-5479	352	29	eq	eq	NOUN
ejpam-5479	352	30	.	.	PUNCT
ejpam-5479	353	1	(	(	PUNCT
ejpam-5479	353	2	9	9	NUM
ejpam-5479	353	3	)	)	PUNCT
ejpam-5479	353	4	in	in	ADP
ejpam-5479	353	5	the	the	DET
ejpam-5479	353	6	absence	absence	NOUN
ejpam-5479	353	7	of	of	ADP
ejpam-5479	353	8	time	time	NOUN
ejpam-5479	353	9	delay	delay	NOUN
ejpam-5479	353	10	and	and	CCONJ
ejpam-5479	353	11	the	the	DET
ejpam-5479	353	12	nps	nps	PROPN
ejpam-5479	353	13	of	of	ADP
ejpam-5479	353	14	eq	eq	PROPN
ejpam-5479	353	15	.	.	PUNCT
ejpam-5479	354	1	(	(	PUNCT
ejpam-5479	354	2	19	19	NUM
ejpam-5479	354	3	)	)	PUNCT
ejpam-5479	354	4	.	.	PUNCT
ejpam-5479	355	1	in	in	ADP
ejpam-5479	355	2	parts	part	NOUN
ejpam-5479	355	3	(	(	PUNCT
ejpam-5479	355	4	a	a	NOUN
ejpam-5479	355	5	)	)	PUNCT
ejpam-5479	355	6	and	and	CCONJ
ejpam-5479	355	7	(	(	PUNCT
ejpam-5479	355	8	b	b	NOUN
ejpam-5479	355	9	)	)	PUNCT
ejpam-5479	355	10	of	of	ADP
ejpam-5479	355	11	these	these	DET
ejpam-5479	355	12	figures	figure	NOUN
ejpam-5479	355	13	.	.	PUNCT
ejpam-5479	356	1	it	it	PRON
ejpam-5479	356	2	is	be	AUX
ejpam-5479	356	3	observed	observe	VERB
ejpam-5479	356	4	that	that	SCONJ
ejpam-5479	356	5	the	the	DET
ejpam-5479	356	6	behavior	behavior	NOUN
ejpam-5479	356	7	of	of	ADP
ejpam-5479	356	8	the	the	DET
ejpam-5479	356	9	waves	wave	NOUN
ejpam-5479	356	10	describing	describe	VERB
ejpam-5479	356	11	the	the	DET
ejpam-5479	356	12	obtained	obtain	VERB
ejpam-5479	356	13	solution	solution	NOUN
ejpam-5479	356	14	using	use	VERB
ejpam-5479	356	15	npa	npa	PROPN
ejpam-5479	356	16	has	have	VERB
ejpam-5479	356	17	periodicity	periodicity	NOUN
ejpam-5479	356	18	manner	manner	NOUN
ejpam-5479	356	19	,	,	PUNCT
ejpam-5479	356	20	which	which	PRON
ejpam-5479	356	21	give	give	VERB
ejpam-5479	356	22	an	an	DET
ejpam-5479	356	23	induction	induction	NOUN
ejpam-5479	356	24	about	about	ADP
ejpam-5479	356	25	the	the	DET
ejpam-5479	356	26	stationary	stationary	ADJ
ejpam-5479	356	27	behavior	behavior	NOUN
ejpam-5479	356	28	of	of	ADP
ejpam-5479	356	29	the	the	DET
ejpam-5479	356	30	obtained	obtain	VERB
ejpam-5479	356	31	solution	solution	NOUN
ejpam-5479	356	32	.	.	PUNCT
ejpam-5479	357	1	moreover	moreover	ADV
ejpam-5479	357	2	,	,	PUNCT
ejpam-5479	357	3	the	the	DET
ejpam-5479	357	4	amplitudes	amplitude	NOUN
ejpam-5479	357	5	of	of	ADP
ejpam-5479	357	6	the	the	DET
ejpam-5479	357	7	drawn	draw	VERB
ejpam-5479	357	8	waves	wave	NOUN
ejpam-5479	357	9	besides	besides	SCONJ
ejpam-5479	357	10	the	the	DET
ejpam-5479	357	11	oscillation	oscillation	NOUN
ejpam-5479	357	12	’s	’s	PART
ejpam-5479	357	13	number	number	NOUN
ejpam-5479	357	14	increase	increase	NOUN
ejpam-5479	357	15	,	,	PUNCT
ejpam-5479	357	16	to	to	ADP
ejpam-5479	357	17	some	some	DET
ejpam-5479	357	18	extent	extent	NOUN
ejpam-5479	357	19	,	,	PUNCT
ejpam-5479	357	20	with	with	ADP
ejpam-5479	357	21	the	the	DET
ejpam-5479	357	22	increase	increase	NOUN
ejpam-5479	357	23	of	of	ADP
ejpam-5479	357	24	r	r	NOUN
ejpam-5479	357	25	and	and	CCONJ
ejpam-5479	357	26	k	k	PROPN
ejpam-5479	357	27	values	value	NOUN
ejpam-5479	357	28	,	,	PUNCT
ejpam-5479	357	29	as	as	SCONJ
ejpam-5479	357	30	illustrated	illustrate	VERB
ejpam-5479	357	31	in	in	ADP
ejpam-5479	357	32	figs	fig	NOUN
ejpam-5479	357	33	.	.	PUNCT
ejpam-5479	358	1	(	(	PUNCT
ejpam-5479	358	2	7a	7a	NUM
ejpam-5479	358	3	)	)	PUNCT
ejpam-5479	358	4	and	and	CCONJ
ejpam-5479	358	5	(	(	PUNCT
ejpam-5479	358	6	8a	8a	NUM
ejpam-5479	358	7	)	)	PUNCT
ejpam-5479	358	8	,	,	PUNCT
ejpam-5479	358	9	respectively	respectively	ADV
ejpam-5479	358	10	.	.	PUNCT
ejpam-5479	359	1	the	the	DET
ejpam-5479	359	2	increase	increase	NOUN
ejpam-5479	359	3	of	of	ADP
ejpam-5479	359	4	τ	τ	PROPN
ejpam-5479	359	5	values	value	NOUN
ejpam-5479	359	6	produces	produce	VERB
ejpam-5479	359	7	standing	stand	VERB
ejpam-5479	359	8	periodic	periodic	ADJ
ejpam-5479	359	9	waves	wave	NOUN
ejpam-5479	359	10	with	with	ADP
ejpam-5479	359	11	some	some	DET
ejpam-5479	359	12	distinct	distinct	ADJ
ejpam-5479	359	13	nodes	node	NOUN
ejpam-5479	359	14	,	,	PUNCT
ejpam-5479	359	15	where	where	SCONJ
ejpam-5479	359	16	the	the	DET
ejpam-5479	359	17	amplitudes	amplitude	NOUN
ejpam-5479	359	18	of	of	ADP
ejpam-5479	359	19	the	the	DET
ejpam-5479	359	20	drawn	draw	VERB
ejpam-5479	359	21	curves	curve	NOUN
ejpam-5479	359	22	are	be	AUX
ejpam-5479	359	23	changed	change	VERB
ejpam-5479	359	24	slightly	slightly	ADV
ejpam-5479	359	25	with	with	ADP
ejpam-5479	359	26	the	the	DET
ejpam-5479	359	27	increase	increase	NOUN
ejpam-5479	359	28	of	of	ADP
ejpam-5479	359	29	τ	τ	PROPN
ejpam-5479	359	30	values	value	NOUN
ejpam-5479	359	31	,	,	PUNCT
ejpam-5479	359	32	as	as	ADP
ejpam-5479	359	33	seen	see	VERB
ejpam-5479	359	34	fig	fig	NOUN
ejpam-5479	359	35	.	.	PUNCT
ejpam-5479	360	1	(	(	PUNCT
ejpam-5479	360	2	9a	9a	NUM
ejpam-5479	360	3	)	)	PUNCT
ejpam-5479	360	4	.	.	PUNCT
ejpam-5479	361	1	based	base	VERB
ejpam-5479	361	2	on	on	ADP
ejpam-5479	361	3	the	the	DET
ejpam-5479	361	4	above	above	NOUN
ejpam-5479	361	5	,	,	PUNCT
ejpam-5479	361	6	one	one	PRON
ejpam-5479	361	7	can	can	AUX
ejpam-5479	361	8	conclude	conclude	VERB
ejpam-5479	361	9	that	that	SCONJ
ejpam-5479	361	10	the	the	DET
ejpam-5479	361	11	obtained	obtain	VERB
ejpam-5479	361	12	solution	solution	NOUN
ejpam-5479	361	13	using	use	VERB
ejpam-5479	361	14	npa	npa	PROPN
ejpam-5479	361	15	has	have	VERB
ejpam-5479	361	16	a	a	DET
ejpam-5479	361	17	stable	stable	ADJ
ejpam-5479	361	18	performance	performance	NOUN
ejpam-5479	361	19	and	and	CCONJ
ejpam-5479	361	20	is	be	AUX
ejpam-5479	361	21	free	free	ADJ
ejpam-5479	361	22	of	of	ADP
ejpam-5479	361	23	chaos	chaos	NOUN
ejpam-5479	361	24	.	.	PUNCT
ejpam-5479	362	1	this	this	DET
ejpam-5479	362	2	supposition	supposition	NOUN
ejpam-5479	362	3	has	have	AUX
ejpam-5479	362	4	been	be	AUX
ejpam-5479	362	5	asserted	assert	VERB
ejpam-5479	362	6	through	through	ADP
ejpam-5479	362	7	the	the	DET
ejpam-5479	362	8	graphed	graphed	ADJ
ejpam-5479	362	9	curves	curve	NOUN
ejpam-5479	362	10	of	of	ADP
ejpam-5479	362	11	the	the	DET
ejpam-5479	362	12	corresponding	corresponding	ADJ
ejpam-5479	362	13	phase	phase	NOUN
ejpam-5479	362	14	plane	plane	NOUN
ejpam-5479	362	15	of	of	ADP
ejpam-5479	362	16	the	the	DET
ejpam-5479	362	17	npa	npa	NOUN
ejpam-5479	362	18	,	,	PUNCT
ejpam-5479	362	19	as	as	SCONJ
ejpam-5479	362	20	seen	see	VERB
ejpam-5479	362	21	in	in	ADP
ejpam-5479	362	22	figs	fig	NOUN
ejpam-5479	362	23	.	.	PUNCT
ejpam-5479	363	1	(	(	PUNCT
ejpam-5479	363	2	7b	7b	NUM
ejpam-5479	363	3	)	)	PUNCT
ejpam-5479	363	4	,	,	PUNCT
ejpam-5479	363	5	(	(	PUNCT
ejpam-5479	363	6	8b	8b	NUM
ejpam-5479	363	7	)	)	PUNCT
ejpam-5479	363	8	,	,	PUNCT
ejpam-5479	363	9	and	and	CCONJ
ejpam-5479	363	10	(	(	PUNCT
ejpam-5479	363	11	9b	9b	NUM
ejpam-5479	363	12	)	)	PUNCT
ejpam-5479	363	13	,	,	PUNCT
ejpam-5479	363	14	in	in	ADP
ejpam-5479	363	15	which	which	PRON
ejpam-5479	363	16	closed	closed	ADJ
ejpam-5479	363	17	curves	curve	NOUN
ejpam-5479	363	18	are	be	AUX
ejpam-5479	363	19	plotted	plot	VERB
ejpam-5479	363	20	for	for	ADP
ejpam-5479	363	21	the	the	DET
ejpam-5479	363	22	identical	identical	ADJ
ejpam-5479	363	23	considered	consider	VERB
ejpam-5479	363	24	values	value	NOUN
ejpam-5479	363	25	of	of	ADP
ejpam-5479	363	26	r	r	NOUN
ejpam-5479	363	27	,	,	PUNCT
ejpam-5479	363	28	k	k	NOUN
ejpam-5479	363	29	,	,	PUNCT
ejpam-5479	363	30	and	and	CCONJ
ejpam-5479	363	31	τ	τ	PROPN
ejpam-5479	363	32	,	,	PUNCT
ejpam-5479	363	33	respectively	respectively	ADV
ejpam-5479	363	34	.	.	PUNCT
ejpam-5479	364	1	within	within	ADP
ejpam-5479	364	2	dynamical	dynamical	ADJ
ejpam-5479	364	3	systems	system	NOUN
ejpam-5479	364	4	analysis	analysis	NOUN
ejpam-5479	364	5	,	,	PUNCT
ejpam-5479	364	6	the	the	DET
ejpam-5479	364	7	phase	phase	NOUN
ejpam-5479	364	8	plane	plane	NOUN
ejpam-5479	364	9	appears	appear	VERB
ejpam-5479	364	10	as	as	ADP
ejpam-5479	364	11	a	a	DET
ejpam-5479	364	12	surface	surface	NOUN
ejpam-5479	364	13	on	on	ADP
ejpam-5479	364	14	which	which	PRON
ejpam-5479	364	15	the	the	DET
ejpam-5479	364	16	interaction	interaction	NOUN
ejpam-5479	364	17	of	of	ADP
ejpam-5479	364	18	variables	variable	NOUN
ejpam-5479	364	19	can	can	AUX
ejpam-5479	364	20	be	be	AUX
ejpam-5479	364	21	graphically	graphically	ADV
ejpam-5479	364	22	represented	represent	VERB
ejpam-5479	364	23	.	.	PUNCT
ejpam-5479	365	1	the	the	DET
ejpam-5479	365	2	plotted	plot	VERB
ejpam-5479	365	3	closed	closed	ADJ
ejpam-5479	365	4	curves	curve	NOUN
ejpam-5479	365	5	provide	provide	VERB
ejpam-5479	365	6	an	an	DET
ejpam-5479	365	7	interesting	interesting	ADJ
ejpam-5479	365	8	story	story	NOUN
ejpam-5479	365	9	about	about	ADP
ejpam-5479	365	10	equilibrium	equilibrium	NOUN
ejpam-5479	365	11	and	and	CCONJ
ejpam-5479	365	12	periodicity	periodicity	NOUN
ejpam-5479	365	13	inside	inside	ADP
ejpam-5479	365	14	these	these	DET
ejpam-5479	365	15	systems	system	NOUN
ejpam-5479	365	16	.	.	PUNCT
ejpam-5479	366	1	these	these	DET
ejpam-5479	366	2	curves	curve	NOUN
ejpam-5479	366	3	,	,	PUNCT
ejpam-5479	366	4	which	which	PRON
ejpam-5479	366	5	elegantly	elegantly	ADV
ejpam-5479	366	6	repeat	repeat	VERB
ejpam-5479	366	7	themselves	themselves	PRON
ejpam-5479	366	8	along	along	ADP
ejpam-5479	366	9	axes	axis	NOUN
ejpam-5479	366	10	of	of	ADP
ejpam-5479	366	11	symmetry	symmetry	NOUN
ejpam-5479	366	12	,	,	PUNCT
ejpam-5479	366	13	capture	capture	VERB
ejpam-5479	366	14	the	the	DET
ejpam-5479	366	15	essence	essence	NOUN
ejpam-5479	366	16	of	of	ADP
ejpam-5479	366	17	stability	stability	NOUN
ejpam-5479	366	18	and	and	CCONJ
ejpam-5479	366	19	cyclic	cyclic	ADJ
ejpam-5479	366	20	behavior	behavior	NOUN
ejpam-5479	366	21	.	.	PUNCT
ejpam-5479	367	1	their	their	PRON
ejpam-5479	367	2	symmetry	symmetry	NOUN
ejpam-5479	367	3	is	be	AUX
ejpam-5479	367	4	evidence	evidence	NOUN
ejpam-5479	367	5	of	of	ADP
ejpam-5479	367	6	the	the	DET
ejpam-5479	367	7	system	system	NOUN
ejpam-5479	367	8	’s	’s	PART
ejpam-5479	367	9	intrinsic	intrinsic	ADJ
ejpam-5479	367	10	balance	balance	NOUN
ejpam-5479	367	11	,	,	PUNCT
ejpam-5479	367	12	where	where	SCONJ
ejpam-5479	367	13	every	every	DET
ejpam-5479	367	14	closed	closed	ADJ
ejpam-5479	367	15	curve	curve	NOUN
ejpam-5479	367	16	draws	draw	VERB
ejpam-5479	367	17	a	a	DET
ejpam-5479	367	18	line	line	NOUN
ejpam-5479	367	19	that	that	PRON
ejpam-5479	367	20	loops	loop	VERB
ejpam-5479	367	21	back	back	ADV
ejpam-5479	367	22	onto	onto	ADP
ejpam-5479	367	23	itself	itself	PRON
ejpam-5479	367	24	with	with	ADP
ejpam-5479	367	25	ease	ease	NOUN
ejpam-5479	367	26	.	.	PUNCT
ejpam-5479	368	1	the	the	DET
ejpam-5479	368	2	notions	notion	NOUN
ejpam-5479	368	3	of	of	ADP
ejpam-5479	368	4	stability	stability	NOUN
ejpam-5479	368	5	and	and	CCONJ
ejpam-5479	368	6	instability	instability	NOUN
ejpam-5479	368	7	zones	zone	NOUN
ejpam-5479	368	8	hold	hold	VERB
ejpam-5479	368	9	significant	significant	ADJ
ejpam-5479	368	10	relevance	relevance	NOUN
ejpam-5479	368	11	across	across	ADP
ejpam-5479	368	12	diverse	diverse	ADJ
ejpam-5479	368	13	disciplines	discipline	NOUN
ejpam-5479	368	14	including	include	VERB
ejpam-5479	368	15	engineering	engineering	NOUN
ejpam-5479	368	16	,	,	PUNCT
ejpam-5479	368	17	physics	physics	NOUN
ejpam-5479	368	18	,	,	PUNCT
ejpam-5479	368	19	and	and	CCONJ
ejpam-5479	368	20	ecology	ecology	NOUN
ejpam-5479	368	21	.	.	PUNCT
ejpam-5479	369	1	these	these	DET
ejpam-5479	369	2	zones	zone	NOUN
ejpam-5479	369	3	help	help	VERB
ejpam-5479	369	4	to	to	PART
ejpam-5479	369	5	determine	determine	VERB
ejpam-5479	369	6	the	the	DET
ejpam-5479	369	7	conditions	condition	NOUN
ejpam-5479	369	8	under	under	ADP
ejpam-5479	369	9	which	which	PRON
ejpam-5479	369	10	a	a	DET
ejpam-5479	369	11	system	system	NOUN
ejpam-5479	369	12	will	will	AUX
ejpam-5479	369	13	remain	remain	VERB
ejpam-5479	369	14	stable	stable	ADJ
ejpam-5479	369	15	or	or	CCONJ
ejpam-5479	369	16	become	become	VERB
ejpam-5479	369	17	unstable	unstable	ADJ
ejpam-5479	369	18	.	.	PUNCT
ejpam-5479	370	1	stability	stability	NOUN
ejpam-5479	370	2	criteria	criterion	NOUN
ejpam-5479	370	3	are	be	AUX
ejpam-5479	370	4	used	use	VERB
ejpam-5479	370	5	to	to	PART
ejpam-5479	370	6	analyze	analyze	VERB
ejpam-5479	370	7	the	the	DET
ejpam-5479	370	8	stability	stability	NOUN
ejpam-5479	370	9	of	of	ADP
ejpam-5479	370	10	a	a	DET
ejpam-5479	370	11	system	system	NOUN
ejpam-5479	370	12	and	and	CCONJ
ejpam-5479	370	13	predict	predict	VERB
ejpam-5479	370	14	its	its	PRON
ejpam-5479	370	15	behavior	behavior	NOUN
ejpam-5479	370	16	under	under	ADP
ejpam-5479	370	17	different	different	ADJ
ejpam-5479	370	18	circumstances	circumstance	NOUN
ejpam-5479	370	19	.	.	PUNCT
ejpam-5479	371	1	to	to	PART
ejpam-5479	371	2	draw	draw	VERB
ejpam-5479	371	3	the	the	DET
ejpam-5479	371	4	stability	stability	NOUN
ejpam-5479	371	5	and	and	CCONJ
ejpam-5479	371	6	instability	instability	NOUN
ejpam-5479	371	7	areas	area	NOUN
ejpam-5479	371	8	,	,	PUNCT
ejpam-5479	371	9	conditions	condition	NOUN
ejpam-5479	371	10	(	(	PUNCT
ejpam-5479	371	11	22	22	NUM
ejpam-5479	371	12	)	)	PUNCT
ejpam-5479	371	13	are	be	AUX
ejpam-5479	371	14	plotted	plot	VERB
ejpam-5479	371	15	when	when	SCONJ
ejpam-5479	371	16	r	r	NOUN
ejpam-5479	371	17	and	and	CCONJ
ejpam-5479	371	18	k	k	PROPN
ejpam-5479	371	19	have	have	VERB
ejpam-5479	371	20	the	the	DET
ejpam-5479	371	21	same	same	ADJ
ejpam-5479	371	22	considered	consider	VERB
ejpam-5479	371	23	values	value	NOUN
ejpam-5479	371	24	above	above	ADV
ejpam-5479	371	25	to	to	PART
ejpam-5479	371	26	produce	produce	VERB
ejpam-5479	371	27	the	the	DET
ejpam-5479	371	28	stable	stable	ADJ
ejpam-5479	371	29	regions	region	NOUN
ejpam-5479	371	30	and	and	CCONJ
ejpam-5479	371	31	the	the	DET
ejpam-5479	371	32	unstable	unstable	ADJ
ejpam-5479	371	33	ones	one	NOUN
ejpam-5479	371	34	,	,	PUNCT
ejpam-5479	371	35	as	as	SCONJ
ejpam-5479	371	36	seen	see	VERB
ejpam-5479	371	37	in	in	ADP
ejpam-5479	371	38	parts	part	NOUN
ejpam-5479	371	39	of	of	ADP
ejpam-5479	371	40	fig	fig	NOUN
ejpam-5479	371	41	.	.	PUNCT
ejpam-5479	372	1	(	(	PUNCT
ejpam-5479	372	2	10	10	NUM
ejpam-5479	372	3	)	)	PUNCT
ejpam-5479	372	4	.	.	PUNCT
ejpam-5479	373	1	it	it	PRON
ejpam-5479	373	2	noted	note	VERB
ejpam-5479	373	3	that	that	SCONJ
ejpam-5479	373	4	the	the	DET
ejpam-5479	373	5	stable	stable	ADJ
ejpam-5479	373	6	zones	zone	NOUN
ejpam-5479	373	7	diminish	diminish	VERB
ejpam-5479	373	8	as	as	ADP
ejpam-5479	373	9	the	the	DET
ejpam-5479	373	10	values	value	NOUN
ejpam-5479	373	11	of	of	ADP
ejpam-5479	373	12	parameters	parameter	NOUN
ejpam-5479	373	13	r	r	NOUN
ejpam-5479	373	14	and	and	CCONJ
ejpam-5479	373	15	k	k	PROPN
ejpam-5479	373	16	increase	increase	NOUN
ejpam-5479	373	17	,	,	PUNCT
ejpam-5479	373	18	as	as	SCONJ
ejpam-5479	373	19	depicted	depict	VERB
ejpam-5479	373	20	in	in	ADP
ejpam-5479	373	21	sections	section	NOUN
ejpam-5479	373	22	(	(	PUNCT
ejpam-5479	373	23	a	a	X
ejpam-5479	373	24	)	)	PUNCT
ejpam-5479	373	25	and	and	CCONJ
ejpam-5479	373	26	(	(	PUNCT
ejpam-5479	373	27	b	b	NOUN
ejpam-5479	373	28	)	)	PUNCT
ejpam-5479	373	29	of	of	ADP
ejpam-5479	373	30	this	this	DET
ejpam-5479	373	31	figure	figure	NOUN
ejpam-5479	373	32	,	,	PUNCT
ejpam-5479	373	33	respectively	respectively	ADV
ejpam-5479	373	34	.	.	PUNCT
ejpam-5479	374	1	k.	k.	PROPN
ejpam-5479	374	2	alluhydan	alluhydan	PROPN
ejpam-5479	374	3	,	,	PUNCT
ejpam-5479	374	4	g.	g.	PROPN
ejpam-5479	374	5	m	m	PROPN
ejpam-5479	374	6	moatimid	moatimid	PROPN
ejpam-5479	374	7	,	,	PUNCT
ejpam-5479	374	8	t.	t.	PROPN
ejpam-5479	374	9	s.	s.	PROPN
ejpam-5479	374	10	amer	amer	PROPN
ejpam-5479	374	11	/	/	SYM
ejpam-5479	374	12	eur	eur	PROPN
ejpam-5479	374	13	.	.	PUNCT
ejpam-5479	375	1	j.	j.	PROPN
ejpam-5479	375	2	pure	pure	PROPN
ejpam-5479	375	3	appl	appl	PROPN
ejpam-5479	375	4	.	.	PROPN
ejpam-5479	375	5	math	math	PROPN
ejpam-5479	375	6	,	,	PUNCT
ejpam-5479	375	7	17	17	NUM
ejpam-5479	375	8	(	(	PUNCT
ejpam-5479	375	9	4	4	NUM
ejpam-5479	375	10	)	)	PUNCT
ejpam-5479	375	11	(	(	PUNCT
ejpam-5479	375	12	2024	2024	NUM
ejpam-5479	375	13	)	)	PUNCT
ejpam-5479	375	14	,	,	PUNCT
ejpam-5479	375	15	3185	3185	NUM
ejpam-5479	375	16	-	-	SYM
ejpam-5479	375	17	3208	3208	NUM
ejpam-5479	375	18	3201	3201	NUM
ejpam-5479	375	19	in	in	ADP
ejpam-5479	375	20	dynamic	dynamic	ADJ
ejpam-5479	375	21	systems	system	NOUN
ejpam-5479	375	22	,	,	PUNCT
ejpam-5479	375	23	especially	especially	ADV
ejpam-5479	375	24	within	within	ADP
ejpam-5479	375	25	control	control	NOUN
ejpam-5479	375	26	theory	theory	NOUN
ejpam-5479	375	27	or	or	CCONJ
ejpam-5479	375	28	odes	ode	NOUN
ejpam-5479	375	29	involving	involve	VERB
ejpam-5479	375	30	delays	delay	NOUN
ejpam-5479	375	31	,	,	PUNCT
ejpam-5479	375	32	time	time	NOUN
ejpam-5479	375	33	delay	delay	NOUN
ejpam-5479	375	34	can	can	AUX
ejpam-5479	375	35	profoundly	profoundly	ADV
ejpam-5479	375	36	influence	influence	VERB
ejpam-5479	375	37	the	the	DET
ejpam-5479	375	38	stability	stability	NOUN
ejpam-5479	375	39	of	of	ADP
ejpam-5479	375	40	the	the	DET
ejpam-5479	375	41	system	system	NOUN
ejpam-5479	375	42	.	.	PUNCT
ejpam-5479	376	1	here	here	ADV
ejpam-5479	376	2	is	be	AUX
ejpam-5479	376	3	a	a	DET
ejpam-5479	376	4	concise	concise	ADJ
ejpam-5479	376	5	elucidation	elucidation	NOUN
ejpam-5479	376	6	:	:	PUNCT
ejpam-5479	376	7	1	1	X
ejpam-5479	376	8	.	.	X
ejpam-5479	376	9	in	in	ADP
ejpam-5479	376	10	instances	instance	NOUN
ejpam-5479	376	11	of	of	ADP
ejpam-5479	376	12	brief	brief	ADJ
ejpam-5479	376	13	time	time	NOUN
ejpam-5479	376	14	delays	delay	NOUN
ejpam-5479	376	15	,	,	PUNCT
ejpam-5479	376	16	the	the	DET
ejpam-5479	376	17	feedback	feedback	NOUN
ejpam-5479	376	18	loop	loop	NOUN
ejpam-5479	376	19	promptly	promptly	ADV
ejpam-5479	376	20	adjusts	adjust	VERB
ejpam-5479	376	21	to	to	ADP
ejpam-5479	376	22	alterations	alteration	NOUN
ejpam-5479	376	23	,	,	PUNCT
ejpam-5479	376	24	enabling	enable	VERB
ejpam-5479	376	25	the	the	DET
ejpam-5479	376	26	system	system	NOUN
ejpam-5479	376	27	to	to	PART
ejpam-5479	376	28	respond	respond	VERB
ejpam-5479	376	29	nearly	nearly	ADV
ejpam-5479	376	30	instantaneously	instantaneously	ADV
ejpam-5479	376	31	to	to	ADP
ejpam-5479	376	32	its	its	PRON
ejpam-5479	376	33	prior	prior	ADJ
ejpam-5479	376	34	conditions	condition	NOUN
ejpam-5479	376	35	.	.	PUNCT
ejpam-5479	377	1	this	this	PRON
ejpam-5479	377	2	may	may	AUX
ejpam-5479	377	3	induce	induce	VERB
ejpam-5479	377	4	quick	quick	ADJ
ejpam-5479	377	5	oscillations	oscillation	NOUN
ejpam-5479	377	6	and	and	CCONJ
ejpam-5479	377	7	overreaction	overreaction	NOUN
ejpam-5479	377	8	,	,	PUNCT
ejpam-5479	377	9	resulting	result	VERB
ejpam-5479	377	10	in	in	ADP
ejpam-5479	377	11	unstable	unstable	ADJ
ejpam-5479	377	12	behavior	behavior	NOUN
ejpam-5479	377	13	,	,	PUNCT
ejpam-5479	377	14	as	as	SCONJ
ejpam-5479	377	15	the	the	DET
ejpam-5479	377	16	system	system	NOUN
ejpam-5479	377	17	lacks	lack	VERB
ejpam-5479	377	18	sufficient	sufficient	ADJ
ejpam-5479	377	19	time	time	NOUN
ejpam-5479	377	20	to	to	PART
ejpam-5479	377	21	stabilize	stabilize	VERB
ejpam-5479	377	22	before	before	ADP
ejpam-5479	377	23	the	the	DET
ejpam-5479	377	24	subsequent	subsequent	ADJ
ejpam-5479	377	25	input	input	NOUN
ejpam-5479	377	26	,	,	PUNCT
ejpam-5479	377	27	influenced	influence	VERB
ejpam-5479	377	28	by	by	ADP
ejpam-5479	377	29	outdates	outdate	NOUN
ejpam-5479	377	30	data	datum	NOUN
ejpam-5479	377	31	,	,	PUNCT
ejpam-5479	377	32	impacts	impact	VERB
ejpam-5479	377	33	it	it	PRON
ejpam-5479	377	34	.	.	PUNCT
ejpam-5479	378	1	the	the	DET
ejpam-5479	378	2	system	system	NOUN
ejpam-5479	378	3	becomes	become	VERB
ejpam-5479	378	4	too	too	ADV
ejpam-5479	378	5	responsive	responsive	ADJ
ejpam-5479	378	6	,	,	PUNCT
ejpam-5479	378	7	exacerbating	exacerbate	VERB
ejpam-5479	378	8	errors	error	NOUN
ejpam-5479	378	9	or	or	CCONJ
ejpam-5479	378	10	disturbances	disturbance	NOUN
ejpam-5479	378	11	rather	rather	ADV
ejpam-5479	378	12	than	than	ADP
ejpam-5479	378	13	mitigating	mitigate	VERB
ejpam-5479	378	14	them	they	PRON
ejpam-5479	378	15	.	.	PUNCT
ejpam-5479	379	1	2	2	X
ejpam-5479	379	2	.	.	X
ejpam-5479	379	3	a	a	DET
ejpam-5479	379	4	prolonged	prolonged	ADJ
ejpam-5479	379	5	latency	latency	NOUN
ejpam-5479	379	6	in	in	ADP
ejpam-5479	379	7	the	the	DET
ejpam-5479	379	8	feedback	feedback	NOUN
ejpam-5479	379	9	loop	loop	NOUN
ejpam-5479	379	10	integrates	integrate	VERB
ejpam-5479	379	11	antiquated	antiquated	ADJ
ejpam-5479	379	12	data	datum	NOUN
ejpam-5479	379	13	,	,	PUNCT
ejpam-5479	379	14	hence	hence	ADV
ejpam-5479	379	15	impeding	impede	VERB
ejpam-5479	379	16	the	the	DET
ejpam-5479	379	17	system	system	NOUN
ejpam-5479	379	18	’s	’s	PART
ejpam-5479	379	19	responsiveness	responsiveness	NOUN
ejpam-5479	379	20	.	.	PUNCT
ejpam-5479	380	1	this	this	DET
ejpam-5479	380	2	delay	delay	NOUN
ejpam-5479	380	3	enables	enable	VERB
ejpam-5479	380	4	the	the	DET
ejpam-5479	380	5	system	system	NOUN
ejpam-5479	380	6	to	to	PART
ejpam-5479	380	7	respond	respond	VERB
ejpam-5479	380	8	more	more	ADV
ejpam-5479	380	9	gradually	gradually	ADV
ejpam-5479	380	10	,	,	PUNCT
ejpam-5479	380	11	mitigating	mitigate	VERB
ejpam-5479	380	12	oscillations	oscillation	NOUN
ejpam-5479	380	13	and	and	CCONJ
ejpam-5479	380	14	averting	avert	VERB
ejpam-5479	380	15	excessive	excessive	ADJ
ejpam-5479	380	16	activity	activity	NOUN
ejpam-5479	380	17	.	.	PUNCT
ejpam-5479	381	1	the	the	DET
ejpam-5479	381	2	postponed	postpone	VERB
ejpam-5479	381	3	reaction	reaction	NOUN
ejpam-5479	381	4	serves	serve	VERB
ejpam-5479	381	5	as	as	ADP
ejpam-5479	381	6	a	a	DET
ejpam-5479	381	7	damping	damp	VERB
ejpam-5479	381	8	mechanism	mechanism	NOUN
ejpam-5479	381	9	,	,	PUNCT
ejpam-5479	381	10	successfully	successfully	ADV
ejpam-5479	381	11	stabilizing	stabilize	VERB
ejpam-5479	381	12	the	the	DET
ejpam-5479	381	13	system	system	NOUN
ejpam-5479	381	14	by	by	ADP
ejpam-5479	381	15	inhibiting	inhibit	VERB
ejpam-5479	381	16	immediate	immediate	ADJ
ejpam-5479	381	17	alterations	alteration	NOUN
ejpam-5479	381	18	that	that	PRON
ejpam-5479	381	19	could	could	AUX
ejpam-5479	381	20	otherwise	otherwise	ADV
ejpam-5479	381	21	lead	lead	VERB
ejpam-5479	381	22	to	to	ADP
ejpam-5479	381	23	instability	instability	NOUN
ejpam-5479	381	24	.	.	PUNCT
ejpam-5479	382	1	in	in	ADP
ejpam-5479	382	2	conclusion	conclusion	NOUN
ejpam-5479	382	3	,	,	PUNCT
ejpam-5479	382	4	brief	brief	ADJ
ejpam-5479	382	5	delays	delay	NOUN
ejpam-5479	382	6	may	may	AUX
ejpam-5479	382	7	induce	induce	VERB
ejpam-5479	382	8	instability	instability	NOUN
ejpam-5479	382	9	through	through	ADP
ejpam-5479	382	10	excessively	excessively	ADV
ejpam-5479	382	11	quick	quick	ADJ
ejpam-5479	382	12	feedback	feedback	NOUN
ejpam-5479	382	13	and	and	CCONJ
ejpam-5479	382	14	adjustments	adjustment	NOUN
ejpam-5479	382	15	,	,	PUNCT
ejpam-5479	382	16	whereas	whereas	SCONJ
ejpam-5479	382	17	prolonged	prolonged	ADJ
ejpam-5479	382	18	delays	delay	NOUN
ejpam-5479	382	19	might	might	AUX
ejpam-5479	382	20	enhance	enhance	VERB
ejpam-5479	382	21	system	system	NOUN
ejpam-5479	382	22	stability	stability	NOUN
ejpam-5479	382	23	by	by	ADP
ejpam-5479	382	24	tempering	temper	VERB
ejpam-5479	382	25	responses	response	NOUN
ejpam-5479	382	26	to	to	ADP
ejpam-5479	382	27	changes	change	NOUN
ejpam-5479	382	28	,	,	PUNCT
ejpam-5479	382	29	so	so	ADV
ejpam-5479	382	30	enabling	enable	VERB
ejpam-5479	382	31	better	well	ADJ
ejpam-5479	382	32	absorption	absorption	NOUN
ejpam-5479	382	33	of	of	ADP
ejpam-5479	382	34	shocks	shock	NOUN
ejpam-5479	382	35	.	.	PUNCT
ejpam-5479	383	1	figure	figure	VERB
ejpam-5479	383	2	7	7	NUM
ejpam-5479	383	3	:	:	PUNCT
ejpam-5479	383	4	(	(	PUNCT
ejpam-5479	383	5	a	a	X
ejpam-5479	383	6	)	)	PUNCT
ejpam-5479	383	7	presents	present	VERB
ejpam-5479	383	8	the	the	DET
ejpam-5479	383	9	time	time	NOUN
ejpam-5479	383	10	history	history	NOUN
ejpam-5479	383	11	of	of	ADP
ejpam-5479	383	12	the	the	DET
ejpam-5479	383	13	obtained	obtain	VERB
ejpam-5479	383	14	solution	solution	NOUN
ejpam-5479	383	15	using	use	VERB
ejpam-5479	383	16	npa	npa	NOUN
ejpam-5479	383	17	at	at	ADP
ejpam-5479	383	18	r(=	r(=	ADJ
ejpam-5479	383	19	0.5	0.5	NUM
ejpam-5479	383	20	,	,	PUNCT
ejpam-5479	383	21	0.7	0.7	NUM
ejpam-5479	383	22	,	,	PUNCT
ejpam-5479	383	23	0.9	0.9	NUM
ejpam-5479	383	24	)	)	PUNCT
ejpam-5479	383	25	,	,	PUNCT
ejpam-5479	383	26	and	and	CCONJ
ejpam-5479	383	27	(	(	PUNCT
ejpam-5479	383	28	b	b	X
ejpam-5479	383	29	)	)	PUNCT
ejpam-5479	383	30	the	the	DET
ejpam-5479	383	31	corresponding	corresponding	ADJ
ejpam-5479	383	32	phase	phase	NOUN
ejpam-5479	383	33	plane	plane	NOUN
ejpam-5479	383	34	curves	curve	NOUN
ejpam-5479	383	35	.	.	PUNCT
ejpam-5479	384	1	k.	k.	PROPN
ejpam-5479	384	2	alluhydan	alluhydan	PROPN
ejpam-5479	384	3	,	,	PUNCT
ejpam-5479	384	4	g.	g.	PROPN
ejpam-5479	384	5	m	m	PROPN
ejpam-5479	384	6	moatimid	moatimid	PROPN
ejpam-5479	384	7	,	,	PUNCT
ejpam-5479	384	8	t.	t.	PROPN
ejpam-5479	384	9	s.	s.	PROPN
ejpam-5479	384	10	amer	amer	PROPN
ejpam-5479	384	11	/	/	SYM
ejpam-5479	384	12	eur	eur	PROPN
ejpam-5479	384	13	.	.	PUNCT
ejpam-5479	385	1	j.	j.	PROPN
ejpam-5479	385	2	pure	pure	PROPN
ejpam-5479	385	3	appl	appl	PROPN
ejpam-5479	385	4	.	.	PROPN
ejpam-5479	385	5	math	math	PROPN
ejpam-5479	385	6	,	,	PUNCT
ejpam-5479	385	7	17	17	NUM
ejpam-5479	385	8	(	(	PUNCT
ejpam-5479	385	9	4	4	NUM
ejpam-5479	385	10	)	)	PUNCT
ejpam-5479	385	11	(	(	PUNCT
ejpam-5479	385	12	2024	2024	NUM
ejpam-5479	385	13	)	)	PUNCT
ejpam-5479	385	14	,	,	PUNCT
ejpam-5479	385	15	3185	3185	NUM
ejpam-5479	385	16	-	-	SYM
ejpam-5479	385	17	3208	3208	NUM
ejpam-5479	385	18	3202	3202	NUM
ejpam-5479	385	19	figure	figure	NOUN
ejpam-5479	385	20	8	8	NUM
ejpam-5479	385	21	:	:	PUNCT
ejpam-5479	385	22	(	(	PUNCT
ejpam-5479	385	23	a	a	X
ejpam-5479	385	24	)	)	PUNCT
ejpam-5479	385	25	shows	show	VERB
ejpam-5479	385	26	the	the	DET
ejpam-5479	385	27	behavior	behavior	NOUN
ejpam-5479	385	28	of	of	ADP
ejpam-5479	385	29	u(t	u(t	NOUN
ejpam-5479	385	30	)	)	PUNCT
ejpam-5479	385	31	at	at	ADP
ejpam-5479	385	32	k(=	k(=	PROPN
ejpam-5479	385	33	0.5	0.5	NUM
ejpam-5479	385	34	,	,	PUNCT
ejpam-5479	385	35	0.7	0.7	NUM
ejpam-5479	385	36	,	,	PUNCT
ejpam-5479	385	37	1	1	NUM
ejpam-5479	385	38	)	)	PUNCT
ejpam-5479	385	39	,	,	PUNCT
ejpam-5479	385	40	and	and	CCONJ
ejpam-5479	385	41	(	(	PUNCT
ejpam-5479	385	42	b	b	X
ejpam-5479	385	43	)	)	PUNCT
ejpam-5479	385	44	the	the	DET
ejpam-5479	385	45	related	relate	VERB
ejpam-5479	385	46	phase	phase	NOUN
ejpam-5479	385	47	plane	plane	NOUN
ejpam-5479	385	48	curves	curve	NOUN
ejpam-5479	385	49	.	.	PUNCT
ejpam-5479	386	1	figure	figure	NOUN
ejpam-5479	386	2	9	9	NUM
ejpam-5479	386	3	:	:	PUNCT
ejpam-5479	386	4	(	(	PUNCT
ejpam-5479	386	5	a	a	X
ejpam-5479	386	6	)	)	PUNCT
ejpam-5479	386	7	describes	describe	VERB
ejpam-5479	386	8	the	the	DET
ejpam-5479	386	9	behavior	behavior	NOUN
ejpam-5479	386	10	of	of	ADP
ejpam-5479	386	11	u(t	u(t	NOUN
ejpam-5479	386	12	)	)	PUNCT
ejpam-5479	386	13	at	at	ADP
ejpam-5479	386	14	τ(=	τ(=	NOUN
ejpam-5479	386	15	0.001	0.001	NUM
ejpam-5479	386	16	,	,	PUNCT
ejpam-5479	386	17	0.01	0.01	NUM
ejpam-5479	386	18	,	,	PUNCT
ejpam-5479	386	19	0.05	0.05	NUM
ejpam-5479	386	20	)	)	PUNCT
ejpam-5479	386	21	,	,	PUNCT
ejpam-5479	386	22	and	and	CCONJ
ejpam-5479	386	23	(	(	PUNCT
ejpam-5479	386	24	b	b	X
ejpam-5479	386	25	)	)	PUNCT
ejpam-5479	386	26	the	the	DET
ejpam-5479	386	27	related	relate	VERB
ejpam-5479	386	28	phase	phase	NOUN
ejpam-5479	386	29	plane	plane	NOUN
ejpam-5479	386	30	curves	curve	NOUN
ejpam-5479	386	31	.	.	PUNCT
ejpam-5479	387	1	k.	k.	PROPN
ejpam-5479	387	2	alluhydan	alluhydan	PROPN
ejpam-5479	387	3	,	,	PUNCT
ejpam-5479	387	4	g.	g.	PROPN
ejpam-5479	387	5	m	m	PROPN
ejpam-5479	387	6	moatimid	moatimid	PROPN
ejpam-5479	387	7	,	,	PUNCT
ejpam-5479	387	8	t.	t.	PROPN
ejpam-5479	387	9	s.	s.	PROPN
ejpam-5479	387	10	amer	amer	PROPN
ejpam-5479	387	11	/	/	SYM
ejpam-5479	387	12	eur	eur	PROPN
ejpam-5479	387	13	.	.	PUNCT
ejpam-5479	388	1	j.	j.	PROPN
ejpam-5479	388	2	pure	pure	PROPN
ejpam-5479	388	3	appl	appl	PROPN
ejpam-5479	388	4	.	.	PROPN
ejpam-5479	388	5	math	math	PROPN
ejpam-5479	388	6	,	,	PUNCT
ejpam-5479	388	7	17	17	NUM
ejpam-5479	388	8	(	(	PUNCT
ejpam-5479	388	9	4	4	NUM
ejpam-5479	388	10	)	)	PUNCT
ejpam-5479	388	11	(	(	PUNCT
ejpam-5479	388	12	2024	2024	NUM
ejpam-5479	388	13	)	)	PUNCT
ejpam-5479	388	14	,	,	PUNCT
ejpam-5479	388	15	3185	3185	NUM
ejpam-5479	388	16	-	-	SYM
ejpam-5479	388	17	3208	3208	NUM
ejpam-5479	388	18	3203	3203	NUM
ejpam-5479	388	19	figure	figure	NOUN
ejpam-5479	388	20	10	10	NUM
ejpam-5479	388	21	:	:	PUNCT
ejpam-5479	388	22	shows	show	VERB
ejpam-5479	388	23	stable	stable	ADJ
ejpam-5479	388	24	and	and	CCONJ
ejpam-5479	388	25	unstable	unstable	ADJ
ejpam-5479	388	26	regions	region	NOUN
ejpam-5479	388	27	:	:	PUNCT
ejpam-5479	388	28	(	(	PUNCT
ejpam-5479	388	29	a	a	X
ejpam-5479	388	30	)	)	PUNCT
ejpam-5479	388	31	at	at	ADP
ejpam-5479	388	32	r(=	r(=	ADJ
ejpam-5479	388	33	0.5	0.5	NUM
ejpam-5479	388	34	,	,	PUNCT
ejpam-5479	388	35	0.7	0.7	NUM
ejpam-5479	388	36	,	,	PUNCT
ejpam-5479	388	37	0.9	0.9	NUM
ejpam-5479	388	38	)	)	PUNCT
ejpam-5479	388	39	and	and	CCONJ
ejpam-5479	388	40	(	(	PUNCT
ejpam-5479	388	41	b	b	X
ejpam-5479	388	42	)	)	PUNCT
ejpam-5479	388	43	at	at	ADP
ejpam-5479	388	44	k(=	k(=	PROPN
ejpam-5479	388	45	0.5	0.5	NUM
ejpam-5479	388	46	,	,	PUNCT
ejpam-5479	388	47	0.7	0.7	NUM
ejpam-5479	388	48	,	,	PUNCT
ejpam-5479	388	49	1	1	NUM
ejpam-5479	388	50	)	)	PUNCT
ejpam-5479	388	51	.	.	PUNCT
ejpam-5479	389	1	5	5	X
ejpam-5479	389	2	.	.	X
ejpam-5479	389	3	conclusions	conclusion	NOUN
ejpam-5479	389	4	the	the	DET
ejpam-5479	389	5	current	current	ADJ
ejpam-5479	389	6	investigation	investigation	NOUN
ejpam-5479	389	7	centers	center	NOUN
ejpam-5479	389	8	on	on	ADP
ejpam-5479	389	9	the	the	DET
ejpam-5479	389	10	analysis	analysis	NOUN
ejpam-5479	389	11	of	of	ADP
ejpam-5479	389	12	the	the	DET
ejpam-5479	389	13	motion	motion	NOUN
ejpam-5479	389	14	of	of	ADP
ejpam-5479	389	15	a	a	DET
ejpam-5479	389	16	sp	sp	NOUN
ejpam-5479	389	17	that	that	PRON
ejpam-5479	389	18	is	be	AUX
ejpam-5479	389	19	linked	link	VERB
ejpam-5479	389	20	to	to	ADP
ejpam-5479	389	21	a	a	DET
ejpam-5479	389	22	rolling	rolling	ADJ
ejpam-5479	389	23	wheel	wheel	NOUN
ejpam-5479	389	24	and	and	CCONJ
ejpam-5479	389	25	attached	attach	VERB
ejpam-5479	389	26	to	to	ADP
ejpam-5479	389	27	a	a	DET
ejpam-5479	389	28	spring	spring	NOUN
ejpam-5479	389	29	that	that	PRON
ejpam-5479	389	30	has	have	VERB
ejpam-5479	389	31	a	a	DET
ejpam-5479	389	32	slight	slight	ADJ
ejpam-5479	389	33	weight	weight	NOUN
ejpam-5479	389	34	.	.	PUNCT
ejpam-5479	390	1	the	the	DET
ejpam-5479	390	2	rationale	rationale	NOUN
ejpam-5479	390	3	behind	behind	ADP
ejpam-5479	390	4	the	the	DET
ejpam-5479	390	5	current	current	ADJ
ejpam-5479	390	6	subject	subject	NOUN
ejpam-5479	390	7	is	be	AUX
ejpam-5479	390	8	seen	see	VERB
ejpam-5479	390	9	in	in	ADP
ejpam-5479	390	10	the	the	DET
ejpam-5479	390	11	potential	potential	ADJ
ejpam-5479	390	12	applications	application	NOUN
ejpam-5479	390	13	of	of	ADP
ejpam-5479	390	14	the	the	DET
ejpam-5479	390	15	sp	sp	NOUN
ejpam-5479	390	16	in	in	ADP
ejpam-5479	390	17	the	the	DET
ejpam-5479	390	18	fields	field	NOUN
ejpam-5479	390	19	of	of	ADP
ejpam-5479	390	20	physics	physics	NOUN
ejpam-5479	390	21	,	,	PUNCT
ejpam-5479	390	22	manufacturing	manufacturing	NOUN
ejpam-5479	390	23	,	,	PUNCT
ejpam-5479	390	24	and	and	CCONJ
ejpam-5479	390	25	practical	practical	ADJ
ejpam-5479	390	26	mechanisms	mechanism	NOUN
ejpam-5479	390	27	.	.	PUNCT
ejpam-5479	391	1	as	as	ADV
ejpam-5479	391	2	well	well	ADV
ejpam-5479	391	3	-	-	PUNCT
ejpam-5479	391	4	known	know	VERB
ejpam-5479	391	5	classical	classical	ADJ
ejpam-5479	391	6	perturbation	perturbation	NOUN
ejpam-5479	391	7	methods	method	NOUN
ejpam-5479	391	8	are	be	AUX
ejpam-5479	391	9	often	often	ADV
ejpam-5479	391	10	employ	employ	VERB
ejpam-5479	391	11	taylor	taylor	NOUN
ejpam-5479	391	12	expansion	expansion	NOUN
ejpam-5479	391	13	to	to	PART
ejpam-5479	391	14	simplify	simplify	VERB
ejpam-5479	391	15	the	the	DET
ejpam-5479	391	16	current	current	ADJ
ejpam-5479	391	17	situation	situation	NOUN
ejpam-5479	391	18	by	by	ADP
ejpam-5479	391	19	increasing	increase	VERB
ejpam-5479	391	20	the	the	DET
ejpam-5479	391	21	existing	exist	VERB
ejpam-5479	391	22	restoring	restore	VERB
ejpam-5479	391	23	forces	force	NOUN
ejpam-5479	391	24	.	.	PUNCT
ejpam-5479	392	1	conversely	conversely	ADV
ejpam-5479	392	2	,	,	PUNCT
ejpam-5479	392	3	the	the	DET
ejpam-5479	392	4	npa	npa	NOUN
ejpam-5479	392	5	as	as	ADP
ejpam-5479	392	6	a	a	DET
ejpam-5479	392	7	novel	novel	ADJ
ejpam-5479	392	8	methodology	methodology	NOUN
ejpam-5479	392	9	converts	convert	VERB
ejpam-5479	392	10	the	the	DET
ejpam-5479	392	11	nonlinear	nonlinear	ADJ
ejpam-5479	392	12	ode	ode	NOUN
ejpam-5479	392	13	into	into	ADP
ejpam-5479	392	14	a	a	DET
ejpam-5479	392	15	linear	linear	ADJ
ejpam-5479	392	16	one	one	NUM
ejpam-5479	392	17	.	.	PUNCT
ejpam-5479	393	1	the	the	DET
ejpam-5479	393	2	npa	npa	NOUN
ejpam-5479	393	3	concept	concept	NOUN
ejpam-5479	393	4	primarily	primarily	ADV
ejpam-5479	393	5	relies	rely	VERB
ejpam-5479	393	6	on	on	ADP
ejpam-5479	393	7	the	the	DET
ejpam-5479	393	8	hff	hff	NOUN
ejpam-5479	393	9	.	.	PUNCT
ejpam-5479	394	1	it	it	PRON
ejpam-5479	394	2	also	also	ADV
ejpam-5479	394	3	allows	allow	VERB
ejpam-5479	394	4	for	for	ADP
ejpam-5479	394	5	the	the	DET
ejpam-5479	394	6	assessment	assessment	NOUN
ejpam-5479	394	7	of	of	ADP
ejpam-5479	394	8	the	the	DET
ejpam-5479	394	9	stability	stability	NOUN
ejpam-5479	394	10	of	of	ADP
ejpam-5479	394	11	the	the	DET
ejpam-5479	394	12	sp	sp	NOUN
ejpam-5479	394	13	.	.	PUNCT
ejpam-5479	395	1	therefore	therefore	ADV
ejpam-5479	395	2	,	,	PUNCT
ejpam-5479	395	3	while	while	SCONJ
ejpam-5479	395	4	analyzing	analyze	VERB
ejpam-5479	395	5	approximations	approximation	NOUN
ejpam-5479	395	6	for	for	ADP
ejpam-5479	395	7	highly	highly	ADV
ejpam-5479	395	8	nonlinear	nonlinear	ADJ
ejpam-5479	395	9	oscillators	oscillator	NOUN
ejpam-5479	395	10	in	in	ADP
ejpam-5479	395	11	the	the	DET
ejpam-5479	395	12	ms	ms	NOUN
ejpam-5479	395	13	,	,	PUNCT
ejpam-5479	395	14	the	the	DET
ejpam-5479	395	15	npa	npa	NOUN
ejpam-5479	395	16	proves	prove	VERB
ejpam-5479	395	17	to	to	PART
ejpam-5479	395	18	be	be	AUX
ejpam-5479	395	19	a	a	DET
ejpam-5479	395	20	more	more	ADV
ejpam-5479	395	21	helpful	helpful	ADJ
ejpam-5479	395	22	instrument	instrument	NOUN
ejpam-5479	395	23	for	for	ADP
ejpam-5479	395	24	guaranteeing	guarantee	VERB
ejpam-5479	395	25	precision	precision	NOUN
ejpam-5479	395	26	and	and	CCONJ
ejpam-5479	395	27	dependability	dependability	NOUN
ejpam-5479	395	28	.	.	PUNCT
ejpam-5479	396	1	to	to	PART
ejpam-5479	396	2	guarantee	guarantee	VERB
ejpam-5479	396	3	the	the	DET
ejpam-5479	396	4	precision	precision	NOUN
ejpam-5479	396	5	of	of	ADP
ejpam-5479	396	6	the	the	DET
ejpam-5479	396	7	outcomes	outcome	NOUN
ejpam-5479	396	8	,	,	PUNCT
ejpam-5479	396	9	a	a	DET
ejpam-5479	396	10	quantitative	quantitative	ADJ
ejpam-5479	396	11	approach	approach	NOUN
ejpam-5479	396	12	utilizing	utilize	VERB
ejpam-5479	396	13	the	the	DET
ejpam-5479	396	14	ms	ms	PROPN
ejpam-5479	396	15	is	be	AUX
ejpam-5479	396	16	utilized	utilize	VERB
ejpam-5479	396	17	to	to	PART
ejpam-5479	396	18	attain	attain	VERB
ejpam-5479	396	19	a	a	DET
ejpam-5479	396	20	strong	strong	ADJ
ejpam-5479	396	21	level	level	NOUN
ejpam-5479	396	22	of	of	ADP
ejpam-5479	396	23	concurrence	concurrence	NOUN
ejpam-5479	396	24	between	between	ADP
ejpam-5479	396	25	the	the	DET
ejpam-5479	396	26	two	two	NUM
ejpam-5479	396	27	systems	system	NOUN
ejpam-5479	396	28	.	.	PUNCT
ejpam-5479	397	1	the	the	DET
ejpam-5479	397	2	derived	derive	VERB
ejpam-5479	397	3	analytical	analytical	ADJ
ejpam-5479	397	4	solution	solution	NOUN
ejpam-5479	397	5	serves	serve	VERB
ejpam-5479	397	6	as	as	ADP
ejpam-5479	397	7	a	a	DET
ejpam-5479	397	8	foundation	foundation	NOUN
ejpam-5479	397	9	for	for	ADP
ejpam-5479	397	10	comprehending	comprehend	VERB
ejpam-5479	397	11	the	the	DET
ejpam-5479	397	12	interrelated	interrelated	ADJ
ejpam-5479	397	13	nonlinear	nonlinear	ADJ
ejpam-5479	397	14	dynamics	dynamic	NOUN
ejpam-5479	397	15	of	of	ADP
ejpam-5479	397	16	the	the	DET
ejpam-5479	397	17	oscillators	oscillator	NOUN
ejpam-5479	397	18	.	.	PUNCT
ejpam-5479	398	1	numerical	numerical	ADJ
ejpam-5479	398	2	computations	computation	NOUN
ejpam-5479	398	3	are	be	AUX
ejpam-5479	398	4	visually	visually	ADV
ejpam-5479	398	5	performed	perform	VERB
ejpam-5479	398	6	to	to	PART
ejpam-5479	398	7	validate	validate	VERB
ejpam-5479	398	8	the	the	DET
ejpam-5479	398	9	new	new	ADJ
ejpam-5479	398	10	approach	approach	NOUN
ejpam-5479	398	11	and	and	CCONJ
ejpam-5479	398	12	assess	assess	VERB
ejpam-5479	398	13	the	the	DET
ejpam-5479	398	14	effectiveness	effectiveness	NOUN
ejpam-5479	398	15	and	and	CCONJ
ejpam-5479	398	16	applicability	applicability	NOUN
ejpam-5479	398	17	of	of	ADP
ejpam-5479	398	18	the	the	DET
ejpam-5479	398	19	strategy	strategy	NOUN
ejpam-5479	398	20	.	.	PUNCT
ejpam-5479	399	1	the	the	DET
ejpam-5479	399	2	results	result	NOUN
ejpam-5479	399	3	were	be	AUX
ejpam-5479	399	4	compared	compare	VERB
ejpam-5479	399	5	to	to	ADP
ejpam-5479	399	6	the	the	DET
ejpam-5479	399	7	precise	precise	ADJ
ejpam-5479	399	8	numerical	numerical	ADJ
ejpam-5479	399	9	responses	response	NOUN
ejpam-5479	399	10	and	and	CCONJ
ejpam-5479	399	11	demonstrated	demonstrate	VERB
ejpam-5479	399	12	complete	complete	ADJ
ejpam-5479	399	13	accuracy	accuracy	NOUN
ejpam-5479	399	14	.	.	PUNCT
ejpam-5479	400	1	the	the	DET
ejpam-5479	400	2	technique	technique	NOUN
ejpam-5479	400	3	is	be	AUX
ejpam-5479	400	4	widely	widely	ADV
ejpam-5479	400	5	relevant	relevant	ADJ
ejpam-5479	400	6	in	in	ADP
ejpam-5479	400	7	engineering	engineering	NOUN
ejpam-5479	400	8	and	and	CCONJ
ejpam-5479	400	9	other	other	ADJ
ejpam-5479	400	10	fields	field	NOUN
ejpam-5479	400	11	since	since	SCONJ
ejpam-5479	400	12	it	it	PRON
ejpam-5479	400	13	can	can	AUX
ejpam-5479	400	14	be	be	AUX
ejpam-5479	400	15	easily	easily	ADV
ejpam-5479	400	16	adapted	adapt	VERB
ejpam-5479	400	17	to	to	ADP
ejpam-5479	400	18	many	many	ADJ
ejpam-5479	400	19	nonlinear	nonlinear	ADJ
ejpam-5479	400	20	systems	system	NOUN
ejpam-5479	400	21	.	.	PUNCT
ejpam-5479	401	1	the	the	DET
ejpam-5479	401	2	empirical	empirical	ADJ
ejpam-5479	401	3	approximation	approximation	NOUN
ejpam-5479	401	4	inquiry	inquiry	NOUN
ejpam-5479	401	5	allows	allow	VERB
ejpam-5479	401	6	for	for	ADP
ejpam-5479	401	7	a	a	DET
ejpam-5479	401	8	qualitative	qualitative	ADJ
ejpam-5479	401	9	analysis	analysis	NOUN
ejpam-5479	401	10	of	of	ADP
ejpam-5479	401	11	the	the	DET
ejpam-5479	401	12	findings	finding	NOUN
ejpam-5479	401	13	.	.	PUNCT
ejpam-5479	402	1	the	the	DET
ejpam-5479	402	2	temporal	temporal	ADJ
ejpam-5479	402	3	results	result	NOUN
ejpam-5479	402	4	are	be	AUX
ejpam-5479	402	5	examined	examine	VERB
ejpam-5479	402	6	for	for	ADP
ejpam-5479	402	7	different	different	ADJ
ejpam-5479	402	8	values	value	NOUN
ejpam-5479	402	9	of	of	ADP
ejpam-5479	402	10	the	the	DET
ejpam-5479	402	11	physical	physical	ADJ
ejpam-5479	402	12	frequency	frequency	NOUN
ejpam-5479	402	13	and	and	CCONJ
ejpam-5479	402	14	time	time	NOUN
ejpam-5479	402	15	-	-	PUNCT
ejpam-5479	402	16	delay	delay	NOUN
ejpam-5479	402	17	parameters	parameter	NOUN
ejpam-5479	402	18	.	.	PUNCT
ejpam-5479	403	1	the	the	DET
ejpam-5479	403	2	results	result	NOUN
ejpam-5479	403	3	are	be	AUX
ejpam-5479	403	4	determined	determine	VERB
ejpam-5479	403	5	based	base	VERB
ejpam-5479	403	6	on	on	ADP
ejpam-5479	403	7	the	the	DET
ejpam-5479	403	8	visible	visible	ADJ
ejpam-5479	403	9	curves	curve	NOUN
ejpam-5479	403	10	.	.	PUNCT
ejpam-5479	404	1	graphical	graphical	ADJ
ejpam-5479	404	2	representations	representation	NOUN
ejpam-5479	404	3	are	be	AUX
ejpam-5479	404	4	employed	employ	VERB
ejpam-5479	404	5	to	to	PART
ejpam-5479	404	6	illustrate	illustrate	VERB
ejpam-5479	404	7	the	the	DET
ejpam-5479	404	8	influence	influence	NOUN
ejpam-5479	404	9	of	of	ADP
ejpam-5479	404	10	parameters	parameter	NOUN
ejpam-5479	404	11	on	on	ADP
ejpam-5479	404	12	the	the	DET
ejpam-5479	404	13	behavior	behavior	NOUN
ejpam-5479	404	14	of	of	ADP
ejpam-5479	404	15	motion	motion	NOUN
ejpam-5479	404	16	.	.	PUNCT
ejpam-5479	405	1	these	these	DET
ejpam-5479	405	2	representations	representation	NOUN
ejpam-5479	405	3	consist	consist	VERB
ejpam-5479	405	4	of	of	ADP
ejpam-5479	405	5	solutions	solution	NOUN
ejpam-5479	405	6	that	that	PRON
ejpam-5479	405	7	have	have	AUX
ejpam-5479	405	8	been	be	AUX
ejpam-5479	405	9	developed	develop	VERB
ejpam-5479	405	10	over	over	ADP
ejpam-5479	405	11	a	a	DET
ejpam-5479	405	12	period	period	NOUN
ejpam-5479	405	13	of	of	ADP
ejpam-5479	405	14	time	time	NOUN
ejpam-5479	405	15	,	,	PUNCT
ejpam-5479	405	16	together	together	ADV
ejpam-5479	405	17	with	with	ADP
ejpam-5479	405	18	their	their	PRON
ejpam-5479	405	19	related	relate	VERB
ejpam-5479	405	20	phase	phase	NOUN
ejpam-5479	405	21	plane	plane	NOUN
ejpam-5479	405	22	graphs	graph	NOUN
ejpam-5479	405	23	.	.	PUNCT
ejpam-5479	406	1	furthermore	furthermore	ADV
ejpam-5479	406	2	,	,	PUNCT
ejpam-5479	406	3	stability	stability	NOUN
ejpam-5479	406	4	and	and	CCONJ
ejpam-5479	406	5	instability	instability	NOUN
ejpam-5479	406	6	zones	zone	NOUN
ejpam-5479	406	7	have	have	AUX
ejpam-5479	406	8	been	be	AUX
ejpam-5479	406	9	drawn	draw	VERB
ejpam-5479	406	10	and	and	CCONJ
ejpam-5479	406	11	examined	examine	VERB
ejpam-5479	406	12	.	.	PUNCT
ejpam-5479	407	1	furthermore	furthermore	ADV
ejpam-5479	407	2	,	,	PUNCT
ejpam-5479	407	3	the	the	DET
ejpam-5479	407	4	npa	npa	NOUN
ejpam-5479	407	5	can	can	AUX
ejpam-5479	407	6	be	be	AUX
ejpam-5479	407	7	expanded	expand	VERB
ejpam-5479	407	8	to	to	PART
ejpam-5479	407	9	encompass	encompass	VERB
ejpam-5479	407	10	further	further	ADJ
ejpam-5479	407	11	categories	category	NOUN
ejpam-5479	407	12	within	within	ADP
ejpam-5479	407	13	the	the	DET
ejpam-5479	407	14	realm	realm	NOUN
ejpam-5479	407	15	of	of	ADP
ejpam-5479	407	16	couples	couple	NOUN
ejpam-5479	407	17	of	of	ADP
ejpam-5479	407	18	dynamical	dynamical	ADJ
ejpam-5479	407	19	systems	system	NOUN
ejpam-5479	407	20	and	and	CCONJ
ejpam-5479	407	21	is	be	AUX
ejpam-5479	407	22	considered	consider	VERB
ejpam-5479	407	23	significant	significant	ADJ
ejpam-5479	407	24	,	,	PUNCT
ejpam-5479	407	25	productive	productive	ADJ
ejpam-5479	407	26	,	,	PUNCT
ejpam-5479	407	27	and	and	CCONJ
ejpam-5479	407	28	captivating	captivating	ADJ
ejpam-5479	407	29	.	.	PUNCT
ejpam-5479	408	1	the	the	DET
ejpam-5479	408	2	main	main	ADJ
ejpam-5479	408	3	outcomes	outcome	NOUN
ejpam-5479	408	4	derived	derive	VERB
ejpam-5479	408	5	from	from	ADP
ejpam-5479	408	6	this	this	DET
ejpam-5479	408	7	study	study	NOUN
ejpam-5479	408	8	can	can	AUX
ejpam-5479	408	9	be	be	AUX
ejpam-5479	408	10	summarized	summarize	VERB
ejpam-5479	408	11	as	as	SCONJ
ejpam-5479	408	12	follows	follow	VERB
ejpam-5479	408	13	:	:	PUNCT
ejpam-5479	408	14	references	reference	NOUN
ejpam-5479	408	15	3204	3204	NUM
ejpam-5479	408	16	i.	i.	PROPN
ejpam-5479	408	17	the	the	DET
ejpam-5479	408	18	taylor	taylor	PROPN
ejpam-5479	408	19	expansion	expansion	NOUN
ejpam-5479	408	20	is	be	AUX
ejpam-5479	408	21	used	use	VERB
ejpam-5479	408	22	by	by	ADP
ejpam-5479	408	23	all	all	DET
ejpam-5479	408	24	conventional	conventional	ADJ
ejpam-5479	408	25	techniques	technique	NOUN
ejpam-5479	408	26	to	to	PART
ejpam-5479	408	27	make	make	VERB
ejpam-5479	408	28	the	the	DET
ejpam-5479	408	29	provided	provide	VERB
ejpam-5479	408	30	problem	problem	NOUN
ejpam-5479	408	31	simpler	simple	ADJ
ejpam-5479	408	32	when	when	SCONJ
ejpam-5479	408	33	restoring	restore	VERB
ejpam-5479	408	34	forces	force	NOUN
ejpam-5479	408	35	are	be	AUX
ejpam-5479	408	36	involved	involve	VERB
ejpam-5479	408	37	.	.	PUNCT
ejpam-5479	409	1	this	this	DET
ejpam-5479	409	2	drawback	drawback	NOUN
ejpam-5479	409	3	is	be	AUX
ejpam-5479	409	4	no	no	ADV
ejpam-5479	409	5	longer	long	ADV
ejpam-5479	409	6	present	present	ADJ
ejpam-5479	409	7	with	with	ADP
ejpam-5479	409	8	the	the	DET
ejpam-5479	409	9	adopted	adopt	VERB
ejpam-5479	409	10	scheme	scheme	NOUN
ejpam-5479	409	11	.	.	PUNCT
ejpam-5479	409	12	ii	ii	PROPN
ejpam-5479	409	13	.	.	PUNCT
ejpam-5479	410	1	this	this	DET
ejpam-5479	410	2	approach	approach	NOUN
ejpam-5479	410	3	,	,	PUNCT
ejpam-5479	410	4	in	in	ADP
ejpam-5479	410	5	contrast	contrast	NOUN
ejpam-5479	410	6	to	to	ADP
ejpam-5479	410	7	earlier	early	ADJ
ejpam-5479	410	8	conventional	conventional	ADJ
ejpam-5479	410	9	methods	method	NOUN
ejpam-5479	410	10	,	,	PUNCT
ejpam-5479	410	11	enables	enable	VERB
ejpam-5479	410	12	us	we	PRON
ejpam-5479	410	13	to	to	PART
ejpam-5479	410	14	examine	examine	VERB
ejpam-5479	410	15	the	the	DET
ejpam-5479	410	16	instability	instability	NOUN
ejpam-5479	410	17	analysis	analysis	NOUN
ejpam-5479	410	18	of	of	ADP
ejpam-5479	410	19	the	the	DET
ejpam-5479	410	20	problem	problem	NOUN
ejpam-5479	410	21	.	.	PUNCT
ejpam-5479	411	1	iii	iii	X
ejpam-5479	411	2	.	.	PUNCT
ejpam-5479	412	1	in	in	ADP
ejpam-5479	412	2	conclusion	conclusion	NOUN
ejpam-5479	412	3	,	,	PUNCT
ejpam-5479	412	4	it	it	PRON
ejpam-5479	412	5	appears	appear	VERB
ejpam-5479	412	6	that	that	SCONJ
ejpam-5479	412	7	the	the	DET
ejpam-5479	412	8	novel	novel	ADJ
ejpam-5479	412	9	technique	technique	NOUN
ejpam-5479	412	10	is	be	AUX
ejpam-5479	412	11	a	a	DET
ejpam-5479	412	12	straightforward	straightforward	ADJ
ejpam-5479	412	13	,	,	PUNCT
ejpam-5479	412	14	valuable	valuable	ADJ
ejpam-5479	412	15	,	,	PUNCT
ejpam-5479	412	16	and	and	CCONJ
ejpam-5479	412	17	efficient	efficient	ADJ
ejpam-5479	412	18	tool	tool	NOUN
ejpam-5479	412	19	.	.	PUNCT
ejpam-5479	413	1	it	it	PRON
ejpam-5479	413	2	has	have	VERB
ejpam-5479	413	3	the	the	DET
ejpam-5479	413	4	potential	potential	NOUN
ejpam-5479	413	5	to	to	PART
ejpam-5479	413	6	be	be	AUX
ejpam-5479	413	7	employed	employ	VERB
ejpam-5479	413	8	in	in	ADP
ejpam-5479	413	9	the	the	DET
ejpam-5479	413	10	analysis	analysis	NOUN
ejpam-5479	413	11	of	of	ADP
ejpam-5479	413	12	various	various	ADJ
ejpam-5479	413	13	classifications	classification	NOUN
ejpam-5479	413	14	of	of	ADP
ejpam-5479	413	15	nonlinear	nonlinear	ADJ
ejpam-5479	413	16	oscillations	oscillation	NOUN
ejpam-5479	413	17	.	.	PUNCT
ejpam-5479	414	1	iv	iv	X
ejpam-5479	414	2	.	.	PUNCT
ejpam-5479	414	3	based	base	VERB
ejpam-5479	414	4	on	on	ADP
ejpam-5479	414	5	the	the	DET
ejpam-5479	414	6	numerical	numerical	ADJ
ejpam-5479	414	7	calculations	calculation	NOUN
ejpam-5479	414	8	and	and	CCONJ
ejpam-5479	414	9	the	the	DET
ejpam-5479	414	10	stability	stability	NOUN
ejpam-5479	414	11	requirements	requirement	NOUN
ejpam-5479	414	12	,	,	PUNCT
ejpam-5479	414	13	it	it	PRON
ejpam-5479	414	14	is	be	AUX
ejpam-5479	414	15	discovered	discover	VERB
ejpam-5479	414	16	that	that	SCONJ
ejpam-5479	414	17	the	the	DET
ejpam-5479	414	18	parameters	parameter	NOUN
ejpam-5479	414	19	rand	rand	VERB
ejpam-5479	414	20	k	k	PROPN
ejpam-5479	414	21	have	have	VERB
ejpam-5479	414	22	a	a	DET
ejpam-5479	414	23	dual	dual	ADJ
ejpam-5479	414	24	role	role	NOUN
ejpam-5479	414	25	in	in	ADP
ejpam-5479	414	26	the	the	DET
ejpam-5479	414	27	stability	stability	NOUN
ejpam-5479	414	28	configuration	configuration	NOUN
ejpam-5479	414	29	.	.	PUNCT
ejpam-5479	415	1	in	in	ADP
ejpam-5479	415	2	light	light	NOUN
ejpam-5479	415	3	of	of	ADP
ejpam-5479	415	4	the	the	DET
ejpam-5479	415	5	great	great	ADJ
ejpam-5479	415	6	significance	significance	NOUN
ejpam-5479	415	7	in	in	ADP
ejpam-5479	415	8	the	the	DET
ejpam-5479	415	9	coupled	couple	VERB
ejpam-5479	415	10	system	system	NOUN
ejpam-5479	415	11	in	in	ADP
ejpam-5479	415	12	various	various	ADJ
ejpam-5479	415	13	classes	class	NOUN
ejpam-5479	415	14	of	of	ADP
ejpam-5479	415	15	the	the	DET
ejpam-5479	415	16	dynamical	dynamical	ADJ
ejpam-5479	415	17	system	system	NOUN
ejpam-5479	415	18	,	,	PUNCT
ejpam-5479	415	19	in	in	ADP
ejpam-5479	415	20	the	the	DET
ejpam-5479	415	21	future	future	ADJ
ejpam-5479	415	22	work	work	NOUN
ejpam-5479	415	23	,	,	PUNCT
ejpam-5479	415	24	the	the	DET
ejpam-5479	415	25	npa	npa	NOUN
ejpam-5479	415	26	will	will	AUX
ejpam-5479	415	27	be	be	AUX
ejpam-5479	415	28	developed	develop	VERB
ejpam-5479	415	29	to	to	PART
ejpam-5479	415	30	analyze	analyze	VERB
ejpam-5479	415	31	such	such	ADJ
ejpam-5479	415	32	problems	problem	NOUN
ejpam-5479	415	33	.	.	PUNCT
ejpam-5479	416	1	fractal	fractal	ADJ
ejpam-5479	416	2	oscillators	oscillator	NOUN
ejpam-5479	416	3	are	be	AUX
ejpam-5479	416	4	technical	technical	ADJ
ejpam-5479	416	5	analysis	analysis	NOUN
ejpam-5479	416	6	tools	tool	NOUN
ejpam-5479	416	7	used	use	VERB
ejpam-5479	416	8	in	in	ADP
ejpam-5479	416	9	financial	financial	ADJ
ejpam-5479	416	10	markets	market	NOUN
ejpam-5479	416	11	to	to	PART
ejpam-5479	416	12	identify	identify	VERB
ejpam-5479	416	13	turning	turn	VERB
ejpam-5479	416	14	points	point	NOUN
ejpam-5479	416	15	or	or	CCONJ
ejpam-5479	416	16	reversals	reversal	NOUN
ejpam-5479	416	17	in	in	ADP
ejpam-5479	416	18	price	price	NOUN
ejpam-5479	416	19	movements	movement	NOUN
ejpam-5479	416	20	by	by	ADP
ejpam-5479	416	21	examining	examine	VERB
ejpam-5479	416	22	patterns	pattern	NOUN
ejpam-5479	416	23	that	that	PRON
ejpam-5479	416	24	repeat	repeat	VERB
ejpam-5479	416	25	at	at	ADP
ejpam-5479	416	26	different	different	ADJ
ejpam-5479	416	27	scales	scale	NOUN
ejpam-5479	416	28	.	.	PUNCT
ejpam-5479	417	1	therefore	therefore	ADV
ejpam-5479	417	2	,	,	PUNCT
ejpam-5479	417	3	another	another	DET
ejpam-5479	417	4	aim	aim	NOUN
ejpam-5479	417	5	of	of	ADP
ejpam-5479	417	6	the	the	DET
ejpam-5479	417	7	progress	progress	NOUN
ejpam-5479	417	8	works	work	VERB
ejpam-5479	417	9	is	be	AUX
ejpam-5479	417	10	to	to	PART
ejpam-5479	417	11	inspect	inspect	VERB
ejpam-5479	417	12	the	the	DET
ejpam-5479	417	13	fractal	fractal	ADJ
ejpam-5479	417	14	oscillators	oscillator	NOUN
ejpam-5479	417	15	.	.	PUNCT
ejpam-5479	418	1	authors	author	NOUN
ejpam-5479	418	2	statements	statement	VERB
ejpam-5479	418	3	khalid	khalid	PROPN
ejpam-5479	418	4	alluhydan	alluhydan	PROPN
ejpam-5479	418	5	:	:	PUNCT
ejpam-5479	418	6	methodology	methodology	NOUN
ejpam-5479	418	7	,	,	PUNCT
ejpam-5479	418	8	resources	resource	NOUN
ejpam-5479	418	9	,	,	PUNCT
ejpam-5479	418	10	validation	validation	NOUN
ejpam-5479	418	11	,	,	PUNCT
ejpam-5479	418	12	formal	formal	ADJ
ejpam-5479	418	13	analysis	analysis	NOUN
ejpam-5479	418	14	,	,	PUNCT
ejpam-5479	418	15	visualization	visualization	NOUN
ejpam-5479	418	16	and	and	CCONJ
ejpam-5479	418	17	reviewing	reviewing	NOUN
ejpam-5479	418	18	.	.	PUNCT
ejpam-5479	419	1	galal	galal	PROPN
ejpam-5479	419	2	m.	m.	PROPN
ejpam-5479	419	3	moatimid	moatimid	PROPN
ejpam-5479	419	4	:	:	PUNCT
ejpam-5479	419	5	resources	resource	NOUN
ejpam-5479	419	6	,	,	PUNCT
ejpam-5479	419	7	conceptualization	conceptualization	NOUN
ejpam-5479	419	8	,	,	PUNCT
ejpam-5479	419	9	formal	formal	ADJ
ejpam-5479	419	10	analysis	analysis	NOUN
ejpam-5479	419	11	,	,	PUNCT
ejpam-5479	419	12	methodology	methodology	NOUN
ejpam-5479	419	13	,	,	PUNCT
ejpam-5479	419	14	validation	validation	NOUN
ejpam-5479	419	15	,	,	PUNCT
ejpam-5479	419	16	writingoriginal	writingoriginal	ADJ
ejpam-5479	419	17	draft	draft	NOUN
ejpam-5479	419	18	preparation	preparation	NOUN
ejpam-5479	419	19	,	,	PUNCT
ejpam-5479	419	20	visualization	visualization	NOUN
ejpam-5479	419	21	and	and	CCONJ
ejpam-5479	419	22	reviewing	reviewing	NOUN
ejpam-5479	419	23	.	.	PUNCT
ejpam-5479	420	1	t.s	t.s	PROPN
ejpam-5479	420	2	.	.	PROPN
ejpam-5479	420	3	amer	amer	PROPN
ejpam-5479	420	4	:	:	PUNCT
ejpam-5479	420	5	methodology	methodology	NOUN
ejpam-5479	420	6	,	,	PUNCT
ejpam-5479	420	7	investigation	investigation	NOUN
ejpam-5479	420	8	,	,	PUNCT
ejpam-5479	420	9	conceptualization	conceptualization	NOUN
ejpam-5479	420	10	,	,	PUNCT
ejpam-5479	420	11	data	data	NOUN
ejpam-5479	420	12	curation	curation	NOUN
ejpam-5479	420	13	,	,	PUNCT
ejpam-5479	420	14	validation	validation	NOUN
ejpam-5479	420	15	,	,	PUNCT
ejpam-5479	420	16	reviewing	reviewing	NOUN
ejpam-5479	420	17	and	and	CCONJ
ejpam-5479	420	18	editing	editing	NOUN
ejpam-5479	420	19	.	.	PUNCT
ejpam-5479	421	1	conflict	conflict	NOUN
ejpam-5479	421	2	of	of	ADP
ejpam-5479	421	3	interest	interest	NOUN
ejpam-5479	421	4	the	the	DET
ejpam-5479	421	5	authors	author	NOUN
ejpam-5479	421	6	have	have	AUX
ejpam-5479	421	7	disclosed	disclose	VERB
ejpam-5479	421	8	no	no	DET
ejpam-5479	421	9	competing	compete	VERB
ejpam-5479	421	10	interests	interest	NOUN
ejpam-5479	421	11	.	.	PUNCT
ejpam-5479	422	1	data	datum	NOUN
ejpam-5479	422	2	availability	availability	NOUN
ejpam-5479	422	3	this	this	DET
ejpam-5479	422	4	work	work	NOUN
ejpam-5479	422	5	contains	contain	VERB
ejpam-5479	422	6	all	all	PRON
ejpam-5479	422	7	of	of	ADP
ejpam-5479	422	8	the	the	DET
ejpam-5479	422	9	data	datum	NOUN
ejpam-5479	422	10	that	that	PRON
ejpam-5479	422	11	were	be	AUX
ejpam-5479	422	12	created	create	VERB
ejpam-5479	422	13	or	or	CCONJ
ejpam-5479	422	14	examined	examine	VERB
ejpam-5479	422	15	during	during	ADP
ejpam-5479	422	16	this	this	DET
ejpam-5479	422	17	study	study	NOUN
ejpam-5479	422	18	.	.	PUNCT
ejpam-5479	423	1	references	reference	NOUN
ejpam-5479	423	2	[	[	X
ejpam-5479	423	3	1	1	NUM
ejpam-5479	423	4	]	]	X
ejpam-5479	423	5	abu	abu	PROPN
ejpam-5479	423	6	-	-	PUNCT
ejpam-5479	423	7	as’ad	as’ad	PROPN
ejpam-5479	423	8	a.	a.	PROPN
ejpam-5479	423	9	and	and	CCONJ
ejpam-5479	423	10	asad	asad	PROPN
ejpam-5479	423	11	j.	j.	PROPN
ejpam-5479	423	12	power	power	PROPN
ejpam-5479	423	13	series	series	PROPN
ejpam-5479	423	14	approach	approach	NOUN
ejpam-5479	423	15	to	to	ADP
ejpam-5479	423	16	nonlinear	nonlinear	ADJ
ejpam-5479	423	17	oscillators	oscillator	NOUN
ejpam-5479	423	18	.	.	PUNCT
ejpam-5479	424	1	journal	journal	NOUN
ejpam-5479	424	2	of	of	ADP
ejpam-5479	424	3	low	low	ADJ
ejpam-5479	424	4	frequency	frequency	NOUN
ejpam-5479	424	5	noise	noise	NOUN
ejpam-5479	424	6	,	,	PUNCT
ejpam-5479	424	7	vibration	vibration	NOUN
ejpam-5479	424	8	and	and	CCONJ
ejpam-5479	424	9	active	active	ADJ
ejpam-5479	424	10	control	control	NOUN
ejpam-5479	424	11	,	,	PUNCT
ejpam-5479	424	12	43(1):220–238	43(1):220–238	NOUN
ejpam-5479	424	13	,	,	PUNCT
ejpam-5479	424	14	2024	2024	NUM
ejpam-5479	424	15	.	.	PUNCT
ejpam-5479	425	1	[	[	X
ejpam-5479	425	2	2	2	NUM
ejpam-5479	425	3	]	]	X
ejpam-5479	425	4	big	big	ADJ
ejpam-5479	425	5	-	-	PUNCT
ejpam-5479	425	6	alabo	alabo	NOUN
ejpam-5479	425	7	a.	a.	NOUN
ejpam-5479	425	8	approximate	approximate	PROPN
ejpam-5479	425	9	period	period	NOUN
ejpam-5479	425	10	for	for	ADP
ejpam-5479	425	11	large	large	ADJ
ejpam-5479	425	12	-	-	PUNCT
ejpam-5479	425	13	amplitude	amplitude	NOUN
ejpam-5479	425	14	oscillations	oscillation	NOUN
ejpam-5479	425	15	of	of	ADP
ejpam-5479	425	16	a	a	DET
ejpam-5479	425	17	simple	simple	ADJ
ejpam-5479	425	18	pendulum	pendulum	NOUN
ejpam-5479	425	19	based	base	VERB
ejpam-5479	425	20	on	on	ADP
ejpam-5479	425	21	quintication	quintication	NOUN
ejpam-5479	425	22	of	of	ADP
ejpam-5479	425	23	the	the	DET
ejpam-5479	425	24	restoring	restore	VERB
ejpam-5479	425	25	force	force	NOUN
ejpam-5479	425	26	.	.	PUNCT
ejpam-5479	426	1	european	european	ADJ
ejpam-5479	426	2	journal	journal	PROPN
ejpam-5479	426	3	of	of	ADP
ejpam-5479	426	4	physics	physics	PROPN
ejpam-5479	426	5	,	,	PUNCT
ejpam-5479	426	6	41(1):015001	41(1):015001	NOUN
ejpam-5479	426	7	,	,	PUNCT
ejpam-5479	426	8	2020	2020	NUM
ejpam-5479	426	9	.	.	PUNCT
ejpam-5479	427	1	[	[	X
ejpam-5479	427	2	3	3	X
ejpam-5479	427	3	]	]	X
ejpam-5479	427	4	chatterjee	chatterjee	PROPN
ejpam-5479	427	5	a.	a.	PROPN
ejpam-5479	427	6	and	and	CCONJ
ejpam-5479	427	7	meng	meng	PROPN
ejpam-5479	427	8	w.	w.	PROPN
ejpam-5479	427	9	nonlinear	nonlinear	PROPN
ejpam-5479	427	10	dynamics	dynamic	NOUN
ejpam-5479	427	11	of	of	ADP
ejpam-5479	427	12	interacting	interact	VERB
ejpam-5479	427	13	population	population	NOUN
ejpam-5479	427	14	in	in	ADP
ejpam-5479	427	15	a	a	DET
ejpam-5479	427	16	marine	marine	ADJ
ejpam-5479	427	17	ecosystem	ecosystem	NOUN
ejpam-5479	427	18	with	with	ADP
ejpam-5479	427	19	a	a	DET
ejpam-5479	427	20	delay	delay	NOUN
ejpam-5479	427	21	effect	effect	NOUN
ejpam-5479	427	22	.	.	PUNCT
ejpam-5479	428	1	nonlinear	nonlinear	ADJ
ejpam-5479	428	2	dynamics	dynamic	NOUN
ejpam-5479	428	3	,	,	PUNCT
ejpam-5479	428	4	112:16639–16656	112:16639–16656	NUM
ejpam-5479	428	5	,	,	PUNCT
ejpam-5479	428	6	2024	2024	NUM
ejpam-5479	428	7	.	.	PUNCT
ejpam-5479	429	1	[	[	X
ejpam-5479	429	2	4	4	NUM
ejpam-5479	429	3	]	]	X
ejpam-5479	429	4	nayfeh	nayfeh	ADJ
ejpam-5479	429	5	a.h	a.h	PROPN
ejpam-5479	429	6	.	.	PROPN
ejpam-5479	429	7	perturbation	perturbation	NOUN
ejpam-5479	429	8	methods	method	NOUN
ejpam-5479	429	9	.	.	PUNCT
ejpam-5479	430	1	wiley	wiley	PROPN
ejpam-5479	430	2	,	,	PUNCT
ejpam-5479	430	3	new	new	PROPN
ejpam-5479	430	4	york	york	PROPN
ejpam-5479	430	5	,	,	PUNCT
ejpam-5479	430	6	1973	1973	NUM
ejpam-5479	430	7	.	.	PUNCT
ejpam-5479	431	1	references	reference	NOUN
ejpam-5479	431	2	3205	3205	NUM
ejpam-5479	431	3	[	[	X
ejpam-5479	431	4	5	5	NUM
ejpam-5479	431	5	]	]	X
ejpam-5479	431	6	rahman	rahman	PROPN
ejpam-5479	431	7	b.	b.	PROPN
ejpam-5479	431	8	time	time	PROPN
ejpam-5479	431	9	-	-	PUNCT
ejpam-5479	431	10	delay	delay	NOUN
ejpam-5479	431	11	systems	system	NOUN
ejpam-5479	431	12	:	:	PUNCT
ejpam-5479	431	13	an	an	DET
ejpam-5479	431	14	overview	overview	NOUN
ejpam-5479	431	15	.	.	PUNCT
ejpam-5479	432	1	nonlinear	nonlinear	ADJ
ejpam-5479	432	2	phenomena	phenomenon	NOUN
ejpam-5479	432	3	in	in	ADP
ejpam-5479	432	4	complex	complex	ADJ
ejpam-5479	432	5	systems	system	NOUN
ejpam-5479	432	6	,	,	PUNCT
ejpam-5479	432	7	23(2):192–195	23(2):192–195	NOUN
ejpam-5479	432	8	,	,	PUNCT
ejpam-5479	432	9	2020	2020	NUM
ejpam-5479	432	10	.	.	PUNCT
ejpam-5479	433	1	[	[	X
ejpam-5479	433	2	6	6	NUM
ejpam-5479	433	3	]	]	X
ejpam-5479	433	4	rath	rath	PROPN
ejpam-5479	433	5	b.	b.	PROPN
ejpam-5479	433	6	,	,	PUNCT
ejpam-5479	433	7	erturk	erturk	PROPN
ejpam-5479	433	8	v.s.	v.s.	PROPN
ejpam-5479	433	9	,	,	PUNCT
ejpam-5479	433	10	asad	asad	PROPN
ejpam-5479	433	11	j.	j.	PROPN
ejpam-5479	433	12	,	,	PUNCT
ejpam-5479	433	13	mallick	mallick	PROPN
ejpam-5479	433	14	p.	p.	PROPN
ejpam-5479	433	15	,	,	PUNCT
ejpam-5479	433	16	and	and	CCONJ
ejpam-5479	433	17	jarrar	jarrar	PROPN
ejpam-5479	433	18	r.	r.	PROPN
ejpam-5479	433	19	an	an	DET
ejpam-5479	433	20	asymmetric	asymmetric	ADJ
ejpam-5479	433	21	model	model	NOUN
ejpam-5479	433	22	two	two	NUM
ejpam-5479	433	23	-	-	PUNCT
ejpam-5479	433	24	dimensional	dimensional	ADJ
ejpam-5479	433	25	oscillator	oscillator	NOUN
ejpam-5479	433	26	.	.	PUNCT
ejpam-5479	434	1	journal	journal	NOUN
ejpam-5479	434	2	of	of	ADP
ejpam-5479	434	3	low	low	ADJ
ejpam-5479	434	4	frequency	frequency	NOUN
ejpam-5479	434	5	noise	noise	NOUN
ejpam-5479	434	6	,	,	PUNCT
ejpam-5479	434	7	vibration	vibration	NOUN
ejpam-5479	434	8	and	and	CCONJ
ejpam-5479	434	9	active	active	ADJ
ejpam-5479	434	10	control	control	NOUN
ejpam-5479	434	11	,	,	PUNCT
ejpam-5479	434	12	43(2):744–754	43(2):744–754	PROPN
ejpam-5479	434	13	,	,	PUNCT
ejpam-5479	434	14	2024	2024	NUM
ejpam-5479	434	15	.	.	PUNCT
ejpam-5479	435	1	[	[	X
ejpam-5479	435	2	7	7	X
ejpam-5479	435	3	]	]	PUNCT
ejpam-5479	435	4	he	he	PRON
ejpam-5479	435	5	c	c	PROPN
ejpam-5479	435	6	-	-	PUNCT
ejpam-5479	435	7	h.	h.	PROPN
ejpam-5479	435	8	and	and	CCONJ
ejpam-5479	435	9	liu	liu	PROPN
ejpam-5479	435	10	c.	c.	PROPN
ejpam-5479	435	11	a	a	DET
ejpam-5479	435	12	modified	modify	VERB
ejpam-5479	435	13	frequency	frequency	NOUN
ejpam-5479	435	14	-	-	PUNCT
ejpam-5479	435	15	amplitude	amplitude	NOUN
ejpam-5479	435	16	formulation	formulation	NOUN
ejpam-5479	435	17	for	for	ADP
ejpam-5479	435	18	fractal	fractal	ADJ
ejpam-5479	435	19	vibration	vibration	NOUN
ejpam-5479	435	20	systems	system	NOUN
ejpam-5479	435	21	.	.	PUNCT
ejpam-5479	436	1	fractals	fractal	NOUN
ejpam-5479	436	2	,	,	PUNCT
ejpam-5479	436	3	30(03):2250046	30(03):2250046	NUM
ejpam-5479	436	4	,	,	PUNCT
ejpam-5479	436	5	2022	2022	NUM
ejpam-5479	436	6	.	.	PUNCT
ejpam-5479	437	1	[	[	X
ejpam-5479	437	2	8	8	NUM
ejpam-5479	437	3	]	]	PUNCT
ejpam-5479	437	4	guiot	guiot	NOUN
ejpam-5479	437	5	e.	e.	PROPN
ejpam-5479	437	6	trajectories	trajectory	NOUN
ejpam-5479	437	7	of	of	ADP
ejpam-5479	437	8	two	two	NUM
ejpam-5479	437	9	-	-	PUNCT
ejpam-5479	437	10	dimensional	dimensional	ADJ
ejpam-5479	437	11	harmonic	harmonic	ADJ
ejpam-5479	437	12	oscillators	oscillator	NOUN
ejpam-5479	437	13	in	in	ADP
ejpam-5479	437	14	a	a	DET
ejpam-5479	437	15	rotating	rotate	VERB
ejpam-5479	437	16	frame	frame	NOUN
ejpam-5479	437	17	:	:	PUNCT
ejpam-5479	437	18	application	application	NOUN
ejpam-5479	437	19	to	to	ADP
ejpam-5479	437	20	foucault	foucault	PROPN
ejpam-5479	437	21	pendulum	pendulum	NOUN
ejpam-5479	437	22	problem	problem	NOUN
ejpam-5479	437	23	.	.	PUNCT
ejpam-5479	438	1	meccanica	meccanica	PROPN
ejpam-5479	438	2	,	,	PUNCT
ejpam-5479	438	3	59:491–501	59:491–501	NUM
ejpam-5479	438	4	,	,	PUNCT
ejpam-5479	438	5	2024	2024	NUM
ejpam-5479	438	6	.	.	PUNCT
ejpam-5479	439	1	[	[	X
ejpam-5479	439	2	9	9	NUM
ejpam-5479	439	3	]	]	X
ejpam-5479	439	4	de	de	PROPN
ejpam-5479	439	5	oliveira	oliveira	PROPN
ejpam-5479	439	6	e.f	e.f	PROPN
ejpam-5479	439	7	.	.	PROPN
ejpam-5479	439	8	and	and	CCONJ
ejpam-5479	439	9	rodrigues	rodrigues	PROPN
ejpam-5479	439	10	c.g	c.g	PROPN
ejpam-5479	439	11	.	.	PROPN
ejpam-5479	439	12	simple	simple	ADJ
ejpam-5479	439	13	pendulum	pendulum	NOUN
ejpam-5479	439	14	:	:	PUNCT
ejpam-5479	439	15	period	period	NOUN
ejpam-5479	439	16	dependent	dependent	ADJ
ejpam-5479	439	17	on	on	ADP
ejpam-5479	439	18	amplitude	amplitude	NOUN
ejpam-5479	439	19	of	of	ADP
ejpam-5479	439	20	oscillation	oscillation	NOUN
ejpam-5479	439	21	.	.	PUNCT
ejpam-5479	440	1	cuadernos	cuaderno	NOUN
ejpam-5479	440	2	de	de	VERB
ejpam-5479	440	3	educación	educación	PROPN
ejpam-5479	440	4	y	y	PROPN
ejpam-5479	440	5	desarrollo	desarrollo	PROPN
ejpam-5479	440	6	,	,	PUNCT
ejpam-5479	440	7	15(12):17662–17685	15(12):17662–17685	NUM
ejpam-5479	440	8	,	,	PUNCT
ejpam-5479	440	9	2023	2023	NUM
ejpam-5479	440	10	.	.	PUNCT
ejpam-5479	441	1	[	[	X
ejpam-5479	441	2	10	10	NUM
ejpam-5479	441	3	]	]	X
ejpam-5479	441	4	ismail	ismail	PROPN
ejpam-5479	441	5	g.m	g.m	PROPN
ejpam-5479	441	6	.	.	PROPN
ejpam-5479	441	7	,	,	PUNCT
ejpam-5479	441	8	moatimid	moatimid	PROPN
ejpam-5479	441	9	g.m	g.m	PROPN
ejpam-5479	441	10	.	.	PROPN
ejpam-5479	441	11	,	,	PUNCT
ejpam-5479	441	12	and	and	CCONJ
ejpam-5479	441	13	yamani	yamani	PROPN
ejpam-5479	441	14	m.i	m.i	PROPN
ejpam-5479	441	15	.	.	PROPN
ejpam-5479	441	16	periodic	periodic	ADJ
ejpam-5479	441	17	solutions	solution	NOUN
ejpam-5479	441	18	of	of	ADP
ejpam-5479	441	19	strongly	strongly	ADV
ejpam-5479	441	20	nonlinear	nonlinear	ADJ
ejpam-5479	441	21	oscillators	oscillator	NOUN
ejpam-5479	441	22	using	use	VERB
ejpam-5479	441	23	he	he	PRON
ejpam-5479	441	24	’s	’s	PART
ejpam-5479	441	25	frequency	frequency	NOUN
ejpam-5479	441	26	formulation	formulation	NOUN
ejpam-5479	441	27	.	.	PUNCT
ejpam-5479	442	1	european	european	ADJ
ejpam-5479	442	2	journal	journal	PROPN
ejpam-5479	442	3	of	of	ADP
ejpam-5479	442	4	pure	pure	ADJ
ejpam-5479	442	5	and	and	CCONJ
ejpam-5479	442	6	applied	applied	ADJ
ejpam-5479	442	7	mathematics	mathematic	NOUN
ejpam-5479	442	8	,	,	PUNCT
ejpam-5479	442	9	17(3):2154–2171	17(3):2154–2171	NUM
ejpam-5479	442	10	,	,	PUNCT
ejpam-5479	442	11	2024	2024	NUM
ejpam-5479	442	12	.	.	PUNCT
ejpam-5479	443	1	[	[	X
ejpam-5479	443	2	11	11	NUM
ejpam-5479	443	3	]	]	X
ejpam-5479	443	4	moatimid	moatimid	PROPN
ejpam-5479	443	5	g.m	g.m	PROPN
ejpam-5479	443	6	.	.	PROPN
ejpam-5479	444	1	and	and	CCONJ
ejpam-5479	444	2	sayed	sayed	PROPN
ejpam-5479	444	3	a.	a.	PROPN
ejpam-5479	444	4	nonlinear	nonlinear	PROPN
ejpam-5479	444	5	ehd	ehd	NOUN
ejpam-5479	444	6	stability	stability	NOUN
ejpam-5479	444	7	of	of	ADP
ejpam-5479	444	8	a	a	DET
ejpam-5479	444	9	cylindrical	cylindrical	ADJ
ejpam-5479	444	10	interface	interface	NOUN
ejpam-5479	444	11	separating	separate	VERB
ejpam-5479	444	12	two	two	NUM
ejpam-5479	444	13	rivlin	rivlin	ADJ
ejpam-5479	444	14	-	-	PUNCT
ejpam-5479	444	15	ericksen	ericksen	ADJ
ejpam-5479	444	16	fluids	fluid	NOUN
ejpam-5479	444	17	:	:	PUNCT
ejpam-5479	444	18	a	a	DET
ejpam-5479	444	19	novel	novel	ADJ
ejpam-5479	444	20	analysis	analysis	NOUN
ejpam-5479	444	21	.	.	PUNCT
ejpam-5479	445	1	chinese	chinese	ADJ
ejpam-5479	445	2	journal	journal	PROPN
ejpam-5479	445	3	of	of	ADP
ejpam-5479	445	4	physics	physics	PROPN
ejpam-5479	445	5	,	,	PUNCT
ejpam-5479	445	6	87:379–397	87:379–397	NUM
ejpam-5479	445	7	,	,	PUNCT
ejpam-5479	445	8	2024	2024	NUM
ejpam-5479	445	9	.	.	PUNCT
ejpam-5479	446	1	[	[	X
ejpam-5479	446	2	12	12	NUM
ejpam-5479	446	3	]	]	X
ejpam-5479	446	4	moatimid	moatimid	PROPN
ejpam-5479	446	5	g.m	g.m	PROPN
ejpam-5479	446	6	.	.	PROPN
ejpam-5479	446	7	,	,	PUNCT
ejpam-5479	446	8	el	el	PROPN
ejpam-5479	446	9	-	-	PUNCT
ejpam-5479	446	10	sayed	say	VERB
ejpam-5479	446	11	a.t	a.t	PROPN
ejpam-5479	446	12	.	.	PROPN
ejpam-5479	446	13	,	,	PUNCT
ejpam-5479	446	14	and	and	CCONJ
ejpam-5479	446	15	salman	salman	PROPN
ejpam-5479	446	16	h.f	h.f	PROPN
ejpam-5479	446	17	.	.	PROPN
ejpam-5479	446	18	dynamical	dynamical	ADJ
ejpam-5479	446	19	analysis	analysis	NOUN
ejpam-5479	446	20	of	of	ADP
ejpam-5479	446	21	an	an	DET
ejpam-5479	446	22	inverted	inverted	ADJ
ejpam-5479	446	23	pendulum	pendulum	NOUN
ejpam-5479	446	24	with	with	ADP
ejpam-5479	446	25	positive	positive	ADJ
ejpam-5479	446	26	position	position	NOUN
ejpam-5479	446	27	feedback	feedback	NOUN
ejpam-5479	446	28	controller	controller	NOUN
ejpam-5479	446	29	approximate	approximate	ADJ
ejpam-5479	446	30	uniform	uniform	NOUN
ejpam-5479	446	31	solution	solution	NOUN
ejpam-5479	446	32	.	.	PUNCT
ejpam-5479	447	1	scientific	scientific	ADJ
ejpam-5479	447	2	reports	report	NOUN
ejpam-5479	447	3	,	,	PUNCT
ejpam-5479	447	4	13:8849	13:8849	NUM
ejpam-5479	447	5	,	,	PUNCT
ejpam-5479	447	6	2023	2023	NUM
ejpam-5479	447	7	.	.	PUNCT
ejpam-5479	448	1	[	[	X
ejpam-5479	448	2	13	13	NUM
ejpam-5479	448	3	]	]	X
ejpam-5479	448	4	moatimid	moatimid	PROPN
ejpam-5479	448	5	g.m	g.m	PROPN
ejpam-5479	448	6	.	.	PROPN
ejpam-5479	448	7	,	,	PUNCT
ejpam-5479	448	8	el	el	PROPN
ejpam-5479	448	9	-	-	PUNCT
ejpam-5479	448	10	sayed	say	VERB
ejpam-5479	448	11	a.t	a.t	PROPN
ejpam-5479	448	12	.	.	PROPN
ejpam-5479	448	13	,	,	PUNCT
ejpam-5479	448	14	and	and	CCONJ
ejpam-5479	448	15	salman	salman	PROPN
ejpam-5479	448	16	h.f	h.f	PROPN
ejpam-5479	448	17	.	.	PUNCT
ejpam-5479	448	18	different	different	ADJ
ejpam-5479	448	19	controllers	controller	NOUN
ejpam-5479	448	20	for	for	ADP
ejpam-5479	448	21	suppressing	suppress	VERB
ejpam-5479	448	22	oscillations	oscillation	NOUN
ejpam-5479	448	23	of	of	ADP
ejpam-5479	448	24	a	a	DET
ejpam-5479	448	25	hybrid	hybrid	ADJ
ejpam-5479	448	26	oscillator	oscillator	NOUN
ejpam-5479	448	27	via	via	ADP
ejpam-5479	448	28	non	non	ADJ
ejpam-5479	448	29	-	-	ADJ
ejpam-5479	448	30	perturbative	perturbative	ADJ
ejpam-5479	448	31	analysis	analysis	NOUN
ejpam-5479	448	32	.	.	PUNCT
ejpam-5479	449	1	scientific	scientific	ADJ
ejpam-5479	449	2	reports	report	NOUN
ejpam-5479	449	3	,	,	PUNCT
ejpam-5479	449	4	14:307	14:307	NUM
ejpam-5479	449	5	,	,	PUNCT
ejpam-5479	449	6	2024	2024	NUM
ejpam-5479	449	7	.	.	PUNCT
ejpam-5479	450	1	[	[	X
ejpam-5479	450	2	14	14	NUM
ejpam-5479	450	3	]	]	X
ejpam-5479	450	4	moatimid	moatimid	PROPN
ejpam-5479	450	5	g.m	g.m	PROPN
ejpam-5479	450	6	.	.	PROPN
ejpam-5479	451	1	and	and	CCONJ
ejpam-5479	451	2	mostafa	mostafa	PROPN
ejpam-5479	451	3	d.m	d.m	PROPN
ejpam-5479	451	4	.	.	PUNCT
ejpam-5479	452	1	nonlinear	nonlinear	ADJ
ejpam-5479	452	2	stability	stability	NOUN
ejpam-5479	452	3	of	of	ADP
ejpam-5479	452	4	two	two	NUM
ejpam-5479	452	5	superimposed	superimpose	VERB
ejpam-5479	452	6	electrified	electrified	ADJ
ejpam-5479	452	7	dusty	dusty	ADJ
ejpam-5479	452	8	fluids	fluid	NOUN
ejpam-5479	452	9	of	of	ADP
ejpam-5479	452	10	type	type	NOUN
ejpam-5479	452	11	rivlin	rivlin	PROPN
ejpam-5479	452	12	-	-	PUNCT
ejpam-5479	452	13	ericksen	ericksen	ADJ
ejpam-5479	452	14	:	:	PUNCT
ejpam-5479	452	15	non	non	ADJ
ejpam-5479	452	16	-	-	ADJ
ejpam-5479	452	17	perturbative	perturbative	ADJ
ejpam-5479	452	18	approach	approach	NOUN
ejpam-5479	452	19	.	.	PUNCT
ejpam-5479	453	1	partial	partial	ADJ
ejpam-5479	453	2	differential	differential	ADJ
ejpam-5479	453	3	equations	equation	NOUN
ejpam-5479	453	4	in	in	ADP
ejpam-5479	453	5	applied	applied	ADJ
ejpam-5479	453	6	mathematics	mathematic	NOUN
ejpam-5479	453	7	,	,	PUNCT
ejpam-5479	453	8	10:100745	10:100745	NUM
ejpam-5479	453	9	,	,	PUNCT
ejpam-5479	453	10	2024	2024	NUM
ejpam-5479	453	11	.	.	PUNCT
ejpam-5479	454	1	[	[	X
ejpam-5479	454	2	15	15	NUM
ejpam-5479	454	3	]	]	X
ejpam-5479	454	4	moatimid	moatimid	PROPN
ejpam-5479	454	5	g.m	g.m	PROPN
ejpam-5479	454	6	.	.	PROPN
ejpam-5479	454	7	,	,	PUNCT
ejpam-5479	454	8	mostafa	mostafa	PROPN
ejpam-5479	454	9	d.m	d.m	PROPN
ejpam-5479	454	10	.	.	PROPN
ejpam-5479	454	11	,	,	PUNCT
ejpam-5479	454	12	and	and	CCONJ
ejpam-5479	454	13	zekry	zekry	PROPN
ejpam-5479	454	14	m.h	m.h	PROPN
ejpam-5479	454	15	.	.	PUNCT
ejpam-5479	455	1	a	a	DET
ejpam-5479	455	2	new	new	ADJ
ejpam-5479	455	3	methodology	methodology	NOUN
ejpam-5479	455	4	in	in	ADP
ejpam-5479	455	5	evaluating	evaluate	VERB
ejpam-5479	455	6	nonlinear	nonlinear	ADJ
ejpam-5479	455	7	electrohydrodynamic	electrohydrodynamic	ADJ
ejpam-5479	455	8	azimuthal	azimuthal	NOUN
ejpam-5479	455	9	stability	stability	NOUN
ejpam-5479	455	10	between	between	ADP
ejpam-5479	455	11	two	two	NUM
ejpam-5479	455	12	dusty	dusty	ADJ
ejpam-5479	455	13	viscous	viscous	ADJ
ejpam-5479	455	14	fluids	fluid	NOUN
ejpam-5479	455	15	.	.	PUNCT
ejpam-5479	456	1	chinese	chinese	ADJ
ejpam-5479	456	2	journal	journal	PROPN
ejpam-5479	456	3	of	of	ADP
ejpam-5479	456	4	physics	physics	PROPN
ejpam-5479	456	5	,	,	PUNCT
ejpam-5479	456	6	90:134–154	90:134–154	NUM
ejpam-5479	456	7	,	,	PUNCT
ejpam-5479	456	8	2024	2024	NUM
ejpam-5479	456	9	.	.	PUNCT
ejpam-5479	457	1	[	[	X
ejpam-5479	457	2	16	16	NUM
ejpam-5479	457	3	]	]	X
ejpam-5479	457	4	moatimid	moatimid	PROPN
ejpam-5479	457	5	g.m	g.m	PROPN
ejpam-5479	457	6	.	.	PROPN
ejpam-5479	457	7	,	,	PUNCT
ejpam-5479	457	8	mohamed	mohamed	PROPN
ejpam-5479	457	9	m.a.a	m.a.a	PROPN
ejpam-5479	457	10	.	.	PUNCT
ejpam-5479	457	11	,	,	PUNCT
ejpam-5479	457	12	and	and	CCONJ
ejpam-5479	457	13	elagamy	elagamy	PROPN
ejpam-5479	457	14	kh	kh	PROPN
ejpam-5479	457	15	.	.	PROPN
ejpam-5479	457	16	nonlinear	nonlinear	PROPN
ejpam-5479	457	17	kelvin	kelvin	PROPN
ejpam-5479	457	18	-	-	PUNCT
ejpam-5479	457	19	helmholtz	helmholtz	PROPN
ejpam-5479	457	20	instability	instability	NOUN
ejpam-5479	457	21	of	of	ADP
ejpam-5479	457	22	a	a	DET
ejpam-5479	457	23	horizontal	horizontal	ADJ
ejpam-5479	457	24	interface	interface	NOUN
ejpam-5479	457	25	separating	separate	VERB
ejpam-5479	457	26	two	two	NUM
ejpam-5479	457	27	electrified	electrify	VERB
ejpam-5479	457	28	walters	walter	NOUN
ejpam-5479	457	29	’	'	PUNCT
ejpam-5479	457	30	b	b	PROPN
ejpam-5479	457	31	liquids	liquid	NOUN
ejpam-5479	457	32	:	:	PUNCT
ejpam-5479	457	33	a	a	DET
ejpam-5479	457	34	new	new	ADJ
ejpam-5479	457	35	approach	approach	NOUN
ejpam-5479	457	36	.	.	PUNCT
ejpam-5479	458	1	chinese	chinese	ADJ
ejpam-5479	458	2	journal	journal	PROPN
ejpam-5479	458	3	of	of	ADP
ejpam-5479	458	4	physics	physics	PROPN
ejpam-5479	458	5	,	,	PUNCT
ejpam-5479	458	6	85:629–648	85:629–648	PROPN
ejpam-5479	458	7	,	,	PUNCT
ejpam-5479	458	8	2023	2023	NUM
ejpam-5479	458	9	.	.	PUNCT
ejpam-5479	459	1	[	[	X
ejpam-5479	459	2	17	17	NUM
ejpam-5479	459	3	]	]	X
ejpam-5479	459	4	moatimid	moatimid	PROPN
ejpam-5479	459	5	g.m	g.m	PROPN
ejpam-5479	459	6	.	.	PROPN
ejpam-5479	459	7	,	,	PUNCT
ejpam-5479	459	8	mohamed	mohamed	PROPN
ejpam-5479	459	9	m.a.a	m.a.a	PROPN
ejpam-5479	459	10	.	.	PUNCT
ejpam-5479	459	11	,	,	PUNCT
ejpam-5479	459	12	and	and	CCONJ
ejpam-5479	459	13	elagamy	elagamy	PROPN
ejpam-5479	459	14	kh	kh	PROPN
ejpam-5479	459	15	.	.	PUNCT
ejpam-5479	460	1	an	an	DET
ejpam-5479	460	2	innovative	innovative	ADJ
ejpam-5479	460	3	approach	approach	NOUN
ejpam-5479	460	4	in	in	ADP
ejpam-5479	460	5	inspecting	inspect	VERB
ejpam-5479	460	6	a	a	DET
ejpam-5479	460	7	damped	damp	VERB
ejpam-5479	460	8	mathieu	mathieu	NOUN
ejpam-5479	460	9	cubic	cubic	ADJ
ejpam-5479	460	10	-	-	PUNCT
ejpam-5479	460	11	quintic	quintic	ADJ
ejpam-5479	460	12	duffing	duffing	NOUN
ejpam-5479	460	13	oscillator	oscillator	NOUN
ejpam-5479	460	14	.	.	PUNCT
ejpam-5479	461	1	journal	journal	NOUN
ejpam-5479	461	2	of	of	ADP
ejpam-5479	461	3	vibration	vibration	NOUN
ejpam-5479	461	4	engineering	engineering	NOUN
ejpam-5479	461	5	&	&	CCONJ
ejpam-5479	461	6	technologies	technology	NOUN
ejpam-5479	461	7	,	,	PUNCT
ejpam-5479	461	8	2024	2024	NUM
ejpam-5479	461	9	.	.	PUNCT
ejpam-5479	462	1	published	publish	VERB
ejpam-5479	462	2	online	online	ADV
ejpam-5479	462	3	:	:	PUNCT
ejpam-5479	462	4	23	23	NUM
ejpam-5479	462	5	july	july	NOUN
ejpam-5479	462	6	.	.	PUNCT
ejpam-5479	463	1	references	reference	NOUN
ejpam-5479	463	2	3206	3206	NUM
ejpam-5479	463	3	[	[	X
ejpam-5479	463	4	18	18	NUM
ejpam-5479	463	5	]	]	X
ejpam-5479	463	6	moatimid	moatimid	PROPN
ejpam-5479	463	7	g.m	g.m	PROPN
ejpam-5479	463	8	.	.	PROPN
ejpam-5479	463	9	,	,	PUNCT
ejpam-5479	463	10	mohamed	mohamed	PROPN
ejpam-5479	463	11	m.a.a	m.a.a	PROPN
ejpam-5479	463	12	.	.	PUNCT
ejpam-5479	463	13	,	,	PUNCT
ejpam-5479	463	14	and	and	CCONJ
ejpam-5479	463	15	elagamy	elagamy	PROPN
ejpam-5479	463	16	kh	kh	PROPN
ejpam-5479	463	17	.	.	PROPN
ejpam-5479	463	18	insightful	insightful	ADJ
ejpam-5479	463	19	inspection	inspection	NOUN
ejpam-5479	463	20	of	of	ADP
ejpam-5479	463	21	the	the	DET
ejpam-5479	463	22	nonlinear	nonlinear	ADJ
ejpam-5479	463	23	instability	instability	NOUN
ejpam-5479	463	24	of	of	ADP
ejpam-5479	463	25	an	an	DET
ejpam-5479	463	26	azimuthal	azimuthal	ADJ
ejpam-5479	463	27	disturbance	disturbance	NOUN
ejpam-5479	463	28	separating	separate	VERB
ejpam-5479	463	29	two	two	NUM
ejpam-5479	463	30	rotating	rotate	VERB
ejpam-5479	463	31	magnetic	magnetic	ADJ
ejpam-5479	463	32	liquid	liquid	ADJ
ejpam-5479	463	33	columns	column	NOUN
ejpam-5479	463	34	.	.	PUNCT
ejpam-5479	464	1	the	the	DET
ejpam-5479	464	2	european	european	PROPN
ejpam-5479	464	3	physical	physical	PROPN
ejpam-5479	464	4	journal	journal	PROPN
ejpam-5479	464	5	plus	plus	CCONJ
ejpam-5479	464	6	,	,	PUNCT
ejpam-5479	464	7	139:590	139:590	NOUN
ejpam-5479	464	8	,	,	PUNCT
ejpam-5479	464	9	2024	2024	NUM
ejpam-5479	464	10	.	.	PUNCT
ejpam-5479	465	1	[	[	X
ejpam-5479	465	2	19	19	NUM
ejpam-5479	465	3	]	]	X
ejpam-5479	465	4	moatimid	moatimid	PROPN
ejpam-5479	465	5	g.m	g.m	PROPN
ejpam-5479	465	6	.	.	PROPN
ejpam-5479	465	7	,	,	PUNCT
ejpam-5479	465	8	mohamed	mohamed	PROPN
ejpam-5479	465	9	m.a.a	m.a.a	PROPN
ejpam-5479	465	10	.	.	PUNCT
ejpam-5479	465	11	,	,	PUNCT
ejpam-5479	465	12	and	and	CCONJ
ejpam-5479	465	13	elagamy	elagamy	PROPN
ejpam-5479	465	14	kh	kh	PROPN
ejpam-5479	465	15	.	.	PROPN
ejpam-5479	465	16	inspection	inspection	NOUN
ejpam-5479	465	17	of	of	ADP
ejpam-5479	465	18	the	the	DET
ejpam-5479	465	19	nonlinear	nonlinear	ADJ
ejpam-5479	465	20	instability	instability	NOUN
ejpam-5479	465	21	of	of	ADP
ejpam-5479	465	22	electrified	electrified	ADJ
ejpam-5479	465	23	casson	casson	PROPN
ejpam-5479	465	24	fluids	fluid	NOUN
ejpam-5479	465	25	:	:	PUNCT
ejpam-5479	465	26	a	a	DET
ejpam-5479	465	27	novel	novel	ADJ
ejpam-5479	465	28	approach	approach	NOUN
ejpam-5479	465	29	.	.	PUNCT
ejpam-5479	466	1	waves	wave	NOUN
ejpam-5479	466	2	in	in	ADP
ejpam-5479	466	3	random	random	ADJ
ejpam-5479	466	4	and	and	CCONJ
ejpam-5479	466	5	complex	complex	ADJ
ejpam-5479	466	6	media	medium	NOUN
ejpam-5479	466	7	,	,	PUNCT
ejpam-5479	466	8	2024	2024	NUM
ejpam-5479	466	9	.	.	PUNCT
ejpam-5479	466	10	published	publish	VERB
ejpam-5479	466	11	online	online	ADV
ejpam-5479	466	12	:	:	PUNCT
ejpam-5479	466	13	02	02	NUM
ejpam-5479	466	14	august	august	NOUN
ejpam-5479	466	15	.	.	PUNCT
ejpam-5479	467	1	[	[	X
ejpam-5479	467	2	20	20	NUM
ejpam-5479	467	3	]	]	X
ejpam-5479	467	4	moatimid	moatimid	PROPN
ejpam-5479	467	5	g.m	g.m	PROPN
ejpam-5479	467	6	.	.	PROPN
ejpam-5479	468	1	and	and	CCONJ
ejpam-5479	468	2	amer	amer	PROPN
ejpam-5479	468	3	t.s	t.s	PROPN
ejpam-5479	468	4	.	.	PROPN
ejpam-5479	468	5	analytical	analytical	ADJ
ejpam-5479	468	6	solution	solution	NOUN
ejpam-5479	468	7	for	for	ADP
ejpam-5479	468	8	the	the	DET
ejpam-5479	468	9	motion	motion	NOUN
ejpam-5479	468	10	of	of	ADP
ejpam-5479	468	11	a	a	DET
ejpam-5479	468	12	pendulum	pendulum	NOUN
ejpam-5479	468	13	with	with	ADP
ejpam-5479	468	14	rolling	rolling	ADJ
ejpam-5479	468	15	wheel	wheel	NOUN
ejpam-5479	468	16	:	:	PUNCT
ejpam-5479	468	17	stability	stability	NOUN
ejpam-5479	468	18	analysis	analysis	NOUN
ejpam-5479	468	19	.	.	PUNCT
ejpam-5479	469	1	scientific	scientific	ADJ
ejpam-5479	469	2	reports	report	NOUN
ejpam-5479	469	3	,	,	PUNCT
ejpam-5479	469	4	12:12628	12:12628	NUM
ejpam-5479	469	5	,	,	PUNCT
ejpam-5479	469	6	2022	2022	NUM
ejpam-5479	469	7	.	.	PUNCT
ejpam-5479	470	1	[	[	X
ejpam-5479	470	2	21	21	NUM
ejpam-5479	470	3	]	]	X
ejpam-5479	470	4	moatimid	moatimid	PROPN
ejpam-5479	470	5	g.m	g.m	PROPN
ejpam-5479	470	6	.	.	PROPN
ejpam-5479	471	1	and	and	CCONJ
ejpam-5479	471	2	amer	amer	PROPN
ejpam-5479	471	3	t.s	t.s	PROPN
ejpam-5479	471	4	.	.	PROPN
ejpam-5479	471	5	analytical	analytical	ADJ
ejpam-5479	471	6	approximate	approximate	ADJ
ejpam-5479	471	7	solutions	solution	NOUN
ejpam-5479	471	8	of	of	ADP
ejpam-5479	471	9	a	a	DET
ejpam-5479	471	10	magnetic	magnetic	ADJ
ejpam-5479	471	11	spherical	spherical	ADJ
ejpam-5479	471	12	pendulum	pendulum	NOUN
ejpam-5479	471	13	:	:	PUNCT
ejpam-5479	471	14	stability	stability	NOUN
ejpam-5479	471	15	analysis	analysis	NOUN
ejpam-5479	471	16	.	.	PUNCT
ejpam-5479	472	1	journal	journal	NOUN
ejpam-5479	472	2	of	of	ADP
ejpam-5479	472	3	vibration	vibration	NOUN
ejpam-5479	472	4	engineering	engineering	NOUN
ejpam-5479	472	5	&	&	CCONJ
ejpam-5479	472	6	technologies	technologies	PROPN
ejpam-5479	472	7	,	,	PUNCT
ejpam-5479	472	8	11:2155–2165	11:2155–2165	NUM
ejpam-5479	472	9	,	,	PUNCT
ejpam-5479	472	10	2023	2023	NUM
ejpam-5479	472	11	.	.	PUNCT
ejpam-5479	473	1	[	[	X
ejpam-5479	473	2	22	22	NUM
ejpam-5479	473	3	]	]	X
ejpam-5479	473	4	moatimid	moatimid	PROPN
ejpam-5479	473	5	g.m	g.m	PROPN
ejpam-5479	473	6	.	.	PROPN
ejpam-5479	474	1	and	and	CCONJ
ejpam-5479	474	2	amer	amer	PROPN
ejpam-5479	474	3	t.s	t.s	PROPN
ejpam-5479	474	4	.	.	PROPN
ejpam-5479	474	5	dynamical	dynamical	ADJ
ejpam-5479	474	6	system	system	NOUN
ejpam-5479	474	7	of	of	ADP
ejpam-5479	474	8	a	a	DET
ejpam-5479	474	9	time	time	NOUN
ejpam-5479	474	10	-	-	PUNCT
ejpam-5479	474	11	delayed	delay	VERB
ejpam-5479	474	12	ϕ6	ϕ6	PROPN
ejpam-5479	474	13	-	-	PUNCT
ejpam-5479	474	14	van	van	PROPN
ejpam-5479	474	15	der	der	PROPN
ejpam-5479	474	16	pole	pole	NOUN
ejpam-5479	474	17	oscillator	oscillator	NOUN
ejpam-5479	474	18	:	:	PUNCT
ejpam-5479	474	19	a	a	DET
ejpam-5479	474	20	non	non	ADJ
ejpam-5479	474	21	-	-	ADJ
ejpam-5479	474	22	perturbative	perturbative	ADJ
ejpam-5479	474	23	approach	approach	NOUN
ejpam-5479	474	24	.	.	PUNCT
ejpam-5479	475	1	scientific	scientific	ADJ
ejpam-5479	475	2	reports	report	NOUN
ejpam-5479	475	3	,	,	PUNCT
ejpam-5479	475	4	13:11942	13:11942	NUM
ejpam-5479	475	5	,	,	PUNCT
ejpam-5479	475	6	2023	2023	NUM
ejpam-5479	475	7	.	.	PUNCT
ejpam-5479	476	1	[	[	X
ejpam-5479	476	2	23	23	NUM
ejpam-5479	476	3	]	]	X
ejpam-5479	476	4	moatimid	moatimid	PROPN
ejpam-5479	476	5	g.m	g.m	AUX
ejpam-5479	476	6	.	.	PROPN
ejpam-5479	476	7	,	,	PUNCT
ejpam-5479	476	8	amer	amer	PROPN
ejpam-5479	476	9	t.s	t.s	PROPN
ejpam-5479	476	10	.	.	PROPN
ejpam-5479	476	11	,	,	PUNCT
ejpam-5479	476	12	and	and	CCONJ
ejpam-5479	476	13	galal	galal	PROPN
ejpam-5479	476	14	a.a	a.a	PROPN
ejpam-5479	476	15	.	.	PROPN
ejpam-5479	476	16	studying	study	VERB
ejpam-5479	476	17	highly	highly	ADV
ejpam-5479	476	18	nonlinear	nonlinear	ADJ
ejpam-5479	476	19	oscillators	oscillator	NOUN
ejpam-5479	476	20	using	use	VERB
ejpam-5479	476	21	the	the	DET
ejpam-5479	476	22	non	non	ADJ
ejpam-5479	476	23	-	-	ADJ
ejpam-5479	476	24	perturbative	perturbative	ADJ
ejpam-5479	476	25	methodology	methodology	NOUN
ejpam-5479	476	26	.	.	PUNCT
ejpam-5479	477	1	scientific	scientific	ADJ
ejpam-5479	477	2	reports	report	NOUN
ejpam-5479	477	3	,	,	PUNCT
ejpam-5479	477	4	13:20288	13:20288	NUM
ejpam-5479	477	5	,	,	PUNCT
ejpam-5479	477	6	2023	2023	NUM
ejpam-5479	477	7	.	.	PUNCT
ejpam-5479	478	1	[	[	X
ejpam-5479	478	2	24	24	NUM
ejpam-5479	478	3	]	]	X
ejpam-5479	478	4	moatimid	moatimid	PROPN
ejpam-5479	478	5	g.m	g.m	PROPN
ejpam-5479	478	6	.	.	PROPN
ejpam-5479	478	7	,	,	PUNCT
ejpam-5479	478	8	amer	amer	PROPN
ejpam-5479	478	9	t.s	t.s	PROPN
ejpam-5479	478	10	.	.	PROPN
ejpam-5479	478	11	,	,	PUNCT
ejpam-5479	478	12	and	and	CCONJ
ejpam-5479	478	13	galal	galal	PROPN
ejpam-5479	478	14	a.a	a.a	PROPN
ejpam-5479	478	15	.	.	PROPN
ejpam-5479	478	16	inspection	inspection	NOUN
ejpam-5479	478	17	of	of	ADP
ejpam-5479	478	18	some	some	DET
ejpam-5479	478	19	extremely	extremely	ADV
ejpam-5479	478	20	nonlinear	nonlinear	ADJ
ejpam-5479	478	21	oscillators	oscillator	NOUN
ejpam-5479	478	22	using	use	VERB
ejpam-5479	478	23	an	an	DET
ejpam-5479	478	24	inventive	inventive	ADJ
ejpam-5479	478	25	approach	approach	NOUN
ejpam-5479	478	26	.	.	PUNCT
ejpam-5479	479	1	journal	journal	NOUN
ejpam-5479	479	2	of	of	ADP
ejpam-5479	479	3	vibration	vibration	NOUN
ejpam-5479	479	4	engineering	engineering	NOUN
ejpam-5479	479	5	&	&	CCONJ
ejpam-5479	479	6	technologies	technology	NOUN
ejpam-5479	479	7	,	,	PUNCT
ejpam-5479	479	8	2024	2024	NUM
ejpam-5479	479	9	.	.	PUNCT
ejpam-5479	480	1	published	publish	VERB
ejpam-5479	480	2	online	online	ADV
ejpam-5479	480	3	:	:	PUNCT
ejpam-5479	480	4	06	06	NUM
ejpam-5479	480	5	july	july	NOUN
ejpam-5479	480	6	.	.	PUNCT
ejpam-5479	481	1	[	[	X
ejpam-5479	481	2	25	25	NUM
ejpam-5479	481	3	]	]	X
ejpam-5479	481	4	moatimid	moatimid	PROPN
ejpam-5479	481	5	g.m	g.m	PROPN
ejpam-5479	481	6	.	.	PROPN
ejpam-5479	481	7	,	,	PUNCT
ejpam-5479	481	8	amer	amer	PROPN
ejpam-5479	481	9	t.s	t.s	PROPN
ejpam-5479	481	10	.	.	PROPN
ejpam-5479	481	11	,	,	PUNCT
ejpam-5479	481	12	and	and	CCONJ
ejpam-5479	481	13	ellabban	ellabban	PROPN
ejpam-5479	481	14	y.y	y.y	PROPN
ejpam-5479	481	15	.	.	PUNCT
ejpam-5479	482	1	a	a	DET
ejpam-5479	482	2	novel	novel	ADJ
ejpam-5479	482	3	methodology	methodology	NOUN
ejpam-5479	482	4	for	for	ADP
ejpam-5479	482	5	a	a	DET
ejpam-5479	482	6	timedelayed	timedelayed	ADJ
ejpam-5479	482	7	controller	controller	NOUN
ejpam-5479	482	8	to	to	PART
ejpam-5479	482	9	prevent	prevent	VERB
ejpam-5479	482	10	nonlinear	nonlinear	ADJ
ejpam-5479	482	11	system	system	NOUN
ejpam-5479	482	12	oscillations	oscillation	NOUN
ejpam-5479	482	13	.	.	PUNCT
ejpam-5479	483	1	journal	journal	NOUN
ejpam-5479	483	2	of	of	ADP
ejpam-5479	483	3	low	low	ADJ
ejpam-5479	483	4	frequency	frequency	NOUN
ejpam-5479	483	5	noise	noise	NOUN
ejpam-5479	483	6	,	,	PUNCT
ejpam-5479	483	7	vibration	vibration	NOUN
ejpam-5479	483	8	and	and	CCONJ
ejpam-5479	483	9	active	active	ADJ
ejpam-5479	483	10	control	control	NOUN
ejpam-5479	483	11	,	,	PUNCT
ejpam-5479	483	12	43(1):525–542	43(1):525–542	PROPN
ejpam-5479	483	13	,	,	PUNCT
ejpam-5479	483	14	2024	2024	NUM
ejpam-5479	483	15	.	.	PUNCT
ejpam-5479	484	1	[	[	X
ejpam-5479	484	2	26	26	NUM
ejpam-5479	484	3	]	]	X
ejpam-5479	484	4	moatimid	moatimid	PROPN
ejpam-5479	484	5	g.m	g.m	PROPN
ejpam-5479	484	6	.	.	PROPN
ejpam-5479	485	1	and	and	CCONJ
ejpam-5479	485	2	mohamed	mohamed	PROPN
ejpam-5479	485	3	y.m	y.m	PROPN
ejpam-5479	485	4	.	.	PROPN
ejpam-5479	486	1	a	a	DET
ejpam-5479	486	2	novel	novel	ADJ
ejpam-5479	486	3	methodology	methodology	NOUN
ejpam-5479	486	4	in	in	ADP
ejpam-5479	486	5	analyzing	analyze	VERB
ejpam-5479	486	6	nonlinear	nonlinear	ADJ
ejpam-5479	486	7	stability	stability	NOUN
ejpam-5479	486	8	of	of	ADP
ejpam-5479	486	9	two	two	NUM
ejpam-5479	486	10	electrified	electrify	VERB
ejpam-5479	486	11	viscoelastic	viscoelastic	ADJ
ejpam-5479	486	12	liquids	liquid	NOUN
ejpam-5479	486	13	.	.	PUNCT
ejpam-5479	487	1	chinese	chinese	ADJ
ejpam-5479	487	2	journal	journal	PROPN
ejpam-5479	487	3	of	of	ADP
ejpam-5479	487	4	physics	physics	PROPN
ejpam-5479	487	5	,	,	PUNCT
ejpam-5479	487	6	89:679	89:679	NUM
ejpam-5479	487	7	–	–	PUNCT
ejpam-5479	487	8	706	706	NUM
ejpam-5479	487	9	,	,	PUNCT
ejpam-5479	487	10	2023	2023	NUM
ejpam-5479	487	11	.	.	PUNCT
ejpam-5479	488	1	[	[	X
ejpam-5479	488	2	27	27	NUM
ejpam-5479	488	3	]	]	X
ejpam-5479	488	4	moatimid	moatimid	PROPN
ejpam-5479	488	5	g.m	g.m	PROPN
ejpam-5479	488	6	.	.	PROPN
ejpam-5479	489	1	and	and	CCONJ
ejpam-5479	489	2	mohamed	mohamed	PROPN
ejpam-5479	489	3	y.m	y.m	PROPN
ejpam-5479	489	4	.	.	PROPN
ejpam-5479	489	5	nonlinear	nonlinear	ADJ
ejpam-5479	489	6	electro	electro	ADJ
ejpam-5479	489	7	-	-	PUNCT
ejpam-5479	489	8	rheological	rheological	ADJ
ejpam-5479	489	9	instability	instability	NOUN
ejpam-5479	489	10	of	of	ADP
ejpam-5479	489	11	two	two	NUM
ejpam-5479	489	12	moving	move	VERB
ejpam-5479	489	13	cylindrical	cylindrical	ADJ
ejpam-5479	489	14	fluids	fluid	NOUN
ejpam-5479	489	15	:	:	PUNCT
ejpam-5479	489	16	an	an	DET
ejpam-5479	489	17	innovative	innovative	ADJ
ejpam-5479	489	18	approach	approach	NOUN
ejpam-5479	489	19	.	.	PUNCT
ejpam-5479	490	1	physics	physics	NOUN
ejpam-5479	490	2	of	of	ADP
ejpam-5479	490	3	fluids	fluid	NOUN
ejpam-5479	490	4	,	,	PUNCT
ejpam-5479	490	5	36(2):024110	36(2):024110	NUM
ejpam-5479	490	6	,	,	PUNCT
ejpam-5479	490	7	2024	2024	NUM
ejpam-5479	490	8	.	.	PUNCT
ejpam-5479	491	1	[	[	X
ejpam-5479	491	2	28	28	NUM
ejpam-5479	491	3	]	]	X
ejpam-5479	491	4	ahmad	ahmad	PROPN
ejpam-5479	491	5	h.	h.	PROPN
ejpam-5479	491	6	,	,	PUNCT
ejpam-5479	491	7	khan	khan	PROPN
ejpam-5479	491	8	t.a	t.a	PROPN
ejpam-5479	491	9	.	.	PROPN
ejpam-5479	491	10	,	,	PUNCT
ejpam-5479	491	11	stanimirović	stanimirović	NOUN
ejpam-5479	491	12	p.	p.	PROPN
ejpam-5479	491	13	s.	s.	PROPN
ejpam-5479	491	14	,	,	PUNCT
ejpam-5479	491	15	chu	chu	PROPN
ejpam-5479	491	16	y	y	PROPN
ejpam-5479	491	17	-	-	PUNCT
ejpam-5479	491	18	m.	m.	NOUN
ejpam-5479	491	19	,	,	PUNCT
ejpam-5479	491	20	and	and	CCONJ
ejpam-5479	491	21	ahmad	ahmad	PROPN
ejpam-5479	491	22	i.	i.	PROPN
ejpam-5479	491	23	modified	modify	VERB
ejpam-5479	491	24	variational	variational	ADJ
ejpam-5479	491	25	iteration	iteration	NOUN
ejpam-5479	491	26	algorithm	algorithm	PROPN
ejpam-5479	491	27	-	-	PUNCT
ejpam-5479	491	28	ii	ii	NOUN
ejpam-5479	491	29	:	:	PUNCT
ejpam-5479	491	30	convergence	convergence	NOUN
ejpam-5479	491	31	and	and	CCONJ
ejpam-5479	491	32	applications	application	NOUN
ejpam-5479	491	33	to	to	ADP
ejpam-5479	491	34	diffusion	diffusion	NOUN
ejpam-5479	491	35	models	model	NOUN
ejpam-5479	491	36	.	.	PUNCT
ejpam-5479	492	1	complexity	complexity	NOUN
ejpam-5479	492	2	,	,	PUNCT
ejpam-5479	492	3	2020	2020	NUM
ejpam-5479	492	4	:	:	PUNCT
ejpam-5479	492	5	article	article	NOUN
ejpam-5479	492	6	i	i	PROPN
ejpam-5479	492	7	d	d	PROPN
ejpam-5479	492	8	8841718	8841718	NUM
ejpam-5479	492	9	,	,	PUNCT
ejpam-5479	492	10	14	14	NUM
ejpam-5479	492	11	pages	page	NOUN
ejpam-5479	492	12	,	,	PUNCT
ejpam-5479	492	13	2020	2020	NUM
ejpam-5479	492	14	.	.	PUNCT
ejpam-5479	493	1	[	[	X
ejpam-5479	493	2	29	29	NUM
ejpam-5479	493	3	]	]	X
ejpam-5479	493	4	fan	fan	PROPN
ejpam-5479	494	1	j.	j.	PROPN
ejpam-5479	495	1	he	he	PRON
ejpam-5479	495	2	’s	’	VERB
ejpam-5479	495	3	frequency	frequency	NOUN
ejpam-5479	495	4	–	–	PUNCT
ejpam-5479	495	5	amplitude	amplitude	NOUN
ejpam-5479	495	6	formulation	formulation	NOUN
ejpam-5479	495	7	for	for	ADP
ejpam-5479	495	8	the	the	DET
ejpam-5479	495	9	duffing	duffing	NOUN
ejpam-5479	495	10	harmonic	harmonic	ADJ
ejpam-5479	495	11	oscillator	oscillator	NOUN
ejpam-5479	495	12	.	.	PUNCT
ejpam-5479	496	1	computers	computer	NOUN
ejpam-5479	496	2	&	&	CCONJ
ejpam-5479	496	3	mathematics	mathematics	PROPN
ejpam-5479	496	4	with	with	ADP
ejpam-5479	496	5	applications	application	NOUN
ejpam-5479	496	6	,	,	PUNCT
ejpam-5479	496	7	58(11	58(11	NUM
ejpam-5479	496	8	-	-	SYM
ejpam-5479	496	9	12):2473–2476	12):2473–2476	NUM
ejpam-5479	496	10	,	,	PUNCT
ejpam-5479	496	11	2009	2009	NUM
ejpam-5479	496	12	.	.	PUNCT
ejpam-5479	497	1	[	[	X
ejpam-5479	497	2	30	30	NUM
ejpam-5479	497	3	]	]	X
ejpam-5479	497	4	shaik	shaik	PROPN
ejpam-5479	497	5	j.	j.	PROPN
ejpam-5479	497	6	,	,	PUNCT
ejpam-5479	497	7	uchida	uchida	PROPN
ejpam-5479	497	8	t.k	t.k	PROPN
ejpam-5479	497	9	.	.	PROPN
ejpam-5479	497	10	,	,	PUNCT
ejpam-5479	497	11	and	and	CCONJ
ejpam-5479	497	12	vyasarayani	vyasarayani	PROPN
ejpam-5479	497	13	c.p	c.p	PROPN
ejpam-5479	497	14	.	.	PROPN
ejpam-5479	497	15	nonlinear	nonlinear	ADJ
ejpam-5479	497	16	dynamics	dynamic	NOUN
ejpam-5479	497	17	near	near	ADP
ejpam-5479	497	18	a	a	DET
ejpam-5479	497	19	double	double	ADJ
ejpam-5479	497	20	hopf	hopf	ADJ
ejpam-5479	497	21	bifurcation	bifurcation	NOUN
ejpam-5479	497	22	for	for	ADP
ejpam-5479	497	23	a	a	DET
ejpam-5479	497	24	ship	ship	NOUN
ejpam-5479	497	25	model	model	NOUN
ejpam-5479	497	26	with	with	ADP
ejpam-5479	497	27	time	time	NOUN
ejpam-5479	497	28	-	-	PUNCT
ejpam-5479	497	29	delay	delay	NOUN
ejpam-5479	497	30	control	control	NOUN
ejpam-5479	497	31	.	.	PUNCT
ejpam-5479	498	1	nonlinear	nonlinear	ADJ
ejpam-5479	498	2	dynamics	dynamic	NOUN
ejpam-5479	498	3	,	,	PUNCT
ejpam-5479	498	4	111:21441	111:21441	NUM
ejpam-5479	498	5	–	–	PUNCT
ejpam-5479	498	6	21460	21460	NUM
ejpam-5479	498	7	,	,	PUNCT
ejpam-5479	498	8	2023	2023	NUM
ejpam-5479	498	9	.	.	PUNCT
ejpam-5479	499	1	references	reference	NOUN
ejpam-5479	499	2	3207	3207	NUM
ejpam-5479	499	3	[	[	X
ejpam-5479	499	4	31	31	NUM
ejpam-5479	499	5	]	]	PUNCT
ejpam-5479	499	6	he	he	PRON
ejpam-5479	499	7	j	j	PROPN
ejpam-5479	499	8	-	-	PROPN
ejpam-5479	499	9	h.	h.	PROPN
ejpam-5479	499	10	homotopy	homotopy	NOUN
ejpam-5479	499	11	perturbation	perturbation	NOUN
ejpam-5479	499	12	technique	technique	NOUN
ejpam-5479	499	13	.	.	PUNCT
ejpam-5479	500	1	computer	computer	NOUN
ejpam-5479	500	2	methods	method	NOUN
ejpam-5479	500	3	in	in	ADP
ejpam-5479	500	4	applied	applied	ADJ
ejpam-5479	500	5	mechanics	mechanic	NOUN
ejpam-5479	500	6	and	and	CCONJ
ejpam-5479	500	7	engineering	engineering	NOUN
ejpam-5479	500	8	,	,	PUNCT
ejpam-5479	500	9	178:257–262	178:257–262	NUM
ejpam-5479	500	10	,	,	PUNCT
ejpam-5479	500	11	1999	1999	NUM
ejpam-5479	500	12	.	.	PUNCT
ejpam-5479	501	1	[	[	X
ejpam-5479	501	2	32	32	NUM
ejpam-5479	501	3	]	]	PUNCT
ejpam-5479	501	4	he	he	PRON
ejpam-5479	501	5	j	j	PROPN
ejpam-5479	501	6	-	-	PUNCT
ejpam-5479	501	7	h.	h.	PROPN
ejpam-5479	501	8	some	some	DET
ejpam-5479	501	9	asymptotic	asymptotic	ADJ
ejpam-5479	501	10	methods	method	NOUN
ejpam-5479	501	11	for	for	ADP
ejpam-5479	501	12	strongly	strongly	ADV
ejpam-5479	501	13	nonlinear	nonlinear	ADJ
ejpam-5479	501	14	equations	equation	NOUN
ejpam-5479	501	15	.	.	PUNCT
ejpam-5479	502	1	international	international	ADJ
ejpam-5479	502	2	journal	journal	NOUN
ejpam-5479	502	3	of	of	ADP
ejpam-5479	502	4	modern	modern	ADJ
ejpam-5479	502	5	physics	physics	PROPN
ejpam-5479	502	6	b	b	PROPN
ejpam-5479	502	7	,	,	PUNCT
ejpam-5479	502	8	20(10):1141–1199	20(10):1141–1199	PROPN
ejpam-5479	502	9	,	,	PUNCT
ejpam-5479	502	10	2006	2006	NUM
ejpam-5479	502	11	.	.	PUNCT
ejpam-5479	503	1	[	[	X
ejpam-5479	503	2	33	33	NUM
ejpam-5479	503	3	]	]	PUNCT
ejpam-5479	503	4	he	he	PRON
ejpam-5479	503	5	j	j	PROPN
ejpam-5479	503	6	-	-	PROPN
ejpam-5479	503	7	h.	h.	PROPN
ejpam-5479	503	8	comment	comment	NOUN
ejpam-5479	503	9	on	on	ADP
ejpam-5479	503	10	‘	'	PUNCT
ejpam-5479	503	11	he	he	PRON
ejpam-5479	503	12	’s	’s	PART
ejpam-5479	503	13	frequency	frequency	NOUN
ejpam-5479	503	14	formulation	formulation	NOUN
ejpam-5479	503	15	for	for	ADP
ejpam-5479	503	16	nonlinear	nonlinear	ADJ
ejpam-5479	503	17	oscillators	oscillator	NOUN
ejpam-5479	503	18	’	'	PUNCT
ejpam-5479	503	19	.	.	PUNCT
ejpam-5479	504	1	european	european	PROPN
ejpam-5479	504	2	journal	journal	PROPN
ejpam-5479	504	3	of	of	ADP
ejpam-5479	504	4	physics	physics	PROPN
ejpam-5479	504	5	,	,	PUNCT
ejpam-5479	504	6	29(4):l19	29(4):l19	NUM
ejpam-5479	504	7	,	,	PUNCT
ejpam-5479	504	8	2008	2008	NUM
ejpam-5479	504	9	.	.	PUNCT
ejpam-5479	505	1	[	[	X
ejpam-5479	505	2	34	34	NUM
ejpam-5479	505	3	]	]	PUNCT
ejpam-5479	505	4	he	he	PRON
ejpam-5479	505	5	j	j	PROPN
ejpam-5479	505	6	-	-	PROPN
ejpam-5479	505	7	h.	h.	PROPN
ejpam-5479	505	8	an	an	DET
ejpam-5479	505	9	improved	improved	ADJ
ejpam-5479	505	10	amplitude	amplitude	NOUN
ejpam-5479	505	11	-	-	PUNCT
ejpam-5479	505	12	frequency	frequency	NOUN
ejpam-5479	505	13	formulation	formulation	NOUN
ejpam-5479	505	14	for	for	ADP
ejpam-5479	505	15	nonlinear	nonlinear	ADJ
ejpam-5479	505	16	oscillators	oscillator	NOUN
ejpam-5479	505	17	.	.	PUNCT
ejpam-5479	506	1	international	international	ADJ
ejpam-5479	506	2	journal	journal	PROPN
ejpam-5479	506	3	of	of	ADP
ejpam-5479	506	4	nonlinear	nonlinear	PROPN
ejpam-5479	506	5	sciences	sciences	PROPN
ejpam-5479	506	6	and	and	CCONJ
ejpam-5479	506	7	numerical	numerical	PROPN
ejpam-5479	506	8	simulation	simulation	PROPN
ejpam-5479	506	9	,	,	PUNCT
ejpam-5479	506	10	9(2):211–212	9(2):211–212	NUM
ejpam-5479	506	11	,	,	PUNCT
ejpam-5479	506	12	2008	2008	NUM
ejpam-5479	506	13	.	.	PUNCT
ejpam-5479	507	1	[	[	X
ejpam-5479	507	2	35	35	NUM
ejpam-5479	507	3	]	]	PUNCT
ejpam-5479	507	4	he	he	PRON
ejpam-5479	507	5	j	j	PROPN
ejpam-5479	507	6	-	-	PUNCT
ejpam-5479	507	7	h.	h.	PROPN
ejpam-5479	507	8	amplitude	amplitude	NOUN
ejpam-5479	507	9	-	-	PUNCT
ejpam-5479	507	10	frequency	frequency	NOUN
ejpam-5479	507	11	relationship	relationship	NOUN
ejpam-5479	507	12	for	for	ADP
ejpam-5479	507	13	conservative	conservative	ADJ
ejpam-5479	507	14	nonlinear	nonlinear	ADJ
ejpam-5479	507	15	oscillators	oscillator	NOUN
ejpam-5479	507	16	with	with	ADP
ejpam-5479	507	17	odd	odd	ADJ
ejpam-5479	507	18	nonlinearities	nonlinearitie	NOUN
ejpam-5479	507	19	.	.	PUNCT
ejpam-5479	508	1	international	international	ADJ
ejpam-5479	508	2	journal	journal	PROPN
ejpam-5479	508	3	of	of	ADP
ejpam-5479	508	4	applied	applied	ADJ
ejpam-5479	508	5	and	and	CCONJ
ejpam-5479	508	6	computational	computational	ADJ
ejpam-5479	508	7	mathematics	mathematic	NOUN
ejpam-5479	508	8	,	,	PUNCT
ejpam-5479	508	9	3:1557–1560	3:1557–1560	PROPN
ejpam-5479	508	10	,	,	PUNCT
ejpam-5479	508	11	2017	2017	NUM
ejpam-5479	508	12	.	.	PUNCT
ejpam-5479	509	1	[	[	X
ejpam-5479	509	2	36	36	NUM
ejpam-5479	509	3	]	]	PUNCT
ejpam-5479	509	4	he	he	PRON
ejpam-5479	509	5	j	j	PROPN
ejpam-5479	509	6	-	-	PROPN
ejpam-5479	509	7	h.	h.	PROPN
ejpam-5479	509	8	special	special	ADJ
ejpam-5479	509	9	functions	function	NOUN
ejpam-5479	509	10	for	for	ADP
ejpam-5479	509	11	solving	solve	VERB
ejpam-5479	509	12	nonlinear	nonlinear	ADJ
ejpam-5479	509	13	differential	differential	ADJ
ejpam-5479	509	14	equations	equation	NOUN
ejpam-5479	509	15	.	.	PUNCT
ejpam-5479	510	1	international	international	ADJ
ejpam-5479	510	2	journal	journal	PROPN
ejpam-5479	510	3	of	of	ADP
ejpam-5479	510	4	applied	applied	ADJ
ejpam-5479	510	5	and	and	CCONJ
ejpam-5479	510	6	computational	computational	ADJ
ejpam-5479	510	7	mathematics	mathematic	NOUN
ejpam-5479	510	8	,	,	PUNCT
ejpam-5479	510	9	7:84	7:84	NUM
ejpam-5479	510	10	,	,	PUNCT
ejpam-5479	510	11	2021	2021	NUM
ejpam-5479	510	12	.	.	PUNCT
ejpam-5479	511	1	6	6	NUM
ejpam-5479	511	2	pages	page	NOUN
ejpam-5479	511	3	.	.	PUNCT
ejpam-5479	512	1	[	[	X
ejpam-5479	512	2	37	37	NUM
ejpam-5479	512	3	]	]	PUNCT
ejpam-5479	512	4	he	he	PRON
ejpam-5479	512	5	j	j	PROPN
ejpam-5479	512	6	-	-	PROPN
ejpam-5479	512	7	h.	h.	PROPN
ejpam-5479	512	8	periodic	periodic	ADJ
ejpam-5479	512	9	solution	solution	NOUN
ejpam-5479	512	10	of	of	ADP
ejpam-5479	512	11	a	a	DET
ejpam-5479	512	12	micro	micro	ADJ
ejpam-5479	512	13	-	-	ADJ
ejpam-5479	512	14	electromechanical	electromechanical	ADJ
ejpam-5479	512	15	system	system	NOUN
ejpam-5479	512	16	.	.	PUNCT
ejpam-5479	513	1	facta	facta	PROPN
ejpam-5479	513	2	universities	universities	PROPN
ejpam-5479	513	3	series	series	PROPN
ejpam-5479	513	4	:	:	PUNCT
ejpam-5479	513	5	mechanical	mechanical	ADJ
ejpam-5479	513	6	engineering	engineering	NOUN
ejpam-5479	513	7	,	,	PUNCT
ejpam-5479	513	8	22(2):187–198	22(2):187–198	PROPN
ejpam-5479	513	9	,	,	PUNCT
ejpam-5479	513	10	2024	2024	NUM
ejpam-5479	513	11	.	.	PUNCT
ejpam-5479	514	1	[	[	X
ejpam-5479	514	2	38	38	NUM
ejpam-5479	514	3	]	]	PUNCT
ejpam-5479	514	4	he	he	PRON
ejpam-5479	514	5	j	j	PROPN
ejpam-5479	514	6	-	-	PROPN
ejpam-5479	514	7	h.	h.	PROPN
ejpam-5479	514	8	and	and	CCONJ
ejpam-5479	514	9	garćıa	garćıa	PROPN
ejpam-5479	514	10	a.	a.	NOUN
ejpam-5479	514	11	the	the	DET
ejpam-5479	514	12	simplest	simple	ADJ
ejpam-5479	514	13	amplitude	amplitude	NOUN
ejpam-5479	514	14	-	-	PUNCT
ejpam-5479	514	15	period	period	NOUN
ejpam-5479	514	16	formula	formula	NOUN
ejpam-5479	514	17	for	for	ADP
ejpam-5479	514	18	non	non	ADJ
ejpam-5479	514	19	-	-	ADJ
ejpam-5479	514	20	conservative	conservative	ADJ
ejpam-5479	514	21	oscillators	oscillator	NOUN
ejpam-5479	514	22	.	.	PUNCT
ejpam-5479	515	1	reports	report	NOUN
ejpam-5479	515	2	in	in	ADP
ejpam-5479	515	3	mechanical	mechanical	ADJ
ejpam-5479	515	4	engineering	engineering	NOUN
ejpam-5479	515	5	,	,	PUNCT
ejpam-5479	515	6	2(1):143–148	2(1):143–148	PROPN
ejpam-5479	515	7	,	,	PUNCT
ejpam-5479	515	8	2021	2021	NUM
ejpam-5479	515	9	.	.	PUNCT
ejpam-5479	516	1	[	[	X
ejpam-5479	516	2	39	39	NUM
ejpam-5479	516	3	]	]	PUNCT
ejpam-5479	516	4	he	he	PRON
ejpam-5479	516	5	j	j	PROPN
ejpam-5479	516	6	-	-	PROPN
ejpam-5479	516	7	h.	h.	PROPN
ejpam-5479	516	8	,	,	PUNCT
ejpam-5479	516	9	he	he	PRON
ejpam-5479	516	10	c	c	PROPN
ejpam-5479	516	11	-	-	PUNCT
ejpam-5479	516	12	h.	h.	PROPN
ejpam-5479	516	13	,	,	PUNCT
ejpam-5479	516	14	qian	qian	PROPN
ejpam-5479	516	15	m	m	PROPN
ejpam-5479	516	16	-	-	PUNCT
ejpam-5479	516	17	y.	y.	PROPN
ejpam-5479	516	18	,	,	PUNCT
ejpam-5479	516	19	and	and	CCONJ
ejpam-5479	516	20	alsolami	alsolami	PROPN
ejpam-5479	516	21	a.a	a.a	PROPN
ejpam-5479	516	22	.	.	PROPN
ejpam-5479	516	23	piezoelectric	piezoelectric	PROPN
ejpam-5479	516	24	biosensor	biosensor	NOUN
ejpam-5479	516	25	based	base	VERB
ejpam-5479	516	26	on	on	ADP
ejpam-5479	516	27	ultrasensitive	ultrasensitive	ADJ
ejpam-5479	516	28	mems	mem	NOUN
ejpam-5479	516	29	system	system	NOUN
ejpam-5479	516	30	.	.	PUNCT
ejpam-5479	517	1	sensors	sensor	NOUN
ejpam-5479	517	2	and	and	CCONJ
ejpam-5479	517	3	actuators	actuator	NOUN
ejpam-5479	517	4	a	a	PRON
ejpam-5479	517	5	:	:	PUNCT
ejpam-5479	517	6	physical	physical	ADJ
ejpam-5479	517	7	,	,	PUNCT
ejpam-5479	517	8	376:115664	376:115664	NUM
ejpam-5479	517	9	,	,	PUNCT
ejpam-5479	517	10	2024	2024	NUM
ejpam-5479	517	11	.	.	PUNCT
ejpam-5479	518	1	[	[	X
ejpam-5479	518	2	40	40	NUM
ejpam-5479	518	3	]	]	PUNCT
ejpam-5479	518	4	alluhydan	alluhydan	PROPN
ejpam-5479	518	5	kh	kh	PROPN
ejpam-5479	518	6	.	.	PROPN
ejpam-5479	518	7	,	,	PUNCT
ejpam-5479	518	8	moatimid	moatimid	PROPN
ejpam-5479	518	9	g.m	g.m	PROPN
ejpam-5479	518	10	.	.	PROPN
ejpam-5479	518	11	,	,	PUNCT
ejpam-5479	518	12	amer	amer	PROPN
ejpam-5479	518	13	t.s	t.s	PROPN
ejpam-5479	518	14	.	.	PROPN
ejpam-5479	518	15	,	,	PUNCT
ejpam-5479	518	16	and	and	CCONJ
ejpam-5479	518	17	galal	galal	PROPN
ejpam-5479	518	18	a.a	a.a	PROPN
ejpam-5479	518	19	.	.	PROPN
ejpam-5479	518	20	inspection	inspection	NOUN
ejpam-5479	518	21	of	of	ADP
ejpam-5479	518	22	a	a	DET
ejpam-5479	518	23	timedelayed	timedelayed	ADJ
ejpam-5479	518	24	excited	excited	ADJ
ejpam-5479	518	25	damping	damp	VERB
ejpam-5479	518	26	duffing	duffing	NOUN
ejpam-5479	518	27	oscillator	oscillator	NOUN
ejpam-5479	518	28	.	.	PUNCT
ejpam-5479	519	1	axioms	axiom	NOUN
ejpam-5479	519	2	,	,	PUNCT
ejpam-5479	519	3	13(6):416	13(6):416	NUM
ejpam-5479	519	4	,	,	PUNCT
ejpam-5479	519	5	2024	2024	NUM
ejpam-5479	519	6	.	.	PUNCT
ejpam-5479	520	1	[	[	X
ejpam-5479	520	2	41	41	NUM
ejpam-5479	520	3	]	]	X
ejpam-5479	520	4	cvetićanin	cvetićanin	PROPN
ejpam-5479	520	5	l.	l.	PROPN
ejpam-5479	520	6	oscillator	oscillator	PROPN
ejpam-5479	520	7	with	with	ADP
ejpam-5479	520	8	strong	strong	ADJ
ejpam-5479	520	9	quadratic	quadratic	ADJ
ejpam-5479	520	10	damping	damp	VERB
ejpam-5479	520	11	force	force	NOUN
ejpam-5479	520	12	.	.	PUNCT
ejpam-5479	521	1	publications	publication	NOUN
ejpam-5479	521	2	de	de	X
ejpam-5479	521	3	l’institut	l’institut	X
ejpam-5479	521	4	mathématique	mathématique	PROPN
ejpam-5479	521	5	,	,	PUNCT
ejpam-5479	521	6	85(99):119–130	85(99):119–130	NUM
ejpam-5479	521	7	,	,	PUNCT
ejpam-5479	521	8	2009	2009	NUM
ejpam-5479	521	9	.	.	PUNCT
ejpam-5479	522	1	[	[	X
ejpam-5479	522	2	42	42	NUM
ejpam-5479	522	3	]	]	X
ejpam-5479	522	4	geng	geng	PROPN
ejpam-5479	522	5	l.	l.	PROPN
ejpam-5479	522	6	and	and	CCONJ
ejpam-5479	522	7	cai	cai	PROPN
ejpam-5479	522	8	x	x	PROPN
ejpam-5479	522	9	-	-	PROPN
ejpam-5479	522	10	c.	c.	NOUN
ejpam-5479	522	11	he	he	PRON
ejpam-5479	522	12	’s	’	VERB
ejpam-5479	522	13	frequency	frequency	NOUN
ejpam-5479	522	14	formulation	formulation	NOUN
ejpam-5479	522	15	for	for	ADP
ejpam-5479	522	16	nonlinear	nonlinear	ADJ
ejpam-5479	522	17	oscillators	oscillator	NOUN
ejpam-5479	522	18	.	.	PUNCT
ejpam-5479	523	1	european	european	ADJ
ejpam-5479	523	2	journal	journal	PROPN
ejpam-5479	523	3	of	of	ADP
ejpam-5479	523	4	physics	physics	PROPN
ejpam-5479	523	5	,	,	PUNCT
ejpam-5479	523	6	28(5):923	28(5):923	NUM
ejpam-5479	523	7	,	,	PUNCT
ejpam-5479	523	8	2007	2007	NUM
ejpam-5479	523	9	.	.	PUNCT
ejpam-5479	524	1	[	[	X
ejpam-5479	524	2	43	43	NUM
ejpam-5479	524	3	]	]	X
ejpam-5479	524	4	dehghan	dehghan	PROPN
ejpam-5479	524	5	m.	m.	NOUN
ejpam-5479	524	6	and	and	CCONJ
ejpam-5479	524	7	ghesmati	ghesmati	PROPN
ejpam-5479	524	8	a.	a.	NOUN
ejpam-5479	524	9	application	application	NOUN
ejpam-5479	524	10	of	of	ADP
ejpam-5479	524	11	the	the	DET
ejpam-5479	524	12	dual	dual	ADJ
ejpam-5479	524	13	reciprocity	reciprocity	NOUN
ejpam-5479	524	14	boundary	boundary	ADJ
ejpam-5479	524	15	integral	integral	ADJ
ejpam-5479	524	16	equation	equation	NOUN
ejpam-5479	524	17	technique	technique	NOUN
ejpam-5479	524	18	to	to	PART
ejpam-5479	524	19	solve	solve	VERB
ejpam-5479	524	20	the	the	DET
ejpam-5479	524	21	nonlinear	nonlinear	PROPN
ejpam-5479	524	22	klein	klein	PROPN
ejpam-5479	524	23	–	–	PUNCT
ejpam-5479	524	24	gordon	gordon	PROPN
ejpam-5479	524	25	equation	equation	NOUN
ejpam-5479	524	26	.	.	PUNCT
ejpam-5479	525	1	computer	computer	NOUN
ejpam-5479	525	2	physics	physics	NOUN
ejpam-5479	525	3	communications	communication	NOUN
ejpam-5479	525	4	,	,	PUNCT
ejpam-5479	525	5	181(8):1410–1418	181(8):1410–1418	NUM
ejpam-5479	525	6	,	,	PUNCT
ejpam-5479	525	7	2010	2010	NUM
ejpam-5479	525	8	.	.	PUNCT
ejpam-5479	526	1	[	[	X
ejpam-5479	526	2	44	44	NUM
ejpam-5479	526	3	]	]	X
ejpam-5479	526	4	khan	khan	PROPN
ejpam-5479	526	5	m.n	m.n	PROPN
ejpam-5479	526	6	.	.	PROPN
ejpam-5479	526	7	,	,	PUNCT
ejpam-5479	526	8	haider	haider	PROPN
ejpam-5479	526	9	j.a	j.a	PROPN
ejpam-5479	526	10	.	.	PROPN
ejpam-5479	526	11	,	,	PUNCT
ejpam-5479	526	12	wang	wang	PROPN
ejpam-5479	526	13	z.	z.	PROPN
ejpam-5479	526	14	,	,	PUNCT
ejpam-5479	526	15	lone	lone	PROPN
ejpam-5479	526	16	s.a	s.a	PROPN
ejpam-5479	526	17	.	.	PROPN
ejpam-5479	526	18	,	,	PUNCT
ejpam-5479	526	19	almutlak	almutlak	PROPN
ejpam-5479	526	20	s.a	s.a	PROPN
ejpam-5479	526	21	.	.	PROPN
ejpam-5479	526	22	,	,	PUNCT
ejpam-5479	526	23	and	and	CCONJ
ejpam-5479	526	24	elseesy	elseesy	ADJ
ejpam-5479	526	25	i.e.	i.e.	X
ejpam-5479	526	26	application	application	NOUN
ejpam-5479	526	27	of	of	ADP
ejpam-5479	526	28	laplace	laplace	NOUN
ejpam-5479	526	29	-	-	PUNCT
ejpam-5479	526	30	based	base	VERB
ejpam-5479	526	31	variational	variational	ADJ
ejpam-5479	526	32	iteration	iteration	NOUN
ejpam-5479	526	33	method	method	NOUN
ejpam-5479	526	34	to	to	PART
ejpam-5479	526	35	analyze	analyze	VERB
ejpam-5479	526	36	generalized	generalized	ADJ
ejpam-5479	526	37	nonlinear	nonlinear	ADJ
ejpam-5479	526	38	oscillations	oscillation	NOUN
ejpam-5479	526	39	in	in	ADP
ejpam-5479	526	40	physical	physical	ADJ
ejpam-5479	526	41	systems	system	NOUN
ejpam-5479	526	42	.	.	PUNCT
ejpam-5479	527	1	modern	modern	ADJ
ejpam-5479	527	2	physics	physics	PROPN
ejpam-5479	527	3	letters	letters	PROPN
ejpam-5479	527	4	b	b	PROPN
ejpam-5479	527	5	,	,	PUNCT
ejpam-5479	527	6	37(34):2350169	37(34):2350169	NUM
ejpam-5479	527	7	,	,	PUNCT
ejpam-5479	527	8	2023	2023	NUM
ejpam-5479	527	9	.	.	PUNCT
ejpam-5479	528	1	[	[	X
ejpam-5479	528	2	45	45	NUM
ejpam-5479	528	3	]	]	X
ejpam-5479	528	4	eĺıas	eĺıas	PROPN
ejpam-5479	528	5	-	-	PUNCT
ejpam-5479	528	6	zú	zú	PROPN
ejpam-5479	528	7	niga	niga	PROPN
ejpam-5479	528	8	a.	a.	NOUN
ejpam-5479	528	9	exact	exact	PROPN
ejpam-5479	528	10	solution	solution	NOUN
ejpam-5479	528	11	of	of	ADP
ejpam-5479	528	12	the	the	DET
ejpam-5479	528	13	cubic	cubic	ADJ
ejpam-5479	528	14	-	-	PUNCT
ejpam-5479	528	15	quintic	quintic	ADJ
ejpam-5479	528	16	duffing	duffing	NOUN
ejpam-5479	528	17	oscillator	oscillator	NOUN
ejpam-5479	528	18	.	.	PUNCT
ejpam-5479	529	1	applied	apply	VERB
ejpam-5479	529	2	mathematical	mathematical	ADJ
ejpam-5479	529	3	modelling	modelling	NOUN
ejpam-5479	529	4	,	,	PUNCT
ejpam-5479	529	5	37(4):2574–2579	37(4):2574–2579	NUM
ejpam-5479	529	6	,	,	PUNCT
ejpam-5479	529	7	2013	2013	NUM
ejpam-5479	529	8	.	.	PUNCT
ejpam-5479	530	1	references	reference	NOUN
ejpam-5479	530	2	3208	3208	NUM
ejpam-5479	530	3	[	[	X
ejpam-5479	530	4	46	46	NUM
ejpam-5479	530	5	]	]	X
ejpam-5479	530	6	eĺıas	eĺıas	PROPN
ejpam-5479	530	7	-	-	PUNCT
ejpam-5479	530	8	zú	zú	PROPN
ejpam-5479	530	9	niga	niga	PROPN
ejpam-5479	530	10	a.	a.	NOUN
ejpam-5479	530	11	,	,	PUNCT
ejpam-5479	530	12	palacios	palacio	NOUN
ejpam-5479	530	13	-	-	PUNCT
ejpam-5479	530	14	pineda	pineda	PROPN
ejpam-5479	530	15	l.m	l.m	PROPN
ejpam-5479	530	16	.	.	PROPN
ejpam-5479	530	17	,	,	PUNCT
ejpam-5479	530	18	jiménez	jiménez	PROPN
ejpam-5479	530	19	-	-	PUNCT
ejpam-5479	530	20	cede	cede	VERB
ejpam-5479	530	21	no	no	DET
ejpam-5479	530	22	i.h	i.h	PROPN
ejpam-5479	530	23	.	.	PROPN
ejpam-5479	530	24	,	,	PUNCT
ejpam-5479	530	25	mart́ınez	mart́ınez	PROPN
ejpam-5479	530	26	-	-	PUNCT
ejpam-5479	530	27	romero	romero	PROPN
ejpam-5479	530	28	o.	o.	PROPN
ejpam-5479	530	29	,	,	PUNCT
ejpam-5479	530	30	and	and	CCONJ
ejpam-5479	530	31	olvera	olvera	PROPN
ejpam-5479	530	32	-	-	PUNCT
ejpam-5479	530	33	trejo	trejo	PROPN
ejpam-5479	530	34	d.	d.	PROPN
ejpam-5479	530	35	enhanced	enhance	VERB
ejpam-5479	530	36	he	he	PRON
ejpam-5479	530	37	’s	’s	PART
ejpam-5479	530	38	frequency	frequency	NOUN
ejpam-5479	530	39	-	-	PUNCT
ejpam-5479	530	40	amplitude	amplitude	NOUN
ejpam-5479	530	41	formulation	formulation	NOUN
ejpam-5479	530	42	for	for	ADP
ejpam-5479	530	43	nonlinear	nonlinear	ADJ
ejpam-5479	530	44	oscillators	oscillator	NOUN
ejpam-5479	530	45	.	.	PUNCT
ejpam-5479	531	1	results	result	NOUN
ejpam-5479	531	2	in	in	ADP
ejpam-5479	531	3	physics	physics	NOUN
ejpam-5479	531	4	,	,	PUNCT
ejpam-5479	531	5	19:103626	19:103626	NUM
ejpam-5479	531	6	,	,	PUNCT
ejpam-5479	531	7	2020	2020	NUM
ejpam-5479	531	8	.	.	PUNCT
ejpam-5479	532	1	[	[	X
ejpam-5479	532	2	47	47	NUM
ejpam-5479	532	3	]	]	X
ejpam-5479	532	4	spanos	spanos	ADJ
ejpam-5479	532	5	p.t.d	p.t.d	NOUN
ejpam-5479	532	6	.	.	PUNCT
ejpam-5479	533	1	and	and	CCONJ
ejpam-5479	533	2	iwan	iwan	PROPN
ejpam-5479	533	3	w.d	w.d	PROPN
ejpam-5479	533	4	.	.	PROPN
ejpam-5479	534	1	on	on	ADP
ejpam-5479	534	2	the	the	DET
ejpam-5479	534	3	existence	existence	NOUN
ejpam-5479	534	4	and	and	CCONJ
ejpam-5479	534	5	uniqueness	uniqueness	NOUN
ejpam-5479	534	6	of	of	ADP
ejpam-5479	534	7	solutions	solution	NOUN
ejpam-5479	534	8	generated	generate	VERB
ejpam-5479	534	9	by	by	ADP
ejpam-5479	534	10	equivalent	equivalent	ADJ
ejpam-5479	534	11	linearization	linearization	NOUN
ejpam-5479	534	12	.	.	PUNCT
ejpam-5479	535	1	international	international	ADJ
ejpam-5479	535	2	journal	journal	PROPN
ejpam-5479	535	3	of	of	ADP
ejpam-5479	535	4	non	non	ADJ
ejpam-5479	535	5	-	-	ADJ
ejpam-5479	535	6	linear	linear	ADJ
ejpam-5479	535	7	mechanics	mechanic	NOUN
ejpam-5479	535	8	,	,	PUNCT
ejpam-5479	535	9	13(2):71	13(2):71	NUM
ejpam-5479	535	10	–	–	PUNCT
ejpam-5479	535	11	78	78	NUM
ejpam-5479	535	12	,	,	PUNCT
ejpam-5479	535	13	1979	1979	NUM
ejpam-5479	535	14	.	.	PUNCT
ejpam-5479	536	1	[	[	X
ejpam-5479	536	2	48	48	NUM
ejpam-5479	536	3	]	]	X
ejpam-5479	536	4	caughey	caughey	PROPN
ejpam-5479	536	5	t.k	t.k	PROPN
ejpam-5479	536	6	.	.	PUNCT
ejpam-5479	536	7	equivalent	equivalent	ADJ
ejpam-5479	536	8	linearization	linearization	NOUN
ejpam-5479	536	9	techniques	technique	NOUN
ejpam-5479	536	10	.	.	PUNCT
ejpam-5479	537	1	the	the	DET
ejpam-5479	537	2	journal	journal	NOUN
ejpam-5479	537	3	of	of	ADP
ejpam-5479	537	4	the	the	DET
ejpam-5479	537	5	acoustical	acoustical	ADJ
ejpam-5479	537	6	society	society	NOUN
ejpam-5479	537	7	of	of	ADP
ejpam-5479	537	8	america	america	PROPN
ejpam-5479	537	9	,	,	PUNCT
ejpam-5479	537	10	35(11):1706–1711	35(11):1706–1711	PROPN
ejpam-5479	537	11	,	,	PUNCT
ejpam-5479	537	12	1963	1963	NUM
ejpam-5479	537	13	.	.	PUNCT
ejpam-5479	538	1	[	[	X
ejpam-5479	538	2	49	49	NUM
ejpam-5479	538	3	]	]	X
ejpam-5479	538	4	mao	mao	PROPN
ejpam-5479	538	5	x.	x.	NOUN
ejpam-5479	538	6	and	and	CCONJ
ejpam-5479	538	7	ding	de	VERB
ejpam-5479	538	8	w.	w.	NOUN
ejpam-5479	538	9	dynamics	dynamic	NOUN
ejpam-5479	538	10	of	of	ADP
ejpam-5479	538	11	a	a	DET
ejpam-5479	538	12	nonlinear	nonlinear	ADJ
ejpam-5479	538	13	vibration	vibration	NOUN
ejpam-5479	538	14	absorption	absorption	NOUN
ejpam-5479	538	15	system	system	NOUN
ejpam-5479	538	16	with	with	ADP
ejpam-5479	538	17	time	time	NOUN
ejpam-5479	538	18	delay	delay	NOUN
ejpam-5479	538	19	.	.	PUNCT
ejpam-5479	539	1	nonlinear	nonlinear	ADJ
ejpam-5479	539	2	dynamics	dynamic	NOUN
ejpam-5479	539	3	,	,	PUNCT
ejpam-5479	539	4	112:5177–5193	112:5177–5193	NUM
ejpam-5479	539	5	,	,	PUNCT
ejpam-5479	539	6	2024	2024	NUM
ejpam-5479	539	7	.	.	PUNCT
ejpam-5479	540	1	[	[	X
ejpam-5479	540	2	50	50	NUM
ejpam-5479	540	3	]	]	X
ejpam-5479	540	4	cai	cai	X
ejpam-5479	540	5	x	x	PROPN
ejpam-5479	540	6	-	-	PROPN
ejpam-5479	540	7	c.	c.	PROPN
ejpam-5479	540	8	and	and	CCONJ
ejpam-5479	540	9	liu	liu	PROPN
ejpam-5479	540	10	j	j	PROPN
ejpam-5479	540	11	-	-	PROPN
ejpam-5479	540	12	f.	f.	PROPN
ejpam-5479	540	13	application	application	NOUN
ejpam-5479	540	14	of	of	ADP
ejpam-5479	540	15	the	the	DET
ejpam-5479	540	16	modified	modify	VERB
ejpam-5479	540	17	frequency	frequency	NOUN
ejpam-5479	540	18	formulation	formulation	NOUN
ejpam-5479	540	19	to	to	ADP
ejpam-5479	540	20	a	a	DET
ejpam-5479	540	21	nonlinear	nonlinear	ADJ
ejpam-5479	540	22	oscillator	oscillator	NOUN
ejpam-5479	540	23	.	.	PUNCT
ejpam-5479	541	1	computers	computer	NOUN
ejpam-5479	541	2	and	and	CCONJ
ejpam-5479	541	3	mathematics	mathematic	NOUN
ejpam-5479	541	4	with	with	ADP
ejpam-5479	541	5	applications	application	NOUN
ejpam-5479	541	6	,	,	PUNCT
ejpam-5479	541	7	61:2237–2240	61:2237–2240	NUM
ejpam-5479	541	8	,	,	PUNCT
ejpam-5479	541	9	2011	2011	NUM
ejpam-5479	541	10	.	.	PUNCT
ejpam-5479	542	1	[	[	X
ejpam-5479	542	2	51	51	NUM
ejpam-5479	542	3	]	]	X
ejpam-5479	542	4	cai	cai	X
ejpam-5479	542	5	x	x	PROPN
ejpam-5479	542	6	-	-	PROPN
ejpam-5479	542	7	c.	c.	PROPN
ejpam-5479	542	8	and	and	CCONJ
ejpam-5479	542	9	wu	wu	PROPN
ejpam-5479	542	10	w	w	PROPN
ejpam-5479	542	11	-	-	PROPN
ejpam-5479	542	12	y.	y.	VERB
ejpam-5479	542	13	he	he	PRON
ejpam-5479	542	14	’s	’	VERB
ejpam-5479	542	15	frequency	frequency	NOUN
ejpam-5479	542	16	formulation	formulation	NOUN
ejpam-5479	542	17	for	for	ADP
ejpam-5479	542	18	the	the	DET
ejpam-5479	542	19	relativistic	relativistic	ADJ
ejpam-5479	542	20	harmonic	harmonic	ADJ
ejpam-5479	542	21	oscillator	oscillator	NOUN
ejpam-5479	542	22	.	.	PUNCT
ejpam-5479	543	1	computers	computer	NOUN
ejpam-5479	543	2	&	&	CCONJ
ejpam-5479	543	3	mathematics	mathematics	PROPN
ejpam-5479	543	4	with	with	ADP
ejpam-5479	543	5	applications	application	NOUN
ejpam-5479	543	6	,	,	PUNCT
ejpam-5479	543	7	58(11	58(11	NUM
ejpam-5479	543	8	-	-	NOUN
ejpam-5479	543	9	12):2358–2359	12):2358–2359	NOUN
ejpam-5479	543	10	,	,	PUNCT
ejpam-5479	543	11	2009	2009	NUM
ejpam-5479	543	12	.	.	PUNCT
ejpam-5479	544	1	[	[	X
ejpam-5479	544	2	52	52	NUM
ejpam-5479	544	3	]	]	X
ejpam-5479	544	4	geng	geng	PROPN
ejpam-5479	544	5	y.	y.	PROPN
ejpam-5479	544	6	exact	exact	PROPN
ejpam-5479	544	7	solutions	solution	NOUN
ejpam-5479	544	8	for	for	ADP
ejpam-5479	544	9	the	the	DET
ejpam-5479	544	10	quadratic	quadratic	ADJ
ejpam-5479	544	11	mixed	mix	VERB
ejpam-5479	544	12	-	-	PUNCT
ejpam-5479	544	13	parity	parity	NOUN
ejpam-5479	544	14	helmholtz	helmholtz	NOUN
ejpam-5479	544	15	–	–	PUNCT
ejpam-5479	544	16	duffing	duffing	NOUN
ejpam-5479	544	17	oscillator	oscillator	NOUN
ejpam-5479	544	18	by	by	ADP
ejpam-5479	544	19	bifurcation	bifurcation	NOUN
ejpam-5479	544	20	theory	theory	NOUN
ejpam-5479	544	21	of	of	ADP
ejpam-5479	544	22	dynamical	dynamical	ADJ
ejpam-5479	544	23	systems	system	NOUN
ejpam-5479	544	24	.	.	PUNCT
ejpam-5479	545	1	chaos	chaos	NOUN
ejpam-5479	545	2	,	,	PUNCT
ejpam-5479	545	3	solitons	soliton	NOUN
ejpam-5479	545	4	&	&	CCONJ
ejpam-5479	545	5	fractals	fractal	NOUN
ejpam-5479	545	6	,	,	PUNCT
ejpam-5479	545	7	81(a):68–77	81(a):68–77	NUM
ejpam-5479	545	8	,	,	PUNCT
ejpam-5479	545	9	2015	2015	NUM
ejpam-5479	545	10	.	.	PUNCT
ejpam-5479	546	1	[	[	X
ejpam-5479	546	2	53	53	NUM
ejpam-5479	546	3	]	]	PUNCT
ejpam-5479	546	4	tian	tian	ADJ
ejpam-5479	546	5	y.	y.	PROPN
ejpam-5479	546	6	frequency	frequency	NOUN
ejpam-5479	546	7	formula	formula	NOUN
ejpam-5479	546	8	for	for	ADP
ejpam-5479	546	9	a	a	DET
ejpam-5479	546	10	class	class	NOUN
ejpam-5479	546	11	of	of	ADP
ejpam-5479	546	12	fractal	fractal	ADJ
ejpam-5479	546	13	vibration	vibration	NOUN
ejpam-5479	546	14	system	system	NOUN
ejpam-5479	546	15	.	.	PUNCT
ejpam-5479	547	1	reports	report	NOUN
ejpam-5479	547	2	in	in	ADP
ejpam-5479	547	3	mechanical	mechanical	ADJ
ejpam-5479	547	4	engineering	engineering	NOUN
ejpam-5479	547	5	,	,	PUNCT
ejpam-5479	547	6	3(1):55–61	3(1):55–61	NUM
ejpam-5479	547	7	,	,	PUNCT
ejpam-5479	547	8	2022	2022	NUM
ejpam-5479	547	9	.	.	PUNCT
ejpam-5479	548	1	[	[	X
ejpam-5479	548	2	54	54	NUM
ejpam-5479	548	3	]	]	PUNCT
ejpam-5479	548	4	tian	tian	PROPN
ejpam-5479	548	5	y.	y.	PROPN
ejpam-5479	548	6	and	and	CCONJ
ejpam-5479	548	7	wang	wang	PROPN
ejpam-5479	548	8	z.	z.	PROPN
ejpam-5479	549	1	a	a	DET
ejpam-5479	549	2	new	new	ADJ
ejpam-5479	549	3	multiple	multiple	ADJ
ejpam-5479	549	4	integral	integral	ADJ
ejpam-5479	549	5	inequality	inequality	NOUN
ejpam-5479	549	6	and	and	CCONJ
ejpam-5479	549	7	its	its	PRON
ejpam-5479	549	8	application	application	NOUN
ejpam-5479	549	9	to	to	PART
ejpam-5479	549	10	stability	stability	VERB
ejpam-5479	549	11	analysis	analysis	NOUN
ejpam-5479	549	12	of	of	ADP
ejpam-5479	549	13	time	time	NOUN
ejpam-5479	549	14	-	-	PUNCT
ejpam-5479	549	15	delay	delay	NOUN
ejpam-5479	549	16	systems	system	NOUN
ejpam-5479	549	17	.	.	PUNCT
ejpam-5479	550	1	applied	apply	VERB
ejpam-5479	550	2	mathematics	mathematics	NOUN
ejpam-5479	550	3	letters	letter	NOUN
ejpam-5479	550	4	,	,	PUNCT
ejpam-5479	550	5	105:106325	105:106325	NUM
ejpam-5479	550	6	,	,	PUNCT
ejpam-5479	550	7	2020	2020	NUM
ejpam-5479	550	8	.	.	PUNCT
ejpam-5479	551	1	[	[	X
ejpam-5479	551	2	55	55	NUM
ejpam-5479	551	3	]	]	X
ejpam-5479	551	4	tian	tian	PROPN
ejpam-5479	551	5	y.	y.	PROPN
ejpam-5479	551	6	and	and	CCONJ
ejpam-5479	551	7	wang	wang	PROPN
ejpam-5479	551	8	z.	z.	PROPN
ejpam-5479	551	9	composite	composite	PROPN
ejpam-5479	551	10	slack	slack	NOUN
ejpam-5479	551	11	-	-	PUNCT
ejpam-5479	551	12	matrix	matrix	NOUN
ejpam-5479	551	13	-	-	PUNCT
ejpam-5479	551	14	based	base	VERB
ejpam-5479	551	15	integral	integral	ADJ
ejpam-5479	551	16	inequality	inequality	NOUN
ejpam-5479	551	17	and	and	CCONJ
ejpam-5479	551	18	its	its	PRON
ejpam-5479	551	19	application	application	NOUN
ejpam-5479	551	20	to	to	PART
ejpam-5479	551	21	stability	stability	VERB
ejpam-5479	551	22	analysis	analysis	NOUN
ejpam-5479	551	23	of	of	ADP
ejpam-5479	551	24	time	time	NOUN
ejpam-5479	551	25	-	-	PUNCT
ejpam-5479	551	26	delay	delay	NOUN
ejpam-5479	551	27	systems	system	NOUN
ejpam-5479	551	28	.	.	PUNCT
ejpam-5479	552	1	applied	apply	VERB
ejpam-5479	552	2	mathematics	mathematics	NOUN
ejpam-5479	552	3	letters	letter	NOUN
ejpam-5479	552	4	,	,	PUNCT
ejpam-5479	552	5	120:107252	120:107252	NUM
ejpam-5479	552	6	,	,	PUNCT
ejpam-5479	552	7	2021	2021	NUM
ejpam-5479	552	8	.	.	PUNCT
ejpam-5479	553	1	[	[	X
ejpam-5479	553	2	56	56	NUM
ejpam-5479	553	3	]	]	X
ejpam-5479	553	4	ren	ren	PROPN
ejpam-5479	553	5	z.	z.	PROPN
ejpam-5479	553	6	theoretical	theoretical	ADJ
ejpam-5479	553	7	basis	basis	NOUN
ejpam-5479	553	8	of	of	ADP
ejpam-5479	553	9	he	he	PRON
ejpam-5479	553	10	’s	’	VERB
ejpam-5479	553	11	frequency	frequency	NOUN
ejpam-5479	553	12	-	-	PUNCT
ejpam-5479	553	13	amplitude	amplitude	NOUN
ejpam-5479	553	14	formulation	formulation	NOUN
ejpam-5479	553	15	for	for	ADP
ejpam-5479	553	16	nonlinear	nonlinear	ADJ
ejpam-5479	553	17	oscillators	oscillator	NOUN
ejpam-5479	553	18	.	.	PUNCT
ejpam-5479	554	1	nonlinear	nonlinear	ADJ
ejpam-5479	554	2	science	science	PROPN
ejpam-5479	554	3	letters	letter	NOUN
ejpam-5479	554	4	a	a	PRON
ejpam-5479	554	5	,	,	PUNCT
ejpam-5479	554	6	9(1):86–90	9(1):86–90	NUM
ejpam-5479	554	7	,	,	PUNCT
ejpam-5479	554	8	2018	2018	NUM
ejpam-5479	554	9	.	.	PUNCT
ejpam-5479	555	1	[	[	X
ejpam-5479	555	2	57	57	NUM
ejpam-5479	555	3	]	]	X
ejpam-5479	555	4	ren	ren	PROPN
ejpam-5479	555	5	z	z	PROPN
ejpam-5479	555	6	-	-	PROPN
ejpam-5479	555	7	f.	f.	PROPN
ejpam-5479	555	8	,	,	PUNCT
ejpam-5479	555	9	liu	liu	PROPN
ejpam-5479	555	10	g	g	PROPN
ejpam-5479	555	11	-	-	PUNCT
ejpam-5479	555	12	q.	q.	PROPN
ejpam-5479	555	13	,	,	PUNCT
ejpam-5479	555	14	kang	kang	PROPN
ejpam-5479	555	15	y	y	PROPN
ejpam-5479	555	16	-	-	PUNCT
ejpam-5479	555	17	x.	x.	PROPN
ejpam-5479	555	18	,	,	PUNCT
ejpam-5479	555	19	fan	fan	PROPN
ejpam-5479	555	20	h	h	PROPN
ejpam-5479	555	21	-	-	PUNCT
ejpam-5479	555	22	y.	y.	PROPN
ejpam-5479	555	23	,	,	PUNCT
ejpam-5479	555	24	li	li	PROPN
ejpam-5479	555	25	h	h	PROPN
ejpam-5479	555	26	-	-	PUNCT
ejpam-5479	555	27	m.	m.	NOUN
ejpam-5479	555	28	,	,	PUNCT
ejpam-5479	555	29	ren	ren	PROPN
ejpam-5479	555	30	x	x	PROPN
ejpam-5479	555	31	-	-	PROPN
ejpam-5479	555	32	d.	d.	PROPN
ejpam-5479	555	33	,	,	PUNCT
ejpam-5479	555	34	and	and	CCONJ
ejpam-5479	555	35	gui	gui	PROPN
ejpam-5479	555	36	w	w	PROPN
ejpam-5479	555	37	-	-	PUNCT
ejpam-5479	555	38	k.	k.	NOUN
ejpam-5479	555	39	application	application	NOUN
ejpam-5479	555	40	of	of	ADP
ejpam-5479	555	41	he	he	PRON
ejpam-5479	555	42	’s	’s	PART
ejpam-5479	555	43	amplitude	amplitude	NOUN
ejpam-5479	555	44	-	-	PUNCT
ejpam-5479	555	45	frequency	frequency	NOUN
ejpam-5479	555	46	formulation	formulation	NOUN
ejpam-5479	555	47	to	to	AUX
ejpam-5479	555	48	nonlinear	nonlinear	ADJ
ejpam-5479	555	49	oscillators	oscillator	NOUN
ejpam-5479	555	50	with	with	ADP
ejpam-5479	555	51	discontinuities	discontinuity	NOUN
ejpam-5479	555	52	.	.	PUNCT
ejpam-5479	556	1	physica	physica	PROPN
ejpam-5479	556	2	scripta	scripta	PROPN
ejpam-5479	556	3	,	,	PUNCT
ejpam-5479	556	4	80(4):045003	80(4):045003	NUM
ejpam-5479	556	5	,	,	PUNCT
ejpam-5479	556	6	2009	2009	NUM
ejpam-5479	556	7	.	.	PUNCT