id	sid	tid	token	lemma	pos
ejpam-4306	1	1	european	european	PROPN
ejpam-4306	1	2	journal	journal	PROPN
ejpam-4306	1	3	of	of	ADP
ejpam-4306	1	4	pure	pure	ADJ
ejpam-4306	1	5	and	and	CCONJ
ejpam-4306	1	6	applied	apply	VERB
ejpam-4306	1	7	mathematics	mathematic	NOUN
ejpam-4306	1	8	vol	vol	NOUN
ejpam-4306	1	9	.	.	PROPN
ejpam-4306	2	1	15	15	NUM
ejpam-4306	2	2	,	,	PUNCT
ejpam-4306	2	3	no	no	INTJ
ejpam-4306	2	4	.	.	NOUN
ejpam-4306	2	5	2	2	NUM
ejpam-4306	2	6	,	,	PUNCT
ejpam-4306	2	7	2022	2022	NUM
ejpam-4306	2	8	,	,	PUNCT
ejpam-4306	2	9	496	496	NUM
ejpam-4306	2	10	-	-	SYM
ejpam-4306	2	11	510	510	NUM
ejpam-4306	2	12	issn	issn	PROPN
ejpam-4306	2	13	1307	1307	NUM
ejpam-4306	2	14	-	-	SYM
ejpam-4306	2	15	5543	5543	NUM
ejpam-4306	2	16	–	–	PUNCT
ejpam-4306	2	17	ejpam.com	ejpam.com	X
ejpam-4306	2	18	published	publish	VERB
ejpam-4306	2	19	by	by	ADP
ejpam-4306	2	20	new	new	PROPN
ejpam-4306	2	21	york	york	PROPN
ejpam-4306	2	22	business	business	PROPN
ejpam-4306	2	23	global	global	ADJ
ejpam-4306	2	24	exact	exact	ADJ
ejpam-4306	2	25	solution	solution	NOUN
ejpam-4306	2	26	for	for	ADP
ejpam-4306	2	27	nonlinear	nonlinear	ADJ
ejpam-4306	2	28	oscillators	oscillator	NOUN
ejpam-4306	2	29	with	with	ADP
ejpam-4306	2	30	coordinate	coordinate	NOUN
ejpam-4306	2	31	-	-	PUNCT
ejpam-4306	2	32	dependent	dependent	ADJ
ejpam-4306	2	33	mass	mass	NOUN
ejpam-4306	2	34	ata	ata	PROPN
ejpam-4306	2	35	abuas’ad1	abuas’ad1	PROPN
ejpam-4306	2	36	,	,	PUNCT
ejpam-4306	2	37	jihad	jihad	VERB
ejpam-4306	2	38	asad2,∗	asad2,∗	PROPN
ejpam-4306	2	39	1	1	NUM
ejpam-4306	2	40	department	department	NOUN
ejpam-4306	2	41	of	of	ADP
ejpam-4306	2	42	applied	apply	VERB
ejpam-4306	2	43	mathematics	mathematic	NOUN
ejpam-4306	2	44	,	,	PUNCT
ejpam-4306	2	45	faculty	faculty	NOUN
ejpam-4306	2	46	of	of	ADP
ejpam-4306	2	47	applied	apply	VERB
ejpam-4306	2	48	science	science	NOUN
ejpam-4306	2	49	,	,	PUNCT
ejpam-4306	2	50	palestine	palestine	PROPN
ejpam-4306	2	51	technical	technical	PROPN
ejpam-4306	2	52	university	university	PROPN
ejpam-4306	2	53	-kadoorie	-kadoorie	PROPN
ejpam-4306	2	54	,	,	PUNCT
ejpam-4306	2	55	tulkarm	tulkarm	NOUN
ejpam-4306	2	56	,	,	PUNCT
ejpam-4306	2	57	palestine	palestine	PROPN
ejpam-4306	2	58	2	2	NUM
ejpam-4306	2	59	department	department	NOUN
ejpam-4306	2	60	of	of	ADP
ejpam-4306	2	61	physics	physics	PROPN
ejpam-4306	2	62	,	,	PUNCT
ejpam-4306	2	63	faculty	faculty	NOUN
ejpam-4306	2	64	of	of	ADP
ejpam-4306	2	65	applied	apply	VERB
ejpam-4306	2	66	science	science	NOUN
ejpam-4306	2	67	,	,	PUNCT
ejpam-4306	2	68	palestine	palestine	PROPN
ejpam-4306	2	69	technical	technical	PROPN
ejpam-4306	2	70	university	university	PROPN
ejpam-4306	2	71	-kadoorie	-kadoorie	PROPN
ejpam-4306	2	72	,	,	PUNCT
ejpam-4306	2	73	tulkarm	tulkarm	NOUN
ejpam-4306	2	74	,	,	PUNCT
ejpam-4306	2	75	palestine	palestine	PROPN
ejpam-4306	2	76	abstract	abstract	NOUN
ejpam-4306	2	77	.	.	PUNCT
ejpam-4306	3	1	in	in	ADP
ejpam-4306	3	2	this	this	DET
ejpam-4306	3	3	work	work	NOUN
ejpam-4306	3	4	,	,	PUNCT
ejpam-4306	3	5	we	we	PRON
ejpam-4306	3	6	aim	aim	VERB
ejpam-4306	3	7	to	to	PART
ejpam-4306	3	8	obtain	obtain	VERB
ejpam-4306	3	9	an	an	DET
ejpam-4306	3	10	exact	exact	ADJ
ejpam-4306	3	11	solution	solution	NOUN
ejpam-4306	3	12	for	for	ADP
ejpam-4306	3	13	a	a	DET
ejpam-4306	3	14	nonlinear	nonlinear	ADJ
ejpam-4306	3	15	oscillator	oscillator	NOUN
ejpam-4306	3	16	with	with	ADP
ejpam-4306	3	17	coordinate	coordinate	NOUN
ejpam-4306	3	18	positiondependent	positiondependent	ADJ
ejpam-4306	3	19	mass	mass	PROPN
ejpam-4306	3	20	.	.	PUNCT
ejpam-4306	4	1	the	the	DET
ejpam-4306	4	2	equation	equation	NOUN
ejpam-4306	4	3	of	of	ADP
ejpam-4306	4	4	motion	motion	NOUN
ejpam-4306	4	5	of	of	ADP
ejpam-4306	4	6	the	the	DET
ejpam-4306	4	7	nonlinear	nonlinear	ADJ
ejpam-4306	4	8	oscillator	oscillator	NOUN
ejpam-4306	4	9	under	under	ADP
ejpam-4306	4	10	investigation	investigation	NOUN
ejpam-4306	4	11	becomes	become	VERB
ejpam-4306	4	12	exact	exact	ADJ
ejpam-4306	4	13	after	after	ADP
ejpam-4306	4	14	making	make	VERB
ejpam-4306	4	15	reduction	reduction	NOUN
ejpam-4306	4	16	of	of	ADP
ejpam-4306	4	17	order	order	NOUN
ejpam-4306	4	18	.	.	PUNCT
ejpam-4306	5	1	the	the	DET
ejpam-4306	5	2	obtained	obtain	VERB
ejpam-4306	5	3	solution	solution	NOUN
ejpam-4306	5	4	was	be	AUX
ejpam-4306	5	5	expressed	express	VERB
ejpam-4306	5	6	in	in	ADP
ejpam-4306	5	7	terms	term	NOUN
ejpam-4306	5	8	of	of	ADP
ejpam-4306	5	9	position	position	NOUN
ejpam-4306	5	10	and	and	CCONJ
ejpam-4306	5	11	time	time	NOUN
ejpam-4306	5	12	.	.	PUNCT
ejpam-4306	6	1	initial	initial	ADJ
ejpam-4306	6	2	conditions	condition	NOUN
ejpam-4306	6	3	were	be	AUX
ejpam-4306	6	4	applied	apply	VERB
ejpam-4306	6	5	,	,	PUNCT
ejpam-4306	6	6	in	in	ADP
ejpam-4306	6	7	addition	addition	NOUN
ejpam-4306	6	8	to	to	ADP
ejpam-4306	6	9	modified	modify	VERB
ejpam-4306	6	10	initial	initial	ADJ
ejpam-4306	6	11	condition	condition	NOUN
ejpam-4306	6	12	.	.	PUNCT
ejpam-4306	7	1	finally	finally	ADV
ejpam-4306	7	2	,	,	PUNCT
ejpam-4306	7	3	fixed	fix	VERB
ejpam-4306	7	4	points	point	NOUN
ejpam-4306	7	5	where	where	SCONJ
ejpam-4306	7	6	studied	study	VERB
ejpam-4306	7	7	with	with	ADP
ejpam-4306	7	8	their	their	PRON
ejpam-4306	7	9	stability	stability	NOUN
ejpam-4306	7	10	,	,	PUNCT
ejpam-4306	7	11	and	and	CCONJ
ejpam-4306	7	12	some	some	DET
ejpam-4306	7	13	plots	plot	NOUN
ejpam-4306	7	14	describing	describe	VERB
ejpam-4306	7	15	the	the	DET
ejpam-4306	7	16	system	system	NOUN
ejpam-4306	7	17	where	where	SCONJ
ejpam-4306	7	18	presented	present	VERB
ejpam-4306	7	19	.	.	PUNCT
ejpam-4306	8	1	2020	2020	NUM
ejpam-4306	8	2	mathematics	mathematics	PROPN
ejpam-4306	8	3	subject	subject	NOUN
ejpam-4306	8	4	classifications	classification	NOUN
ejpam-4306	8	5	:	:	PUNCT
ejpam-4306	8	6	34d10	34d10	NUM
ejpam-4306	8	7	,	,	PUNCT
ejpam-4306	8	8	34l15	34l15	NUM
ejpam-4306	8	9	,	,	PUNCT
ejpam-4306	8	10	34d20	34d20	NUM
ejpam-4306	8	11	,	,	PUNCT
ejpam-4306	8	12	37c25	37c25	NUM
ejpam-4306	8	13	,	,	PUNCT
ejpam-4306	8	14	31a15	31a15	NUM
ejpam-4306	8	15	,	,	PUNCT
ejpam-4306	8	16	37m05	37m05	NUM
ejpam-4306	8	17	,	,	PUNCT
ejpam-4306	8	18	key	key	ADJ
ejpam-4306	8	19	words	word	NOUN
ejpam-4306	8	20	and	and	CCONJ
ejpam-4306	8	21	phrases	phrase	NOUN
ejpam-4306	8	22	:	:	PUNCT
ejpam-4306	8	23	homotopoty	homotopoty	NOUN
ejpam-4306	8	24	perturbation	perturbation	NOUN
ejpam-4306	8	25	,	,	PUNCT
ejpam-4306	8	26	equilibrium	equilibrium	NOUN
ejpam-4306	8	27	(	(	PUNCT
ejpam-4306	8	28	fixed	fix	VERB
ejpam-4306	8	29	)	)	PUNCT
ejpam-4306	8	30	points	point	NOUN
ejpam-4306	8	31	,	,	PUNCT
ejpam-4306	8	32	simulation	simulation	NOUN
ejpam-4306	8	33	,	,	PUNCT
ejpam-4306	8	34	stability	stability	NOUN
ejpam-4306	8	35	,	,	PUNCT
ejpam-4306	8	36	conservative	conservative	ADJ
ejpam-4306	8	37	,	,	PUNCT
ejpam-4306	8	38	potential	potential	ADJ
ejpam-4306	8	39	function	function	NOUN
ejpam-4306	8	40	,	,	PUNCT
ejpam-4306	8	41	exact	exact	ADJ
ejpam-4306	8	42	differential	differential	ADJ
ejpam-4306	8	43	equation	equation	NOUN
ejpam-4306	8	44	,	,	PUNCT
ejpam-4306	8	45	reduction	reduction	NOUN
ejpam-4306	8	46	of	of	ADP
ejpam-4306	8	47	order	order	NOUN
ejpam-4306	8	48	,	,	PUNCT
ejpam-4306	8	49	center	center	NOUN
ejpam-4306	8	50	point	point	NOUN
ejpam-4306	8	51	1	1	NUM
ejpam-4306	8	52	.	.	PUNCT
ejpam-4306	9	1	introduction	introduction	NOUN
ejpam-4306	9	2	simple	simple	ADJ
ejpam-4306	9	3	oscillating	oscillate	VERB
ejpam-4306	9	4	systems	system	NOUN
ejpam-4306	9	5	are	be	AUX
ejpam-4306	9	6	modeled	model	VERB
ejpam-4306	9	7	in	in	ADP
ejpam-4306	9	8	general	general	ADJ
ejpam-4306	9	9	as	as	ADP
ejpam-4306	9	10	a	a	DET
ejpam-4306	9	11	mass	mass	NOUN
ejpam-4306	9	12	attached	attach	VERB
ejpam-4306	9	13	to	to	ADP
ejpam-4306	9	14	a	a	DET
ejpam-4306	9	15	spring	spring	NOUN
ejpam-4306	9	16	(	(	PUNCT
ejpam-4306	9	17	i.e.	i.e.	X
ejpam-4306	9	18	,	,	PUNCT
ejpam-4306	9	19	simple	simple	ADJ
ejpam-4306	9	20	oscillators	oscillator	NOUN
ejpam-4306	9	21	)	)	PUNCT
ejpam-4306	9	22	.	.	PUNCT
ejpam-4306	10	1	the	the	DET
ejpam-4306	10	2	equation	equation	NOUN
ejpam-4306	10	3	of	of	ADP
ejpam-4306	10	4	motion	motion	NOUN
ejpam-4306	10	5	describing	describe	VERB
ejpam-4306	10	6	such	such	ADJ
ejpam-4306	10	7	systems	system	NOUN
ejpam-4306	10	8	are	be	AUX
ejpam-4306	10	9	obtained	obtain	VERB
ejpam-4306	10	10	either	either	CCONJ
ejpam-4306	10	11	using	use	VERB
ejpam-4306	10	12	newtonian	newtonian	ADJ
ejpam-4306	10	13	mechanics	mechanic	NOUN
ejpam-4306	10	14	or	or	CCONJ
ejpam-4306	10	15	lagrangian	lagrangian	ADJ
ejpam-4306	10	16	method	method	NOUN
ejpam-4306	10	17	,	,	PUNCT
ejpam-4306	10	18	and	and	CCONJ
ejpam-4306	10	19	it	it	PRON
ejpam-4306	10	20	can	can	AUX
ejpam-4306	10	21	be	be	AUX
ejpam-4306	10	22	solved	solve	VERB
ejpam-4306	10	23	exactly	exactly	ADV
ejpam-4306	10	24	in	in	ADP
ejpam-4306	10	25	some	some	DET
ejpam-4306	10	26	simple	simple	ADJ
ejpam-4306	10	27	cases	case	NOUN
ejpam-4306	10	28	.	.	PUNCT
ejpam-4306	11	1	unfortunately	unfortunately	ADV
ejpam-4306	11	2	,	,	PUNCT
ejpam-4306	11	3	no	no	DET
ejpam-4306	11	4	such	such	ADJ
ejpam-4306	11	5	systems	system	NOUN
ejpam-4306	11	6	present	present	ADJ
ejpam-4306	11	7	in	in	ADP
ejpam-4306	11	8	the	the	DET
ejpam-4306	11	9	macroscopic	macroscopic	ADJ
ejpam-4306	11	10	world	world	NOUN
ejpam-4306	11	11	and	and	CCONJ
ejpam-4306	11	12	this	this	PRON
ejpam-4306	11	13	is	be	AUX
ejpam-4306	11	14	due	due	ADJ
ejpam-4306	11	15	to	to	ADP
ejpam-4306	11	16	dissipative	dissipative	ADJ
ejpam-4306	11	17	forces	force	NOUN
ejpam-4306	11	18	that	that	PRON
ejpam-4306	11	19	are	be	AUX
ejpam-4306	11	20	always	always	ADV
ejpam-4306	11	21	present	present	ADJ
ejpam-4306	11	22	in	in	ADP
ejpam-4306	11	23	nature	nature	NOUN
ejpam-4306	11	24	.	.	PUNCT
ejpam-4306	12	1	dissipative	dissipative	ADJ
ejpam-4306	12	2	forces	force	NOUN
ejpam-4306	12	3	can	can	AUX
ejpam-4306	12	4	be	be	AUX
ejpam-4306	12	5	ignored	ignore	VERB
ejpam-4306	12	6	if	if	SCONJ
ejpam-4306	12	7	they	they	PRON
ejpam-4306	12	8	have	have	VERB
ejpam-4306	12	9	small	small	ADJ
ejpam-4306	12	10	effects	effect	NOUN
ejpam-4306	12	11	,	,	PUNCT
ejpam-4306	12	12	but	but	CCONJ
ejpam-4306	12	13	in	in	ADP
ejpam-4306	12	14	many	many	ADJ
ejpam-4306	12	15	cases	case	NOUN
ejpam-4306	12	16	they	they	PRON
ejpam-4306	12	17	lead	lead	VERB
ejpam-4306	12	18	to	to	ADP
ejpam-4306	12	19	damping	damp	VERB
ejpam-4306	12	20	oscillators	oscillator	NOUN
ejpam-4306	12	21	.	.	PUNCT
ejpam-4306	13	1	linear	linear	ADJ
ejpam-4306	13	2	oscillators	oscillator	NOUN
ejpam-4306	13	3	are	be	AUX
ejpam-4306	13	4	those	those	PRON
ejpam-4306	13	5	that	that	PRON
ejpam-4306	13	6	oscillate	oscillate	VERB
ejpam-4306	13	7	with	with	ADP
ejpam-4306	13	8	one	one	NUM
ejpam-4306	13	9	frequency	frequency	NOUN
ejpam-4306	13	10	and	and	CCONJ
ejpam-4306	13	11	its	its	PRON
ejpam-4306	13	12	motion	motion	NOUN
ejpam-4306	13	13	is	be	AUX
ejpam-4306	13	14	sinusoidal	sinusoidal	ADJ
ejpam-4306	13	15	and	and	CCONJ
ejpam-4306	13	16	periodic	periodic	ADJ
ejpam-4306	13	17	,	,	PUNCT
ejpam-4306	13	18	for	for	ADP
ejpam-4306	13	19	more	more	ADJ
ejpam-4306	13	20	information	information	NOUN
ejpam-4306	13	21	related	relate	VERB
ejpam-4306	13	22	to	to	ADP
ejpam-4306	13	23	oscillators	oscillator	NOUN
ejpam-4306	13	24	(	(	PUNCT
ejpam-4306	13	25	simple	simple	ADJ
ejpam-4306	13	26	and	and	CCONJ
ejpam-4306	13	27	damped	damped	ADJ
ejpam-4306	13	28	)	)	PUNCT
ejpam-4306	13	29	we	we	PRON
ejpam-4306	13	30	advise	advise	VERB
ejpam-4306	13	31	interested	interested	ADJ
ejpam-4306	13	32	people	people	NOUN
ejpam-4306	13	33	to	to	PART
ejpam-4306	13	34	refer	refer	VERB
ejpam-4306	13	35	to	to	ADP
ejpam-4306	13	36	some	some	DET
ejpam-4306	13	37	classical	classical	ADJ
ejpam-4306	13	38	mechanics	mechanic	NOUN
ejpam-4306	13	39	texts	text	NOUN
ejpam-4306	13	40	[	[	X
ejpam-4306	13	41	5	5	NUM
ejpam-4306	13	42	,	,	PUNCT
ejpam-4306	13	43	9	9	NUM
ejpam-4306	13	44	,	,	PUNCT
ejpam-4306	13	45	10	10	NUM
ejpam-4306	13	46	]	]	PUNCT
ejpam-4306	13	47	.	.	PUNCT
ejpam-4306	14	1	nonlinear	nonlinear	ADJ
ejpam-4306	14	2	oscillators	oscillator	NOUN
ejpam-4306	14	3	result	result	VERB
ejpam-4306	14	4	in	in	ADP
ejpam-4306	14	5	complex	complex	ADJ
ejpam-4306	14	6	motion	motion	NOUN
ejpam-4306	14	7	and	and	CCONJ
ejpam-4306	14	8	there	there	PRON
ejpam-4306	14	9	are	be	VERB
ejpam-4306	14	10	mainly	mainly	ADV
ejpam-4306	14	11	two	two	NUM
ejpam-4306	14	12	important	important	ADJ
ejpam-4306	14	13	features	feature	NOUN
ejpam-4306	14	14	for	for	ADP
ejpam-4306	14	15	such	such	ADJ
ejpam-4306	14	16	systems	system	NOUN
ejpam-4306	14	17	:	:	PUNCT
ejpam-4306	14	18	as	as	SCONJ
ejpam-4306	14	19	the	the	DET
ejpam-4306	14	20	amplitude	amplitude	NOUN
ejpam-4306	14	21	increases	increase	VERB
ejpam-4306	14	22	then	then	ADV
ejpam-4306	14	23	the	the	DET
ejpam-4306	14	24	non	non	ADJ
ejpam-4306	14	25	linearity	linearity	PROPN
ejpam-4306	14	26	motion	motion	NOUN
ejpam-4306	14	27	becomes	become	VERB
ejpam-4306	14	28	more	more	ADV
ejpam-4306	14	29	important	important	ADJ
ejpam-4306	14	30	,	,	PUNCT
ejpam-4306	14	31	and	and	CCONJ
ejpam-4306	14	32	in	in	ADP
ejpam-4306	14	33	some	some	DET
ejpam-4306	14	34	cases	case	NOUN
ejpam-4306	14	35	,	,	PUNCT
ejpam-4306	14	36	the	the	DET
ejpam-4306	14	37	frequency	frequency	NOUN
ejpam-4306	14	38	will	will	AUX
ejpam-4306	14	39	change	change	VERB
ejpam-4306	14	40	with	with	ADP
ejpam-4306	14	41	amplitude	amplitude	NOUN
ejpam-4306	14	42	.	.	PUNCT
ejpam-4306	15	1	in	in	ADP
ejpam-4306	15	2	real	real	ADJ
ejpam-4306	15	3	∗corresponding	∗corresponde	VERB
ejpam-4306	15	4	author	author	NOUN
ejpam-4306	15	5	.	.	PUNCT
ejpam-4306	16	1	doi	doi	NOUN
ejpam-4306	16	2	:	:	PUNCT
ejpam-4306	16	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4306	https://doi.org/10.29020/nybg.ejpam.v15i2.4306	ADJ
ejpam-4306	16	4	email	email	NOUN
ejpam-4306	16	5	addresses	address	NOUN
ejpam-4306	16	6	:	:	PUNCT
ejpam-4306	16	7	a.asad@ptuk.edu.ps	a.asad@ptuk.edu.ps	PROPN
ejpam-4306	16	8	(	(	PUNCT
ejpam-4306	16	9	a.	a.	NOUN
ejpam-4306	16	10	abuas’ad	abuas’ad	PROPN
ejpam-4306	16	11	)	)	PUNCT
ejpam-4306	16	12	,	,	PUNCT
ejpam-4306	16	13	j.asad@ptuk.edu.ps	j.asad@ptuk.edu.ps	NOUN
ejpam-4306	16	14	(	(	PUNCT
ejpam-4306	16	15	j.	j.	PROPN
ejpam-4306	16	16	asad	asad	PROPN
ejpam-4306	16	17	)	)	PUNCT
ejpam-4306	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4306	17	1	496	496	NUM
ejpam-4306	18	1	©	©	ADP
ejpam-4306	18	2	2022	2022	NUM
ejpam-4306	18	3	ejpam	ejpam	VERB
ejpam-4306	18	4	all	all	DET
ejpam-4306	18	5	rights	right	NOUN
ejpam-4306	18	6	reserved	reserve	VERB
ejpam-4306	18	7	.	.	PUNCT
ejpam-4306	19	1	a.	a.	PROPN
ejpam-4306	19	2	abuas’ad	abuas’ad	PROPN
ejpam-4306	19	3	,	,	PUNCT
ejpam-4306	19	4	j.	j.	PROPN
ejpam-4306	19	5	asad	asad	PROPN
ejpam-4306	19	6	/	/	SYM
ejpam-4306	19	7	eur	eur	PROPN
ejpam-4306	19	8	.	.	PUNCT
ejpam-4306	20	1	j.	j.	PROPN
ejpam-4306	20	2	pure	pure	PROPN
ejpam-4306	20	3	appl	appl	PROPN
ejpam-4306	20	4	.	.	PROPN
ejpam-4306	20	5	math	math	PROPN
ejpam-4306	20	6	,	,	PUNCT
ejpam-4306	20	7	15	15	NUM
ejpam-4306	20	8	(	(	PUNCT
ejpam-4306	20	9	2	2	NUM
ejpam-4306	20	10	)	)	PUNCT
ejpam-4306	20	11	(	(	PUNCT
ejpam-4306	20	12	2022	2022	NUM
ejpam-4306	20	13	)	)	PUNCT
ejpam-4306	20	14	,	,	PUNCT
ejpam-4306	20	15	496	496	NUM
ejpam-4306	20	16	-	-	SYM
ejpam-4306	20	17	510	510	NUM
ejpam-4306	20	18	497	497	NUM
ejpam-4306	20	19	world	world	NOUN
ejpam-4306	20	20	one	one	PRON
ejpam-4306	20	21	can	can	AUX
ejpam-4306	20	22	find	find	VERB
ejpam-4306	20	23	many	many	ADJ
ejpam-4306	20	24	such	such	ADJ
ejpam-4306	20	25	nonlinear	nonlinear	ADJ
ejpam-4306	20	26	oscillators	oscillator	NOUN
ejpam-4306	20	27	and	and	CCONJ
ejpam-4306	20	28	one	one	PRON
ejpam-4306	20	29	has	have	VERB
ejpam-4306	20	30	to	to	PART
ejpam-4306	20	31	note	note	VERB
ejpam-4306	20	32	that	that	SCONJ
ejpam-4306	20	33	coupled	couple	VERB
ejpam-4306	20	34	nonlinear	nonlinear	ADJ
ejpam-4306	20	35	oscillators	oscillator	NOUN
ejpam-4306	20	36	are	be	AUX
ejpam-4306	20	37	a	a	DET
ejpam-4306	20	38	subject	subject	NOUN
ejpam-4306	20	39	founded	found	VERB
ejpam-4306	20	40	in	in	ADP
ejpam-4306	20	41	many	many	ADJ
ejpam-4306	20	42	branches	branch	NOUN
ejpam-4306	20	43	of	of	ADP
ejpam-4306	20	44	science	science	NOUN
ejpam-4306	20	45	as	as	ADP
ejpam-4306	20	46	:	:	PUNCT
ejpam-4306	20	47	biology	biology	NOUN
ejpam-4306	20	48	,	,	PUNCT
ejpam-4306	20	49	physics	physics	NOUN
ejpam-4306	20	50	,	,	PUNCT
ejpam-4306	20	51	and	and	CCONJ
ejpam-4306	20	52	many	many	ADJ
ejpam-4306	20	53	others	other	NOUN
ejpam-4306	20	54	.	.	PUNCT
ejpam-4306	21	1	in	in	ADP
ejpam-4306	21	2	literature	literature	NOUN
ejpam-4306	21	3	there	there	PRON
ejpam-4306	21	4	are	be	VERB
ejpam-4306	21	5	a	a	DET
ejpam-4306	21	6	lot	lot	NOUN
ejpam-4306	21	7	of	of	ADP
ejpam-4306	21	8	efforts	effort	NOUN
ejpam-4306	21	9	paid	pay	VERB
ejpam-4306	21	10	on	on	ADP
ejpam-4306	21	11	studying	study	VERB
ejpam-4306	21	12	these	these	DET
ejpam-4306	21	13	systems	system	NOUN
ejpam-4306	21	14	[	[	X
ejpam-4306	21	15	13	13	NUM
ejpam-4306	21	16	,	,	PUNCT
ejpam-4306	21	17	16	16	NUM
ejpam-4306	21	18	,	,	PUNCT
ejpam-4306	21	19	20	20	NUM
ejpam-4306	21	20	]	]	PUNCT
ejpam-4306	21	21	.	.	PUNCT
ejpam-4306	22	1	an	an	DET
ejpam-4306	22	2	important	important	ADJ
ejpam-4306	22	3	example	example	NOUN
ejpam-4306	22	4	is	be	AUX
ejpam-4306	22	5	the	the	DET
ejpam-4306	22	6	van	van	PROPN
ejpam-4306	22	7	der	der	ADJ
ejpam-4306	22	8	pol	pol	PROPN
ejpam-4306	22	9	oscillator	oscillator	NOUN
ejpam-4306	22	10	which	which	PRON
ejpam-4306	22	11	is	be	AUX
ejpam-4306	22	12	an	an	DET
ejpam-4306	22	13	oscillator	oscillator	NOUN
ejpam-4306	22	14	with	with	ADP
ejpam-4306	22	15	nonlinear	nonlinear	ADJ
ejpam-4306	22	16	damping	damping	NOUN
ejpam-4306	22	17	introduced	introduce	VERB
ejpam-4306	22	18	in	in	ADP
ejpam-4306	22	19	the	the	DET
ejpam-4306	22	20	1920	1920	NUM
ejpam-4306	22	21	’s	’s	NOUN
ejpam-4306	22	22	by	by	ADP
ejpam-4306	22	23	balthasar	balthasar	PROPN
ejpam-4306	22	24	van	van	PROPN
ejpam-4306	22	25	der	der	PROPN
ejpam-4306	22	26	pol	pol	PROPN
ejpam-4306	22	27	(	(	PUNCT
ejpam-4306	22	28	1889	1889	NUM
ejpam-4306	22	29	1959).the	1959).the	NUM
ejpam-4306	22	30	van	van	PROPN
ejpam-4306	22	31	der	der	PROPN
ejpam-4306	22	32	pol	pol	PROPN
ejpam-4306	22	33	oscillator	oscillator	NOUN
ejpam-4306	22	34	is	be	AUX
ejpam-4306	22	35	considered	consider	VERB
ejpam-4306	22	36	as	as	ADP
ejpam-4306	22	37	an	an	DET
ejpam-4306	22	38	example	example	NOUN
ejpam-4306	22	39	of	of	ADP
ejpam-4306	22	40	an	an	DET
ejpam-4306	22	41	oscillator	oscillator	NOUN
ejpam-4306	22	42	with	with	ADP
ejpam-4306	22	43	nonlinear	nonlinear	ADJ
ejpam-4306	22	44	damping	damping	NOUN
ejpam-4306	22	45	,	,	PUNCT
ejpam-4306	22	46	energy	energy	NOUN
ejpam-4306	22	47	being	be	AUX
ejpam-4306	22	48	dissipated	dissipate	VERB
ejpam-4306	22	49	at	at	ADP
ejpam-4306	22	50	large	large	ADJ
ejpam-4306	22	51	amplitudes	amplitude	NOUN
ejpam-4306	22	52	and	and	CCONJ
ejpam-4306	22	53	generated	generate	VERB
ejpam-4306	22	54	as	as	ADP
ejpam-4306	22	55	low	low	ADJ
ejpam-4306	22	56	amplitude	amplitude	NOUN
ejpam-4306	22	57	,	,	PUNCT
ejpam-4306	22	58	and	and	CCONJ
ejpam-4306	22	59	it	it	PRON
ejpam-4306	22	60	attracts	attract	VERB
ejpam-4306	22	61	the	the	DET
ejpam-4306	22	62	attention	attention	NOUN
ejpam-4306	22	63	of	of	ADP
ejpam-4306	22	64	many	many	ADJ
ejpam-4306	22	65	researchers	researcher	NOUN
ejpam-4306	22	66	where	where	SCONJ
ejpam-4306	22	67	many	many	ADJ
ejpam-4306	22	68	method	method	NOUN
ejpam-4306	22	69	have	have	AUX
ejpam-4306	22	70	been	be	AUX
ejpam-4306	22	71	applied	apply	VERB
ejpam-4306	22	72	in	in	ADP
ejpam-4306	22	73	dealing	deal	VERB
ejpam-4306	22	74	with	with	ADP
ejpam-4306	22	75	this	this	DET
ejpam-4306	22	76	oscillator	oscillator	NOUN
ejpam-4306	22	77	either	either	CCONJ
ejpam-4306	22	78	analytically	analytically	ADV
ejpam-4306	22	79	using	use	VERB
ejpam-4306	22	80	homotopy	homotopy	NOUN
ejpam-4306	22	81	analysis	analysis	NOUN
ejpam-4306	22	82	method	method	NOUN
ejpam-4306	22	83	(	(	PUNCT
ejpam-4306	22	84	ham	ham	NOUN
ejpam-4306	22	85	)	)	PUNCT
ejpam-4306	22	86	as	as	ADP
ejpam-4306	22	87	in[4	in[4	NOUN
ejpam-4306	22	88	,	,	PUNCT
ejpam-4306	22	89	14	14	NUM
ejpam-4306	22	90	]	]	PUNCT
ejpam-4306	22	91	.	.	PUNCT
ejpam-4306	23	1	homotopy	homotopy	NOUN
ejpam-4306	23	2	perturbation	perturbation	NOUN
ejpam-4306	23	3	method	method	NOUN
ejpam-4306	23	4	(	(	PUNCT
ejpam-4306	23	5	hpm	hpm	NOUN
ejpam-4306	23	6	)	)	PUNCT
ejpam-4306	23	7	as	as	ADP
ejpam-4306	23	8	in	in	ADP
ejpam-4306	23	9	[	[	X
ejpam-4306	23	10	18	18	NUM
ejpam-4306	23	11	]	]	PUNCT
ejpam-4306	23	12	or	or	CCONJ
ejpam-4306	23	13	numerically	numerically	ADV
ejpam-4306	23	14	using	use	VERB
ejpam-4306	23	15	for	for	ADP
ejpam-4306	23	16	example	example	NOUN
ejpam-4306	23	17	perturbation	perturbation	NOUN
ejpam-4306	23	18	algorithm	algorithm	NOUN
ejpam-4306	23	19	combining	combine	VERB
ejpam-4306	23	20	the	the	DET
ejpam-4306	23	21	method	method	NOUN
ejpam-4306	23	22	of	of	ADP
ejpam-4306	23	23	multiple	multiple	ADJ
ejpam-4306	23	24	scales	scale	NOUN
ejpam-4306	23	25	and	and	CCONJ
ejpam-4306	23	26	modified	modify	VERB
ejpam-4306	23	27	lindstedt	lindstedt	PROPN
ejpam-4306	23	28	–	–	PUNCT
ejpam-4306	23	29	poincare	poincare	PROPN
ejpam-4306	23	30	techniques	technique	NOUN
ejpam-4306	23	31	as	as	ADP
ejpam-4306	23	32	in	in	ADP
ejpam-4306	23	33	[	[	X
ejpam-4306	23	34	15	15	NUM
ejpam-4306	23	35	]	]	X
ejpam-4306	23	36	,	,	PUNCT
ejpam-4306	23	37	a	a	DET
ejpam-4306	23	38	domain	domain	NOUN
ejpam-4306	23	39	decomposition	decomposition	NOUN
ejpam-4306	23	40	method	method	NOUN
ejpam-4306	23	41	(	(	PUNCT
ejpam-4306	23	42	adm	adm	PROPN
ejpam-4306	23	43	)	)	PUNCT
ejpam-4306	23	44	as	as	ADP
ejpam-4306	23	45	in	in	ADP
ejpam-4306	23	46	[	[	X
ejpam-4306	23	47	2	2	NUM
ejpam-4306	23	48	,	,	PUNCT
ejpam-4306	23	49	8	8	NUM
ejpam-4306	23	50	]	]	PUNCT
ejpam-4306	23	51	and	and	CCONJ
ejpam-4306	23	52	many	many	ADJ
ejpam-4306	23	53	other	other	ADJ
ejpam-4306	23	54	methods	method	NOUN
ejpam-4306	23	55	.	.	PUNCT
ejpam-4306	24	1	nonlinear	nonlinear	ADJ
ejpam-4306	24	2	oscillations	oscillation	NOUN
ejpam-4306	24	3	have	have	AUX
ejpam-4306	24	4	been	be	AUX
ejpam-4306	24	5	of	of	ADP
ejpam-4306	24	6	paramount	paramount	ADJ
ejpam-4306	24	7	importance	importance	NOUN
ejpam-4306	24	8	in	in	ADP
ejpam-4306	24	9	practical	practical	ADJ
ejpam-4306	24	10	engineering	engineering	NOUN
ejpam-4306	24	11	,	,	PUNCT
ejpam-4306	24	12	physics	physic	NOUN
ejpam-4306	24	13	,	,	PUNCT
ejpam-4306	24	14	applied	apply	VERB
ejpam-4306	24	15	mathematics	mathematic	NOUN
ejpam-4306	24	16	,	,	PUNCT
ejpam-4306	24	17	and	and	CCONJ
ejpam-4306	24	18	several	several	ADJ
ejpam-4306	24	19	real	real	ADJ
ejpam-4306	24	20	-	-	PUNCT
ejpam-4306	24	21	world	world	NOUN
ejpam-4306	24	22	requirements	requirement	NOUN
ejpam-4306	24	23	for	for	ADP
ejpam-4306	24	24	many	many	ADJ
ejpam-4306	24	25	years	year	NOUN
ejpam-4306	24	26	.	.	PUNCT
ejpam-4306	25	1	in	in	ADP
ejpam-4306	25	2	literature	literature	NOUN
ejpam-4306	25	3	,	,	PUNCT
ejpam-4306	25	4	one	one	PRON
ejpam-4306	25	5	can	can	AUX
ejpam-4306	25	6	find	find	VERB
ejpam-4306	25	7	many	many	ADJ
ejpam-4306	25	8	various	various	ADJ
ejpam-4306	25	9	analytical	analytical	ADJ
ejpam-4306	25	10	approaches	approach	NOUN
ejpam-4306	25	11	for	for	ADP
ejpam-4306	25	12	solving	solve	VERB
ejpam-4306	25	13	nonlinear	nonlinear	ADJ
ejpam-4306	25	14	systems	system	NOUN
ejpam-4306	25	15	,	,	PUNCT
ejpam-4306	25	16	such	such	ADJ
ejpam-4306	25	17	as	as	ADP
ejpam-4306	25	18	the	the	DET
ejpam-4306	25	19	iteration	iteration	NOUN
ejpam-4306	25	20	perturbation	perturbation	NOUN
ejpam-4306	25	21	method	method	NOUN
ejpam-4306	25	22	[	[	X
ejpam-4306	25	23	7	7	NUM
ejpam-4306	25	24	]	]	PUNCT
ejpam-4306	25	25	,	,	PUNCT
ejpam-4306	25	26	the	the	DET
ejpam-4306	25	27	homotopy	homotopy	NOUN
ejpam-4306	25	28	perturbation	perturbation	NOUN
ejpam-4306	25	29	method	method	NOUN
ejpam-4306	25	30	(	(	PUNCT
ejpam-4306	25	31	hmp	hmp	PROPN
ejpam-4306	25	32	)	)	PUNCT
ejpam-4306	26	1	[	[	X
ejpam-4306	26	2	21	21	NUM
ejpam-4306	26	3	]	]	PUNCT
ejpam-4306	26	4	,	,	PUNCT
ejpam-4306	26	5	the	the	DET
ejpam-4306	26	6	variational	variational	ADJ
ejpam-4306	26	7	method	method	NOUN
ejpam-4306	26	8	[	[	X
ejpam-4306	26	9	17	17	NUM
ejpam-4306	26	10	]	]	PUNCT
ejpam-4306	26	11	,	,	PUNCT
ejpam-4306	26	12	and	and	CCONJ
ejpam-4306	26	13	many	many	ADJ
ejpam-4306	26	14	other	other	ADJ
ejpam-4306	26	15	methods[6	methods[6	PRON
ejpam-4306	26	16	]	]	PUNCT
ejpam-4306	26	17	.	.	PUNCT
ejpam-4306	27	1	interested	interested	ADJ
ejpam-4306	27	2	researchers	researcher	NOUN
ejpam-4306	27	3	in	in	ADP
ejpam-4306	27	4	this	this	DET
ejpam-4306	27	5	topic	topic	NOUN
ejpam-4306	27	6	can	can	AUX
ejpam-4306	27	7	refer	refer	VERB
ejpam-4306	27	8	to	to	ADP
ejpam-4306	27	9	[	[	X
ejpam-4306	27	10	12	12	NUM
ejpam-4306	27	11	,	,	PUNCT
ejpam-4306	27	12	12	12	NUM
ejpam-4306	27	13	]	]	PUNCT
ejpam-4306	27	14	therein	therein	ADV
ejpam-4306	27	15	.	.	PUNCT
ejpam-4306	28	1	in	in	ADP
ejpam-4306	28	2	principle	principle	NOUN
ejpam-4306	28	3	,	,	PUNCT
ejpam-4306	28	4	the	the	DET
ejpam-4306	28	5	solution	solution	NOUN
ejpam-4306	28	6	for	for	ADP
ejpam-4306	28	7	such	such	ADJ
ejpam-4306	28	8	nonlinear	nonlinear	ADJ
ejpam-4306	28	9	oscillators	oscillator	NOUN
ejpam-4306	28	10	is	be	AUX
ejpam-4306	28	11	difficult	difficult	ADJ
ejpam-4306	28	12	to	to	PART
ejpam-4306	28	13	obtain	obtain	VERB
ejpam-4306	28	14	analytically	analytically	ADV
ejpam-4306	28	15	and	and	CCONJ
ejpam-4306	28	16	researchers	researcher	NOUN
ejpam-4306	28	17	resort	resort	VERB
ejpam-4306	28	18	to	to	PART
ejpam-4306	28	19	use	use	VERB
ejpam-4306	28	20	different	different	ADJ
ejpam-4306	28	21	numerical	numerical	ADJ
ejpam-4306	28	22	methods	method	NOUN
ejpam-4306	28	23	[	[	X
ejpam-4306	28	24	1	1	NUM
ejpam-4306	28	25	,	,	PUNCT
ejpam-4306	28	26	3	3	NUM
ejpam-4306	28	27	,	,	PUNCT
ejpam-4306	28	28	21	21	NUM
ejpam-4306	28	29	,	,	PUNCT
ejpam-4306	28	30	21	21	NUM
ejpam-4306	28	31	]	]	PUNCT
ejpam-4306	28	32	.	.	PUNCT
ejpam-4306	29	1	in	in	ADP
ejpam-4306	29	2	[	[	X
ejpam-4306	29	3	21	21	NUM
ejpam-4306	29	4	]	]	PUNCT
ejpam-4306	29	5	the	the	DET
ejpam-4306	29	6	authors	author	NOUN
ejpam-4306	29	7	consider	consider	VERB
ejpam-4306	29	8	a	a	DET
ejpam-4306	29	9	nonlinear	nonlinear	ADJ
ejpam-4306	29	10	oscillator	oscillator	NOUN
ejpam-4306	29	11	with	with	ADP
ejpam-4306	29	12	coordinate	coordinate	NOUN
ejpam-4306	29	13	-	-	PUNCT
ejpam-4306	29	14	dependent	dependent	ADJ
ejpam-4306	29	15	mass	mass	NOUN
ejpam-4306	29	16	,	,	PUNCT
ejpam-4306	29	17	where	where	SCONJ
ejpam-4306	29	18	they	they	PRON
ejpam-4306	29	19	proposed	propose	VERB
ejpam-4306	29	20	a	a	DET
ejpam-4306	29	21	nonlinear	nonlinear	ADJ
ejpam-4306	29	22	oscillator	oscillator	NOUN
ejpam-4306	29	23	with	with	ADP
ejpam-4306	29	24	negative	negative	ADJ
ejpam-4306	29	25	coefficient	coefficient	NOUN
ejpam-4306	29	26	of	of	ADP
ejpam-4306	29	27	linear	linear	ADJ
ejpam-4306	29	28	term	term	NOUN
ejpam-4306	29	29	(	(	PUNCT
ejpam-4306	29	30	see	see	VERB
ejpam-4306	29	31	eq	eq	NOUN
ejpam-4306	29	32	.	.	NOUN
ejpam-4306	29	33	3	3	NUM
ejpam-4306	29	34	in	in	ADP
ejpam-4306	29	35	[	[	X
ejpam-4306	29	36	21	21	NUM
ejpam-4306	29	37	]	]	PUNCT
ejpam-4306	29	38	)	)	PUNCT
ejpam-4306	29	39	and	and	CCONJ
ejpam-4306	29	40	apply	apply	VERB
ejpam-4306	29	41	the	the	DET
ejpam-4306	29	42	homotopy	homotopy	NOUN
ejpam-4306	29	43	perturbation	perturbation	NOUN
ejpam-4306	29	44	method	method	NOUN
ejpam-4306	29	45	to	to	PART
ejpam-4306	29	46	find	find	VERB
ejpam-4306	29	47	an	an	DET
ejpam-4306	29	48	approximate	approximate	ADJ
ejpam-4306	29	49	period	period	NOUN
ejpam-4306	29	50	for	for	ADP
ejpam-4306	29	51	their	their	PRON
ejpam-4306	29	52	equation	equation	NOUN
ejpam-4306	29	53	.	.	PUNCT
ejpam-4306	30	1	in	in	ADP
ejpam-4306	30	2	this	this	DET
ejpam-4306	30	3	paper	paper	NOUN
ejpam-4306	30	4	we	we	PRON
ejpam-4306	30	5	are	be	AUX
ejpam-4306	30	6	going	go	VERB
ejpam-4306	30	7	to	to	PART
ejpam-4306	30	8	find	find	VERB
ejpam-4306	30	9	an	an	DET
ejpam-4306	30	10	exact	exact	ADJ
ejpam-4306	30	11	solution	solution	NOUN
ejpam-4306	30	12	for	for	ADP
ejpam-4306	30	13	the	the	DET
ejpam-4306	30	14	above	above	ADJ
ejpam-4306	30	15	equation	equation	NOUN
ejpam-4306	30	16	in	in	ADP
ejpam-4306	30	17	section	section	NOUN
ejpam-4306	30	18	2	2	NUM
ejpam-4306	30	19	,	,	PUNCT
ejpam-4306	30	20	while	while	SCONJ
ejpam-4306	30	21	in	in	ADP
ejpam-4306	30	22	section	section	NOUN
ejpam-4306	30	23	3	3	NUM
ejpam-4306	30	24	the	the	DET
ejpam-4306	30	25	exact	exact	ADJ
ejpam-4306	30	26	solution	solution	NOUN
ejpam-4306	30	27	with	with	ADP
ejpam-4306	30	28	modifying	modify	VERB
ejpam-4306	30	29	in	in	ADP
ejpam-4306	30	30	the	the	DET
ejpam-4306	30	31	potential	potential	ADJ
ejpam-4306	30	32	function	function	NOUN
ejpam-4306	30	33	will	will	AUX
ejpam-4306	30	34	be	be	AUX
ejpam-4306	30	35	presented	present	VERB
ejpam-4306	30	36	and	and	CCONJ
ejpam-4306	30	37	explained	explain	VERB
ejpam-4306	30	38	,	,	PUNCT
ejpam-4306	30	39	an	an	DET
ejpam-4306	30	40	equilibrium	equilibrium	NOUN
ejpam-4306	30	41	points	point	NOUN
ejpam-4306	30	42	of	of	ADP
ejpam-4306	30	43	the	the	DET
ejpam-4306	30	44	system	system	NOUN
ejpam-4306	30	45	and	and	CCONJ
ejpam-4306	30	46	their	their	PRON
ejpam-4306	30	47	stability	stability	NOUN
ejpam-4306	30	48	with	with	ADP
ejpam-4306	30	49	graphical	graphical	ADJ
ejpam-4306	30	50	simulation	simulation	NOUN
ejpam-4306	30	51	are	be	AUX
ejpam-4306	30	52	given	give	VERB
ejpam-4306	30	53	finally	finally	ADV
ejpam-4306	30	54	close	close	VERB
ejpam-4306	30	55	the	the	DET
ejpam-4306	30	56	paper	paper	NOUN
ejpam-4306	30	57	with	with	ADP
ejpam-4306	30	58	a	a	DET
ejpam-4306	30	59	conclusion	conclusion	NOUN
ejpam-4306	30	60	.	.	PUNCT
ejpam-4306	31	1	2	2	X
ejpam-4306	31	2	.	.	X
ejpam-4306	31	3	exact	exact	ADJ
ejpam-4306	31	4	solution	solution	NOUN
ejpam-4306	31	5	for	for	ADP
ejpam-4306	31	6	nonlinear	nonlinear	ADJ
ejpam-4306	31	7	oscillators	oscillator	NOUN
ejpam-4306	31	8	with	with	ADP
ejpam-4306	31	9	coordinate	coordinate	NOUN
ejpam-4306	31	10	-	-	PUNCT
ejpam-4306	31	11	dependent	dependent	ADJ
ejpam-4306	31	12	mass	mass	NOUN
ejpam-4306	31	13	consider	consider	VERB
ejpam-4306	31	14	the	the	DET
ejpam-4306	31	15	following	follow	VERB
ejpam-4306	31	16	equation	equation	NOUN
ejpam-4306	31	17	(	(	PUNCT
ejpam-4306	31	18	1	1	NUM
ejpam-4306	31	19	+	+	NUM
ejpam-4306	31	20	αx2)ẍ+	αx2)ẍ+	PRON
ejpam-4306	32	1	αxẋ2	αxẋ2	NUM
ejpam-4306	32	2	−	−	NOUN
ejpam-4306	32	3	x(1−	x(1−	PROPN
ejpam-4306	33	1	x2	x2	PROPN
ejpam-4306	33	2	)	)	PUNCT
ejpam-4306	34	1	=	=	SYM
ejpam-4306	34	2	0	0	PUNCT
ejpam-4306	34	3	(	(	PUNCT
ejpam-4306	34	4	1	1	X
ejpam-4306	34	5	)	)	PUNCT
ejpam-4306	34	6	an	an	DET
ejpam-4306	34	7	important	important	ADJ
ejpam-4306	34	8	property	property	NOUN
ejpam-4306	34	9	of	of	ADP
ejpam-4306	34	10	(	(	PUNCT
ejpam-4306	34	11	1	1	NUM
ejpam-4306	34	12	)	)	PUNCT
ejpam-4306	34	13	is	be	AUX
ejpam-4306	34	14	the	the	DET
ejpam-4306	34	15	frequencyamplitude	frequencyamplitude	NOUN
ejpam-4306	34	16	relationship	relationship	NOUN
ejpam-4306	34	17	,	,	PUNCT
ejpam-4306	34	18	where	where	SCONJ
ejpam-4306	34	19	in	in	ADP
ejpam-4306	34	20	principle	principle	ADJ
ejpam-4306	34	21	frequency	frequency	NOUN
ejpam-4306	34	22	of	of	ADP
ejpam-4306	34	23	a	a	DET
ejpam-4306	34	24	nonlinear	nonlinear	ADJ
ejpam-4306	34	25	oscillating	oscillate	VERB
ejpam-4306	34	26	system	system	NOUN
ejpam-4306	34	27	as	as	ADP
ejpam-4306	34	28	(	(	PUNCT
ejpam-4306	34	29	1	1	NUM
ejpam-4306	34	30	)	)	PUNCT
ejpam-4306	34	31	is	be	AUX
ejpam-4306	34	32	nonlinearly	nonlinearly	ADV
ejpam-4306	34	33	related	relate	VERB
ejpam-4306	34	34	to	to	ADP
ejpam-4306	34	35	its	its	PRON
ejpam-4306	34	36	amplitude	amplitude	NOUN
ejpam-4306	34	37	.	.	PUNCT
ejpam-4306	35	1	this	this	DET
ejpam-4306	35	2	property	property	NOUN
ejpam-4306	35	3	was	be	AUX
ejpam-4306	35	4	the	the	DET
ejpam-4306	35	5	aim	aim	NOUN
ejpam-4306	35	6	of	of	ADP
ejpam-4306	35	7	study	study	NOUN
ejpam-4306	35	8	of	of	ADP
ejpam-4306	35	9	many	many	ADJ
ejpam-4306	35	10	researchers	researcher	NOUN
ejpam-4306	35	11	such	such	ADJ
ejpam-4306	35	12	as	as	ADP
ejpam-4306	35	13	[	[	X
ejpam-4306	35	14	12	12	NUM
ejpam-4306	35	15	]	]	PUNCT
ejpam-4306	35	16	,	,	PUNCT
ejpam-4306	35	17	where	where	SCONJ
ejpam-4306	35	18	he	he	PRON
ejpam-4306	35	19	suggests	suggest	VERB
ejpam-4306	35	20	a	a	DET
ejpam-4306	35	21	direct	direct	ADJ
ejpam-4306	35	22	frequency	frequency	NOUN
ejpam-4306	35	23	estimate	estimate	NOUN
ejpam-4306	35	24	method	method	NOUN
ejpam-4306	35	25	for	for	ADP
ejpam-4306	35	26	nonlinear	nonlinear	ADJ
ejpam-4306	35	27	oscillators	oscillator	NOUN
ejpam-4306	35	28	with	with	ADP
ejpam-4306	35	29	arbitrary	arbitrary	ADJ
ejpam-4306	35	30	initial	initial	ADJ
ejpam-4306	35	31	conditions	condition	NOUN
ejpam-4306	35	32	and	and	CCONJ
ejpam-4306	35	33	the	the	DET
ejpam-4306	35	34	method	method	NOUN
ejpam-4306	35	35	used	use	VERB
ejpam-4306	35	36	is	be	AUX
ejpam-4306	35	37	based	base	VERB
ejpam-4306	35	38	on	on	ADP
ejpam-4306	35	39	the	the	DET
ejpam-4306	35	40	work	work	NOUN
ejpam-4306	35	41	presented	present	VERB
ejpam-4306	35	42	in	in	ADP
ejpam-4306	35	43	[	[	X
ejpam-4306	35	44	11	11	NUM
ejpam-4306	35	45	]	]	PUNCT
ejpam-4306	35	46	,	,	PUNCT
ejpam-4306	35	47	[	[	X
ejpam-4306	35	48	19	19	NUM
ejpam-4306	35	49	]	]	PUNCT
ejpam-4306	35	50	shows	show	VERB
ejpam-4306	35	51	that	that	SCONJ
ejpam-4306	35	52	it	it	PRON
ejpam-4306	35	53	can	can	AUX
ejpam-4306	35	54	be	be	AUX
ejpam-4306	35	55	greatly	greatly	ADV
ejpam-4306	35	56	interesting	interesting	ADJ
ejpam-4306	35	57	for	for	ADP
ejpam-4306	35	58	nonlinear	nonlinear	NOUN
ejpam-4306	35	59	oscillations.firstly	oscillations.firstly	ADV
ejpam-4306	35	60	,	,	PUNCT
ejpam-4306	35	61	we	we	PRON
ejpam-4306	35	62	make	make	VERB
ejpam-4306	35	63	reduction	reduction	NOUN
ejpam-4306	35	64	of	of	ADP
ejpam-4306	35	65	order	order	NOUN
ejpam-4306	35	66	for	for	ADP
ejpam-4306	35	67	the	the	DET
ejpam-4306	35	68	differential	differential	ADJ
ejpam-4306	35	69	equation	equation	NOUN
ejpam-4306	35	70	(	(	PUNCT
ejpam-4306	35	71	1	1	NUM
ejpam-4306	35	72	)	)	PUNCT
ejpam-4306	35	73	.	.	PUNCT
ejpam-4306	36	1	let	let	VERB
ejpam-4306	36	2	v	v	NOUN
ejpam-4306	36	3	=	=	SYM
ejpam-4306	36	4	dx	dx	PROPN
ejpam-4306	37	1	dt	dt	X
ejpam-4306	37	2	then	then	ADV
ejpam-4306	37	3	d2x	d2x	PROPN
ejpam-4306	37	4	dt2	dt2	PROPN
ejpam-4306	37	5	=	=	PROPN
ejpam-4306	37	6	dv	dv	PROPN
ejpam-4306	37	7	dt	dt	PROPN
ejpam-4306	38	1	=	=	PROPN
ejpam-4306	38	2	dv	dv	PROPN
ejpam-4306	38	3	dx	dx	PROPN
ejpam-4306	38	4	.	.	PUNCT
ejpam-4306	39	1	dx	dx	PROPN
ejpam-4306	40	1	dt	dt	X
ejpam-4306	41	1	=	=	X
ejpam-4306	41	2	v	v	PROPN
ejpam-4306	41	3	dv	dv	PROPN
ejpam-4306	41	4	dx	dx	PROPN
ejpam-4306	41	5	,	,	PUNCT
ejpam-4306	41	6	so	so	ADV
ejpam-4306	41	7	we	we	PRON
ejpam-4306	41	8	transform	transform	VERB
ejpam-4306	41	9	a.	a.	NOUN
ejpam-4306	41	10	abuas’ad	abuas’ad	PROPN
ejpam-4306	41	11	,	,	PUNCT
ejpam-4306	41	12	j.	j.	PROPN
ejpam-4306	41	13	asad	asad	PROPN
ejpam-4306	41	14	/	/	SYM
ejpam-4306	41	15	eur	eur	PROPN
ejpam-4306	41	16	.	.	PUNCT
ejpam-4306	42	1	j.	j.	PROPN
ejpam-4306	42	2	pure	pure	PROPN
ejpam-4306	42	3	appl	appl	PROPN
ejpam-4306	42	4	.	.	PROPN
ejpam-4306	42	5	math	math	PROPN
ejpam-4306	42	6	,	,	PUNCT
ejpam-4306	42	7	15	15	NUM
ejpam-4306	42	8	(	(	PUNCT
ejpam-4306	42	9	2	2	NUM
ejpam-4306	42	10	)	)	PUNCT
ejpam-4306	42	11	(	(	PUNCT
ejpam-4306	42	12	2022	2022	NUM
ejpam-4306	42	13	)	)	PUNCT
ejpam-4306	42	14	,	,	PUNCT
ejpam-4306	42	15	496	496	NUM
ejpam-4306	42	16	-	-	SYM
ejpam-4306	42	17	510	510	NUM
ejpam-4306	42	18	498	498	NUM
ejpam-4306	42	19	equation(1	equation(1	NOUN
ejpam-4306	42	20	)	)	PUNCT
ejpam-4306	42	21	into	into	ADP
ejpam-4306	42	22	the	the	DET
ejpam-4306	42	23	following	follow	VERB
ejpam-4306	42	24	first	first	ADJ
ejpam-4306	42	25	order	order	NOUN
ejpam-4306	42	26	nonlinear	nonlinear	ADJ
ejpam-4306	42	27	differential	differential	ADJ
ejpam-4306	42	28	equation	equation	NOUN
ejpam-4306	42	29	(	(	PUNCT
ejpam-4306	42	30	1	1	NUM
ejpam-4306	42	31	+	+	NUM
ejpam-4306	42	32	αx2)v	αx2)v	NUM
ejpam-4306	42	33	dv	dv	PROPN
ejpam-4306	42	34	dx	dx	PROPN
ejpam-4306	42	35	+	+	CCONJ
ejpam-4306	43	1	αxv2	αxv2	ADJ
ejpam-4306	43	2	−	−	PROPN
ejpam-4306	43	3	x(1−	x(1−	PROPN
ejpam-4306	43	4	x2	x2	PROPN
ejpam-4306	43	5	)	)	PUNCT
ejpam-4306	44	1	=	=	SYM
ejpam-4306	44	2	0	0	NUM
ejpam-4306	44	3	which	which	PRON
ejpam-4306	44	4	can	can	AUX
ejpam-4306	44	5	be	be	AUX
ejpam-4306	44	6	rewriiten	rewriiten	VERB
ejpam-4306	44	7	as	as	ADP
ejpam-4306	44	8	:	:	PUNCT
ejpam-4306	44	9	(	(	PUNCT
ejpam-4306	44	10	1	1	NUM
ejpam-4306	44	11	+	+	CCONJ
ejpam-4306	44	12	αx2)vdv	αx2)vdv	ADJ
ejpam-4306	44	13	+	+	CCONJ
ejpam-4306	44	14	(	(	PUNCT
ejpam-4306	44	15	αxv2	αxv2	ADJ
ejpam-4306	44	16	−	−	PROPN
ejpam-4306	44	17	x(1−	x(1−	PROPN
ejpam-4306	44	18	x2	x2	PROPN
ejpam-4306	44	19	)	)	PUNCT
ejpam-4306	44	20	)	)	PUNCT
ejpam-4306	45	1	dx	dx	PROPN
ejpam-4306	46	1	=	=	SYM
ejpam-4306	46	2	0	0	PUNCT
ejpam-4306	46	3	(	(	PUNCT
ejpam-4306	46	4	2	2	NUM
ejpam-4306	46	5	)	)	PUNCT
ejpam-4306	46	6	now	now	ADV
ejpam-4306	46	7	,	,	PUNCT
ejpam-4306	46	8	we	we	PRON
ejpam-4306	46	9	will	will	AUX
ejpam-4306	46	10	discuss	discuss	VERB
ejpam-4306	46	11	the	the	DET
ejpam-4306	46	12	exactness	exactness	ADJ
ejpam-4306	46	13	solution	solution	NOUN
ejpam-4306	46	14	of	of	ADP
ejpam-4306	46	15	equation(2	equation(2	PROPN
ejpam-4306	46	16	)	)	PUNCT
ejpam-4306	46	17	(	(	PUNCT
ejpam-4306	46	18	i.e.	i.e.	X
ejpam-4306	46	19	,	,	PUNCT
ejpam-4306	46	20	show	show	VERB
ejpam-4306	46	21	if	if	SCONJ
ejpam-4306	46	22	it	it	PRON
ejpam-4306	46	23	is	be	AUX
ejpam-4306	46	24	conservative	conservative	ADJ
ejpam-4306	46	25	or	or	CCONJ
ejpam-4306	46	26	not	not	PART
ejpam-4306	46	27	)	)	PUNCT
ejpam-4306	46	28	.	.	PUNCT
ejpam-4306	47	1	letting	let	VERB
ejpam-4306	47	2	m(x	m(x	PROPN
ejpam-4306	47	3	,	,	PUNCT
ejpam-4306	47	4	v	v	NOUN
ejpam-4306	47	5	)	)	PUNCT
ejpam-4306	47	6	=	=	PUNCT
ejpam-4306	48	1	(	(	PUNCT
ejpam-4306	48	2	1	1	NUM
ejpam-4306	48	3	+	+	CCONJ
ejpam-4306	48	4	αx2)v	αx2)v	NOUN
ejpam-4306	48	5	,	,	PUNCT
ejpam-4306	48	6	n(x	n(x	X
ejpam-4306	48	7	,	,	PUNCT
ejpam-4306	48	8	v	v	NOUN
ejpam-4306	48	9	)	)	PUNCT
ejpam-4306	48	10	=	=	SYM
ejpam-4306	48	11	αxv2	αxv2	ADJ
ejpam-4306	48	12	−	−	PROPN
ejpam-4306	48	13	x(1−	x(1−	PROPN
ejpam-4306	48	14	x2	x2	PROPN
ejpam-4306	48	15	)	)	PUNCT
ejpam-4306	48	16	,	,	PUNCT
ejpam-4306	49	1	then	then	ADV
ejpam-4306	49	2	∂m	∂m	PROPN
ejpam-4306	49	3	∂x	∂x	PROPN
ejpam-4306	49	4	=	=	SYM
ejpam-4306	49	5	2αxv	2αxv	PROPN
ejpam-4306	49	6	and	and	CCONJ
ejpam-4306	49	7	∂n	∂n	PROPN
ejpam-4306	49	8	∂v	∂v	PROPN
ejpam-4306	50	1	=	=	PUNCT
ejpam-4306	50	2	2αxv	2αxv	PROPN
ejpam-4306	50	3	this	this	PRON
ejpam-4306	50	4	means	mean	VERB
ejpam-4306	50	5	that	that	SCONJ
ejpam-4306	50	6	equation	equation	NOUN
ejpam-4306	50	7	(	(	PUNCT
ejpam-4306	50	8	2	2	X
ejpam-4306	50	9	)	)	PUNCT
ejpam-4306	50	10	is	be	AUX
ejpam-4306	50	11	exact	exact	ADJ
ejpam-4306	50	12	(	(	PUNCT
ejpam-4306	50	13	conservative	conservative	ADJ
ejpam-4306	50	14	)	)	PUNCT
ejpam-4306	50	15	.	.	PUNCT
ejpam-4306	51	1	according	accord	VERB
ejpam-4306	51	2	to	to	ADP
ejpam-4306	51	3	differential	differential	ADJ
ejpam-4306	51	4	equations	equation	NOUN
ejpam-4306	51	5	anslysis	anslysis	NOUN
ejpam-4306	51	6	there	there	PRON
ejpam-4306	51	7	must	must	AUX
ejpam-4306	51	8	exists	exist	VERB
ejpam-4306	51	9	a	a	DET
ejpam-4306	51	10	potential	potential	ADJ
ejpam-4306	51	11	function	function	NOUN
ejpam-4306	51	12	ψ(x	ψ(x	NOUN
ejpam-4306	51	13	,	,	PUNCT
ejpam-4306	51	14	v	v	NOUN
ejpam-4306	51	15	)	)	PUNCT
ejpam-4306	51	16	such	such	ADJ
ejpam-4306	51	17	that	that	PRON
ejpam-4306	51	18	.	.	PUNCT
ejpam-4306	52	1	ψ(x	ψ(x	PROPN
ejpam-4306	52	2	,	,	PUNCT
ejpam-4306	52	3	v	v	NOUN
ejpam-4306	52	4	)	)	PUNCT
ejpam-4306	52	5	=	=	PUNCT
ejpam-4306	52	6	(	(	PUNCT
ejpam-4306	52	7	1	1	NUM
ejpam-4306	52	8	+	+	CCONJ
ejpam-4306	52	9	αx2)vdv	αx2)vdv	ADJ
ejpam-4306	52	10	=	=	NOUN
ejpam-4306	52	11	1	1	NUM
ejpam-4306	52	12	2	2	NUM
ejpam-4306	52	13	(	(	PUNCT
ejpam-4306	52	14	1	1	NUM
ejpam-4306	52	15	+	+	CCONJ
ejpam-4306	52	16	αx2)v2	αx2)v2	NOUN
ejpam-4306	52	17	+	+	CCONJ
ejpam-4306	52	18	f(x	f(x	PROPN
ejpam-4306	52	19	)	)	PUNCT
ejpam-4306	52	20	where	where	SCONJ
ejpam-4306	52	21	f(x	f(x	PROPN
ejpam-4306	52	22	)	)	PUNCT
ejpam-4306	52	23	is	be	AUX
ejpam-4306	52	24	a	a	DET
ejpam-4306	52	25	constant	constant	ADJ
ejpam-4306	52	26	function	function	NOUN
ejpam-4306	52	27	respect	respect	NOUN
ejpam-4306	52	28	to	to	ADP
ejpam-4306	52	29	v.	v.	NOUN
ejpam-4306	52	30	in	in	ADP
ejpam-4306	52	31	the	the	DET
ejpam-4306	52	32	following	following	NOUN
ejpam-4306	52	33	we	we	PRON
ejpam-4306	52	34	aim	aim	VERB
ejpam-4306	52	35	to	to	PART
ejpam-4306	52	36	find	find	VERB
ejpam-4306	52	37	f(x	f(x	PROPN
ejpam-4306	52	38	)	)	PUNCT
ejpam-4306	52	39	∂ψ(x	∂ψ(x	NOUN
ejpam-4306	52	40	,	,	PUNCT
ejpam-4306	52	41	v	v	NOUN
ejpam-4306	52	42	)	)	PUNCT
ejpam-4306	52	43	∂x	∂x	NOUN
ejpam-4306	52	44	=	=	SYM
ejpam-4306	52	45	n(x	n(x	PROPN
ejpam-4306	52	46	,	,	PUNCT
ejpam-4306	52	47	v	v	NOUN
ejpam-4306	52	48	)	)	PUNCT
ejpam-4306	52	49	thus	thus	ADV
ejpam-4306	52	50	αxv2	αxv2	ADJ
ejpam-4306	52	51	+	+	CCONJ
ejpam-4306	52	52	df	df	PROPN
ejpam-4306	52	53	dx	dx	PROPN
ejpam-4306	52	54	=	=	SYM
ejpam-4306	52	55	αxv2	αxv2	ADJ
ejpam-4306	52	56	−	−	PROPN
ejpam-4306	52	57	x(1−	x(1−	PROPN
ejpam-4306	52	58	x2	x2	PROPN
ejpam-4306	52	59	)	)	PUNCT
ejpam-4306	52	60	.	.	PUNCT
ejpam-4306	53	1	this	this	PRON
ejpam-4306	53	2	means	mean	VERB
ejpam-4306	53	3	that	that	SCONJ
ejpam-4306	53	4	:	:	PUNCT
ejpam-4306	53	5	f(x	f(x	PROPN
ejpam-4306	53	6	)	)	PUNCT
ejpam-4306	53	7	=	=	SYM
ejpam-4306	54	1	−x(1−	−x(1−	PROPN
ejpam-4306	54	2	x2)dx	x2)dx	VERB
ejpam-4306	54	3	=	=	PUNCT
ejpam-4306	55	1	−x2	−x2	NOUN
ejpam-4306	55	2	2	2	NUM
ejpam-4306	55	3	+	+	CCONJ
ejpam-4306	55	4	x4	x4	PROPN
ejpam-4306	55	5	4	4	NUM
ejpam-4306	55	6	+	+	CCONJ
ejpam-4306	55	7	c	c	AUX
ejpam-4306	55	8	therefore	therefore	ADV
ejpam-4306	55	9	the	the	DET
ejpam-4306	55	10	potential	potential	ADJ
ejpam-4306	55	11	function	function	NOUN
ejpam-4306	55	12	ψ(x	ψ(x	PROPN
ejpam-4306	55	13	,	,	PUNCT
ejpam-4306	55	14	v	v	NOUN
ejpam-4306	55	15	)	)	PUNCT
ejpam-4306	55	16	becomes	become	VERB
ejpam-4306	55	17	ψ(x	ψ(x	PROPN
ejpam-4306	55	18	,	,	PUNCT
ejpam-4306	55	19	v	v	NOUN
ejpam-4306	55	20	)	)	PUNCT
ejpam-4306	55	21	=	=	SYM
ejpam-4306	55	22	1	1	NUM
ejpam-4306	55	23	2	2	NUM
ejpam-4306	55	24	(	(	PUNCT
ejpam-4306	55	25	1	1	NUM
ejpam-4306	55	26	+	+	CCONJ
ejpam-4306	55	27	αx2)v2	αx2)v2	NOUN
ejpam-4306	55	28	−	−	NOUN
ejpam-4306	55	29	x2	x2	NOUN
ejpam-4306	55	30	2	2	NUM
ejpam-4306	55	31	+	+	CCONJ
ejpam-4306	55	32	x4	x4	PROPN
ejpam-4306	55	33	4	4	NUM
ejpam-4306	55	34	+	+	NUM
ejpam-4306	55	35	c	c	NOUN
ejpam-4306	55	36	set	set	VERB
ejpam-4306	55	37	1	1	NUM
ejpam-4306	55	38	2	2	NUM
ejpam-4306	55	39	(	(	PUNCT
ejpam-4306	55	40	1	1	NUM
ejpam-4306	55	41	+	+	CCONJ
ejpam-4306	55	42	αx2)v2	αx2)v2	NOUN
ejpam-4306	55	43	−	−	NOUN
ejpam-4306	55	44	x2	x2	NOUN
ejpam-4306	55	45	2	2	NUM
ejpam-4306	55	46	+	+	CCONJ
ejpam-4306	55	47	x4	x4	PROPN
ejpam-4306	55	48	4	4	NUM
ejpam-4306	55	49	=	=	SYM
ejpam-4306	55	50	c	c	NOUN
ejpam-4306	55	51	now	now	ADV
ejpam-4306	55	52	substituting	substitute	VERB
ejpam-4306	55	53	the	the	DET
ejpam-4306	55	54	initial	initial	ADJ
ejpam-4306	55	55	conditions	condition	NOUN
ejpam-4306	55	56	x(0	x(0	PRON
ejpam-4306	55	57	)	)	PUNCT
ejpam-4306	55	58	=	=	SYM
ejpam-4306	55	59	a	a	PRON
ejpam-4306	55	60	,	,	PUNCT
ejpam-4306	55	61	and	and	CCONJ
ejpam-4306	55	62	ẋ(0	ẋ(0	NOUN
ejpam-4306	55	63	)	)	PUNCT
ejpam-4306	56	1	=	=	SYM
ejpam-4306	56	2	0	0	PUNCT
ejpam-4306	56	3	=	=	SYM
ejpam-4306	56	4	v	v	NOUN
ejpam-4306	56	5	,	,	PUNCT
ejpam-4306	56	6	the	the	DET
ejpam-4306	56	7	potential	potential	ADJ
ejpam-4306	56	8	function	function	NOUN
ejpam-4306	56	9	is	be	AUX
ejpam-4306	56	10	ψ(x	ψ(x	NOUN
ejpam-4306	56	11	,	,	PUNCT
ejpam-4306	56	12	v	v	NOUN
ejpam-4306	56	13	)	)	PUNCT
ejpam-4306	56	14	=	=	SYM
ejpam-4306	56	15	1	1	NUM
ejpam-4306	56	16	2	2	NUM
ejpam-4306	56	17	(	(	PUNCT
ejpam-4306	56	18	1	1	NUM
ejpam-4306	56	19	+	+	CCONJ
ejpam-4306	56	20	αx2)v2	αx2)v2	NOUN
ejpam-4306	56	21	−	−	NOUN
ejpam-4306	56	22	x2	x2	NOUN
ejpam-4306	56	23	2	2	NUM
ejpam-4306	56	24	+	+	CCONJ
ejpam-4306	56	25	x4	x4	PROPN
ejpam-4306	56	26	4	4	NUM
ejpam-4306	56	27	+	+	NUM
ejpam-4306	56	28	a2	a2	PROPN
ejpam-4306	56	29	2	2	NUM
ejpam-4306	56	30	−	−	NOUN
ejpam-4306	56	31	a4	a4	NOUN
ejpam-4306	56	32	4	4	NUM
ejpam-4306	56	33	a.	a.	NOUN
ejpam-4306	56	34	abuas’ad	abuas’ad	PROPN
ejpam-4306	56	35	,	,	PUNCT
ejpam-4306	56	36	j.	j.	PROPN
ejpam-4306	56	37	asad	asad	PROPN
ejpam-4306	56	38	/	/	SYM
ejpam-4306	56	39	eur	eur	PROPN
ejpam-4306	56	40	.	.	PUNCT
ejpam-4306	57	1	j.	j.	PROPN
ejpam-4306	57	2	pure	pure	PROPN
ejpam-4306	57	3	appl	appl	PROPN
ejpam-4306	57	4	.	.	PROPN
ejpam-4306	57	5	math	math	PROPN
ejpam-4306	57	6	,	,	PUNCT
ejpam-4306	57	7	15	15	NUM
ejpam-4306	57	8	(	(	PUNCT
ejpam-4306	57	9	2	2	NUM
ejpam-4306	57	10	)	)	PUNCT
ejpam-4306	57	11	(	(	PUNCT
ejpam-4306	57	12	2022	2022	NUM
ejpam-4306	57	13	)	)	PUNCT
ejpam-4306	57	14	,	,	PUNCT
ejpam-4306	57	15	496	496	NUM
ejpam-4306	57	16	-	-	SYM
ejpam-4306	57	17	510	510	NUM
ejpam-4306	57	18	499	499	NUM
ejpam-4306	57	19	setting	set	VERB
ejpam-4306	57	20	c	c	NOUN
ejpam-4306	57	21	=	=	SYM
ejpam-4306	57	22	0	0	PUNCT
ejpam-4306	58	1	(	(	PUNCT
ejpam-4306	58	2	arbitrary	arbitrary	ADJ
ejpam-4306	58	3	constant	constant	ADJ
ejpam-4306	58	4	)	)	PUNCT
ejpam-4306	58	5	in	in	ADP
ejpam-4306	58	6	ψ(x	ψ(x	PROPN
ejpam-4306	58	7	,	,	PUNCT
ejpam-4306	58	8	v	v	NOUN
ejpam-4306	58	9	)	)	PUNCT
ejpam-4306	58	10	.	.	PUNCT
ejpam-4306	59	1	then	then	ADV
ejpam-4306	59	2	we	we	PRON
ejpam-4306	59	3	have	have	VERB
ejpam-4306	59	4	v2	v2	NOUN
ejpam-4306	59	5	=	=	SYM
ejpam-4306	59	6	x2	x2	PROPN
ejpam-4306	59	7	−	−	PROPN
ejpam-4306	59	8	x4	x4	PROPN
ejpam-4306	59	9	2	2	NUM
ejpam-4306	59	10	(	(	PUNCT
ejpam-4306	59	11	1	1	NUM
ejpam-4306	59	12	+	+	NUM
ejpam-4306	59	13	αx2	αx2	NOUN
ejpam-4306	59	14	)	)	PUNCT
ejpam-4306	59	15	dx	dx	PROPN
ejpam-4306	60	1	dt	dt	NOUN
ejpam-4306	60	2	=	=	SYM
ejpam-4306	60	3	v	v	PROPN
ejpam-4306	60	4	=	=	SYM
ejpam-4306	60	5	√	√	ADP
ejpam-4306	60	6	2x2	2x2	NUM
ejpam-4306	60	7	−	−	PUNCT
ejpam-4306	60	8	x4	x4	PROPN
ejpam-4306	60	9	2(1	2(1	NUM
ejpam-4306	60	10	+	+	NUM
ejpam-4306	60	11	αx2	αx2	NOUN
ejpam-4306	60	12	)	)	PUNCT
ejpam-4306	60	13	dt	dt	X
ejpam-4306	61	1	dx	dx	PROPN
ejpam-4306	61	2	=	=	PUNCT
ejpam-4306	62	1	√	√	NUM
ejpam-4306	62	2	2(1	2(1	NUM
ejpam-4306	62	3	+	+	CCONJ
ejpam-4306	62	4	αx2	αx2	NOUN
ejpam-4306	62	5	)	)	PUNCT
ejpam-4306	62	6	2x2	2x2	NUM
ejpam-4306	62	7	−	−	NOUN
ejpam-4306	63	1	x4	x4	NOUN
ejpam-4306	63	2	integrating	integrate	VERB
ejpam-4306	63	3	the	the	DET
ejpam-4306	63	4	above	above	ADJ
ejpam-4306	63	5	equation	equation	NOUN
ejpam-4306	63	6	to	to	PART
ejpam-4306	63	7	get	get	VERB
ejpam-4306	63	8	t	t	NOUN
ejpam-4306	63	9	=	=	SYM
ejpam-4306	63	10	√	√	NUM
ejpam-4306	63	11	2	2	NUM
ejpam-4306	63	12	1	1	NUM
ejpam-4306	63	13	x	x	SYM
ejpam-4306	63	14	√	√	PROPN
ejpam-4306	63	15	(	(	PUNCT
ejpam-4306	63	16	1	1	NUM
ejpam-4306	63	17	+	+	NUM
ejpam-4306	63	18	αx2	αx2	NOUN
ejpam-4306	63	19	)	)	PUNCT
ejpam-4306	63	20	2−	2−	NUM
ejpam-4306	64	1	x2	x2	NOUN
ejpam-4306	64	2	dx	dx	PROPN
ejpam-4306	64	3	t	t	PROPN
ejpam-4306	64	4	=	=	PUNCT
ejpam-4306	65	1	√	√	PROPN
ejpam-4306	65	2	2	2	NUM
ejpam-4306	65	3	1	1	NUM
ejpam-4306	65	4	x	x	SYM
ejpam-4306	65	5	√	√	PROPN
ejpam-4306	65	6	(	(	PUNCT
ejpam-4306	65	7	1	1	NUM
ejpam-4306	65	8	+	+	NUM
ejpam-4306	65	9	αx2	αx2	NOUN
ejpam-4306	65	10	)	)	PUNCT
ejpam-4306	65	11	2−	2−	NUM
ejpam-4306	66	1	x2	x2	NOUN
ejpam-4306	66	2	dx	dx	PROPN
ejpam-4306	66	3	t	t	PROPN
ejpam-4306	66	4	=	=	PUNCT
ejpam-4306	67	1	√	√	PROPN
ejpam-4306	67	2	2	2	NUM
ejpam-4306	67	3	1	1	NUM
ejpam-4306	67	4	x	x	SYM
ejpam-4306	67	5	√	√	PROPN
ejpam-4306	67	6	(	(	PUNCT
ejpam-4306	67	7	1	1	NUM
ejpam-4306	67	8	+	+	NUM
ejpam-4306	67	9	αx2	αx2	NOUN
ejpam-4306	67	10	+	+	CCONJ
ejpam-4306	67	11	α−	α−	ADP
ejpam-4306	67	12	α	α	NOUN
ejpam-4306	67	13	)	)	PUNCT
ejpam-4306	67	14	1	1	NUM
ejpam-4306	67	15	+	+	SYM
ejpam-4306	67	16	1−	1−	NUM
ejpam-4306	68	1	x2	x2	NUM
ejpam-4306	68	2	dx	dx	PROPN
ejpam-4306	68	3	t	t	PROPN
ejpam-4306	68	4	=	=	PUNCT
ejpam-4306	69	1	√	√	PROPN
ejpam-4306	69	2	2	2	NUM
ejpam-4306	69	3	1	1	NUM
ejpam-4306	69	4	x	x	SYM
ejpam-4306	69	5	√	√	ADP
ejpam-4306	69	6	1	1	NUM
ejpam-4306	69	7	+	+	CCONJ
ejpam-4306	69	8	α−	α−	ADP
ejpam-4306	69	9	α(1−	α(1−	PROPN
ejpam-4306	69	10	x2	x2	PROPN
ejpam-4306	69	11	)	)	PUNCT
ejpam-4306	69	12	1	1	NUM
ejpam-4306	70	1	+	+	CCONJ
ejpam-4306	70	2	(	(	PUNCT
ejpam-4306	70	3	1−	1−	NUM
ejpam-4306	70	4	x2	x2	NOUN
ejpam-4306	70	5	)	)	PUNCT
ejpam-4306	70	6	dx	dx	PROPN
ejpam-4306	70	7	now	now	ADV
ejpam-4306	70	8	y	y	PROPN
ejpam-4306	70	9	=	=	SYM
ejpam-4306	70	10	1−	1−	NUM
ejpam-4306	70	11	x2	x2	NOUN
ejpam-4306	70	12	,	,	PUNCT
ejpam-4306	70	13	dy	dy	X
ejpam-4306	70	14	=	=	SYM
ejpam-4306	70	15	−2xdx	−2xdx	PROPN
ejpam-4306	70	16	,	,	PUNCT
ejpam-4306	70	17	and	and	CCONJ
ejpam-4306	71	1	dx	dx	PROPN
ejpam-4306	71	2	=	=	SYM
ejpam-4306	71	3	−dy√	−dy√	PROPN
ejpam-4306	71	4	1−y	1−y	PROPN
ejpam-4306	71	5	t	t	NOUN
ejpam-4306	71	6	=	=	SYM
ejpam-4306	72	1	−	−	PROPN
ejpam-4306	72	2	1√	1√	NUM
ejpam-4306	72	3	2	2	NUM
ejpam-4306	72	4	1	1	NUM
ejpam-4306	72	5	1−	1−	NUM
ejpam-4306	72	6	y	y	NOUN
ejpam-4306	72	7	√	√	ADV
ejpam-4306	72	8	1	1	NUM
ejpam-4306	72	9	+	+	CCONJ
ejpam-4306	72	10	α(1−	α(1−	PROPN
ejpam-4306	72	11	y	y	PROPN
ejpam-4306	72	12	)	)	PUNCT
ejpam-4306	72	13	1	1	NUM
ejpam-4306	73	1	+	+	CCONJ
ejpam-4306	73	2	y	y	NOUN
ejpam-4306	73	3	dy	dy	NOUN
ejpam-4306	73	4	we	we	PRON
ejpam-4306	73	5	can	can	AUX
ejpam-4306	73	6	write	write	VERB
ejpam-4306	73	7	the	the	DET
ejpam-4306	73	8	integration	integration	NOUN
ejpam-4306	73	9	as	as	ADP
ejpam-4306	73	10	t	t	PROPN
ejpam-4306	73	11	=	=	SYM
ejpam-4306	73	12	−	−	PROPN
ejpam-4306	73	13	1√	1√	PROPN
ejpam-4306	73	14	2	2	NUM
ejpam-4306	73	15	1	1	NUM
ejpam-4306	73	16	1−	1−	NUM
ejpam-4306	73	17	y	y	NOUN
ejpam-4306	73	18	√	√	ADV
ejpam-4306	73	19	1	1	NUM
ejpam-4306	74	1	+	+	CCONJ
ejpam-4306	74	2	2α	2α	NOUN
ejpam-4306	74	3	1	1	NUM
ejpam-4306	74	4	+	+	NUM
ejpam-4306	74	5	y	y	PROPN
ejpam-4306	74	6	−	−	PROPN
ejpam-4306	74	7	αdy	αdy	NOUN
ejpam-4306	74	8	again	again	ADV
ejpam-4306	74	9	,	,	PUNCT
ejpam-4306	74	10	let	let	VERB
ejpam-4306	74	11	w	w	NOUN
ejpam-4306	74	12	=	=	SYM
ejpam-4306	74	13	1	1	NUM
ejpam-4306	74	14	+	+	NUM
ejpam-4306	74	15	2α	2α	NOUN
ejpam-4306	74	16	1+y	1+y	NUM
ejpam-4306	74	17	−α	−α	NOUN
ejpam-4306	74	18	,	,	PUNCT
ejpam-4306	74	19	then	then	ADV
ejpam-4306	74	20	y	y	PROPN
ejpam-4306	74	21	=	=	SYM
ejpam-4306	74	22	1	1	NUM
ejpam-4306	74	23	+	+	NOUN
ejpam-4306	74	24	2α	2α	X
ejpam-4306	74	25	w+α	w+α	NUM
ejpam-4306	74	26	−1	−1	NOUN
ejpam-4306	74	27	,	,	PUNCT
ejpam-4306	74	28	and	and	CCONJ
ejpam-4306	74	29	dy	dy	X
ejpam-4306	74	30	=	=	SYM
ejpam-4306	75	1	−(1	−(1	X
ejpam-4306	75	2	+	+	NOUN
ejpam-4306	75	3	2α	2α	NOUN
ejpam-4306	75	4	)	)	PUNCT
ejpam-4306	75	5	(	(	PUNCT
ejpam-4306	75	6	w+α)2	w+α)2	PROPN
ejpam-4306	75	7	dw	dw	PROPN
ejpam-4306	75	8	,	,	PUNCT
ejpam-4306	75	9	the	the	DET
ejpam-4306	75	10	equation	equation	NOUN
ejpam-4306	76	1	integral	integral	ADJ
ejpam-4306	76	2	reads	read	NOUN
ejpam-4306	76	3	t	t	NOUN
ejpam-4306	76	4	=	=	SYM
ejpam-4306	76	5	1√	1√	NUM
ejpam-4306	76	6	2	2	NUM
ejpam-4306	76	7	1	1	NUM
ejpam-4306	76	8	2w−1	2w−1	NUM
ejpam-4306	76	9	w+α	w+α	X
ejpam-4306	76	10	√	√	INTJ
ejpam-4306	76	11	w	w	NOUN
ejpam-4306	76	12	(	(	PUNCT
ejpam-4306	76	13	1	1	NUM
ejpam-4306	76	14	+	+	NUM
ejpam-4306	76	15	2α	2α	NOUN
ejpam-4306	76	16	)	)	PUNCT
ejpam-4306	76	17	(	(	PUNCT
ejpam-4306	76	18	w	w	X
ejpam-4306	76	19	+	+	SYM
ejpam-4306	76	20	α)2	α)2	PROPN
ejpam-4306	76	21	dw	dw	NOUN
ejpam-4306	76	22	t	t	PROPN
ejpam-4306	76	23	=	=	PUNCT
ejpam-4306	76	24	(	(	PUNCT
ejpam-4306	76	25	1	1	NUM
ejpam-4306	76	26	+	+	CCONJ
ejpam-4306	76	27	2α)√	2α)√	PROPN
ejpam-4306	76	28	2	2	NUM
ejpam-4306	76	29	√	√	NUM
ejpam-4306	76	30	w	w	NOUN
ejpam-4306	76	31	(	(	PUNCT
ejpam-4306	76	32	2w	2w	NUM
ejpam-4306	76	33	−	−	PROPN
ejpam-4306	76	34	1)(w	1)(w	NUM
ejpam-4306	76	35	+	+	CCONJ
ejpam-4306	76	36	α	α	X
ejpam-4306	76	37	)	)	PUNCT
ejpam-4306	76	38	dw	dw	NOUN
ejpam-4306	76	39	substituting	substitute	VERB
ejpam-4306	76	40	u	u	NOUN
ejpam-4306	76	41	=	=	PROPN
ejpam-4306	76	42	√	√	PROPN
ejpam-4306	76	43	w	w	PROPN
ejpam-4306	76	44	,	,	PUNCT
ejpam-4306	76	45	du	du	PROPN
ejpam-4306	76	46	=	=	SYM
ejpam-4306	76	47	1	1	NUM
ejpam-4306	76	48	2udw	2udw	NUM
ejpam-4306	76	49	,	,	PUNCT
ejpam-4306	76	50	then	then	ADV
ejpam-4306	76	51	t	t	PROPN
ejpam-4306	76	52	=	=	PUNCT
ejpam-4306	76	53	(	(	PUNCT
ejpam-4306	76	54	1	1	NUM
ejpam-4306	76	55	+	+	CCONJ
ejpam-4306	76	56	2α)√	2α)√	NUM
ejpam-4306	76	57	2	2	NUM
ejpam-4306	76	58	2u2	2u2	NUM
ejpam-4306	76	59	(	(	PUNCT
ejpam-4306	76	60	2u2	2u2	NUM
ejpam-4306	76	61	−	−	NOUN
ejpam-4306	76	62	1)(u2	1)(u2	NUM
ejpam-4306	76	63	+	+	CCONJ
ejpam-4306	76	64	α	α	X
ejpam-4306	76	65	)	)	PUNCT
ejpam-4306	76	66	du	du	PROPN
ejpam-4306	76	67	a.	a.	NOUN
ejpam-4306	76	68	abuas’ad	abuas’ad	PROPN
ejpam-4306	76	69	,	,	PUNCT
ejpam-4306	76	70	j.	j.	PROPN
ejpam-4306	76	71	asad	asad	PROPN
ejpam-4306	76	72	/	/	SYM
ejpam-4306	76	73	eur	eur	PROPN
ejpam-4306	76	74	.	.	PUNCT
ejpam-4306	77	1	j.	j.	PROPN
ejpam-4306	77	2	pure	pure	PROPN
ejpam-4306	77	3	appl	appl	PROPN
ejpam-4306	77	4	.	.	PROPN
ejpam-4306	77	5	math	math	PROPN
ejpam-4306	77	6	,	,	PUNCT
ejpam-4306	77	7	15	15	NUM
ejpam-4306	77	8	(	(	PUNCT
ejpam-4306	77	9	2	2	NUM
ejpam-4306	77	10	)	)	PUNCT
ejpam-4306	77	11	(	(	PUNCT
ejpam-4306	77	12	2022	2022	NUM
ejpam-4306	77	13	)	)	PUNCT
ejpam-4306	77	14	,	,	PUNCT
ejpam-4306	77	15	496	496	NUM
ejpam-4306	77	16	-	-	SYM
ejpam-4306	77	17	510	510	NUM
ejpam-4306	77	18	500	500	NUM
ejpam-4306	77	19	=	=	SYM
ejpam-4306	77	20	(	(	PUNCT
ejpam-4306	77	21	1	1	NUM
ejpam-4306	77	22	+	+	NUM
ejpam-4306	77	23	2α	2α	NOUN
ejpam-4306	77	24	)	)	PUNCT
ejpam-4306	77	25	√	√	NOUN
ejpam-4306	77	26	2	2	NUM
ejpam-4306	77	27	u2	u2	NOUN
ejpam-4306	77	28	(	(	PUNCT
ejpam-4306	77	29	2u2	2u2	NUM
ejpam-4306	77	30	−	−	NOUN
ejpam-4306	77	31	1)(u2	1)(u2	NUM
ejpam-4306	77	32	+	+	CCONJ
ejpam-4306	77	33	α	α	X
ejpam-4306	77	34	)	)	PUNCT
ejpam-4306	77	35	du	du	PROPN
ejpam-4306	77	36	making	make	VERB
ejpam-4306	77	37	use	use	NOUN
ejpam-4306	77	38	of	of	ADP
ejpam-4306	77	39	partial	partial	ADJ
ejpam-4306	77	40	fraction	fraction	NOUN
ejpam-4306	77	41	t	t	NOUN
ejpam-4306	77	42	=	=	SYM
ejpam-4306	77	43	1	1	NUM
ejpam-4306	77	44	2	2	NUM
ejpam-4306	77	45	ln	ln	NOUN
ejpam-4306	77	46	(	(	PUNCT
ejpam-4306	77	47	√	√	PROPN
ejpam-4306	77	48	2u−	2u−	NUM
ejpam-4306	77	49	1√	1√	NOUN
ejpam-4306	77	50	2u+	2u+	NUM
ejpam-4306	77	51	1	1	NUM
ejpam-4306	77	52	)	)	PUNCT
ejpam-4306	78	1	+	+	CCONJ
ejpam-4306	78	2	√	√	NUM
ejpam-4306	78	3	2	2	NUM
ejpam-4306	78	4	α	α	NOUN
ejpam-4306	78	5	tan−1	tan−1	PROPN
ejpam-4306	78	6	(	(	PUNCT
ejpam-4306	78	7	u√	u√	NOUN
ejpam-4306	78	8	α	α	NOUN
ejpam-4306	78	9	)	)	PUNCT
ejpam-4306	79	1	+	+	CCONJ
ejpam-4306	79	2	c	c	NOUN
ejpam-4306	79	3	but	but	CCONJ
ejpam-4306	79	4	u	u	NOUN
ejpam-4306	79	5	=	=	PROPN
ejpam-4306	79	6	√	√	PROPN
ejpam-4306	79	7	w	w	NOUN
ejpam-4306	79	8	=	=	NOUN
ejpam-4306	80	1	√	√	NUM
ejpam-4306	80	2	1	1	NUM
ejpam-4306	81	1	+	+	NOUN
ejpam-4306	81	2	2α	2α	NOUN
ejpam-4306	81	3	1+y	1+y	NUM
ejpam-4306	81	4	−	−	NOUN
ejpam-4306	81	5	α	α	NOUN
ejpam-4306	81	6	=	=	NOUN
ejpam-4306	81	7	√	√	PROPN
ejpam-4306	81	8	1+αx2	1+αx2	NUM
ejpam-4306	81	9	2−x2	2−x2	NUM
ejpam-4306	81	10	,	,	PUNCT
ejpam-4306	81	11	which	which	PRON
ejpam-4306	81	12	imply	imply	VERB
ejpam-4306	81	13	to	to	ADP
ejpam-4306	81	14	the	the	DET
ejpam-4306	81	15	solution	solution	NOUN
ejpam-4306	81	16	t	t	NOUN
ejpam-4306	81	17	=	=	SYM
ejpam-4306	81	18	1	1	NUM
ejpam-4306	81	19	2	2	NUM
ejpam-4306	81	20	ln	ln	NOUN
ejpam-4306	81	21			PROPN
ejpam-4306	81	22	√	√	NUM
ejpam-4306	81	23	2(1+αx2	2(1+αx2	NUM
ejpam-4306	81	24	)	)	PUNCT
ejpam-4306	81	25	2−x2	2−x2	NUM
ejpam-4306	82	1	−	−	NUM
ejpam-4306	82	2	1√	1√	PROPN
ejpam-4306	82	3	2(1+αx2	2(1+αx2	NUM
ejpam-4306	82	4	)	)	PUNCT
ejpam-4306	83	1	2−x2	2−x2	NUM
ejpam-4306	84	1	+	+	CCONJ
ejpam-4306	84	2	1	1	NUM
ejpam-4306	84	3	+	+	NOUN
ejpam-4306	84	4	√	√	ADV
ejpam-4306	84	5	2	2	NUM
ejpam-4306	84	6	α	α	NOUN
ejpam-4306	84	7	tan−1	tan−1	PROPN
ejpam-4306	84	8	(	(	PUNCT
ejpam-4306	84	9	√	√	NUM
ejpam-4306	84	10	2	2	NUM
ejpam-4306	84	11	(	(	PUNCT
ejpam-4306	84	12	1	1	NUM
ejpam-4306	84	13	+	+	NUM
ejpam-4306	84	14	αx2	αx2	NOUN
ejpam-4306	84	15	)	)	PUNCT
ejpam-4306	84	16	α	α	PROPN
ejpam-4306	84	17	(	(	PUNCT
ejpam-4306	84	18	2−	2−	NUM
ejpam-4306	84	19	x2	x2	NOUN
ejpam-4306	84	20	)	)	PUNCT
ejpam-4306	84	21	)	)	PUNCT
ejpam-4306	85	1	+	+	CCONJ
ejpam-4306	85	2	c	c	X
ejpam-4306	85	3	(	(	PUNCT
ejpam-4306	85	4	3	3	X
ejpam-4306	85	5	)	)	PUNCT
ejpam-4306	85	6	using	use	VERB
ejpam-4306	85	7	x(0	x(0	PROPN
ejpam-4306	85	8	)	)	PUNCT
ejpam-4306	85	9	=	=	PUNCT
ejpam-4306	86	1	a	a	X
ejpam-4306	86	2	,	,	PUNCT
ejpam-4306	86	3	we	we	PRON
ejpam-4306	86	4	get	get	VERB
ejpam-4306	86	5	c	c	NOUN
ejpam-4306	86	6	=	=	SYM
ejpam-4306	86	7	1	1	NUM
ejpam-4306	86	8	2	2	NUM
ejpam-4306	86	9	ln	ln	NOUN
ejpam-4306	86	10			PROPN
ejpam-4306	86	11	√	√	ADJ
ejpam-4306	86	12	2(1+αa2	2(1+αa2	NUM
ejpam-4306	86	13	)	)	PUNCT
ejpam-4306	86	14	2−a2	2−a2	NUM
ejpam-4306	87	1	+	+	CCONJ
ejpam-4306	87	2	1√	1√	ADJ
ejpam-4306	87	3	2(1+αa2	2(1+αa2	NUM
ejpam-4306	87	4	)	)	PUNCT
ejpam-4306	87	5	2−a2	2−a2	NUM
ejpam-4306	88	1	−	−	NOUN
ejpam-4306	88	2	1	1	NUM
ejpam-4306	88	3	−	−	ADV
ejpam-4306	89	1	√	√	NOUN
ejpam-4306	89	2	2	2	NUM
ejpam-4306	89	3	α	α	NOUN
ejpam-4306	89	4	tan−1	tan−1	PROPN
ejpam-4306	89	5	(	(	PUNCT
ejpam-4306	89	6	√	√	NUM
ejpam-4306	89	7	2	2	NUM
ejpam-4306	89	8	(	(	PUNCT
ejpam-4306	89	9	1	1	NUM
ejpam-4306	89	10	+	+	NUM
ejpam-4306	89	11	αa2	αa2	NOUN
ejpam-4306	89	12	)	)	PUNCT
ejpam-4306	89	13	α	α	PROPN
ejpam-4306	89	14	(	(	PUNCT
ejpam-4306	89	15	2−a2	2−a2	NUM
ejpam-4306	89	16	)	)	PUNCT
ejpam-4306	89	17	)	)	PUNCT
ejpam-4306	89	18	the	the	DET
ejpam-4306	89	19	solution	solution	NOUN
ejpam-4306	89	20	of	of	ADP
ejpam-4306	89	21	equation	equation	NOUN
ejpam-4306	89	22	(	(	PUNCT
ejpam-4306	89	23	3	3	X
ejpam-4306	89	24	)	)	PUNCT
ejpam-4306	89	25	has	have	VERB
ejpam-4306	89	26	a	a	DET
ejpam-4306	89	27	discrete	discrete	ADJ
ejpam-4306	89	28	two	two	NUM
ejpam-4306	89	29	motional	motional	ADJ
ejpam-4306	89	30	oscillation	oscillation	NOUN
ejpam-4306	89	31	when	when	SCONJ
ejpam-4306	89	32	2	2	NUM
ejpam-4306	89	33	−	−	NOUN
ejpam-4306	89	34	x2	x2	INTJ
ejpam-4306	89	35	>	>	X
ejpam-4306	89	36	0	0	NUM
ejpam-4306	89	37	,	,	PUNCT
ejpam-4306	89	38	|x|	|x|	PROPN
ejpam-4306	89	39	<	<	X
ejpam-4306	89	40	√	√	PROPN
ejpam-4306	89	41	2	2	NUM
ejpam-4306	89	42	otherwise	otherwise	ADV
ejpam-4306	89	43	we	we	PRON
ejpam-4306	89	44	have	have	VERB
ejpam-4306	89	45	the	the	DET
ejpam-4306	89	46	two	two	NUM
ejpam-4306	89	47	motional	motional	ADJ
ejpam-4306	89	48	oscillation	oscillation	NOUN
ejpam-4306	89	49	intersect	intersect	ADJ
ejpam-4306	89	50	,	,	PUNCT
ejpam-4306	89	51	provided	provide	VERB
ejpam-4306	89	52	that	that	SCONJ
ejpam-4306	89	53	α	α	PRON
ejpam-4306	89	54	is	be	AUX
ejpam-4306	89	55	positive	positive	ADJ
ejpam-4306	89	56	in	in	ADP
ejpam-4306	89	57	the	the	DET
ejpam-4306	89	58	term	term	NOUN
ejpam-4306	89	59	√	√	ADV
ejpam-4306	89	60	2	2	NUM
ejpam-4306	89	61	α	α	NOUN
ejpam-4306	89	62	.	.	PUNCT
ejpam-4306	90	1	3	3	X
ejpam-4306	90	2	.	.	X
ejpam-4306	90	3	the	the	DET
ejpam-4306	90	4	exact	exact	ADJ
ejpam-4306	90	5	solution	solution	NOUN
ejpam-4306	90	6	with	with	ADP
ejpam-4306	90	7	modifying	modify	VERB
ejpam-4306	90	8	in	in	ADP
ejpam-4306	90	9	the	the	DET
ejpam-4306	90	10	potential	potential	ADJ
ejpam-4306	90	11	function	function	NOUN
ejpam-4306	90	12	in	in	ADP
ejpam-4306	90	13	section	section	NOUN
ejpam-4306	90	14	2	2	NUM
ejpam-4306	90	15	,	,	PUNCT
ejpam-4306	90	16	the	the	DET
ejpam-4306	90	17	following	follow	VERB
ejpam-4306	90	18	scalar	scalar	ADJ
ejpam-4306	90	19	function	function	NOUN
ejpam-4306	90	20	was	be	AUX
ejpam-4306	90	21	obtained	obtain	VERB
ejpam-4306	90	22	ψ(x	ψ(x	PROPN
ejpam-4306	90	23	,	,	PUNCT
ejpam-4306	90	24	v	v	NOUN
ejpam-4306	90	25	)	)	PUNCT
ejpam-4306	90	26	=	=	SYM
ejpam-4306	90	27	1	1	NUM
ejpam-4306	90	28	2	2	NUM
ejpam-4306	90	29	(	(	PUNCT
ejpam-4306	90	30	1	1	NUM
ejpam-4306	90	31	+	+	CCONJ
ejpam-4306	91	1	αx2)v2	αx2)v2	NOUN
ejpam-4306	91	2	−	−	NOUN
ejpam-4306	91	3	x2	x2	NOUN
ejpam-4306	91	4	2	2	NUM
ejpam-4306	91	5	+	+	CCONJ
ejpam-4306	91	6	x4	x4	PROPN
ejpam-4306	91	7	4	4	NUM
ejpam-4306	91	8	+	+	NUM
ejpam-4306	91	9	a2	a2	PROPN
ejpam-4306	91	10	2	2	NUM
ejpam-4306	91	11	−	−	NOUN
ejpam-4306	91	12	a4	a4	NOUN
ejpam-4306	91	13	4	4	NUM
ejpam-4306	91	14	(	(	PUNCT
ejpam-4306	91	15	4	4	NUM
ejpam-4306	91	16	)	)	PUNCT
ejpam-4306	91	17	if	if	SCONJ
ejpam-4306	91	18	we	we	PRON
ejpam-4306	91	19	replace	replace	VERB
ejpam-4306	91	20	the	the	DET
ejpam-4306	91	21	constant	constant	ADJ
ejpam-4306	91	22	position	position	NOUN
ejpam-4306	91	23	term	term	NOUN
ejpam-4306	91	24	from	from	ADP
ejpam-4306	91	25	the	the	DET
ejpam-4306	91	26	potintial	potintial	ADJ
ejpam-4306	91	27	function	function	NOUN
ejpam-4306	91	28	ψ(x	ψ(x	PROPN
ejpam-4306	91	29	,	,	PUNCT
ejpam-4306	91	30	v	v	NOUN
ejpam-4306	91	31	)	)	PUNCT
ejpam-4306	91	32	to	to	PART
ejpam-4306	91	33	be	be	AUX
ejpam-4306	91	34	propotinal	propotinal	ADJ
ejpam-4306	91	35	by	by	ADP
ejpam-4306	91	36	a2	a2	PROPN
ejpam-4306	91	37	2	2	NUM
ejpam-4306	91	38	−	−	NOUN
ejpam-4306	91	39	a4	a4	NOUN
ejpam-4306	91	40	4	4	NUM
ejpam-4306	91	41	=	=	SYM
ejpam-4306	91	42	βx2,where	βx2,where	X
ejpam-4306	91	43	β	β	X
ejpam-4306	91	44	≥	≥	NOUN
ejpam-4306	91	45	0,then	0,then	X
ejpam-4306	91	46	equation	equation	NOUN
ejpam-4306	91	47	(	(	PUNCT
ejpam-4306	91	48	4	4	X
ejpam-4306	91	49	)	)	PUNCT
ejpam-4306	91	50	becomes	become	VERB
ejpam-4306	91	51	ψ(x	ψ(x	PROPN
ejpam-4306	91	52	,	,	PUNCT
ejpam-4306	91	53	v	v	NOUN
ejpam-4306	91	54	)	)	PUNCT
ejpam-4306	91	55	=	=	SYM
ejpam-4306	91	56	1	1	NUM
ejpam-4306	91	57	2	2	NUM
ejpam-4306	91	58	(	(	PUNCT
ejpam-4306	91	59	1	1	NUM
ejpam-4306	91	60	+	+	CCONJ
ejpam-4306	91	61	αx2)v2	αx2)v2	NOUN
ejpam-4306	91	62	−	−	NOUN
ejpam-4306	91	63	x2	x2	NOUN
ejpam-4306	91	64	2	2	NUM
ejpam-4306	91	65	+	+	CCONJ
ejpam-4306	91	66	x4	x4	PROPN
ejpam-4306	91	67	4	4	NUM
ejpam-4306	92	1	+	+	CCONJ
ejpam-4306	92	2	βx2	βx2	PROPN
ejpam-4306	93	1	so	so	ADV
ejpam-4306	93	2	1	1	NUM
ejpam-4306	93	3	2	2	NUM
ejpam-4306	93	4	(	(	PUNCT
ejpam-4306	93	5	1	1	NUM
ejpam-4306	93	6	+	+	CCONJ
ejpam-4306	93	7	αx2)v2	αx2)v2	NOUN
ejpam-4306	93	8	−	−	NOUN
ejpam-4306	93	9	x2	x2	NOUN
ejpam-4306	93	10	2	2	NUM
ejpam-4306	93	11	+	+	CCONJ
ejpam-4306	93	12	x4	x4	PROPN
ejpam-4306	93	13	4	4	NUM
ejpam-4306	93	14	+	+	CCONJ
ejpam-4306	93	15	βx2	βx2	NOUN
ejpam-4306	93	16	=	=	SYM
ejpam-4306	93	17	0	0	NUM
ejpam-4306	93	18	t	t	NOUN
ejpam-4306	93	19	=	=	PUNCT
ejpam-4306	93	20	√	√	NUM
ejpam-4306	93	21	2	2	NUM
ejpam-4306	93	22	1	1	NUM
ejpam-4306	93	23	x	x	SYM
ejpam-4306	93	24	√	√	PROPN
ejpam-4306	93	25	(	(	PUNCT
ejpam-4306	93	26	1	1	NUM
ejpam-4306	93	27	+	+	NUM
ejpam-4306	93	28	αx2	αx2	NOUN
ejpam-4306	93	29	)	)	PUNCT
ejpam-4306	93	30	2(1−	2(1−	NUM
ejpam-4306	94	1	2β)−	2β)−	NUM
ejpam-4306	94	2	x2	x2	INTJ
ejpam-4306	94	3	dx	dx	PROPN
ejpam-4306	94	4	a.	a.	PROPN
ejpam-4306	94	5	abuas’ad	abuas’ad	PROPN
ejpam-4306	94	6	,	,	PUNCT
ejpam-4306	94	7	j.	j.	PROPN
ejpam-4306	94	8	asad	asad	PROPN
ejpam-4306	94	9	/	/	SYM
ejpam-4306	94	10	eur	eur	PROPN
ejpam-4306	94	11	.	.	PUNCT
ejpam-4306	95	1	j.	j.	PROPN
ejpam-4306	95	2	pure	pure	PROPN
ejpam-4306	95	3	appl	appl	PROPN
ejpam-4306	95	4	.	.	PROPN
ejpam-4306	95	5	math	math	PROPN
ejpam-4306	95	6	,	,	PUNCT
ejpam-4306	95	7	15	15	NUM
ejpam-4306	95	8	(	(	PUNCT
ejpam-4306	95	9	2	2	NUM
ejpam-4306	95	10	)	)	PUNCT
ejpam-4306	95	11	(	(	PUNCT
ejpam-4306	95	12	2022	2022	NUM
ejpam-4306	95	13	)	)	PUNCT
ejpam-4306	95	14	,	,	PUNCT
ejpam-4306	95	15	496	496	NUM
ejpam-4306	95	16	-	-	SYM
ejpam-4306	95	17	510	510	NUM
ejpam-4306	95	18	501	501	NUM
ejpam-4306	95	19	let	let	VERB
ejpam-4306	95	20	x2	x2	NOUN
ejpam-4306	95	21	=	=	PUNCT
ejpam-4306	95	22	u	u	PROPN
ejpam-4306	95	23	,	,	PUNCT
ejpam-4306	95	24	and	and	CCONJ
ejpam-4306	95	25	2(1−	2(1−	NUM
ejpam-4306	95	26	2β	2β	NUM
ejpam-4306	95	27	)	)	PUNCT
ejpam-4306	95	28	=	=	SYM
ejpam-4306	96	1	λ	λ	NOUN
ejpam-4306	96	2	,	,	PUNCT
ejpam-4306	96	3	then	then	ADV
ejpam-4306	96	4	t	t	PROPN
ejpam-4306	96	5	=	=	SYM
ejpam-4306	96	6	1√	1√	PROPN
ejpam-4306	96	7	2	2	NUM
ejpam-4306	96	8	1	1	NUM
ejpam-4306	96	9	u	u	NOUN
ejpam-4306	96	10	√	√	ADV
ejpam-4306	96	11	1	1	NUM
ejpam-4306	96	12	+	+	NUM
ejpam-4306	96	13	αu	αu	VERB
ejpam-4306	96	14	λ−	λ−	PROPN
ejpam-4306	96	15	u	u	PROPN
ejpam-4306	96	16	du	du	X
ejpam-4306	96	17	(	(	PUNCT
ejpam-4306	96	18	5	5	NUM
ejpam-4306	96	19	)	)	PUNCT
ejpam-4306	96	20	integrating	integrate	VERB
ejpam-4306	96	21	the	the	DET
ejpam-4306	96	22	equation	equation	NOUN
ejpam-4306	96	23	(	(	PUNCT
ejpam-4306	96	24	5	5	NUM
ejpam-4306	96	25	)	)	PUNCT
ejpam-4306	96	26	as	as	ADP
ejpam-4306	96	27	previouse	previouse	NOUN
ejpam-4306	96	28	calculation	calculation	NOUN
ejpam-4306	96	29	we	we	PRON
ejpam-4306	96	30	get	get	VERB
ejpam-4306	96	31	t	t	NOUN
ejpam-4306	96	32	=	=	SYM
ejpam-4306	96	33	1√	1√	PROPN
ejpam-4306	96	34	2λ	2λ	NOUN
ejpam-4306	96	35	ln	ln	NOUN
ejpam-4306	96	36	(	(	PUNCT
ejpam-4306	96	37	√	√	PROPN
ejpam-4306	96	38	λu−	λu−	SYM
ejpam-4306	96	39	1√	1√	NUM
ejpam-4306	96	40	λu+	λu+	NOUN
ejpam-4306	96	41	1	1	NUM
ejpam-4306	96	42	)	)	PUNCT
ejpam-4306	97	1	+	+	CCONJ
ejpam-4306	97	2	1√	1√	PROPN
ejpam-4306	97	3	2λα	2λα	NOUN
ejpam-4306	98	1	tan−1	tan−1	PROPN
ejpam-4306	98	2	(	(	PUNCT
ejpam-4306	98	3	u√	u√	NOUN
ejpam-4306	98	4	α	α	NOUN
ejpam-4306	98	5	)	)	PUNCT
ejpam-4306	99	1	+	+	PUNCT
ejpam-4306	99	2	c	c	NOUN
ejpam-4306	99	3	t	t	NOUN
ejpam-4306	99	4	=	=	SYM
ejpam-4306	99	5	1√	1√	PROPN
ejpam-4306	99	6	4(1−	4(1−	NUM
ejpam-4306	99	7	2β	2β	NUM
ejpam-4306	99	8	)	)	PUNCT
ejpam-4306	100	1	ln	ln	PROPN
ejpam-4306	100	2			PROPN
ejpam-4306	100	3	√	√	NUM
ejpam-4306	100	4	2(1−2β)(1+αx2	2(1−2β)(1+αx2	NUM
ejpam-4306	100	5	)	)	PUNCT
ejpam-4306	100	6	2(1−2β)−x2	2(1−2β)−x2	NUM
ejpam-4306	101	1	−	−	PROPN
ejpam-4306	101	2	1√	1√	PROPN
ejpam-4306	101	3	2(1−2β)(1+αx2	2(1−2β)(1+αx2	NUM
ejpam-4306	101	4	)	)	PUNCT
ejpam-4306	102	1	2(1−2β)−x2	2(1−2β)−x2	NOUN
ejpam-4306	103	1	+	+	SYM
ejpam-4306	103	2	1	1	NUM
ejpam-4306	103	3	+	+	PROPN
ejpam-4306	103	4	1√	1√	NUM
ejpam-4306	103	5	4α(1−	4α(1−	NUM
ejpam-4306	103	6	2β	2β	NOUN
ejpam-4306	103	7	)	)	PUNCT
ejpam-4306	104	1	tan−1	tan−1	PROPN
ejpam-4306	104	2	(	(	PUNCT
ejpam-4306	104	3	√	√	ADP
ejpam-4306	104	4	2(1−	2(1−	NUM
ejpam-4306	104	5	2β	2β	NUM
ejpam-4306	104	6	)	)	PUNCT
ejpam-4306	104	7	(	(	PUNCT
ejpam-4306	104	8	1	1	NUM
ejpam-4306	104	9	+	+	NUM
ejpam-4306	104	10	αx2	αx2	NOUN
ejpam-4306	104	11	)	)	PUNCT
ejpam-4306	105	1	2(1−	2(1−	NUM
ejpam-4306	106	1	2β)−	2β)−	NUM
ejpam-4306	106	2	x2	x2	PROPN
ejpam-4306	106	3	)	)	PUNCT
ejpam-4306	107	1	+	+	CCONJ
ejpam-4306	107	2	c	c	X
ejpam-4306	107	3	applying	apply	VERB
ejpam-4306	107	4	the	the	DET
ejpam-4306	107	5	boundary	boundary	ADJ
ejpam-4306	107	6	condition	condition	NOUN
ejpam-4306	107	7	x(0	x(0	PROPN
ejpam-4306	107	8	)	)	PUNCT
ejpam-4306	107	9	=	=	SYM
ejpam-4306	107	10	a	a	X
ejpam-4306	107	11	,	,	PUNCT
ejpam-4306	107	12	we	we	PRON
ejpam-4306	107	13	obtain	obtain	VERB
ejpam-4306	107	14	c=	c=	NOUN
ejpam-4306	107	15	1√	1√	PROPN
ejpam-4306	107	16	4(1−2β	4(1−2β	NUM
ejpam-4306	107	17	)	)	PUNCT
ejpam-4306	108	1	ln	ln	ADJ
ejpam-4306	108	2			NOUN
ejpam-4306	108	3	√	√	ADV
ejpam-4306	108	4	2(1−2β	2(1−2β	NUM
ejpam-4306	108	5	)	)	PUNCT
ejpam-4306	108	6	(	(	PUNCT
ejpam-4306	108	7	1+αa2	1+αa2	NUM
ejpam-4306	108	8	)	)	PUNCT
ejpam-4306	108	9	2(1−2β)−a2	2(1−2β)−a2	PROPN
ejpam-4306	109	1	+1√	+1√	NUM
ejpam-4306	109	2	2(1−2β	2(1−2β	NUM
ejpam-4306	109	3	)	)	PUNCT
ejpam-4306	109	4	(	(	PUNCT
ejpam-4306	109	5	1+αa2	1+αa2	NUM
ejpam-4306	109	6	)	)	PUNCT
ejpam-4306	109	7	2(1−2β)−a2	2(1−2β)−a2	NUM
ejpam-4306	109	8	−1	−1	NOUN
ejpam-4306	109	9	−	−	PROPN
ejpam-4306	109	10	1√	1√	PROPN
ejpam-4306	109	11	4α(1−2β	4α(1−2β	PROPN
ejpam-4306	109	12	)	)	PUNCT
ejpam-4306	110	1	tan−1	tan−1	PROPN
ejpam-4306	110	2	(	(	PUNCT
ejpam-4306	110	3	√	√	NUM
ejpam-4306	110	4	2(1−2β)(1+αa2	2(1−2β)(1+αa2	NUM
ejpam-4306	110	5	)	)	PUNCT
ejpam-4306	110	6	2(1−2β)−a2	2(1−2β)−a2	NUM
ejpam-4306	110	7	)	)	PUNCT
ejpam-4306	111	1	it	it	PRON
ejpam-4306	111	2	is	be	AUX
ejpam-4306	111	3	important	important	ADJ
ejpam-4306	111	4	to	to	PART
ejpam-4306	111	5	notice	notice	VERB
ejpam-4306	111	6	that	that	SCONJ
ejpam-4306	111	7	|x|	|x|	PROPN
ejpam-4306	111	8	<	<	X
ejpam-4306	111	9	√	√	ADJ
ejpam-4306	111	10	4(1−	4(1−	NUM
ejpam-4306	111	11	2β	2β	NOUN
ejpam-4306	111	12	)	)	PUNCT
ejpam-4306	111	13	<	<	X
ejpam-4306	111	14	√	√	NUM
ejpam-4306	111	15	2	2	NUM
ejpam-4306	111	16	,	,	PUNCT
ejpam-4306	111	17	0	0	NUM
ejpam-4306	111	18	≤	≤	NUM
ejpam-4306	111	19	β	β	X
ejpam-4306	111	20	<	<	X
ejpam-4306	111	21	1	1	NUM
ejpam-4306	111	22	2	2	NUM
ejpam-4306	111	23	,	,	PUNCT
ejpam-4306	111	24	and	and	CCONJ
ejpam-4306	111	25	α	α	X
ejpam-4306	111	26	>	>	X
ejpam-4306	111	27	0	0	NUM
ejpam-4306	111	28	due	due	ADP
ejpam-4306	111	29	to	to	ADP
ejpam-4306	111	30	the	the	DET
ejpam-4306	111	31	present	present	NOUN
ejpam-4306	111	32	the	the	DET
ejpam-4306	111	33	following	follow	VERB
ejpam-4306	111	34	term	term	NOUN
ejpam-4306	111	35	√	√	ADP
ejpam-4306	111	36	2(1−	2(1−	NUM
ejpam-4306	111	37	2β	2β	NUM
ejpam-4306	111	38	)	)	PUNCT
ejpam-4306	111	39	(	(	PUNCT
ejpam-4306	111	40	1	1	NUM
ejpam-4306	111	41	+	+	NUM
ejpam-4306	111	42	αx2	αx2	NOUN
ejpam-4306	111	43	)	)	PUNCT
ejpam-4306	111	44	2(1−	2(1−	NUM
ejpam-4306	112	1	2β)−	2β)−	NUM
ejpam-4306	112	2	x2	x2	INTJ
ejpam-4306	112	3	>	>	X
ejpam-4306	113	1	1	1	NUM
ejpam-4306	114	1	here	here	ADV
ejpam-4306	114	2	we	we	PRON
ejpam-4306	114	3	have	have	VERB
ejpam-4306	114	4	a	a	DET
ejpam-4306	114	5	solution	solution	NOUN
ejpam-4306	114	6	for	for	ADP
ejpam-4306	114	7	this	this	DET
ejpam-4306	114	8	equation	equation	NOUN
ejpam-4306	114	9	to	to	PART
ejpam-4306	114	10	make	make	VERB
ejpam-4306	114	11	a	a	DET
ejpam-4306	114	12	two	two	NUM
ejpam-4306	114	13	discrete	discrete	ADJ
ejpam-4306	114	14	oscillate	oscillate	NOUN
ejpam-4306	114	15	motion	motion	NOUN
ejpam-4306	114	16	(	(	PUNCT
ejpam-4306	114	17	see	see	VERB
ejpam-4306	114	18	figs	fig	NOUN
ejpam-4306	114	19	.	.	PUNCT
ejpam-4306	115	1	1314	1314	NUM
ejpam-4306	115	2	,	,	PUNCT
ejpam-4306	115	3	when	when	SCONJ
ejpam-4306	115	4	|x|	|x|	PROPN
ejpam-4306	115	5	<	<	X
ejpam-4306	115	6	√	√	ADP
ejpam-4306	115	7	2(1−	2(1−	NUM
ejpam-4306	115	8	2β	2β	NUM
ejpam-4306	115	9	)	)	PUNCT
ejpam-4306	115	10	<	<	X
ejpam-4306	115	11	√	√	NUM
ejpam-4306	115	12	2	2	NUM
ejpam-4306	115	13	,	,	PUNCT
ejpam-4306	115	14	0	0	NUM
ejpam-4306	115	15	≤	≤	NUM
ejpam-4306	115	16	β	β	X
ejpam-4306	115	17	<	<	X
ejpam-4306	115	18	1	1	NUM
ejpam-4306	115	19	2	2	NUM
ejpam-4306	115	20	otherwise	otherwise	ADV
ejpam-4306	115	21	we	we	PRON
ejpam-4306	115	22	have	have	VERB
ejpam-4306	115	23	overlapping	overlap	VERB
ejpam-4306	115	24	by	by	ADP
ejpam-4306	115	25	two	two	NUM
ejpam-4306	115	26	oscillate	oscillate	ADJ
ejpam-4306	115	27	motion	motion	NOUN
ejpam-4306	115	28	(	(	PUNCT
ejpam-4306	115	29	see	see	VERB
ejpam-4306	115	30	figs	fig	NOUN
ejpam-4306	115	31	.	.	PUNCT
ejpam-4306	116	1	24	24	NUM
ejpam-4306	116	2	)	)	PUNCT
ejpam-4306	116	3	.	.	PUNCT
ejpam-4306	117	1	4	4	X
ejpam-4306	117	2	.	.	X
ejpam-4306	117	3	an	an	DET
ejpam-4306	117	4	equilibrium	equilibrium	NOUN
ejpam-4306	117	5	points	point	NOUN
ejpam-4306	117	6	and	and	CCONJ
ejpam-4306	117	7	their	their	PRON
ejpam-4306	117	8	stability	stability	NOUN
ejpam-4306	117	9	with	with	ADP
ejpam-4306	117	10	graphical	graphical	ADJ
ejpam-4306	117	11	simulation	simulation	NOUN
ejpam-4306	117	12	in	in	ADP
ejpam-4306	117	13	this	this	DET
ejpam-4306	117	14	section	section	NOUN
ejpam-4306	117	15	,	,	PUNCT
ejpam-4306	117	16	we	we	PRON
ejpam-4306	117	17	are	be	AUX
ejpam-4306	117	18	going	go	VERB
ejpam-4306	117	19	to	to	PART
ejpam-4306	117	20	find	find	VERB
ejpam-4306	117	21	the	the	DET
ejpam-4306	117	22	equilibrium	equilibrium	NOUN
ejpam-4306	117	23	points	point	NOUN
ejpam-4306	117	24	and	and	CCONJ
ejpam-4306	117	25	analyse	analyse	VERB
ejpam-4306	117	26	their	their	PRON
ejpam-4306	117	27	stability	stability	NOUN
ejpam-4306	117	28	.	.	PUNCT
ejpam-4306	118	1	for	for	SCONJ
ejpam-4306	118	2	this	this	DET
ejpam-4306	118	3	issue	issue	NOUN
ejpam-4306	118	4	convert	convert	VERB
ejpam-4306	118	5	equation(1	equation(1	NOUN
ejpam-4306	118	6	)	)	PUNCT
ejpam-4306	118	7	to	to	ADP
ejpam-4306	118	8	a	a	DET
ejpam-4306	118	9	system	system	NOUN
ejpam-4306	118	10	of	of	ADP
ejpam-4306	118	11	nonlinear	nonlinear	ADJ
ejpam-4306	118	12	equation	equation	NOUN
ejpam-4306	118	13	by	by	ADP
ejpam-4306	118	14	y1	y1	NOUN
ejpam-4306	118	15	=	=	SYM
ejpam-4306	118	16	x	x	NOUN
ejpam-4306	118	17	,	,	PUNCT
ejpam-4306	118	18	y2	y2	PROPN
ejpam-4306	118	19	=	=	PUNCT
ejpam-4306	119	1	ẋ,then	ẋ,then	PROPN
ejpam-4306	119	2	we	we	PRON
ejpam-4306	119	3	get	get	VERB
ejpam-4306	119	4	the	the	DET
ejpam-4306	119	5	following	follow	VERB
ejpam-4306	119	6	two	two	NUM
ejpam-4306	119	7	nonlinear	nonlinear	ADJ
ejpam-4306	119	8	system	system	NOUN
ejpam-4306	119	9	of	of	ADP
ejpam-4306	119	10	equation	equation	NOUN
ejpam-4306	119	11	.	.	PUNCT
ejpam-4306	120	1	ẏ1	ẏ1	NOUN
ejpam-4306	120	2	=	=	SYM
ejpam-4306	120	3	y2	y2	PROPN
ejpam-4306	120	4	(	(	PUNCT
ejpam-4306	120	5	6	6	NUM
ejpam-4306	120	6	)	)	PUNCT
ejpam-4306	120	7	ẏ2	ẏ2	NOUN
ejpam-4306	120	8	=	=	SYM
ejpam-4306	120	9	−(αy1y	−(αy1y	PROPN
ejpam-4306	120	10	2	2	NUM
ejpam-4306	120	11	2	2	NUM
ejpam-4306	120	12	−	−	NOUN
ejpam-4306	120	13	y1(1−	y1(1−	NOUN
ejpam-4306	121	1	y21)/(1	y21)/(1	PROPN
ejpam-4306	121	2	+	+	PUNCT
ejpam-4306	121	3	αy21	αy21	PROPN
ejpam-4306	121	4	)	)	PUNCT
ejpam-4306	121	5	now	now	ADV
ejpam-4306	121	6	let	let	VERB
ejpam-4306	121	7	[	[	PUNCT
ejpam-4306	121	8	y2	y2	NOUN
ejpam-4306	121	9	−(αy1y	−(αy1y	PROPN
ejpam-4306	121	10	2	2	NUM
ejpam-4306	121	11	2	2	NUM
ejpam-4306	121	12	−	−	NOUN
ejpam-4306	121	13	y1(1−	y1(1−	NOUN
ejpam-4306	122	1	y21)/(1	y21)/(1	PROPN
ejpam-4306	122	2	+	+	PUNCT
ejpam-4306	122	3	αy21	αy21	PROPN
ejpam-4306	122	4	)	)	PUNCT
ejpam-4306	123	1	=	=	PUNCT
ejpam-4306	124	1	[	[	PUNCT
ejpam-4306	124	2	0	0	NUM
ejpam-4306	124	3	0	0	NUM
ejpam-4306	124	4	]	]	X
ejpam-4306	124	5	]	]	X
ejpam-4306	124	6	(	(	PUNCT
ejpam-4306	124	7	7	7	X
ejpam-4306	124	8	)	)	PUNCT
ejpam-4306	124	9	a.	a.	NOUN
ejpam-4306	124	10	abuas’ad	abuas’ad	PROPN
ejpam-4306	124	11	,	,	PUNCT
ejpam-4306	124	12	j.	j.	PROPN
ejpam-4306	124	13	asad	asad	PROPN
ejpam-4306	124	14	/	/	SYM
ejpam-4306	124	15	eur	eur	PROPN
ejpam-4306	124	16	.	.	PUNCT
ejpam-4306	125	1	j.	j.	PROPN
ejpam-4306	125	2	pure	pure	PROPN
ejpam-4306	125	3	appl	appl	PROPN
ejpam-4306	125	4	.	.	PROPN
ejpam-4306	125	5	math	math	PROPN
ejpam-4306	125	6	,	,	PUNCT
ejpam-4306	125	7	15	15	NUM
ejpam-4306	125	8	(	(	PUNCT
ejpam-4306	125	9	2	2	NUM
ejpam-4306	125	10	)	)	PUNCT
ejpam-4306	125	11	(	(	PUNCT
ejpam-4306	125	12	2022	2022	NUM
ejpam-4306	125	13	)	)	PUNCT
ejpam-4306	125	14	,	,	PUNCT
ejpam-4306	125	15	496	496	NUM
ejpam-4306	125	16	-	-	SYM
ejpam-4306	125	17	510	510	NUM
ejpam-4306	125	18	502	502	NUM
ejpam-4306	125	19	solving	solving	NOUN
ejpam-4306	125	20	equations(7	equations(7	NOUN
ejpam-4306	125	21	)	)	PUNCT
ejpam-4306	126	1	one	one	PRON
ejpam-4306	126	2	gets	get	VERB
ejpam-4306	126	3	three	three	NUM
ejpam-4306	126	4	equilibrium	equilibrium	NOUN
ejpam-4306	126	5	points	point	NOUN
ejpam-4306	126	6	(	(	PUNCT
ejpam-4306	126	7	y∗1	y∗1	NOUN
ejpam-4306	126	8	,	,	PUNCT
ejpam-4306	126	9	y	y	PROPN
ejpam-4306	126	10	∗	∗	NOUN
ejpam-4306	126	11	2	2	NUM
ejpam-4306	126	12	)	)	PUNCT
ejpam-4306	126	13	=	=	SYM
ejpam-4306	126	14	(	(	PUNCT
ejpam-4306	126	15	0	0	NUM
ejpam-4306	126	16	,	,	PUNCT
ejpam-4306	126	17	0	0	NUM
ejpam-4306	126	18	)	)	PUNCT
ejpam-4306	126	19	,	,	PUNCT
ejpam-4306	126	20	(	(	PUNCT
ejpam-4306	126	21	1	1	NUM
ejpam-4306	126	22	,	,	PUNCT
ejpam-4306	126	23	0	0	NUM
ejpam-4306	126	24	)	)	PUNCT
ejpam-4306	126	25	,	,	PUNCT
ejpam-4306	126	26	(	(	PUNCT
ejpam-4306	126	27	−1	−1	NOUN
ejpam-4306	126	28	,	,	PUNCT
ejpam-4306	126	29	0	0	NUM
ejpam-4306	126	30	)	)	PUNCT
ejpam-4306	126	31	.	.	PUNCT
ejpam-4306	127	1	to	to	PART
ejpam-4306	127	2	determine	determine	VERB
ejpam-4306	127	3	their	their	PRON
ejpam-4306	127	4	stability	stability	NOUN
ejpam-4306	127	5	of	of	ADP
ejpam-4306	127	6	the	the	DET
ejpam-4306	127	7	equilibrium	equilibrium	NOUN
ejpam-4306	127	8	points	point	NOUN
ejpam-4306	127	9	we	we	PRON
ejpam-4306	127	10	find	find	VERB
ejpam-4306	127	11	the	the	DET
ejpam-4306	127	12	jacobian	jacobian	ADJ
ejpam-4306	127	13	matrix	matrix	NOUN
ejpam-4306	127	14	for	for	ADP
ejpam-4306	127	15	the	the	DET
ejpam-4306	127	16	system(6	system(6	PROPN
ejpam-4306	127	17	)	)	PUNCT
ejpam-4306	127	18	j	j	PROPN
ejpam-4306	128	1	=	=	PUNCT
ejpam-4306	128	2	[	[	PUNCT
ejpam-4306	128	3	0	0	NUM
ejpam-4306	128	4	1	1	NUM
ejpam-4306	128	5	−	−	NOUN
ejpam-4306	128	6	[	[	PUNCT
ejpam-4306	128	7	(	(	PUNCT
ejpam-4306	128	8	1	1	NUM
ejpam-4306	128	9	+	+	CCONJ
ejpam-4306	128	10	αy21)(αy	αy21)(αy	NOUN
ejpam-4306	128	11	2	2	NUM
ejpam-4306	128	12	2	2	NUM
ejpam-4306	128	13	+	+	NUM
ejpam-4306	128	14	3y21	3y21	NUM
ejpam-4306	129	1	−	−	PROPN
ejpam-4306	129	2	1)−	1)−	PROPN
ejpam-4306	129	3	(	(	PUNCT
ejpam-4306	129	4	αy1y	αy1y	PROPN
ejpam-4306	129	5	2	2	NUM
ejpam-4306	129	6	2	2	NUM
ejpam-4306	129	7	−	−	NOUN
ejpam-4306	129	8	y1(1−	y1(1−	NOUN
ejpam-4306	129	9	y21))2αy1	y21))2αy1	NOUN
ejpam-4306	129	10	]	]	PUNCT
ejpam-4306	129	11	/(1	/(1	PUNCT
ejpam-4306	130	1	+	+	CCONJ
ejpam-4306	130	2	αy21	αy21	PROPN
ejpam-4306	130	3	)	)	PUNCT
ejpam-4306	130	4	2	2	NUM
ejpam-4306	130	5	−2αy1y2/(1	−2αy1y2/(1	NOUN
ejpam-4306	130	6	+	+	X
ejpam-4306	130	7	αy21	αy21	PROPN
ejpam-4306	130	8	)	)	PUNCT
ejpam-4306	130	9	]	]	PUNCT
ejpam-4306	130	10	at	at	ADP
ejpam-4306	130	11	the	the	DET
ejpam-4306	130	12	point	point	NOUN
ejpam-4306	130	13	(	(	PUNCT
ejpam-4306	130	14	0	0	NUM
ejpam-4306	130	15	,	,	PUNCT
ejpam-4306	130	16	0)the	0)the	PRON
ejpam-4306	130	17	jacobian	jacobian	PROPN
ejpam-4306	130	18	j	j	PROPN
ejpam-4306	131	1	=	=	PUNCT
ejpam-4306	132	1	[	[	PUNCT
ejpam-4306	132	2	0	0	NUM
ejpam-4306	132	3	1	1	NUM
ejpam-4306	132	4	1	1	NUM
ejpam-4306	132	5	0	0	NUM
ejpam-4306	132	6	]	]	PUNCT
ejpam-4306	132	7	since	since	SCONJ
ejpam-4306	132	8	the	the	DET
ejpam-4306	132	9	charactrestic	charactrestic	ADJ
ejpam-4306	132	10	equation	equation	NOUN
ejpam-4306	132	11	is	be	AUX
ejpam-4306	132	12	λ2−	λ2−	NOUN
ejpam-4306	132	13	1	1	NUM
ejpam-4306	132	14	=	=	SYM
ejpam-4306	132	15	0	0	NUM
ejpam-4306	133	1	so	so	ADV
ejpam-4306	133	2	the	the	DET
ejpam-4306	133	3	eigenvalues	eigenvalue	NOUN
ejpam-4306	133	4	are	be	AUX
ejpam-4306	133	5	λ1,2	λ1,2	ADJ
ejpam-4306	133	6	=	=	SYM
ejpam-4306	133	7	±1	±1	VERB
ejpam-4306	133	8	so	so	SCONJ
ejpam-4306	133	9	the	the	DET
ejpam-4306	133	10	fixed	fix	VERB
ejpam-4306	133	11	point	point	NOUN
ejpam-4306	133	12	is	be	AUX
ejpam-4306	133	13	unstable	unstable	ADJ
ejpam-4306	133	14	as	as	SCONJ
ejpam-4306	133	15	shown	show	VERB
ejpam-4306	133	16	in	in	ADP
ejpam-4306	133	17	the	the	DET
ejpam-4306	133	18	graphical	graphical	ADJ
ejpam-4306	133	19	analysis	analysis	NOUN
ejpam-4306	133	20	(	(	PUNCT
ejpam-4306	133	21	see	see	VERB
ejpam-4306	133	22	figs	fig	NOUN
ejpam-4306	133	23	.	.	PUNCT
ejpam-4306	134	1	23	23	NUM
ejpam-4306	134	2	)	)	PUNCT
ejpam-4306	134	3	.	.	PUNCT
ejpam-4306	135	1	for	for	ADP
ejpam-4306	135	2	the	the	DET
ejpam-4306	135	3	other	other	ADJ
ejpam-4306	135	4	two	two	NUM
ejpam-4306	135	5	equilibrium	equilibrium	NOUN
ejpam-4306	135	6	points	point	NOUN
ejpam-4306	135	7	(	(	PUNCT
ejpam-4306	135	8	±1	±1	VERB
ejpam-4306	135	9	,	,	PUNCT
ejpam-4306	135	10	0	0	NUM
ejpam-4306	135	11	)	)	PUNCT
ejpam-4306	135	12	,	,	PUNCT
ejpam-4306	135	13	the	the	DET
ejpam-4306	135	14	jacobian	jacobian	PROPN
ejpam-4306	135	15	takes	take	VERB
ejpam-4306	135	16	the	the	DET
ejpam-4306	135	17	following	follow	VERB
ejpam-4306	135	18	form	form	NOUN
ejpam-4306	135	19	:	:	PUNCT
ejpam-4306	136	1	j	j	X
ejpam-4306	137	1	=	=	PUNCT
ejpam-4306	138	1	[	[	PUNCT
ejpam-4306	138	2	0	0	NUM
ejpam-4306	138	3	1	1	NUM
ejpam-4306	138	4	−2	−2	NOUN
ejpam-4306	138	5	1+α	1+α	NUM
ejpam-4306	138	6	0	0	NUM
ejpam-4306	138	7	]	]	PUNCT
ejpam-4306	138	8	.	.	PUNCT
ejpam-4306	139	1	so	so	ADV
ejpam-4306	139	2	λ1,2	λ1,2	PROPN
ejpam-4306	139	3	=	=	SYM
ejpam-4306	139	4	±	±	NOUN
ejpam-4306	139	5	√	√	ADV
ejpam-4306	139	6	2	2	NUM
ejpam-4306	139	7	1+α	1+α	NUM
ejpam-4306	140	1	i	i	PRON
ejpam-4306	140	2	this	this	PRON
ejpam-4306	140	3	means	mean	VERB
ejpam-4306	140	4	that	that	SCONJ
ejpam-4306	140	5	the	the	DET
ejpam-4306	140	6	points	point	NOUN
ejpam-4306	140	7	(	(	PUNCT
ejpam-4306	140	8	±1	±1	VERB
ejpam-4306	140	9	,	,	PUNCT
ejpam-4306	140	10	0	0	NUM
ejpam-4306	140	11	)	)	PUNCT
ejpam-4306	140	12	are	be	AUX
ejpam-4306	140	13	center	center	NOUN
ejpam-4306	140	14	points	point	NOUN
ejpam-4306	140	15	when	when	SCONJ
ejpam-4306	140	16	α	α	X
ejpam-4306	140	17	∈	∈	PROPN
ejpam-4306	140	18	(	(	PUNCT
ejpam-4306	140	19	−∞,−1	−∞,−1	NOUN
ejpam-4306	140	20	)	)	PUNCT
ejpam-4306	140	21	goes	go	VERB
ejpam-4306	140	22	to	to	PART
ejpam-4306	140	23	limit	limit	VERB
ejpam-4306	140	24	cycle	cycle	NOUN
ejpam-4306	140	25	and	and	CCONJ
ejpam-4306	140	26	unstable	unstable	ADJ
ejpam-4306	140	27	when	when	SCONJ
ejpam-4306	140	28	α	α	PROPN
ejpam-4306	140	29	∈	∈	PROPN
ejpam-4306	140	30	(	(	PUNCT
ejpam-4306	140	31	−1,∞	−1,∞	NOUN
ejpam-4306	140	32	)	)	PUNCT
ejpam-4306	140	33	since	since	SCONJ
ejpam-4306	140	34	one	one	NUM
ejpam-4306	140	35	of	of	ADP
ejpam-4306	140	36	the	the	DET
ejpam-4306	140	37	eigenvalues	eigenvalue	NOUN
ejpam-4306	140	38	is	be	AUX
ejpam-4306	140	39	positive	positive	ADJ
ejpam-4306	140	40	and	and	CCONJ
ejpam-4306	140	41	the	the	DET
ejpam-4306	140	42	other	other	ADJ
ejpam-4306	140	43	is	be	AUX
ejpam-4306	140	44	negative	negative	ADJ
ejpam-4306	140	45	.	.	PUNCT
ejpam-4306	141	1	since	since	SCONJ
ejpam-4306	141	2	the	the	DET
ejpam-4306	141	3	fixed	fix	VERB
ejpam-4306	141	4	points	point	NOUN
ejpam-4306	141	5	does	do	AUX
ejpam-4306	141	6	not	not	PART
ejpam-4306	141	7	depend	depend	VERB
ejpam-4306	141	8	on	on	ADP
ejpam-4306	141	9	the	the	DET
ejpam-4306	141	10	value	value	NOUN
ejpam-4306	141	11	of	of	ADP
ejpam-4306	141	12	α	α	NOUN
ejpam-4306	141	13	so	so	SCONJ
ejpam-4306	141	14	we	we	PRON
ejpam-4306	141	15	can	can	AUX
ejpam-4306	141	16	take	take	VERB
ejpam-4306	141	17	it	it	PRON
ejpam-4306	141	18	any	any	DET
ejpam-4306	141	19	real	real	ADJ
ejpam-4306	141	20	value	value	NOUN
ejpam-4306	141	21	so	so	SCONJ
ejpam-4306	141	22	we	we	PRON
ejpam-4306	141	23	can	can	AUX
ejpam-4306	141	24	make	make	VERB
ejpam-4306	141	25	simulation	simulation	NOUN
ejpam-4306	141	26	for	for	ADP
ejpam-4306	141	27	the	the	DET
ejpam-4306	141	28	solution	solution	NOUN
ejpam-4306	141	29	graphically	graphically	ADV
ejpam-4306	141	30	.	.	PUNCT
ejpam-4306	142	1	below	below	ADV
ejpam-4306	142	2	,	,	PUNCT
ejpam-4306	142	3	we	we	PRON
ejpam-4306	142	4	plot	plot	VERB
ejpam-4306	142	5	the	the	DET
ejpam-4306	142	6	oscillator	oscillator	NOUN
ejpam-4306	142	7	equation	equation	NOUN
ejpam-4306	142	8	of	of	ADP
ejpam-4306	142	9	motion	motion	NOUN
ejpam-4306	142	10	with	with	ADP
ejpam-4306	142	11	the	the	DET
ejpam-4306	142	12	following	follow	VERB
ejpam-4306	142	13	cases	case	NOUN
ejpam-4306	142	14	.	.	PUNCT
ejpam-4306	143	1	case	case	NOUN
ejpam-4306	143	2	i.	i.	NOUN
ejpam-4306	143	3	for	for	ADP
ejpam-4306	143	4	fixed	fix	VERB
ejpam-4306	143	5	point	point	NOUN
ejpam-4306	143	6	(	(	PUNCT
ejpam-4306	143	7	0	0	NUM
ejpam-4306	143	8	,	,	PUNCT
ejpam-4306	143	9	0	0	NUM
ejpam-4306	143	10	)	)	PUNCT
ejpam-4306	143	11	,	,	PUNCT
ejpam-4306	143	12	where	where	SCONJ
ejpam-4306	143	13	α	α	X
ejpam-4306	143	14	any	any	DET
ejpam-4306	143	15	real	real	ADJ
ejpam-4306	143	16	figure	figure	NOUN
ejpam-4306	143	17	1	1	NUM
ejpam-4306	143	18	:	:	PUNCT
ejpam-4306	143	19	(	(	PUNCT
ejpam-4306	143	20	0	0	NUM
ejpam-4306	143	21	,	,	PUNCT
ejpam-4306	143	22	0	0	NUM
ejpam-4306	143	23	)	)	PUNCT
ejpam-4306	143	24	α	α	PROPN
ejpam-4306	143	25	∈	∈	PROPN
ejpam-4306	143	26	r.	r.	NOUN
ejpam-4306	143	27	we	we	PRON
ejpam-4306	143	28	see	see	VERB
ejpam-4306	143	29	that	that	SCONJ
ejpam-4306	143	30	the	the	DET
ejpam-4306	143	31	fixed	fixed	ADJ
ejpam-4306	143	32	point	point	NOUN
ejpam-4306	143	33	still	still	ADV
ejpam-4306	143	34	(	(	PUNCT
ejpam-4306	143	35	0	0	NUM
ejpam-4306	143	36	,	,	PUNCT
ejpam-4306	143	37	0)despite	0)despite	NUM
ejpam-4306	143	38	the	the	DET
ejpam-4306	143	39	changes	change	NOUN
ejpam-4306	143	40	in	in	ADP
ejpam-4306	143	41	α	α	PROPN
ejpam-4306	143	42	(	(	PUNCT
ejpam-4306	143	43	see	see	VERB
ejpam-4306	143	44	fig	fig	NOUN
ejpam-4306	143	45	.	.	PUNCT
ejpam-4306	144	1	1	1	NUM
ejpam-4306	144	2	)	)	PUNCT
ejpam-4306	144	3	so	so	SCONJ
ejpam-4306	144	4	the	the	DET
ejpam-4306	144	5	fixed	fix	VERB
ejpam-4306	144	6	point	point	NOUN
ejpam-4306	144	7	does	do	AUX
ejpam-4306	144	8	not	not	PART
ejpam-4306	144	9	depend	depend	VERB
ejpam-4306	144	10	in	in	ADP
ejpam-4306	144	11	α	α	NOUN
ejpam-4306	144	12	,	,	PUNCT
ejpam-4306	144	13	while	while	SCONJ
ejpam-4306	144	14	if	if	SCONJ
ejpam-4306	144	15	we	we	PRON
ejpam-4306	144	16	move	move	VERB
ejpam-4306	144	17	a	a	DET
ejpam-4306	144	18	little	little	ADJ
ejpam-4306	144	19	bet	bet	NOUN
ejpam-4306	144	20	from	from	ADP
ejpam-4306	144	21	this	this	DET
ejpam-4306	144	22	fixed	fix	VERB
ejpam-4306	144	23	point	point	NOUN
ejpam-4306	144	24	oscillation	oscillation	NOUN
ejpam-4306	144	25	intersect	intersect	ADJ
ejpam-4306	144	26	as	as	ADP
ejpam-4306	144	27	in	in	ADP
ejpam-4306	144	28	(	(	PUNCT
ejpam-4306	144	29	figs	fig	NOUN
ejpam-4306	144	30	.	.	PUNCT
ejpam-4306	145	1	2	2	NUM
ejpam-4306	145	2	-	-	SYM
ejpam-4306	145	3	3	3	NUM
ejpam-4306	145	4	)	)	PUNCT
ejpam-4306	145	5	this	this	PRON
ejpam-4306	145	6	is	be	AUX
ejpam-4306	145	7	show	show	NOUN
ejpam-4306	145	8	how	how	SCONJ
ejpam-4306	145	9	the	the	DET
ejpam-4306	145	10	fixed	fixed	ADJ
ejpam-4306	145	11	point	point	NOUN
ejpam-4306	145	12	(	(	PUNCT
ejpam-4306	145	13	0	0	NUM
ejpam-4306	145	14	,	,	PUNCT
ejpam-4306	145	15	0	0	NUM
ejpam-4306	145	16	)	)	PUNCT
ejpam-4306	145	17	unstable	unstable	ADJ
ejpam-4306	145	18	.	.	PUNCT
ejpam-4306	145	19	caseii	caseii	NOUN
ejpam-4306	145	20	.	.	PUNCT
ejpam-4306	146	1	we	we	PRON
ejpam-4306	146	2	see	see	VERB
ejpam-4306	146	3	that	that	SCONJ
ejpam-4306	146	4	after	after	ADP
ejpam-4306	146	5	this	this	DET
ejpam-4306	146	6	little	little	ADJ
ejpam-4306	146	7	change	change	NOUN
ejpam-4306	146	8	of	of	ADP
ejpam-4306	146	9	initial	initial	ADJ
ejpam-4306	146	10	value	value	NOUN
ejpam-4306	146	11	away	away	ADV
ejpam-4306	146	12	from	from	ADP
ejpam-4306	146	13	the	the	DET
ejpam-4306	146	14	fixed	fixed	ADJ
ejpam-4306	146	15	point	point	NOUN
ejpam-4306	146	16	the	the	DET
ejpam-4306	146	17	equation	equation	NOUN
ejpam-4306	146	18	will	will	AUX
ejpam-4306	146	19	depend	depend	VERB
ejpam-4306	146	20	in	in	ADP
ejpam-4306	146	21	the	the	DET
ejpam-4306	146	22	changes	change	NOUN
ejpam-4306	146	23	of	of	ADP
ejpam-4306	146	24	α	α	PROPN
ejpam-4306	146	25	.	.	PUNCT
ejpam-4306	146	26	a.	a.	PROPN
ejpam-4306	146	27	abuas’ad	abuas’ad	PROPN
ejpam-4306	146	28	,	,	PUNCT
ejpam-4306	146	29	j.	j.	PROPN
ejpam-4306	146	30	asad	asad	PROPN
ejpam-4306	146	31	/	/	SYM
ejpam-4306	146	32	eur	eur	PROPN
ejpam-4306	146	33	.	.	PUNCT
ejpam-4306	147	1	j.	j.	PROPN
ejpam-4306	147	2	pure	pure	PROPN
ejpam-4306	147	3	appl	appl	PROPN
ejpam-4306	147	4	.	.	PROPN
ejpam-4306	147	5	math	math	PROPN
ejpam-4306	147	6	,	,	PUNCT
ejpam-4306	147	7	15	15	NUM
ejpam-4306	147	8	(	(	PUNCT
ejpam-4306	147	9	2	2	NUM
ejpam-4306	147	10	)	)	PUNCT
ejpam-4306	147	11	(	(	PUNCT
ejpam-4306	147	12	2022	2022	NUM
ejpam-4306	147	13	)	)	PUNCT
ejpam-4306	147	14	,	,	PUNCT
ejpam-4306	147	15	496	496	NUM
ejpam-4306	147	16	-	-	SYM
ejpam-4306	147	17	510	510	NUM
ejpam-4306	147	18	503	503	NUM
ejpam-4306	147	19	figure	figure	NOUN
ejpam-4306	147	20	2	2	NUM
ejpam-4306	147	21	:	:	PUNCT
ejpam-4306	147	22	(	(	PUNCT
ejpam-4306	147	23	0.001	0.001	NUM
ejpam-4306	147	24	,	,	PUNCT
ejpam-4306	147	25	0	0	NUM
ejpam-4306	147	26	)	)	PUNCT
ejpam-4306	147	27	α	α	NOUN
ejpam-4306	147	28	=	=	SYM
ejpam-4306	147	29	0.5	0.5	NUM
ejpam-4306	147	30	.	.	PUNCT
ejpam-4306	147	31	figure	figure	NOUN
ejpam-4306	147	32	3	3	NUM
ejpam-4306	147	33	:	:	PUNCT
ejpam-4306	147	34	(	(	PUNCT
ejpam-4306	147	35	0.001	0.001	NUM
ejpam-4306	147	36	,	,	PUNCT
ejpam-4306	147	37	0	0	NUM
ejpam-4306	147	38	)	)	PUNCT
ejpam-4306	147	39	α	α	NOUN
ejpam-4306	148	1	=	=	SYM
ejpam-4306	148	2	1.5	1.5	NUM
ejpam-4306	148	3	.	.	PUNCT
ejpam-4306	148	4	caseiii.for	caseiii.for	ADP
ejpam-4306	148	5	changing	change	VERB
ejpam-4306	148	6	0.5	0.5	NUM
ejpam-4306	148	7	<	<	X
ejpam-4306	148	8	α	α	PROPN
ejpam-4306	148	9	<	<	X
ejpam-4306	148	10	4.72	4.72	NUM
ejpam-4306	148	11	we	we	PRON
ejpam-4306	148	12	have	have	VERB
ejpam-4306	148	13	the	the	DET
ejpam-4306	148	14	change	change	NOUN
ejpam-4306	148	15	of	of	ADP
ejpam-4306	148	16	oscillation	oscillation	NOUN
ejpam-4306	148	17	while	while	SCONJ
ejpam-4306	148	18	α	α	NOUN
ejpam-4306	148	19	increase	increase	NOUN
ejpam-4306	148	20	as	as	SCONJ
ejpam-4306	148	21	shown	show	VERB
ejpam-4306	148	22	in	in	ADP
ejpam-4306	148	23	fig.4	fig.4	PROPN
ejpam-4306	148	24	.	.	PROPN
ejpam-4306	148	25	figure	figure	NOUN
ejpam-4306	148	26	4	4	NUM
ejpam-4306	148	27	:	:	PUNCT
ejpam-4306	148	28	(	(	PUNCT
ejpam-4306	148	29	0.001	0.001	NUM
ejpam-4306	148	30	,	,	PUNCT
ejpam-4306	148	31	0	0	NUM
ejpam-4306	148	32	)	)	PUNCT
ejpam-4306	149	1	α	α	NOUN
ejpam-4306	149	2	=	=	SYM
ejpam-4306	149	3	4.57	4.57	NUM
ejpam-4306	149	4	.	.	PUNCT
ejpam-4306	149	5	a.	a.	PROPN
ejpam-4306	149	6	abuas’ad	abuas’ad	PROPN
ejpam-4306	149	7	,	,	PUNCT
ejpam-4306	149	8	j.	j.	PROPN
ejpam-4306	149	9	asad	asad	PROPN
ejpam-4306	149	10	/	/	SYM
ejpam-4306	149	11	eur	eur	PROPN
ejpam-4306	149	12	.	.	PUNCT
ejpam-4306	150	1	j.	j.	PROPN
ejpam-4306	150	2	pure	pure	PROPN
ejpam-4306	150	3	appl	appl	PROPN
ejpam-4306	150	4	.	.	PROPN
ejpam-4306	150	5	math	math	PROPN
ejpam-4306	150	6	,	,	PUNCT
ejpam-4306	150	7	15	15	NUM
ejpam-4306	150	8	(	(	PUNCT
ejpam-4306	150	9	2	2	NUM
ejpam-4306	150	10	)	)	PUNCT
ejpam-4306	150	11	(	(	PUNCT
ejpam-4306	150	12	2022	2022	NUM
ejpam-4306	150	13	)	)	PUNCT
ejpam-4306	150	14	,	,	PUNCT
ejpam-4306	150	15	496	496	NUM
ejpam-4306	150	16	-	-	SYM
ejpam-4306	150	17	510	510	NUM
ejpam-4306	150	18	504	504	NUM
ejpam-4306	150	19	caseiv	caseiv	NOUN
ejpam-4306	150	20	now	now	ADV
ejpam-4306	150	21	for	for	ADP
ejpam-4306	150	22	changing	change	VERB
ejpam-4306	150	23	α	α	NOUN
ejpam-4306	150	24	to	to	PART
ejpam-4306	150	25	be	be	AUX
ejpam-4306	150	26	non	non	X
ejpam-4306	150	27	positive	positive	ADJ
ejpam-4306	150	28	real	real	ADJ
ejpam-4306	150	29	number	number	NOUN
ejpam-4306	150	30	we	we	PRON
ejpam-4306	150	31	see	see	VERB
ejpam-4306	150	32	that	that	SCONJ
ejpam-4306	150	33	the	the	DET
ejpam-4306	150	34	nonlinear	nonlinear	ADJ
ejpam-4306	150	35	oscillator	oscillator	NOUN
ejpam-4306	150	36	intersect	intersect	ADJ
ejpam-4306	150	37	to	to	ADP
ejpam-4306	150	38	each	each	DET
ejpam-4306	150	39	other	other	ADJ
ejpam-4306	150	40	when	when	SCONJ
ejpam-4306	150	41	,	,	PUNCT
ejpam-4306	150	42	−0.5	−0.5	PROPN
ejpam-4306	150	43	<	<	X
ejpam-4306	150	44	α	α	X
ejpam-4306	150	45	≤	≤	NUM
ejpam-4306	150	46	0	0	PUNCT
ejpam-4306	150	47	like	like	ADP
ejpam-4306	150	48	figs	fig	NOUN
ejpam-4306	150	49	.	.	PUNCT
ejpam-4306	151	1	57	57	NUM
ejpam-4306	151	2	,	,	PUNCT
ejpam-4306	151	3	while	while	SCONJ
ejpam-4306	151	4	when	when	SCONJ
ejpam-4306	151	5	α	α	PROPN
ejpam-4306	151	6	≤	≤	NOUN
ejpam-4306	151	7	−0.5	−0.5	NOUN
ejpam-4306	151	8	we	we	PRON
ejpam-4306	151	9	see	see	VERB
ejpam-4306	151	10	that	that	SCONJ
ejpam-4306	151	11	the	the	DET
ejpam-4306	151	12	solution	solution	NOUN
ejpam-4306	151	13	goes	go	VERB
ejpam-4306	151	14	to	to	ADP
ejpam-4306	151	15	infinity	infinity	NOUN
ejpam-4306	151	16	’s	’	VERB
ejpam-4306	151	17	shown	show	VERB
ejpam-4306	151	18	in	in	ADP
ejpam-4306	151	19	fig	fig	NOUN
ejpam-4306	151	20	.	.	PUNCT
ejpam-4306	152	1	8	8	X
ejpam-4306	152	2	.	.	X
ejpam-4306	152	3	figure	figure	NOUN
ejpam-4306	152	4	5	5	NUM
ejpam-4306	152	5	:	:	PUNCT
ejpam-4306	152	6	(	(	PUNCT
ejpam-4306	152	7	0.001	0.001	NUM
ejpam-4306	152	8	,	,	PUNCT
ejpam-4306	152	9	0	0	NUM
ejpam-4306	152	10	)	)	PUNCT
ejpam-4306	152	11	α	α	NOUN
ejpam-4306	152	12	=	=	SYM
ejpam-4306	152	13	0	0	X
ejpam-4306	152	14	.	.	PUNCT
ejpam-4306	152	15	figure	figure	VERB
ejpam-4306	152	16	6	6	NUM
ejpam-4306	152	17	:	:	PUNCT
ejpam-4306	152	18	(	(	PUNCT
ejpam-4306	152	19	0.001	0.001	NUM
ejpam-4306	152	20	,	,	PUNCT
ejpam-4306	152	21	0	0	NUM
ejpam-4306	152	22	)	)	PUNCT
ejpam-4306	153	1	α	α	NOUN
ejpam-4306	153	2	=	=	PUNCT
ejpam-4306	153	3	−0.29	−0.29	NOUN
ejpam-4306	153	4	.	.	NOUN
ejpam-4306	153	5	figure	figure	VERB
ejpam-4306	153	6	7	7	NUM
ejpam-4306	153	7	:	:	PUNCT
ejpam-4306	153	8	(	(	PUNCT
ejpam-4306	153	9	0.001	0.001	NUM
ejpam-4306	153	10	,	,	PUNCT
ejpam-4306	153	11	0	0	NUM
ejpam-4306	153	12	)	)	PUNCT
ejpam-4306	153	13	α	α	NOUN
ejpam-4306	153	14	=	=	PUNCT
ejpam-4306	153	15	−0.4	−0.4	PROPN
ejpam-4306	153	16	.	.	PUNCT
ejpam-4306	154	1	a.	a.	PROPN
ejpam-4306	154	2	abuas’ad	abuas’ad	PROPN
ejpam-4306	154	3	,	,	PUNCT
ejpam-4306	154	4	j.	j.	PROPN
ejpam-4306	154	5	asad	asad	PROPN
ejpam-4306	154	6	/	/	SYM
ejpam-4306	154	7	eur	eur	PROPN
ejpam-4306	154	8	.	.	PUNCT
ejpam-4306	155	1	j.	j.	PROPN
ejpam-4306	155	2	pure	pure	PROPN
ejpam-4306	155	3	appl	appl	PROPN
ejpam-4306	155	4	.	.	PROPN
ejpam-4306	155	5	math	math	PROPN
ejpam-4306	155	6	,	,	PUNCT
ejpam-4306	155	7	15	15	NUM
ejpam-4306	155	8	(	(	PUNCT
ejpam-4306	155	9	2	2	NUM
ejpam-4306	155	10	)	)	PUNCT
ejpam-4306	155	11	(	(	PUNCT
ejpam-4306	155	12	2022	2022	NUM
ejpam-4306	155	13	)	)	PUNCT
ejpam-4306	155	14	,	,	PUNCT
ejpam-4306	155	15	496	496	NUM
ejpam-4306	155	16	-	-	SYM
ejpam-4306	155	17	510	510	NUM
ejpam-4306	155	18	505	505	NUM
ejpam-4306	155	19	figure	figure	NOUN
ejpam-4306	155	20	8	8	NUM
ejpam-4306	155	21	:	:	PUNCT
ejpam-4306	155	22	(	(	PUNCT
ejpam-4306	155	23	0.001	0.001	NUM
ejpam-4306	155	24	,	,	PUNCT
ejpam-4306	155	25	0	0	NUM
ejpam-4306	155	26	)	)	PUNCT
ejpam-4306	155	27	α	α	NOUN
ejpam-4306	155	28	=	=	SYM
ejpam-4306	155	29	−0.5	−0.5	PROPN
ejpam-4306	155	30	.	.	PUNCT
ejpam-4306	155	31	casev	casev	NOUN
ejpam-4306	155	32	.	.	PUNCT
ejpam-4306	156	1	we	we	PRON
ejpam-4306	156	2	see	see	VERB
ejpam-4306	156	3	that	that	SCONJ
ejpam-4306	156	4	around	around	ADP
ejpam-4306	156	5	the	the	DET
ejpam-4306	156	6	fixed	fix	VERB
ejpam-4306	156	7	point	point	NOUN
ejpam-4306	156	8	(	(	PUNCT
ejpam-4306	156	9	0	0	NUM
ejpam-4306	156	10	,	,	PUNCT
ejpam-4306	156	11	0	0	NUM
ejpam-4306	156	12	)	)	PUNCT
ejpam-4306	156	13	,	,	PUNCT
ejpam-4306	156	14	we	we	PRON
ejpam-4306	156	15	have	have	VERB
ejpam-4306	156	16	an	an	DET
ejpam-4306	156	17	intersection	intersection	NOUN
ejpam-4306	156	18	between	between	ADP
ejpam-4306	156	19	two	two	NUM
ejpam-4306	156	20	oscillate	oscillate	NOUN
ejpam-4306	156	21	system	system	NOUN
ejpam-4306	156	22	and	and	CCONJ
ejpam-4306	156	23	they	they	PRON
ejpam-4306	156	24	began	begin	VERB
ejpam-4306	156	25	to	to	PART
ejpam-4306	156	26	disjoint	disjoint	VERB
ejpam-4306	156	27	if	if	SCONJ
ejpam-4306	156	28	we	we	PRON
ejpam-4306	156	29	increase	increase	VERB
ejpam-4306	156	30	the	the	DET
ejpam-4306	156	31	vaues	vaue	NOUN
ejpam-4306	156	32	to	to	PART
ejpam-4306	156	33	be	be	AUX
ejpam-4306	156	34	near	near	ADP
ejpam-4306	156	35	the	the	DET
ejpam-4306	156	36	fixed	fix	VERB
ejpam-4306	156	37	point	point	NOUN
ejpam-4306	156	38	(	(	PUNCT
ejpam-4306	156	39	1	1	NUM
ejpam-4306	156	40	,	,	PUNCT
ejpam-4306	156	41	0	0	NUM
ejpam-4306	156	42	)	)	PUNCT
ejpam-4306	156	43	or	or	CCONJ
ejpam-4306	156	44	(	(	PUNCT
ejpam-4306	156	45	−1	−1	NOUN
ejpam-4306	156	46	,	,	PUNCT
ejpam-4306	156	47	0	0	NUM
ejpam-4306	156	48	)	)	PUNCT
ejpam-4306	156	49	see	see	VERB
ejpam-4306	156	50	figs	fig	NOUN
ejpam-4306	156	51	.	.	PUNCT
ejpam-4306	157	1	910	910	NUM
ejpam-4306	157	2	figure	figure	NOUN
ejpam-4306	157	3	9	9	NUM
ejpam-4306	157	4	:	:	PUNCT
ejpam-4306	157	5	(	(	PUNCT
ejpam-4306	157	6	0.5	0.5	NUM
ejpam-4306	157	7	,	,	PUNCT
ejpam-4306	157	8	0	0	NUM
ejpam-4306	157	9	)	)	PUNCT
ejpam-4306	157	10	α	α	NOUN
ejpam-4306	157	11	=	=	SYM
ejpam-4306	157	12	−0.5	−0.5	PROPN
ejpam-4306	157	13	.	.	PUNCT
ejpam-4306	158	1	figure	figure	NOUN
ejpam-4306	158	2	10	10	NUM
ejpam-4306	158	3	:	:	PUNCT
ejpam-4306	158	4	(	(	PUNCT
ejpam-4306	158	5	−0.5	−0.5	PROPN
ejpam-4306	158	6	,	,	PUNCT
ejpam-4306	158	7	0	0	NUM
ejpam-4306	158	8	)	)	PUNCT
ejpam-4306	158	9	α	α	NOUN
ejpam-4306	158	10	=	=	SYM
ejpam-4306	158	11	−0.5	−0.5	PROPN
ejpam-4306	158	12	.	.	PUNCT
ejpam-4306	159	1	a.	a.	PROPN
ejpam-4306	159	2	abuas’ad	abuas’ad	PROPN
ejpam-4306	159	3	,	,	PUNCT
ejpam-4306	159	4	j.	j.	PROPN
ejpam-4306	159	5	asad	asad	PROPN
ejpam-4306	159	6	/	/	SYM
ejpam-4306	159	7	eur	eur	PROPN
ejpam-4306	159	8	.	.	PUNCT
ejpam-4306	160	1	j.	j.	PROPN
ejpam-4306	160	2	pure	pure	PROPN
ejpam-4306	160	3	appl	appl	PROPN
ejpam-4306	160	4	.	.	PROPN
ejpam-4306	160	5	math	math	PROPN
ejpam-4306	160	6	,	,	PUNCT
ejpam-4306	160	7	15	15	NUM
ejpam-4306	160	8	(	(	PUNCT
ejpam-4306	160	9	2	2	NUM
ejpam-4306	160	10	)	)	PUNCT
ejpam-4306	160	11	(	(	PUNCT
ejpam-4306	160	12	2022	2022	NUM
ejpam-4306	160	13	)	)	PUNCT
ejpam-4306	160	14	,	,	PUNCT
ejpam-4306	160	15	496	496	NUM
ejpam-4306	160	16	-	-	SYM
ejpam-4306	160	17	510	510	NUM
ejpam-4306	160	18	506	506	NUM
ejpam-4306	160	19	casevi	casevi	NOUN
ejpam-4306	160	20	.	.	PUNCT
ejpam-4306	161	1	we	we	PRON
ejpam-4306	161	2	see	see	VERB
ejpam-4306	161	3	if	if	SCONJ
ejpam-4306	161	4	we	we	PRON
ejpam-4306	161	5	increase	increase	VERB
ejpam-4306	161	6	the	the	DET
ejpam-4306	161	7	value	value	NOUN
ejpam-4306	161	8	to	to	PART
ejpam-4306	161	9	reach	reach	VERB
ejpam-4306	161	10	the	the	DET
ejpam-4306	161	11	fixed	fix	VERB
ejpam-4306	161	12	point	point	NOUN
ejpam-4306	161	13	(	(	PUNCT
ejpam-4306	161	14	±1	±1	VERB
ejpam-4306	161	15	,	,	PUNCT
ejpam-4306	161	16	0	0	NUM
ejpam-4306	161	17	)	)	PUNCT
ejpam-4306	161	18	which	which	PRON
ejpam-4306	161	19	they	they	PRON
ejpam-4306	161	20	are	be	AUX
ejpam-4306	161	21	unstable	unstable	ADJ
ejpam-4306	161	22	for	for	ADP
ejpam-4306	161	23	any	any	DET
ejpam-4306	161	24	real	real	ADJ
ejpam-4306	161	25	number	number	NOUN
ejpam-4306	161	26	α	α	NOUN
ejpam-4306	161	27	see	see	VERB
ejpam-4306	161	28	fig	fig	NOUN
ejpam-4306	161	29	.	.	PUNCT
ejpam-4306	162	1	11	11	NUM
ejpam-4306	162	2	figure	figure	NOUN
ejpam-4306	162	3	11	11	NUM
ejpam-4306	162	4	:	:	PUNCT
ejpam-4306	162	5	fixed	fix	VERB
ejpam-4306	162	6	points	point	NOUN
ejpam-4306	162	7	(	(	PUNCT
ejpam-4306	162	8	0	0	NUM
ejpam-4306	162	9	,	,	PUNCT
ejpam-4306	162	10	0	0	NUM
ejpam-4306	162	11	)	)	PUNCT
ejpam-4306	162	12	and	and	CCONJ
ejpam-4306	162	13	(	(	PUNCT
ejpam-4306	162	14	1	1	NUM
ejpam-4306	162	15	,	,	PUNCT
ejpam-4306	162	16	0	0	NUM
ejpam-4306	162	17	)	)	PUNCT
ejpam-4306	162	18	where	where	SCONJ
ejpam-4306	162	19	α	α	PROPN
ejpam-4306	162	20	∈	∈	PROPN
ejpam-4306	162	21	r.	r.	PROPN
ejpam-4306	162	22	case	case	NOUN
ejpam-4306	162	23	vii	vii	PROPN
ejpam-4306	162	24	.	.	PUNCT
ejpam-4306	163	1	now	now	ADV
ejpam-4306	163	2	if	if	SCONJ
ejpam-4306	163	3	we	we	PRON
ejpam-4306	163	4	change	change	VERB
ejpam-4306	163	5	the	the	DET
ejpam-4306	163	6	initial	initial	ADJ
ejpam-4306	163	7	value	value	NOUN
ejpam-4306	163	8	we	we	PRON
ejpam-4306	163	9	see	see	VERB
ejpam-4306	163	10	the	the	DET
ejpam-4306	163	11	oscillate	oscillate	NOUN
ejpam-4306	163	12	movement	movement	NOUN
ejpam-4306	163	13	has	have	VERB
ejpam-4306	163	14	to	to	PART
ejpam-4306	163	15	periodic	periodic	VERB
ejpam-4306	163	16	in	in	ADP
ejpam-4306	163	17	two	two	NUM
ejpam-4306	163	18	different	different	ADJ
ejpam-4306	163	19	time	time	NOUN
ejpam-4306	163	20	see	see	VERB
ejpam-4306	163	21	fig	fig	NOUN
ejpam-4306	163	22	.	.	PUNCT
ejpam-4306	164	1	12	12	NUM
ejpam-4306	164	2	figure	figure	NOUN
ejpam-4306	164	3	12	12	NUM
ejpam-4306	164	4	:	:	PUNCT
ejpam-4306	164	5	initial	initial	ADJ
ejpam-4306	164	6	value	value	NOUN
ejpam-4306	164	7	(	(	PUNCT
ejpam-4306	164	8	1.37	1.37	NUM
ejpam-4306	164	9	,	,	PUNCT
ejpam-4306	164	10	0	0	NUM
ejpam-4306	164	11	)	)	PUNCT
ejpam-4306	164	12	α	α	NOUN
ejpam-4306	164	13	=	=	SYM
ejpam-4306	164	14	0	0	PROPN
ejpam-4306	164	15	.	.	PUNCT
ejpam-4306	164	16	a.	a.	PROPN
ejpam-4306	164	17	abuas’ad	abuas’ad	PROPN
ejpam-4306	164	18	,	,	PUNCT
ejpam-4306	164	19	j.	j.	PROPN
ejpam-4306	164	20	asad	asad	PROPN
ejpam-4306	164	21	/	/	SYM
ejpam-4306	164	22	eur	eur	PROPN
ejpam-4306	164	23	.	.	PUNCT
ejpam-4306	165	1	j.	j.	PROPN
ejpam-4306	165	2	pure	pure	PROPN
ejpam-4306	165	3	appl	appl	PROPN
ejpam-4306	165	4	.	.	PROPN
ejpam-4306	165	5	math	math	PROPN
ejpam-4306	165	6	,	,	PUNCT
ejpam-4306	165	7	15	15	NUM
ejpam-4306	165	8	(	(	PUNCT
ejpam-4306	165	9	2	2	NUM
ejpam-4306	165	10	)	)	PUNCT
ejpam-4306	165	11	(	(	PUNCT
ejpam-4306	165	12	2022	2022	NUM
ejpam-4306	165	13	)	)	PUNCT
ejpam-4306	165	14	,	,	PUNCT
ejpam-4306	165	15	496	496	NUM
ejpam-4306	165	16	-	-	SYM
ejpam-4306	165	17	510	510	NUM
ejpam-4306	165	18	507	507	NUM
ejpam-4306	165	19	finally	finally	ADV
ejpam-4306	165	20	we	we	PRON
ejpam-4306	165	21	see	see	VERB
ejpam-4306	165	22	an	an	DET
ejpam-4306	165	23	socialite	socialite	ADJ
ejpam-4306	165	24	movement	movement	NOUN
ejpam-4306	165	25	for	for	ADP
ejpam-4306	165	26	this	this	DET
ejpam-4306	165	27	equation	equation	NOUN
ejpam-4306	165	28	with	with	ADP
ejpam-4306	165	29	periodic	periodic	ADJ
ejpam-4306	165	30	motion	motion	NOUN
ejpam-4306	165	31	just	just	ADV
ejpam-4306	165	32	when	when	SCONJ
ejpam-4306	165	33	we	we	PRON
ejpam-4306	165	34	begin	begin	VERB
ejpam-4306	165	35	a	a	DET
ejpam-4306	165	36	little	little	ADJ
ejpam-4306	165	37	bet	bet	NOUN
ejpam-4306	165	38	a	a	DET
ejpam-4306	165	39	way	way	NOUN
ejpam-4306	165	40	from	from	ADP
ejpam-4306	165	41	the	the	DET
ejpam-4306	165	42	fixed	fix	VERB
ejpam-4306	165	43	point	point	NOUN
ejpam-4306	165	44	when	when	SCONJ
ejpam-4306	165	45	α	α	PRON
ejpam-4306	165	46	≥	≥	NUM
ejpam-4306	165	47	2	2	NUM
ejpam-4306	165	48	there	there	PRON
ejpam-4306	165	49	is	be	VERB
ejpam-4306	165	50	two	two	NUM
ejpam-4306	165	51	disjoint	disjoint	ADJ
ejpam-4306	165	52	oscillate	oscillate	NOUN
ejpam-4306	165	53	like	like	ADP
ejpam-4306	165	54	figs	fig	NOUN
ejpam-4306	165	55	1314	1314	NUM
ejpam-4306	165	56	,	,	PUNCT
ejpam-4306	165	57	but	but	CCONJ
ejpam-4306	165	58	when	when	SCONJ
ejpam-4306	165	59	−0.53	−0.53	VERB
ejpam-4306	165	60	≤	≤	NOUN
ejpam-4306	165	61	α	α	NOUN
ejpam-4306	165	62	<	<	X
ejpam-4306	165	63	2	2	NUM
ejpam-4306	165	64	the	the	DET
ejpam-4306	165	65	oscillate	oscillate	NOUN
ejpam-4306	165	66	movement	movement	NOUN
ejpam-4306	165	67	will	will	AUX
ejpam-4306	165	68	intersect	intersect	VERB
ejpam-4306	165	69	see	see	VERB
ejpam-4306	165	70	fig.15	fig.15	NOUN
ejpam-4306	165	71	,	,	PUNCT
ejpam-4306	165	72	while	while	SCONJ
ejpam-4306	165	73	the	the	DET
ejpam-4306	165	74	solution	solution	NOUN
ejpam-4306	165	75	goes	go	VERB
ejpam-4306	165	76	to	to	ADP
ejpam-4306	165	77	infinty	infinty	PRON
ejpam-4306	165	78	when	when	SCONJ
ejpam-4306	165	79	α	α	X
ejpam-4306	165	80	>	>	X
ejpam-4306	165	81	−0.53	−0.53	PROPN
ejpam-4306	165	82	as	as	SCONJ
ejpam-4306	165	83	shown	show	VERB
ejpam-4306	165	84	in	in	ADP
ejpam-4306	165	85	fig.16	fig.16	PROPN
ejpam-4306	165	86	.	.	PUNCT
ejpam-4306	165	87	figure	figure	NOUN
ejpam-4306	165	88	13	13	NUM
ejpam-4306	165	89	:	:	PUNCT
ejpam-4306	165	90	initial	initial	ADJ
ejpam-4306	165	91	value	value	NOUN
ejpam-4306	165	92	(	(	PUNCT
ejpam-4306	165	93	1.37	1.37	NUM
ejpam-4306	165	94	,	,	PUNCT
ejpam-4306	165	95	0	0	NUM
ejpam-4306	165	96	)	)	PUNCT
ejpam-4306	165	97	α	α	NOUN
ejpam-4306	165	98	=	=	SYM
ejpam-4306	165	99	0	0	X
ejpam-4306	165	100	.	.	PUNCT
ejpam-4306	165	101	figure	figure	NOUN
ejpam-4306	165	102	14	14	NUM
ejpam-4306	165	103	:	:	PUNCT
ejpam-4306	165	104	initial	initial	ADJ
ejpam-4306	165	105	value	value	NOUN
ejpam-4306	165	106	(	(	PUNCT
ejpam-4306	165	107	1.37	1.37	NUM
ejpam-4306	165	108	,	,	PUNCT
ejpam-4306	165	109	0	0	NUM
ejpam-4306	165	110	)	)	PUNCT
ejpam-4306	165	111	α	α	NOUN
ejpam-4306	165	112	=	=	SYM
ejpam-4306	165	113	5	5	X
ejpam-4306	165	114	.	.	X
ejpam-4306	165	115	figure	figure	NOUN
ejpam-4306	165	116	15	15	NUM
ejpam-4306	165	117	:	:	PUNCT
ejpam-4306	165	118	initial	initial	ADJ
ejpam-4306	165	119	value	value	NOUN
ejpam-4306	165	120	(	(	PUNCT
ejpam-4306	165	121	1.37	1.37	NUM
ejpam-4306	165	122	,	,	PUNCT
ejpam-4306	165	123	0	0	NUM
ejpam-4306	165	124	)	)	PUNCT
ejpam-4306	165	125	α	α	NOUN
ejpam-4306	165	126	=	=	SYM
ejpam-4306	165	127	−0.53	−0.53	PROPN
ejpam-4306	165	128	.	.	NOUN
ejpam-4306	165	129	a.	a.	PROPN
ejpam-4306	165	130	abuas’ad	abuas’ad	PROPN
ejpam-4306	165	131	,	,	PUNCT
ejpam-4306	165	132	j.	j.	PROPN
ejpam-4306	165	133	asad	asad	PROPN
ejpam-4306	165	134	/	/	SYM
ejpam-4306	165	135	eur	eur	PROPN
ejpam-4306	165	136	.	.	PUNCT
ejpam-4306	166	1	j.	j.	PROPN
ejpam-4306	166	2	pure	pure	PROPN
ejpam-4306	166	3	appl	appl	PROPN
ejpam-4306	166	4	.	.	PROPN
ejpam-4306	166	5	math	math	PROPN
ejpam-4306	166	6	,	,	PUNCT
ejpam-4306	166	7	15	15	NUM
ejpam-4306	166	8	(	(	PUNCT
ejpam-4306	166	9	2	2	NUM
ejpam-4306	166	10	)	)	PUNCT
ejpam-4306	166	11	(	(	PUNCT
ejpam-4306	166	12	2022	2022	NUM
ejpam-4306	166	13	)	)	PUNCT
ejpam-4306	166	14	,	,	PUNCT
ejpam-4306	166	15	496	496	NUM
ejpam-4306	166	16	-	-	SYM
ejpam-4306	166	17	510	510	NUM
ejpam-4306	166	18	508	508	NUM
ejpam-4306	166	19	figure	figure	NOUN
ejpam-4306	166	20	16	16	NUM
ejpam-4306	166	21	:	:	PUNCT
ejpam-4306	166	22	initial	initial	ADJ
ejpam-4306	166	23	value	value	NOUN
ejpam-4306	166	24	(	(	PUNCT
ejpam-4306	166	25	1.37	1.37	NUM
ejpam-4306	166	26	,	,	PUNCT
ejpam-4306	166	27	0	0	NUM
ejpam-4306	166	28	)	)	PUNCT
ejpam-4306	166	29	α	α	NOUN
ejpam-4306	166	30	=	=	PUNCT
ejpam-4306	167	1	−0.54	−0.54	X
ejpam-4306	167	2	.	.	PUNCT
ejpam-4306	168	1	studying	study	VERB
ejpam-4306	168	2	the	the	DET
ejpam-4306	168	3	direction	direction	NOUN
ejpam-4306	168	4	field	field	NOUN
ejpam-4306	168	5	around	around	ADP
ejpam-4306	168	6	the	the	DET
ejpam-4306	168	7	fixed	fix	VERB
ejpam-4306	168	8	points	point	NOUN
ejpam-4306	168	9	of	of	ADP
ejpam-4306	168	10	the	the	DET
ejpam-4306	168	11	system	system	NOUN
ejpam-4306	168	12	,	,	PUNCT
ejpam-4306	168	13	we	we	PRON
ejpam-4306	168	14	see	see	VERB
ejpam-4306	168	15	first	first	ADV
ejpam-4306	168	16	how	how	SCONJ
ejpam-4306	168	17	the	the	DET
ejpam-4306	168	18	solution	solution	NOUN
ejpam-4306	168	19	goes	go	VERB
ejpam-4306	168	20	a	a	DET
ejpam-4306	168	21	way	way	NOUN
ejpam-4306	168	22	from	from	ADP
ejpam-4306	168	23	(	(	PUNCT
ejpam-4306	168	24	0,0	0,0	NOUN
ejpam-4306	168	25	)	)	PUNCT
ejpam-4306	168	26	,	,	PUNCT
ejpam-4306	168	27	then	then	ADV
ejpam-4306	168	28	the	the	DET
ejpam-4306	168	29	fixed	fixed	ADJ
ejpam-4306	168	30	points	point	NOUN
ejpam-4306	168	31	(	(	PUNCT
ejpam-4306	168	32	±1	±1	VERB
ejpam-4306	168	33	,	,	PUNCT
ejpam-4306	168	34	0	0	NUM
ejpam-4306	168	35	)	)	PUNCT
ejpam-4306	168	36	.	.	PUNCT
ejpam-4306	169	1	since	since	SCONJ
ejpam-4306	169	2	every	every	DET
ejpam-4306	169	3	fixed	fix	VERB
ejpam-4306	169	4	point	point	NOUN
ejpam-4306	169	5	change	change	NOUN
ejpam-4306	169	6	it	it	PRON
ejpam-4306	169	7	direction	direction	NOUN
ejpam-4306	169	8	when	when	SCONJ
ejpam-4306	169	9	it	it	PRON
ejpam-4306	169	10	go	go	VERB
ejpam-4306	169	11	away	away	ADV
ejpam-4306	169	12	from	from	ADP
ejpam-4306	169	13	left	left	ADJ
ejpam-4306	169	14	or	or	CCONJ
ejpam-4306	169	15	right	right	ADJ
ejpam-4306	169	16	side	side	NOUN
ejpam-4306	169	17	as	as	ADP
ejpam-4306	169	18	an	an	DET
ejpam-4306	169	19	opposite	opposite	ADJ
ejpam-4306	169	20	position	position	NOUN
ejpam-4306	169	21	from	from	ADP
ejpam-4306	169	22	each	each	DET
ejpam-4306	169	23	other	other	ADJ
ejpam-4306	169	24	,	,	PUNCT
ejpam-4306	169	25	now	now	ADV
ejpam-4306	169	26	the	the	DET
ejpam-4306	169	27	graph	graph	NOUN
ejpam-4306	169	28	of	of	ADP
ejpam-4306	169	29	the	the	DET
ejpam-4306	169	30	direction	direction	NOUN
ejpam-4306	169	31	field	field	NOUN
ejpam-4306	169	32	contain	contain	VERB
ejpam-4306	169	33	the	the	DET
ejpam-4306	169	34	three	three	NUM
ejpam-4306	169	35	fixed	fix	VERB
ejpam-4306	169	36	points	point	NOUN
ejpam-4306	169	37	that	that	PRON
ejpam-4306	169	38	shows	show	VERB
ejpam-4306	169	39	their	their	PRON
ejpam-4306	169	40	stability	stability	NOUN
ejpam-4306	169	41	see	see	VERB
ejpam-4306	169	42	fig	fig	NOUN
ejpam-4306	169	43	.	.	PUNCT
ejpam-4306	170	1	17	17	NUM
ejpam-4306	170	2	.	.	X
ejpam-4306	170	3	figure	figure	NOUN
ejpam-4306	170	4	17	17	NUM
ejpam-4306	170	5	:	:	PUNCT
ejpam-4306	170	6	direction	direction	NOUN
ejpam-4306	170	7	field	field	NOUN
ejpam-4306	170	8	about	about	ADP
ejpam-4306	170	9	the	the	DET
ejpam-4306	170	10	points	point	NOUN
ejpam-4306	170	11	(	(	PUNCT
ejpam-4306	170	12	0	0	NUM
ejpam-4306	170	13	,	,	PUNCT
ejpam-4306	170	14	0	0	NUM
ejpam-4306	170	15	)	)	PUNCT
ejpam-4306	170	16	,	,	PUNCT
ejpam-4306	170	17	(	(	PUNCT
ejpam-4306	170	18	1	1	NUM
ejpam-4306	170	19	,	,	PUNCT
ejpam-4306	170	20	0	0	NUM
ejpam-4306	170	21	)	)	PUNCT
ejpam-4306	170	22	,	,	PUNCT
ejpam-4306	170	23	(	(	PUNCT
ejpam-4306	170	24	−1	−1	NOUN
ejpam-4306	170	25	,	,	PUNCT
ejpam-4306	170	26	0	0	NUM
ejpam-4306	170	27	)	)	PUNCT
ejpam-4306	170	28	.	.	PUNCT
ejpam-4306	171	1	5	5	X
ejpam-4306	171	2	.	.	X
ejpam-4306	171	3	conclusion	conclusion	NOUN
ejpam-4306	171	4	an	an	DET
ejpam-4306	171	5	exact	exact	ADJ
ejpam-4306	171	6	analytical	analytical	ADJ
ejpam-4306	171	7	solution	solution	NOUN
ejpam-4306	171	8	for	for	ADP
ejpam-4306	171	9	a	a	DET
ejpam-4306	171	10	nonlinear	nonlinear	ADJ
ejpam-4306	171	11	oscillator	oscillator	NOUN
ejpam-4306	171	12	with	with	ADP
ejpam-4306	171	13	coordinate	coordinate	NOUN
ejpam-4306	171	14	dependentmass	dependentmass	NOUN
ejpam-4306	171	15	was	be	AUX
ejpam-4306	171	16	obtained	obtain	VERB
ejpam-4306	171	17	.	.	PUNCT
ejpam-4306	172	1	from	from	ADP
ejpam-4306	172	2	the	the	DET
ejpam-4306	172	3	obtained	obtain	VERB
ejpam-4306	172	4	figures	figure	NOUN
ejpam-4306	172	5	we	we	PRON
ejpam-4306	172	6	conclude	conclude	VERB
ejpam-4306	172	7	that	that	SCONJ
ejpam-4306	172	8	the	the	DET
ejpam-4306	172	9	oscillator	oscillator	NOUN
ejpam-4306	172	10	have	have	VERB
ejpam-4306	172	11	a	a	DET
ejpam-4306	172	12	periodic	periodic	ADJ
ejpam-4306	172	13	oscillation	oscillation	NOUN
ejpam-4306	172	14	at	at	ADP
ejpam-4306	172	15	all	all	DET
ejpam-4306	172	16	time	time	NOUN
ejpam-4306	172	17	and	and	CCONJ
ejpam-4306	172	18	in	in	ADP
ejpam-4306	172	19	all	all	DET
ejpam-4306	172	20	position	position	NOUN
ejpam-4306	172	21	except	except	SCONJ
ejpam-4306	172	22	at	at	ADP
ejpam-4306	172	23	the	the	DET
ejpam-4306	172	24	equilibrium	equilibrium	NOUN
ejpam-4306	172	25	points	point	NOUN
ejpam-4306	172	26	,	,	PUNCT
ejpam-4306	172	27	that	that	PRON
ejpam-4306	172	28	change	change	VERB
ejpam-4306	172	29	the	the	DET
ejpam-4306	172	30	direction	direction	NOUN
ejpam-4306	172	31	and	and	CCONJ
ejpam-4306	172	32	make	make	VERB
ejpam-4306	172	33	intersection	intersection	NOUN
ejpam-4306	172	34	of	of	ADP
ejpam-4306	172	35	oscillator	oscillator	NOUN
ejpam-4306	172	36	or	or	CCONJ
ejpam-4306	172	37	disconnect	disconnect	VERB
ejpam-4306	172	38	each	each	DET
ejpam-4306	172	39	other	other	ADJ
ejpam-4306	172	40	in	in	ADP
ejpam-4306	172	41	different	different	ADJ
ejpam-4306	172	42	time	time	NOUN
ejpam-4306	172	43	and	and	CCONJ
ejpam-4306	172	44	position	position	NOUN
ejpam-4306	172	45	.	.	PUNCT
ejpam-4306	173	1	references	reference	NOUN
ejpam-4306	173	2	509	509	NUM
ejpam-4306	173	3	acknowledgements	acknowledgement	NOUN
ejpam-4306	173	4	the	the	DET
ejpam-4306	173	5	authors	author	NOUN
ejpam-4306	173	6	would	would	AUX
ejpam-4306	173	7	like	like	VERB
ejpam-4306	173	8	to	to	PART
ejpam-4306	173	9	thank	thank	VERB
ejpam-4306	173	10	palestine	palestine	PROPN
ejpam-4306	173	11	technical	technical	PROPN
ejpam-4306	173	12	universitykadoorie	universitykadoorie	PROPN
ejpam-4306	173	13	.	.	PUNCT
ejpam-4306	174	1	scientific	scientific	ADJ
ejpam-4306	174	2	research	research	NOUN
ejpam-4306	174	3	funding	fund	VERB
ejpam-4306	174	4	2022	2022	NUM
ejpam-4306	174	5	for	for	ADP
ejpam-4306	174	6	their	their	PRON
ejpam-4306	174	7	support	support	NOUN
ejpam-4306	174	8	.	.	PUNCT
ejpam-4306	175	1	references	reference	NOUN
ejpam-4306	175	2	[	[	X
ejpam-4306	175	3	1	1	NUM
ejpam-4306	175	4	]	]	PUNCT
ejpam-4306	175	5	homotopy	homotopy	VERB
ejpam-4306	175	6	perturbation	perturbation	NOUN
ejpam-4306	175	7	technique	technique	NOUN
ejpam-4306	175	8	.	.	PUNCT
ejpam-4306	176	1	computer	computer	NOUN
ejpam-4306	176	2	methods	method	NOUN
ejpam-4306	176	3	in	in	ADP
ejpam-4306	176	4	applied	applied	ADJ
ejpam-4306	176	5	mechanics	mechanic	NOUN
ejpam-4306	176	6	and	and	CCONJ
ejpam-4306	176	7	engineering	engineering	NOUN
ejpam-4306	176	8	,	,	PUNCT
ejpam-4306	176	9	178(3):257–262	178(3):257–262	NUM
ejpam-4306	176	10	,	,	PUNCT
ejpam-4306	176	11	1999	1999	NUM
ejpam-4306	176	12	.	.	PUNCT
ejpam-4306	177	1	[	[	X
ejpam-4306	177	2	2	2	X
ejpam-4306	177	3	]	]	PUNCT
ejpam-4306	177	4	z.	z.	PROPN
ejpam-4306	177	5	azimzadeh	azimzadeh	PROPN
ejpam-4306	177	6	a.	a.	PROPN
ejpam-4306	177	7	r.	r.	PROPN
ejpam-4306	177	8	vahidi	vahidi	PROPN
ejpam-4306	177	9	and	and	CCONJ
ejpam-4306	177	10	s.	s.	PROPN
ejpam-4306	177	11	mohammadifar	mohammadifar	PROPN
ejpam-4306	177	12	.	.	PUNCT
ejpam-4306	178	1	restarted	restart	VERB
ejpam-4306	178	2	adomian	adomian	NOUN
ejpam-4306	178	3	decomposition	decomposition	NOUN
ejpam-4306	178	4	method	method	NOUN
ejpam-4306	178	5	for	for	ADP
ejpam-4306	178	6	solving	solve	VERB
ejpam-4306	178	7	duffing	duffing	NOUN
ejpam-4306	178	8	-	-	PUNCT
ejpam-4306	178	9	van	van	PROPN
ejpam-4306	178	10	der	der	ADJ
ejpam-4306	178	11	pol	pol	NOUN
ejpam-4306	178	12	equation	equation	NOUN
ejpam-4306	178	13	.	.	PUNCT
ejpam-4306	179	1	applied	apply	VERB
ejpam-4306	179	2	mathematical	mathematical	ADJ
ejpam-4306	179	3	sciences	science	NOUN
ejpam-4306	179	4	,	,	PUNCT
ejpam-4306	179	5	10:499	10:499	NUM
ejpam-4306	179	6	–	–	PUNCT
ejpam-4306	179	7	507	507	NUM
ejpam-4306	179	8	,	,	PUNCT
ejpam-4306	179	9	2012	2012	NUM
ejpam-4306	179	10	.	.	PUNCT
ejpam-4306	180	1	[	[	X
ejpam-4306	180	2	3	3	NUM
ejpam-4306	180	3	]	]	X
ejpam-4306	180	4	magaji	magaji	PROPN
ejpam-4306	180	5	adamu	adamu	PROPN
ejpam-4306	180	6	yunbunga	yunbunga	PROPN
ejpam-4306	180	7	and	and	CCONJ
ejpam-4306	180	8	ogenyi	ogenyi	PROPN
ejpam-4306	180	9	.	.	PUNCT
ejpam-4306	181	1	parameterized	parameterized	ADJ
ejpam-4306	181	2	homotopy	homotopy	PROPN
ejpam-4306	181	3	perturbation	perturbation	NOUN
ejpam-4306	181	4	method	method	NOUN
ejpam-4306	181	5	.	.	PUNCT
ejpam-4306	182	1	nonlinear	nonlinear	PROPN
ejpam-4306	182	2	sci	sci	PROPN
ejpam-4306	182	3	,	,	PUNCT
ejpam-4306	182	4	8:240–243	8:240–243	NOUN
ejpam-4306	182	5	,	,	PUNCT
ejpam-4306	182	6	06	06	NUM
ejpam-4306	182	7	2017	2017	NUM
ejpam-4306	182	8	.	.	PUNCT
ejpam-4306	183	1	[	[	X
ejpam-4306	183	2	4	4	X
ejpam-4306	183	3	]	]	PUNCT
ejpam-4306	183	4	aiyong	aiyong	PROPN
ejpam-4306	183	5	chen	chen	PROPN
ejpam-4306	183	6	and	and	CCONJ
ejpam-4306	183	7	guirong	guirong	PROPN
ejpam-4306	183	8	jiang	jiang	PROPN
ejpam-4306	183	9	.	.	PUNCT
ejpam-4306	184	1	periodic	periodic	ADJ
ejpam-4306	184	2	solution	solution	NOUN
ejpam-4306	184	3	of	of	ADP
ejpam-4306	184	4	the	the	DET
ejpam-4306	184	5	duffing	duffing	NOUN
ejpam-4306	184	6	-	-	PUNCT
ejpam-4306	184	7	van	van	PROPN
ejpam-4306	184	8	der	der	ADJ
ejpam-4306	184	9	pol	pol	PROPN
ejpam-4306	184	10	oscillator	oscillator	NOUN
ejpam-4306	184	11	by	by	ADP
ejpam-4306	184	12	homotopy	homotopy	NOUN
ejpam-4306	184	13	perturbation	perturbation	NOUN
ejpam-4306	184	14	method	method	NOUN
ejpam-4306	184	15	.	.	PUNCT
ejpam-4306	185	1	international	international	ADJ
ejpam-4306	185	2	journal	journal	PROPN
ejpam-4306	185	3	of	of	ADP
ejpam-4306	185	4	computer	computer	NOUN
ejpam-4306	185	5	mathematics	mathematic	NOUN
ejpam-4306	185	6	,	,	PUNCT
ejpam-4306	185	7	87(12):2688–2696	87(12):2688–2696	NUM
ejpam-4306	185	8	,	,	PUNCT
ejpam-4306	185	9	2010	2010	NUM
ejpam-4306	185	10	.	.	PUNCT
ejpam-4306	186	1	[	[	X
ejpam-4306	186	2	5	5	X
ejpam-4306	186	3	]	]	X
ejpam-4306	186	4	g.	g.	PROPN
ejpam-4306	186	5	r	r	PROPN
ejpam-4306	186	6	fowles	fowles	PROPN
ejpam-4306	186	7	.	.	PUNCT
ejpam-4306	187	1	analytical	analytical	ADJ
ejpam-4306	187	2	mechanics	mechanic	NOUN
ejpam-4306	187	3	.	.	PUNCT
ejpam-4306	188	1	thompson	thompson	PROPN
ejpam-4306	188	2	brooks	brooks	PROPN
ejpam-4306	188	3	/	/	SYM
ejpam-4306	188	4	cole	cole	PROPN
ejpam-4306	188	5	,	,	PUNCT
ejpam-4306	188	6	belmont	belmont	PROPN
ejpam-4306	188	7	,	,	PUNCT
ejpam-4306	188	8	ca	ca	NOUN
ejpam-4306	188	9	,	,	PUNCT
ejpam-4306	188	10	2005	2005	NUM
ejpam-4306	188	11	.	.	PUNCT
ejpam-4306	189	1	[	[	X
ejpam-4306	189	2	6	6	X
ejpam-4306	189	3	]	]	PUNCT
ejpam-4306	189	4	davood	davood	ADJ
ejpam-4306	189	5	domiri	domiri	PROPN
ejpam-4306	189	6	ganji	ganji	PROPN
ejpam-4306	189	7	,	,	PUNCT
ejpam-4306	189	8	m	m	PROPN
ejpam-4306	189	9	gorji	gorji	PROPN
ejpam-4306	189	10	,	,	PUNCT
ejpam-4306	189	11	s	s	VERB
ejpam-4306	189	12	soleimani	soleimani	NOUN
ejpam-4306	189	13	,	,	PUNCT
ejpam-4306	189	14	and	and	CCONJ
ejpam-4306	189	15	mohsen	mohsen	PROPN
ejpam-4306	189	16	esmaeilpour	esmaeilpour	PROPN
ejpam-4306	189	17	.	.	PUNCT
ejpam-4306	190	1	solution	solution	NOUN
ejpam-4306	190	2	of	of	ADP
ejpam-4306	190	3	nonlinear	nonlinear	ADJ
ejpam-4306	190	4	cubic	cubic	ADJ
ejpam-4306	190	5	-	-	PUNCT
ejpam-4306	190	6	quintic	quintic	ADJ
ejpam-4306	190	7	duffing	duffing	NOUN
ejpam-4306	190	8	oscillators	oscillator	NOUN
ejpam-4306	190	9	using	use	VERB
ejpam-4306	190	10	he	he	PRON
ejpam-4306	190	11	’s	’s	PART
ejpam-4306	190	12	energy	energy	NOUN
ejpam-4306	190	13	balance	balance	NOUN
ejpam-4306	190	14	method	method	NOUN
ejpam-4306	190	15	.	.	PUNCT
ejpam-4306	191	1	journal	journal	PROPN
ejpam-4306	191	2	of	of	ADP
ejpam-4306	191	3	zhejiang	zhejiang	PROPN
ejpam-4306	191	4	university	university	PROPN
ejpam-4306	191	5	-	-	PUNCT
ejpam-4306	191	6	science	science	PROPN
ejpam-4306	191	7	a	a	PRON
ejpam-4306	191	8	,	,	PUNCT
ejpam-4306	191	9	10(9):1263–1268	10(9):1263–1268	NUM
ejpam-4306	191	10	,	,	PUNCT
ejpam-4306	191	11	2009	2009	NUM
ejpam-4306	191	12	.	.	PUNCT
ejpam-4306	192	1	[	[	X
ejpam-4306	192	2	7	7	X
ejpam-4306	192	3	]	]	X
ejpam-4306	192	4	seyed	seyed	PROPN
ejpam-4306	192	5	s	s	PROPN
ejpam-4306	192	6	ganji	ganji	X
ejpam-4306	192	7	,	,	PUNCT
ejpam-4306	192	8	amin	amin	NOUN
ejpam-4306	192	9	barari	barari	PROPN
ejpam-4306	192	10	,	,	PUNCT
ejpam-4306	192	11	s	s	PART
ejpam-4306	192	12	karimpour	karimpour	NOUN
ejpam-4306	192	13	,	,	PUNCT
ejpam-4306	192	14	and	and	CCONJ
ejpam-4306	192	15	g	g	PROPN
ejpam-4306	192	16	domairry	domairry	NOUN
ejpam-4306	192	17	.	.	PUNCT
ejpam-4306	193	1	motion	motion	NOUN
ejpam-4306	193	2	of	of	ADP
ejpam-4306	193	3	a	a	DET
ejpam-4306	193	4	rigid	rigid	ADJ
ejpam-4306	193	5	rod	rod	NOUN
ejpam-4306	193	6	rocking	rock	VERB
ejpam-4306	193	7	back	back	ADV
ejpam-4306	193	8	and	and	CCONJ
ejpam-4306	193	9	forth	forth	ADV
ejpam-4306	193	10	and	and	CCONJ
ejpam-4306	193	11	cubic	cubic	ADJ
ejpam-4306	193	12	-	-	PUNCT
ejpam-4306	193	13	quintic	quintic	ADJ
ejpam-4306	193	14	duffing	duffing	NOUN
ejpam-4306	193	15	oscillators	oscillator	NOUN
ejpam-4306	193	16	.	.	PUNCT
ejpam-4306	194	1	journal	journal	NOUN
ejpam-4306	194	2	of	of	ADP
ejpam-4306	194	3	theoretical	theoretical	ADJ
ejpam-4306	194	4	and	and	CCONJ
ejpam-4306	194	5	applied	applied	ADJ
ejpam-4306	194	6	mechanics	mechanic	NOUN
ejpam-4306	194	7	,	,	PUNCT
ejpam-4306	194	8	50(1):215–229	50(1):215–229	PROPN
ejpam-4306	194	9	,	,	PUNCT
ejpam-4306	194	10	2012	2012	NUM
ejpam-4306	194	11	.	.	PUNCT
ejpam-4306	195	1	[	[	X
ejpam-4306	195	2	8	8	NUM
ejpam-4306	195	3	]	]	X
ejpam-4306	195	4	asadi	asadi	PROPN
ejpam-4306	195	5	cordshooli	cordshooli	PROPN
ejpam-4306	195	6	gh	gh	PROPN
ejpam-4306	195	7	and	and	CCONJ
ejpam-4306	195	8	ar	ar	PROPN
ejpam-4306	195	9	vahidi	vahidi	PROPN
ejpam-4306	195	10	.	.	PUNCT
ejpam-4306	196	1	solutions	solution	NOUN
ejpam-4306	196	2	of	of	ADP
ejpam-4306	196	3	duffing	duffing	PROPN
ejpam-4306	196	4	-	-	PUNCT
ejpam-4306	196	5	van	van	PROPN
ejpam-4306	196	6	der	der	ADJ
ejpam-4306	196	7	pol	pol	NOUN
ejpam-4306	196	8	equation	equation	NOUN
ejpam-4306	196	9	using	use	VERB
ejpam-4306	196	10	decomposition	decomposition	NOUN
ejpam-4306	196	11	method	method	NOUN
ejpam-4306	196	12	,	,	PUNCT
ejpam-4306	196	13	adv	adv	PROPN
ejpam-4306	196	14	.	.	PUNCT
ejpam-4306	197	1	studies	study	NOUN
ejpam-4306	197	2	theorist	theorist	NOUN
ejpam-4306	197	3	physics	physic	NOUN
ejpam-4306	197	4	,	,	PUNCT
ejpam-4306	197	5	5:121–129	5:121–129	NUM
ejpam-4306	197	6	,	,	PUNCT
ejpam-4306	197	7	2011	2011	NUM
ejpam-4306	197	8	.	.	PUNCT
ejpam-4306	198	1	[	[	X
ejpam-4306	198	2	9	9	NUM
ejpam-4306	198	3	]	]	X
ejpam-4306	198	4	h	h	PROPN
ejpam-4306	198	5	goldstein	goldstein	PROPN
ejpam-4306	198	6	.	.	PUNCT
ejpam-4306	199	1	classical	classical	ADJ
ejpam-4306	199	2	mechanic	mechanic	NOUN
ejpam-4306	199	3	.	.	PUNCT
ejpam-4306	200	1	addison	addison	PROPN
ejpam-4306	200	2	-	-	PUNCT
ejpam-4306	200	3	wesley	wesley	PROPN
ejpam-4306	200	4	,	,	PUNCT
ejpam-4306	200	5	united	united	PROPN
ejpam-4306	200	6	states	states	PROPN
ejpam-4306	200	7	of	of	ADP
ejpam-4306	200	8	america	america	PROPN
ejpam-4306	200	9	,	,	PUNCT
ejpam-4306	200	10	1950	1950	NUM
ejpam-4306	200	11	.	.	PUNCT
ejpam-4306	201	1	[	[	X
ejpam-4306	201	2	10	10	NUM
ejpam-4306	201	3	]	]	SYM
ejpam-4306	201	4	louis	louis	PROPN
ejpam-4306	201	5	n.	n.	PROPN
ejpam-4306	201	6	hand	hand	NOUN
ejpam-4306	201	7	.	.	PUNCT
ejpam-4306	202	1	analytical	analytical	ADJ
ejpam-4306	202	2	mechanics	mechanic	NOUN
ejpam-4306	202	3	.	.	PUNCT
ejpam-4306	203	1	cambridge	cambridge	PROPN
ejpam-4306	203	2	university	university	PROPN
ejpam-4306	203	3	press	press	PROPN
ejpam-4306	203	4	,	,	PUNCT
ejpam-4306	203	5	united	united	PROPN
ejpam-4306	203	6	states	states	PROPN
ejpam-4306	203	7	of	of	ADP
ejpam-4306	203	8	america	america	PROPN
ejpam-4306	203	9	,	,	PUNCT
ejpam-4306	203	10	1998	1998	NUM
ejpam-4306	203	11	.	.	PUNCT
ejpam-4306	204	1	[	[	X
ejpam-4306	204	2	11	11	NUM
ejpam-4306	204	3	]	]	X
ejpam-4306	204	4	ji	ji	PROPN
ejpam-4306	204	5	-	-	PROPN
ejpam-4306	204	6	huan	huan	PROPN
ejpam-4306	204	7	he	he	PROPN
ejpam-4306	204	8	.	.	PUNCT
ejpam-4306	205	1	the	the	DET
ejpam-4306	205	2	simpler	simple	ADJ
ejpam-4306	205	3	,	,	PUNCT
ejpam-4306	205	4	the	the	PRON
ejpam-4306	205	5	better	well	ADJ
ejpam-4306	205	6	:	:	PUNCT
ejpam-4306	205	7	analytical	analytical	ADJ
ejpam-4306	205	8	methods	method	NOUN
ejpam-4306	205	9	for	for	ADP
ejpam-4306	205	10	nonlinear	nonlinear	ADJ
ejpam-4306	205	11	oscillators	oscillator	NOUN
ejpam-4306	205	12	and	and	CCONJ
ejpam-4306	205	13	fractional	fractional	ADJ
ejpam-4306	205	14	oscillators	oscillator	NOUN
ejpam-4306	205	15	.	.	PUNCT
ejpam-4306	206	1	journal	journal	NOUN
ejpam-4306	206	2	of	of	ADP
ejpam-4306	206	3	low	low	ADJ
ejpam-4306	206	4	frequency	frequency	NOUN
ejpam-4306	206	5	noise	noise	NOUN
ejpam-4306	206	6	,	,	PUNCT
ejpam-4306	206	7	vibration	vibration	NOUN
ejpam-4306	206	8	and	and	CCONJ
ejpam-4306	206	9	active	active	ADJ
ejpam-4306	206	10	control	control	NOUN
ejpam-4306	206	11	,	,	PUNCT
ejpam-4306	206	12	38(3	38(3	PROPN
ejpam-4306	206	13	-	-	PUNCT
ejpam-4306	206	14	4):1252–1260	4):1252–1260	NOUN
ejpam-4306	206	15	,	,	PUNCT
ejpam-4306	206	16	2019	2019	NUM
ejpam-4306	206	17	.	.	PUNCT
ejpam-4306	207	1	[	[	X
ejpam-4306	207	2	12	12	NUM
ejpam-4306	207	3	]	]	X
ejpam-4306	207	4	ji	ji	PROPN
ejpam-4306	207	5	-	-	PROPN
ejpam-4306	207	6	huan	huan	PROPN
ejpam-4306	207	7	he	he	PRON
ejpam-4306	207	8	,	,	PUNCT
ejpam-4306	207	9	qian	qian	PROPN
ejpam-4306	207	10	yang	yang	PROPN
ejpam-4306	207	11	,	,	PUNCT
ejpam-4306	207	12	chun	chun	PROPN
ejpam-4306	207	13	-	-	PUNCT
ejpam-4306	207	14	hui	hui	PROPN
ejpam-4306	207	15	he	he	PRON
ejpam-4306	207	16	,	,	PUNCT
ejpam-4306	207	17	and	and	CCONJ
ejpam-4306	207	18	yasir	yasir	PROPN
ejpam-4306	207	19	khan	khan	PROPN
ejpam-4306	207	20	.	.	PUNCT
ejpam-4306	208	1	a	a	DET
ejpam-4306	208	2	simple	simple	ADJ
ejpam-4306	208	3	frequency	frequency	NOUN
ejpam-4306	208	4	formulation	formulation	NOUN
ejpam-4306	208	5	for	for	ADP
ejpam-4306	208	6	the	the	DET
ejpam-4306	208	7	tangent	tangent	NOUN
ejpam-4306	208	8	oscillator	oscillator	NOUN
ejpam-4306	208	9	.	.	PUNCT
ejpam-4306	209	1	axioms	axiom	NOUN
ejpam-4306	209	2	,	,	PUNCT
ejpam-4306	209	3	10(4	10(4	NUM
ejpam-4306	209	4	)	)	PUNCT
ejpam-4306	209	5	,	,	PUNCT
ejpam-4306	209	6	2021	2021	NUM
ejpam-4306	209	7	.	.	PUNCT
ejpam-4306	210	1	[	[	X
ejpam-4306	210	2	13	13	NUM
ejpam-4306	210	3	]	]	X
ejpam-4306	210	4	natalia	natalia	PROPN
ejpam-4306	210	5	janson	janson	PROPN
ejpam-4306	210	6	,	,	PUNCT
ejpam-4306	210	7	dmitry	dmitry	PROPN
ejpam-4306	210	8	postnov	postnov	NOUN
ejpam-4306	210	9	,	,	PUNCT
ejpam-4306	210	10	and	and	CCONJ
ejpam-4306	210	11	olga	olga	PROPN
ejpam-4306	210	12	sosnovtseva	sosnovtseva	PROPN
ejpam-4306	210	13	.	.	PUNCT
ejpam-4306	211	1	synchronization	synchronization	NOUN
ejpam-4306	211	2	:	:	PUNCT
ejpam-4306	211	3	from	from	ADP
ejpam-4306	211	4	simple	simple	ADJ
ejpam-4306	211	5	to	to	ADP
ejpam-4306	211	6	complex	complex	ADJ
ejpam-4306	211	7	.	.	PUNCT
ejpam-4306	212	1	springer	springer	NOUN
ejpam-4306	212	2	complexity	complexity	NOUN
ejpam-4306	212	3	.	.	PUNCT
ejpam-4306	213	1	springer	springer	NOUN
ejpam-4306	213	2	,	,	PUNCT
ejpam-4306	213	3	2009	2009	NUM
ejpam-4306	213	4	.	.	PUNCT
ejpam-4306	214	1	references	reference	NOUN
ejpam-4306	214	2	510	510	NUM
ejpam-4306	214	3	[	[	X
ejpam-4306	214	4	14	14	NUM
ejpam-4306	214	5	]	]	X
ejpam-4306	214	6	a	a	DET
ejpam-4306	214	7	kimiaeifar	kimiaeifar	PROPN
ejpam-4306	214	8	,	,	PUNCT
ejpam-4306	214	9	ar	ar	PROPN
ejpam-4306	214	10	saidi	saidi	PROPN
ejpam-4306	214	11	,	,	PUNCT
ejpam-4306	214	12	gh	gh	PROPN
ejpam-4306	214	13	bagheri	bagheri	PROPN
ejpam-4306	214	14	,	,	PUNCT
ejpam-4306	214	15	m	m	NOUN
ejpam-4306	214	16	rahimpour	rahimpour	NOUN
ejpam-4306	214	17	,	,	PUNCT
ejpam-4306	214	18	and	and	CCONJ
ejpam-4306	214	19	dg	dg	AUX
ejpam-4306	214	20	domairry	domairry	VERB
ejpam-4306	214	21	.	.	PUNCT
ejpam-4306	215	1	analytical	analytical	ADJ
ejpam-4306	215	2	solution	solution	NOUN
ejpam-4306	215	3	for	for	ADP
ejpam-4306	215	4	van	van	PROPN
ejpam-4306	215	5	der	der	PROPN
ejpam-4306	215	6	pol	pol	PROPN
ejpam-4306	215	7	–	–	PUNCT
ejpam-4306	215	8	duffing	duffe	VERB
ejpam-4306	215	9	oscillators	oscillator	NOUN
ejpam-4306	215	10	.	.	PUNCT
ejpam-4306	216	1	chaos	chaos	NOUN
ejpam-4306	216	2	,	,	PUNCT
ejpam-4306	216	3	solitons	soliton	NOUN
ejpam-4306	216	4	&	&	CCONJ
ejpam-4306	216	5	fractals	fractal	NOUN
ejpam-4306	216	6	,	,	PUNCT
ejpam-4306	216	7	42(5):2660–2666	42(5):2660–2666	NOUN
ejpam-4306	216	8	,	,	PUNCT
ejpam-4306	216	9	2009	2009	NUM
ejpam-4306	216	10	.	.	PUNCT
ejpam-4306	217	1	[	[	X
ejpam-4306	217	2	15	15	X
ejpam-4306	217	3	]	]	X
ejpam-4306	217	4	manoj	manoj	PROPN
ejpam-4306	217	5	kumar	kumar	PROPN
ejpam-4306	217	6	and	and	CCONJ
ejpam-4306	217	7	parul	parul	PROPN
ejpam-4306	217	8	varshney	varshney	NOUN
ejpam-4306	217	9	.	.	PUNCT
ejpam-4306	218	1	numerical	numerical	PROPN
ejpam-4306	218	2	simulation	simulation	PROPN
ejpam-4306	218	3	of	of	ADP
ejpam-4306	218	4	van	van	PROPN
ejpam-4306	218	5	der	der	PROPN
ejpam-4306	218	6	pol	pol	NOUN
ejpam-4306	218	7	equation	equation	NOUN
ejpam-4306	218	8	using	use	VERB
ejpam-4306	218	9	multiple	multiple	ADJ
ejpam-4306	218	10	scales	scale	NOUN
ejpam-4306	218	11	modified	modify	VERB
ejpam-4306	218	12	lindstedt	lindstedt	PROPN
ejpam-4306	218	13	-	-	PUNCT
ejpam-4306	218	14	poincare	poincare	PROPN
ejpam-4306	218	15	method	method	NOUN
ejpam-4306	218	16	.	.	PUNCT
ejpam-4306	219	1	proceedings	proceeding	NOUN
ejpam-4306	219	2	of	of	ADP
ejpam-4306	219	3	the	the	DET
ejpam-4306	219	4	national	national	PROPN
ejpam-4306	219	5	academy	academy	PROPN
ejpam-4306	219	6	of	of	ADP
ejpam-4306	219	7	sciences	sciences	PROPN
ejpam-4306	219	8	,	,	PUNCT
ejpam-4306	219	9	india	india	PROPN
ejpam-4306	219	10	section	section	PROPN
ejpam-4306	219	11	a	a	DET
ejpam-4306	219	12	:	:	PUNCT
ejpam-4306	219	13	physical	physical	ADJ
ejpam-4306	219	14	sciences	science	NOUN
ejpam-4306	219	15	,	,	PUNCT
ejpam-4306	219	16	91(1):55–65	91(1):55–65	NUM
ejpam-4306	219	17	,	,	PUNCT
ejpam-4306	219	18	2021	2021	NUM
ejpam-4306	219	19	.	.	PUNCT
ejpam-4306	220	1	[	[	X
ejpam-4306	220	2	16	16	NUM
ejpam-4306	220	3	]	]	X
ejpam-4306	220	4	n.	n.	NOUN
ejpam-4306	220	5	minorsky	minorsky	PROPN
ejpam-4306	220	6	.	.	PUNCT
ejpam-4306	221	1	introduction	introduction	NOUN
ejpam-4306	221	2	to	to	ADP
ejpam-4306	221	3	non	non	ADJ
ejpam-4306	221	4	-	-	ADJ
ejpam-4306	221	5	linear	linear	ADJ
ejpam-4306	221	6	mechanics	mechanic	NOUN
ejpam-4306	221	7	.	.	PUNCT
ejpam-4306	222	1	edwards	edwards	PROPN
ejpam-4306	222	2	brothers	brothers	PROPN
ejpam-4306	222	3	,	,	PUNCT
ejpam-4306	222	4	united	united	PROPN
ejpam-4306	222	5	states	states	PROPN
ejpam-4306	222	6	of	of	ADP
ejpam-4306	222	7	america	america	PROPN
ejpam-4306	222	8	,	,	PUNCT
ejpam-4306	222	9	1947	1947	NUM
ejpam-4306	222	10	.	.	PUNCT
ejpam-4306	223	1	[	[	X
ejpam-4306	223	2	17	17	NUM
ejpam-4306	223	3	]	]	X
ejpam-4306	223	4	yasir	yasir	PROPN
ejpam-4306	223	5	nawaz	nawaz	PROPN
ejpam-4306	223	6	,	,	PUNCT
ejpam-4306	223	7	muhammad	muhammad	PROPN
ejpam-4306	223	8	shoaib	shoaib	PROPN
ejpam-4306	223	9	arif	arif	PROPN
ejpam-4306	223	10	,	,	PUNCT
ejpam-4306	223	11	mairaj	mairaj	ADJ
ejpam-4306	223	12	bibi	bibi	NOUN
ejpam-4306	223	13	,	,	PUNCT
ejpam-4306	223	14	mehvish	mehvish	PROPN
ejpam-4306	223	15	naz	naz	PROPN
ejpam-4306	223	16	,	,	PUNCT
ejpam-4306	223	17	and	and	CCONJ
ejpam-4306	223	18	rabia	rabia	PROPN
ejpam-4306	223	19	fayyaz	fayyaz	NOUN
ejpam-4306	223	20	.	.	PUNCT
ejpam-4306	224	1	an	an	DET
ejpam-4306	224	2	effective	effective	ADJ
ejpam-4306	224	3	modification	modification	NOUN
ejpam-4306	224	4	of	of	ADP
ejpam-4306	224	5	he	he	PRON
ejpam-4306	224	6	’s	’	VERB
ejpam-4306	224	7	variational	variational	ADJ
ejpam-4306	224	8	approach	approach	NOUN
ejpam-4306	224	9	to	to	ADP
ejpam-4306	224	10	a	a	DET
ejpam-4306	224	11	nonlinear	nonlinear	ADJ
ejpam-4306	224	12	oscillator	oscillator	NOUN
ejpam-4306	224	13	.	.	PUNCT
ejpam-4306	225	1	journal	journal	NOUN
ejpam-4306	225	2	of	of	ADP
ejpam-4306	225	3	low	low	ADJ
ejpam-4306	225	4	frequency	frequency	NOUN
ejpam-4306	225	5	noise	noise	NOUN
ejpam-4306	225	6	,	,	PUNCT
ejpam-4306	225	7	vibration	vibration	NOUN
ejpam-4306	225	8	and	and	CCONJ
ejpam-4306	225	9	active	active	ADJ
ejpam-4306	225	10	control	control	NOUN
ejpam-4306	225	11	,	,	PUNCT
ejpam-4306	225	12	38(3	38(3	PROPN
ejpam-4306	225	13	-	-	PUNCT
ejpam-4306	225	14	4):1013–1022	4):1013–1022	NOUN
ejpam-4306	225	15	,	,	PUNCT
ejpam-4306	225	16	2019	2019	NUM
ejpam-4306	225	17	.	.	PUNCT
ejpam-4306	226	1	[	[	X
ejpam-4306	226	2	18	18	NUM
ejpam-4306	226	3	]	]	X
ejpam-4306	226	4	yh	yh	PROPN
ejpam-4306	226	5	qian	qian	PROPN
ejpam-4306	226	6	,	,	PUNCT
ejpam-4306	226	7	wk	wk	PROPN
ejpam-4306	226	8	liu	liu	PROPN
ejpam-4306	226	9	,	,	PUNCT
ejpam-4306	226	10	and	and	CCONJ
ejpam-4306	226	11	sm	sm	PROPN
ejpam-4306	226	12	chen	chen	PROPN
ejpam-4306	226	13	.	.	PUNCT
ejpam-4306	227	1	construction	construction	NOUN
ejpam-4306	227	2	of	of	ADP
ejpam-4306	227	3	approximate	approximate	ADJ
ejpam-4306	227	4	analytical	analytical	ADJ
ejpam-4306	227	5	solutions	solution	NOUN
ejpam-4306	227	6	to	to	PART
ejpam-4306	227	7	strongly	strongly	ADV
ejpam-4306	227	8	nonlinear	nonlinear	VERB
ejpam-4306	227	9	coupled	couple	VERB
ejpam-4306	227	10	van	van	PROPN
ejpam-4306	227	11	der	der	PROPN
ejpam-4306	227	12	pol	pol	PROPN
ejpam-4306	227	13	oscillators	oscillator	NOUN
ejpam-4306	227	14	.	.	PUNCT
ejpam-4306	228	1	advances	advance	NOUN
ejpam-4306	228	2	in	in	ADP
ejpam-4306	228	3	mechanical	mechanical	ADJ
ejpam-4306	228	4	engineering	engineering	NOUN
ejpam-4306	228	5	,	,	PUNCT
ejpam-4306	228	6	6	6	NUM
ejpam-4306	228	7	,	,	PUNCT
ejpam-4306	228	8	2014	2014	NUM
ejpam-4306	228	9	.	.	PUNCT
ejpam-4306	229	1	[	[	X
ejpam-4306	229	2	19	19	NUM
ejpam-4306	229	3	]	]	PUNCT
ejpam-4306	229	4	na	na	PART
ejpam-4306	229	5	qie	qie	PROPN
ejpam-4306	229	6	,	,	PUNCT
ejpam-4306	229	7	wei	wei	PROPN
ejpam-4306	229	8	-	-	PUNCT
ejpam-4306	229	9	fan	fan	PROPN
ejpam-4306	229	10	houa	houa	NOUN
ejpam-4306	229	11	,	,	PUNCT
ejpam-4306	229	12	and	and	CCONJ
ejpam-4306	229	13	ji	ji	PROPN
ejpam-4306	229	14	-	-	PROPN
ejpam-4306	229	15	huan	huan	PROPN
ejpam-4306	229	16	he	he	PROPN
ejpam-4306	229	17	.	.	PUNCT
ejpam-4306	230	1	the	the	DET
ejpam-4306	230	2	fastest	fast	ADJ
ejpam-4306	230	3	insight	insight	NOUN
ejpam-4306	230	4	into	into	ADP
ejpam-4306	230	5	the	the	DET
ejpam-4306	230	6	large	large	ADJ
ejpam-4306	230	7	amplitude	amplitude	NOUN
ejpam-4306	230	8	vibration	vibration	NOUN
ejpam-4306	230	9	of	of	ADP
ejpam-4306	230	10	a	a	DET
ejpam-4306	230	11	string	string	NOUN
ejpam-4306	230	12	.	.	PUNCT
ejpam-4306	231	1	reports	report	NOUN
ejpam-4306	231	2	in	in	ADP
ejpam-4306	231	3	mechanical	mechanical	ADJ
ejpam-4306	231	4	engineering	engineering	NOUN
ejpam-4306	231	5	,	,	PUNCT
ejpam-4306	231	6	2(1):1–5	2(1):1–5	NUM
ejpam-4306	231	7	,	,	PUNCT
ejpam-4306	231	8	2021	2021	NUM
ejpam-4306	231	9	.	.	PUNCT
ejpam-4306	232	1	[	[	X
ejpam-4306	232	2	20	20	NUM
ejpam-4306	232	3	]	]	PUNCT
ejpam-4306	232	4	sh	sh	PROPN
ejpam-4306	232	5	strogatz	strogatz	PROPN
ejpam-4306	232	6	.	.	PUNCT
ejpam-4306	233	1	nonlinear	nonlinear	ADJ
ejpam-4306	233	2	dynamics	dynamic	NOUN
ejpam-4306	233	3	and	and	CCONJ
ejpam-4306	233	4	chaos	chaos	NOUN
ejpam-4306	233	5	,	,	PUNCT
ejpam-4306	233	6	vol	vol	NOUN
ejpam-4306	233	7	1	1	NUM
ejpam-4306	233	8	-	-	SYM
ejpam-4306	233	9	9	9	NUM
ejpam-4306	233	10	.	.	PUNCT
ejpam-4306	233	11	westview	westview	PROPN
ejpam-4306	233	12	press	press	PROPN
ejpam-4306	233	13	,	,	PUNCT
ejpam-4306	233	14	us	us	PROPN
ejpam-4306	233	15	perseus	perseus	NOUN
ejpam-4306	233	16	books	book	NOUN
ejpam-4306	233	17	publishing	publishing	NOUN
ejpam-4306	233	18	,	,	PUNCT
ejpam-4306	233	19	llc	llc	PROPN
ejpam-4306	233	20	,	,	PUNCT
ejpam-4306	233	21	1994	1994	NUM
ejpam-4306	233	22	.	.	PUNCT
ejpam-4306	234	1	[	[	X
ejpam-4306	234	2	21	21	NUM
ejpam-4306	234	3	]	]	X
ejpam-4306	234	4	yue	yue	PROPN
ejpam-4306	234	5	wu	wu	PROPN
ejpam-4306	234	6	and	and	CCONJ
ejpam-4306	234	7	ji	ji	PROPN
ejpam-4306	234	8	-	-	PROPN
ejpam-4306	234	9	huan	huan	PROPN
ejpam-4306	234	10	he	he	PROPN
ejpam-4306	234	11	.	.	PUNCT
ejpam-4306	235	1	homotopy	homotopy	VERB
ejpam-4306	235	2	perturbation	perturbation	NOUN
ejpam-4306	235	3	method	method	NOUN
ejpam-4306	235	4	for	for	ADP
ejpam-4306	235	5	nonlinear	nonlinear	ADJ
ejpam-4306	235	6	oscillators	oscillator	NOUN
ejpam-4306	235	7	with	with	ADP
ejpam-4306	235	8	coordinate	coordinate	NOUN
ejpam-4306	235	9	dependent	dependent	ADJ
ejpam-4306	235	10	mass	mass	PROPN
ejpam-4306	235	11	.	.	PUNCT
ejpam-4306	236	1	results	result	VERB
ejpam-4306	236	2	phys	phy	NOUN
ejpam-4306	236	3	,	,	PUNCT
ejpam-4306	236	4	10:270–271	10:270–271	PROPN
ejpam-4306	236	5	,	,	PUNCT
ejpam-4306	236	6	2018	2018	NUM
ejpam-4306	236	7	.	.	PUNCT