id	sid	tid	token	lemma	pos
fumecheng-12201	1	1	12201	12201	NUM
fumecheng-12201	1	2	facta	facta	PROPN
fumecheng-12201	1	3	universitatis	universitatis	PROPN
fumecheng-12201	1	4	series	series	NOUN
fumecheng-12201	1	5	:	:	PUNCT
fumecheng-12201	1	6	mechanical	mechanical	ADJ
fumecheng-12201	1	7	engineering	engineering	NOUN
fumecheng-12201	1	8	vol	vol	NOUN
fumecheng-12201	1	9	.	.	PROPN
fumecheng-12201	1	10	21	21	NUM
fumecheng-12201	1	11	,	,	PUNCT
fumecheng-12201	1	12	no	no	DET
fumecheng-12201	1	13	4	4	NUM
fumecheng-12201	1	14	,	,	PUNCT
fumecheng-12201	1	15	2023	2023	NUM
fumecheng-12201	1	16	,	,	PUNCT
fumecheng-12201	1	17	pp	pp	ADJ
fumecheng-12201	1	18	.	.	PUNCT
fumecheng-12201	2	1	701	701	NUM
fumecheng-12201	2	2	712	712	NUM
fumecheng-12201	2	3	https://doi.org/10.22190/fume230909047z	https://doi.org/10.22190/fume230909047z	NOUN
fumecheng-12201	2	4	©	©	PROPN
fumecheng-12201	2	5	2023	2023	NUM
fumecheng-12201	2	6	by	by	ADP
fumecheng-12201	2	7	university	university	PROPN
fumecheng-12201	2	8	of	of	ADP
fumecheng-12201	2	9	niš	niš	PROPN
fumecheng-12201	2	10	,	,	PUNCT
fumecheng-12201	2	11	serbia	serbia	PROPN
fumecheng-12201	2	12	|	|	ADV
fumecheng-12201	2	13	creative	creative	ADJ
fumecheng-12201	2	14	commons	common	NOUN
fumecheng-12201	2	15	license	license	NOUN
fumecheng-12201	2	16	:	:	PUNCT
fumecheng-12201	2	17	cc	cc	VERB
fumecheng-12201	2	18	by	by	ADP
fumecheng-12201	2	19	-	-	PUNCT
fumecheng-12201	2	20	nc	nc	VERB
fumecheng-12201	2	21	-	-	PUNCT
fumecheng-12201	2	22	nd	nd	ADV
fumecheng-12201	2	23	original	original	ADJ
fumecheng-12201	2	24	scientific	scientific	ADJ
fumecheng-12201	2	25	paper	paper	NUM
fumecheng-12201	2	26	application	application	NOUN
fumecheng-12201	2	27	of	of	ADP
fumecheng-12201	2	28	he	he	PRON
fumecheng-12201	2	29	’s	’s	PART
fumecheng-12201	2	30	frequency	frequency	NOUN
fumecheng-12201	2	31	formula	formula	NOUN
fumecheng-12201	2	32	to	to	PART
fumecheng-12201	2	33	nonlinear	nonlinear	ADJ
fumecheng-12201	2	34	oscillators	oscillator	NOUN
fumecheng-12201	2	35	with	with	ADP
fumecheng-12201	2	36	generalized	generalized	ADJ
fumecheng-12201	2	37	initial	initial	ADJ
fumecheng-12201	2	38	conditions	condition	NOUN
fumecheng-12201	2	39	jian	jian	PROPN
fumecheng-12201	2	40	-	-	PUNCT
fumecheng-12201	2	41	gang	gang	NOUN
fumecheng-12201	2	42	zhang1	zhang1	PROPN
fumecheng-12201	2	43	,	,	PUNCT
fumecheng-12201	2	44	qing	qing	NOUN
fumecheng-12201	2	45	-	-	PUNCT
fumecheng-12201	2	46	ru	ru	PROPN
fumecheng-12201	2	47	song1	song1	NOUN
fumecheng-12201	2	48	,	,	PUNCT
fumecheng-12201	2	49	jian	jian	PROPN
fumecheng-12201	2	50	-	-	PUNCT
fumecheng-12201	2	51	qiang	qiang	PROPN
fumecheng-12201	2	52	zhang2	zhang2	PROPN
fumecheng-12201	2	53	,	,	PUNCT
fumecheng-12201	2	54	fang	fang	X
fumecheng-12201	2	55	wang1	wang1	PROPN
fumecheng-12201	3	1	1school	1school	NUM
fumecheng-12201	3	2	of	of	ADP
fumecheng-12201	3	3	mathematics	mathematic	NOUN
fumecheng-12201	3	4	and	and	CCONJ
fumecheng-12201	3	5	physics	physics	PROPN
fumecheng-12201	3	6	,	,	PUNCT
fumecheng-12201	3	7	lanzhou	lanzhou	PROPN
fumecheng-12201	3	8	jiaotong	jiaotong	PROPN
fumecheng-12201	3	9	university	university	PROPN
fumecheng-12201	3	10	,	,	PUNCT
fumecheng-12201	3	11	lanzhou	lanzhou	PROPN
fumecheng-12201	3	12	,	,	PUNCT
fumecheng-12201	3	13	china	china	PROPN
fumecheng-12201	3	14	2school	2school	NUM
fumecheng-12201	3	15	of	of	ADP
fumecheng-12201	3	16	automation	automation	NOUN
fumecheng-12201	3	17	and	and	CCONJ
fumecheng-12201	3	18	electrical	electrical	ADJ
fumecheng-12201	3	19	engineering	engineering	NOUN
fumecheng-12201	3	20	,	,	PUNCT
fumecheng-12201	3	21	lanzhou	lanzhou	PROPN
fumecheng-12201	3	22	jiaotong	jiaotong	PROPN
fumecheng-12201	3	23	university	university	PROPN
fumecheng-12201	3	24	,	,	PUNCT
fumecheng-12201	3	25	lanzhou	lanzhou	PROPN
fumecheng-12201	3	26	,	,	PUNCT
fumecheng-12201	3	27	china	china	PROPN
fumecheng-12201	3	28	abstract	abstract	NOUN
fumecheng-12201	3	29	.	.	PUNCT
fumecheng-12201	4	1	this	this	DET
fumecheng-12201	4	2	paper	paper	NOUN
fumecheng-12201	4	3	focuses	focus	VERB
fumecheng-12201	4	4	on	on	ADP
fumecheng-12201	4	5	the	the	DET
fumecheng-12201	4	6	vibration	vibration	NOUN
fumecheng-12201	4	7	periodic	periodic	ADJ
fumecheng-12201	4	8	property	property	NOUN
fumecheng-12201	4	9	of	of	ADP
fumecheng-12201	4	10	duffing	duffe	VERB
fumecheng-12201	4	11	oscillator	oscillator	NOUN
fumecheng-12201	4	12	with	with	ADP
fumecheng-12201	4	13	generalized	generalized	ADJ
fumecheng-12201	4	14	initial	initial	ADJ
fumecheng-12201	4	15	conditions	condition	NOUN
fumecheng-12201	4	16	.	.	PUNCT
fumecheng-12201	5	1	firstly	firstly	ADV
fumecheng-12201	5	2	,	,	PUNCT
fumecheng-12201	5	3	the	the	DET
fumecheng-12201	5	4	undamped	undampe	VERB
fumecheng-12201	5	5	case	case	NOUN
fumecheng-12201	5	6	is	be	AUX
fumecheng-12201	5	7	solved	solve	VERB
fumecheng-12201	5	8	by	by	ADP
fumecheng-12201	5	9	ji	ji	PROPN
fumecheng-12201	5	10	-	-	PROPN
fumecheng-12201	5	11	huan	huan	PROPN
fumecheng-12201	5	12	he	he	PRON
fumecheng-12201	5	13	’s	’	VERB
fumecheng-12201	5	14	frequency	frequency	NOUN
fumecheng-12201	5	15	formulation	formulation	NOUN
fumecheng-12201	5	16	;	;	PUNCT
fumecheng-12201	5	17	secondly	secondly	ADV
fumecheng-12201	5	18	,	,	PUNCT
fumecheng-12201	5	19	the	the	DET
fumecheng-12201	5	20	formulation	formulation	NOUN
fumecheng-12201	5	21	is	be	AUX
fumecheng-12201	5	22	extended	extend	VERB
fumecheng-12201	5	23	to	to	ADP
fumecheng-12201	5	24	the	the	DET
fumecheng-12201	5	25	damped	damped	NOUN
fumecheng-12201	5	26	case	case	NOUN
fumecheng-12201	5	27	.	.	PUNCT
fumecheng-12201	6	1	numerical	numerical	PROPN
fumecheng-12201	6	2	verification	verification	PROPN
fumecheng-12201	6	3	shows	show	VERB
fumecheng-12201	6	4	that	that	SCONJ
fumecheng-12201	6	5	the	the	DET
fumecheng-12201	6	6	frequency	frequency	NOUN
fumecheng-12201	6	7	formulation	formulation	NOUN
fumecheng-12201	6	8	is	be	AUX
fumecheng-12201	6	9	mathematically	mathematically	ADV
fumecheng-12201	6	10	simple	simple	ADJ
fumecheng-12201	6	11	and	and	CCONJ
fumecheng-12201	6	12	physically	physically	ADV
fumecheng-12201	6	13	insightful	insightful	ADJ
fumecheng-12201	6	14	and	and	CCONJ
fumecheng-12201	6	15	practically	practically	ADV
fumecheng-12201	6	16	applicable	applicable	ADJ
fumecheng-12201	6	17	.	.	PUNCT
fumecheng-12201	7	1	this	this	DET
fumecheng-12201	7	2	paper	paper	NOUN
fumecheng-12201	7	3	paves	pave	VERB
fumecheng-12201	7	4	a	a	DET
fumecheng-12201	7	5	novel	novel	ADJ
fumecheng-12201	7	6	way	way	NOUN
fumecheng-12201	7	7	for	for	SCONJ
fumecheng-12201	7	8	engineers	engineer	NOUN
fumecheng-12201	7	9	to	to	PART
fumecheng-12201	7	10	use	use	VERB
fumecheng-12201	7	11	the	the	DET
fumecheng-12201	7	12	formulation	formulation	NOUN
fumecheng-12201	7	13	to	to	PART
fumecheng-12201	7	14	study	study	VERB
fumecheng-12201	7	15	nonlinear	nonlinear	ADJ
fumecheng-12201	7	16	vibration	vibration	NOUN
fumecheng-12201	7	17	system	system	NOUN
fumecheng-12201	7	18	with	with	ADP
fumecheng-12201	7	19	ease	ease	NOUN
fumecheng-12201	7	20	and	and	CCONJ
fumecheng-12201	7	21	reliability	reliability	NOUN
fumecheng-12201	7	22	.	.	PUNCT
fumecheng-12201	8	1	key	key	ADJ
fumecheng-12201	8	2	words	word	NOUN
fumecheng-12201	8	3	:	:	PUNCT
fumecheng-12201	8	4	duffing	duffe	VERB
fumecheng-12201	8	5	equation	equation	NOUN
fumecheng-12201	8	6	,	,	PUNCT
fumecheng-12201	8	7	he	he	PRON
fumecheng-12201	8	8	’s	’	VERB
fumecheng-12201	8	9	frequency	frequency	NOUN
fumecheng-12201	8	10	formulation	formulation	NOUN
fumecheng-12201	8	11	,	,	PUNCT
fumecheng-12201	8	12	ancient	ancient	ADJ
fumecheng-12201	8	13	chinese	chinese	ADJ
fumecheng-12201	8	14	mathematics	mathematic	NOUN
fumecheng-12201	8	15	,	,	PUNCT
fumecheng-12201	8	16	residual	residual	ADJ
fumecheng-12201	8	17	equation	equation	NOUN
fumecheng-12201	8	18	,	,	PUNCT
fumecheng-12201	8	19	nonlinear	nonlinear	ADJ
fumecheng-12201	8	20	vibrations	vibration	NOUN
fumecheng-12201	8	21	1	1	NUM
fumecheng-12201	8	22	.	.	PUNCT
fumecheng-12201	9	1	introduction	introduction	NOUN
fumecheng-12201	9	2	nonlinear	nonlinear	PROPN
fumecheng-12201	9	3	systems	system	NOUN
fumecheng-12201	9	4	are	be	AUX
fumecheng-12201	9	5	widely	widely	ADV
fumecheng-12201	9	6	present	present	ADJ
fumecheng-12201	9	7	in	in	ADP
fumecheng-12201	9	8	the	the	DET
fumecheng-12201	9	9	field	field	NOUN
fumecheng-12201	9	10	of	of	ADP
fumecheng-12201	9	11	mechanical	mechanical	ADJ
fumecheng-12201	9	12	engineering	engineering	NOUN
fumecheng-12201	9	13	and	and	CCONJ
fumecheng-12201	9	14	hold	hold	VERB
fumecheng-12201	9	15	significant	significant	ADJ
fumecheng-12201	9	16	importance	importance	NOUN
fumecheng-12201	9	17	in	in	ADP
fumecheng-12201	9	18	unraveling	unravel	VERB
fumecheng-12201	9	19	the	the	DET
fumecheng-12201	9	20	dynamical	dynamical	ADJ
fumecheng-12201	9	21	characteristics	characteristic	NOUN
fumecheng-12201	9	22	of	of	ADP
fumecheng-12201	9	23	nonlinear	nonlinear	ADJ
fumecheng-12201	9	24	vibration	vibration	NOUN
fumecheng-12201	9	25	systems	system	NOUN
fumecheng-12201	9	26	.	.	PUNCT
fumecheng-12201	10	1	in	in	ADP
fumecheng-12201	10	2	the	the	DET
fumecheng-12201	10	3	realm	realm	NOUN
fumecheng-12201	10	4	of	of	ADP
fumecheng-12201	10	5	mechanical	mechanical	ADJ
fumecheng-12201	10	6	engineering	engineering	NOUN
fumecheng-12201	10	7	,	,	PUNCT
fumecheng-12201	10	8	nonlinear	nonlinear	ADJ
fumecheng-12201	10	9	vibration	vibration	NOUN
fumecheng-12201	10	10	systems	system	NOUN
fumecheng-12201	10	11	are	be	AUX
fumecheng-12201	10	12	omnipresent	omnipresent	ADJ
fumecheng-12201	10	13	,	,	PUNCT
fumecheng-12201	10	14	encompassing	encompass	VERB
fumecheng-12201	10	15	nano	nano	NOUN
fumecheng-12201	10	16	-	-	PUNCT
fumecheng-12201	10	17	scale	scale	NOUN
fumecheng-12201	10	18	vibrations	vibration	NOUN
fumecheng-12201	10	19	[	[	X
fumecheng-12201	10	20	1	1	NUM
fumecheng-12201	10	21	]	]	PUNCT
fumecheng-12201	10	22	,	,	PUNCT
fumecheng-12201	10	23	atomic	atomic	ADJ
fumecheng-12201	10	24	-	-	PUNCT
fumecheng-12201	10	25	level	level	NOUN
fumecheng-12201	10	26	lattice	lattice	NOUN
fumecheng-12201	10	27	vibrations	vibration	NOUN
fumecheng-12201	10	28	[	[	X
fumecheng-12201	10	29	2	2	NUM
fumecheng-12201	10	30	]	]	PUNCT
fumecheng-12201	10	31	,	,	PUNCT
fumecheng-12201	10	32	and	and	CCONJ
fumecheng-12201	10	33	microelectromechanical	microelectromechanical	ADJ
fumecheng-12201	10	34	systems	system	NOUN
fumecheng-12201	10	35	[	[	X
fumecheng-12201	10	36	3,4	3,4	NUM
fumecheng-12201	10	37	]	]	PUNCT
fumecheng-12201	10	38	,	,	PUNCT
fumecheng-12201	10	39	among	among	ADP
fumecheng-12201	10	40	others	other	NOUN
fumecheng-12201	10	41	.	.	PUNCT
fumecheng-12201	11	1	the	the	DET
fumecheng-12201	11	2	most	most	ADV
fumecheng-12201	11	3	renowned	renowned	ADJ
fumecheng-12201	11	4	nonlinear	nonlinear	ADJ
fumecheng-12201	11	5	oscillators	oscillator	NOUN
fumecheng-12201	11	6	in	in	ADP
fumecheng-12201	11	7	these	these	DET
fumecheng-12201	11	8	systems	system	NOUN
fumecheng-12201	11	9	include	include	VERB
fumecheng-12201	11	10	pendulum	pendulum	NOUN
fumecheng-12201	11	11	oscillators	oscillator	NOUN
fumecheng-12201	11	12	[	[	X
fumecheng-12201	11	13	5,6	5,6	NUM
fumecheng-12201	11	14	]	]	PUNCT
fumecheng-12201	11	15	,	,	PUNCT
fumecheng-12201	11	16	van	van	PROPN
fumecheng-12201	11	17	der	der	ADJ
fumecheng-12201	11	18	pol	pol	PROPN
fumecheng-12201	11	19	oscillators	oscillator	NOUN
fumecheng-12201	11	20	,	,	PUNCT
fumecheng-12201	11	21	and	and	CCONJ
fumecheng-12201	11	22	duffing	duffe	VERB
fumecheng-12201	11	23	oscillators	oscillator	NOUN
fumecheng-12201	11	24	[	[	X
fumecheng-12201	11	25	7	7	NUM
fumecheng-12201	11	26	]	]	PUNCT
fumecheng-12201	11	27	.	.	PUNCT
fumecheng-12201	12	1	with	with	ADP
fumecheng-12201	12	2	the	the	DET
fumecheng-12201	12	3	rapid	rapid	ADJ
fumecheng-12201	12	4	development	development	NOUN
fumecheng-12201	12	5	of	of	ADP
fumecheng-12201	12	6	nonlinear	nonlinear	ADJ
fumecheng-12201	12	7	science	science	NOUN
fumecheng-12201	12	8	,	,	PUNCT
fumecheng-12201	12	9	more	more	ADJ
fumecheng-12201	12	10	and	and	CCONJ
fumecheng-12201	12	11	more	more	ADJ
fumecheng-12201	12	12	scholars	scholar	NOUN
fumecheng-12201	12	13	have	have	AUX
fumecheng-12201	12	14	shown	show	VERB
fumecheng-12201	12	15	great	great	ADJ
fumecheng-12201	12	16	interest	interest	NOUN
fumecheng-12201	12	17	in	in	ADP
fumecheng-12201	12	18	nonlinear	nonlinear	ADJ
fumecheng-12201	12	19	problems	problem	NOUN
fumecheng-12201	12	20	.	.	PUNCT
fumecheng-12201	13	1	solving	solve	VERB
fumecheng-12201	13	2	large	large	ADJ
fumecheng-12201	13	3	-	-	PUNCT
fumecheng-12201	13	4	scale	scale	NOUN
fumecheng-12201	13	5	linear	linear	NOUN
fumecheng-12201	13	6	equation	equation	NOUN
fumecheng-12201	13	7	systems	system	NOUN
fumecheng-12201	13	8	is	be	AUX
fumecheng-12201	13	9	no	no	ADV
fumecheng-12201	13	10	longer	long	ADV
fumecheng-12201	13	11	a	a	DET
fumecheng-12201	13	12	challenge	challenge	NOUN
fumecheng-12201	13	13	,	,	PUNCT
fumecheng-12201	13	14	however	however	ADV
fumecheng-12201	13	15	,	,	PUNCT
fumecheng-12201	13	16	for	for	ADP
fumecheng-12201	13	17	nonlinear	nonlinear	ADJ
fumecheng-12201	13	18	equation	equation	NOUN
fumecheng-12201	13	19	systems	system	NOUN
fumecheng-12201	13	20	,	,	PUNCT
fumecheng-12201	13	21	traditional	traditional	ADJ
fumecheng-12201	13	22	perturbation	perturbation	NOUN
fumecheng-12201	13	23	methods	method	NOUN
fumecheng-12201	13	24	[	[	X
fumecheng-12201	13	25	8	8	X
fumecheng-12201	13	26	]	]	PUNCT
fumecheng-12201	13	27	have	have	AUX
fumecheng-12201	13	28	been	be	AUX
fumecheng-12201	13	29	widely	widely	ADV
fumecheng-12201	13	30	applied	apply	VERB
fumecheng-12201	13	31	in	in	ADP
fumecheng-12201	13	32	the	the	DET
fumecheng-12201	13	33	nonlinear	nonlinear	ADJ
fumecheng-12201	13	34	analysis	analysis	NOUN
fumecheng-12201	13	35	of	of	ADP
fumecheng-12201	13	36	engineering	engineering	NOUN
fumecheng-12201	13	37	problems	problem	NOUN
fumecheng-12201	13	38	.	.	PUNCT
fumecheng-12201	14	1	however	however	ADV
fumecheng-12201	14	2	,	,	PUNCT
fumecheng-12201	14	3	like	like	ADP
fumecheng-12201	14	4	other	other	ADJ
fumecheng-12201	14	5	nonlinear	nonlinear	ADJ
fumecheng-12201	14	6	asymptotic	asymptotic	ADJ
fumecheng-12201	14	7	techniques	technique	NOUN
fumecheng-12201	14	8	,	,	PUNCT
fumecheng-12201	14	9	perturbation	perturbation	NOUN
fumecheng-12201	14	10	methods	method	NOUN
fumecheng-12201	14	11	are	be	AUX
fumecheng-12201	14	12	also	also	ADV
fumecheng-12201	14	13	affected	affect	VERB
fumecheng-12201	14	14	by	by	ADP
fumecheng-12201	14	15	limitations	limitation	NOUN
fumecheng-12201	14	16	imposed	impose	VERB
fumecheng-12201	14	17	by	by	ADP
fumecheng-12201	14	18	small	small	ADJ
fumecheng-12201	14	19	parameters	parameter	NOUN
fumecheng-12201	14	20	,	,	PUNCT
fumecheng-12201	14	21	and	and	CCONJ
fumecheng-12201	14	22	this	this	DET
fumecheng-12201	14	23	point	point	NOUN
fumecheng-12201	14	24	should	should	AUX
fumecheng-12201	14	25	received	received	VERB
fumecheng-12201	14	26	:	:	PUNCT
fumecheng-12201	14	27	september	september	PROPN
fumecheng-12201	14	28	09	09	NUM
fumecheng-12201	14	29	,	,	PUNCT
fumecheng-12201	14	30	2023	2023	NUM
fumecheng-12201	14	31	/	/	PUNCT
fumecheng-12201	14	32	accepted	accept	VERB
fumecheng-12201	14	33	november	november	PROPN
fumecheng-12201	14	34	30	30	NUM
fumecheng-12201	14	35	,	,	PUNCT
fumecheng-12201	14	36	2023	2023	NUM
fumecheng-12201	14	37	corresponding	correspond	VERB
fumecheng-12201	14	38	author	author	NOUN
fumecheng-12201	14	39	:	:	PUNCT
fumecheng-12201	14	40	jian	jian	PROPN
fumecheng-12201	14	41	-	-	PUNCT
fumecheng-12201	14	42	gang	gang	PROPN
fumecheng-12201	14	43	zhang	zhang	PROPN
fumecheng-12201	14	44	school	school	PROPN
fumecheng-12201	14	45	of	of	ADP
fumecheng-12201	14	46	mathematics	mathematics	PROPN
fumecheng-12201	14	47	and	and	CCONJ
fumecheng-12201	14	48	physics	physics	PROPN
fumecheng-12201	14	49	,	,	PUNCT
fumecheng-12201	14	50	lanzhou	lanzhou	PROPN
fumecheng-12201	14	51	jiaotong	jiaotong	PROPN
fumecheng-12201	14	52	university	university	PROPN
fumecheng-12201	14	53	,	,	PUNCT
fumecheng-12201	14	54	lanzhou	lanzhou	PROPN
fumecheng-12201	14	55	,	,	PUNCT
fumecheng-12201	15	1	p.	p.	PROPN
fumecheng-12201	15	2	r.	r.	PROPN
fumecheng-12201	15	3	china	china	PROPN
fumecheng-12201	16	1	e	e	PROPN
fumecheng-12201	16	2	-	-	NOUN
fumecheng-12201	16	3	mail	mail	NOUN
fumecheng-12201	16	4	:	:	PUNCT
fumecheng-12201	16	5	zhangjg7715776@126.com	zhangjg7715776@126.com	NUM
fumecheng-12201	16	6	702	702	NUM
fumecheng-12201	16	7	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	16	8	,	,	PUNCT
fumecheng-12201	16	9	q.r.song	q.r.song	PROPN
fumecheng-12201	16	10	,	,	PUNCT
fumecheng-12201	16	11	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	16	12	,	,	PUNCT
fumecheng-12201	16	13	f.wang	f.wang	PROPN
fumecheng-12201	16	14	also	also	ADV
fumecheng-12201	16	15	be	be	AUX
fumecheng-12201	16	16	taken	take	VERB
fumecheng-12201	16	17	into	into	ADP
fumecheng-12201	16	18	consideration	consideration	NOUN
fumecheng-12201	16	19	.	.	PUNCT
fumecheng-12201	17	1	as	as	SCONJ
fumecheng-12201	17	2	is	be	AUX
fumecheng-12201	17	3	well	well	ADV
fumecheng-12201	17	4	known	know	VERB
fumecheng-12201	17	5	,	,	PUNCT
fumecheng-12201	17	6	most	most	ADJ
fumecheng-12201	17	7	nonlinear	nonlinear	ADJ
fumecheng-12201	17	8	problems	problem	NOUN
fumecheng-12201	17	9	do	do	AUX
fumecheng-12201	17	10	not	not	PART
fumecheng-12201	17	11	involve	involve	VERB
fumecheng-12201	17	12	small	small	ADJ
fumecheng-12201	17	13	parameters	parameter	NOUN
fumecheng-12201	17	14	.	.	PUNCT
fumecheng-12201	18	1	even	even	ADV
fumecheng-12201	18	2	if	if	SCONJ
fumecheng-12201	18	3	appropriate	appropriate	ADJ
fumecheng-12201	18	4	small	small	ADJ
fumecheng-12201	18	5	parameters	parameter	NOUN
fumecheng-12201	18	6	exist	exist	VERB
fumecheng-12201	18	7	,	,	PUNCT
fumecheng-12201	18	8	the	the	DET
fumecheng-12201	18	9	approximate	approximate	ADJ
fumecheng-12201	18	10	solutions	solution	NOUN
fumecheng-12201	18	11	obtained	obtain	VERB
fumecheng-12201	18	12	through	through	ADP
fumecheng-12201	18	13	perturbation	perturbation	NOUN
fumecheng-12201	18	14	methods	method	NOUN
fumecheng-12201	18	15	are	be	AUX
fumecheng-12201	18	16	only	only	ADV
fumecheng-12201	18	17	effective	effective	ADJ
fumecheng-12201	18	18	for	for	ADP
fumecheng-12201	18	19	weakly	weakly	ADJ
fumecheng-12201	18	20	nonlinear	nonlinear	ADJ
fumecheng-12201	18	21	cases	case	NOUN
fumecheng-12201	18	22	[	[	X
fumecheng-12201	18	23	9	9	NUM
fumecheng-12201	18	24	]	]	PUNCT
fumecheng-12201	18	25	.	.	PUNCT
fumecheng-12201	19	1	furthermore	furthermore	ADV
fumecheng-12201	19	2	,	,	PUNCT
fumecheng-12201	19	3	the	the	DET
fumecheng-12201	19	4	approximate	approximate	ADJ
fumecheng-12201	19	5	solutions	solution	NOUN
fumecheng-12201	19	6	obtained	obtain	VERB
fumecheng-12201	19	7	through	through	ADP
fumecheng-12201	19	8	perturbation	perturbation	NOUN
fumecheng-12201	19	9	methods	method	NOUN
fumecheng-12201	19	10	often	often	ADV
fumecheng-12201	19	11	lose	lose	VERB
fumecheng-12201	19	12	some	some	DET
fumecheng-12201	19	13	crucial	crucial	ADJ
fumecheng-12201	19	14	information	information	NOUN
fumecheng-12201	19	15	,	,	PUNCT
fumecheng-12201	19	16	thereby	thereby	ADV
fumecheng-12201	19	17	failing	fail	VERB
fumecheng-12201	19	18	to	to	PART
fumecheng-12201	19	19	accurately	accurately	ADV
fumecheng-12201	19	20	reflect	reflect	VERB
fumecheng-12201	19	21	the	the	DET
fumecheng-12201	19	22	important	important	ADJ
fumecheng-12201	19	23	relationship	relationship	NOUN
fumecheng-12201	19	24	between	between	ADP
fumecheng-12201	19	25	amplitude	amplitude	NOUN
fumecheng-12201	19	26	and	and	CCONJ
fumecheng-12201	19	27	frequency	frequency	NOUN
fumecheng-12201	19	28	.	.	PUNCT
fumecheng-12201	20	1	the	the	DET
fumecheng-12201	20	2	duffing	duffing	NOUN
fumecheng-12201	20	3	equation	equation	NOUN
fumecheng-12201	20	4	serves	serve	VERB
fumecheng-12201	20	5	as	as	ADP
fumecheng-12201	20	6	an	an	DET
fumecheng-12201	20	7	example	example	NOUN
fumecheng-12201	20	8	of	of	ADP
fumecheng-12201	20	9	this	this	DET
fumecheng-12201	20	10	case	case	NOUN
fumecheng-12201	20	11	.	.	PUNCT
fumecheng-12201	21	1	therefore	therefore	ADV
fumecheng-12201	21	2	,	,	PUNCT
fumecheng-12201	21	3	to	to	PART
fumecheng-12201	21	4	solve	solve	VERB
fumecheng-12201	21	5	this	this	DET
fumecheng-12201	21	6	problem	problem	NOUN
fumecheng-12201	21	7	,	,	PUNCT
fumecheng-12201	21	8	chinese	chinese	ADJ
fumecheng-12201	21	9	mathematician	mathematician	NOUN
fumecheng-12201	21	10	,	,	PUNCT
fumecheng-12201	21	11	ji	ji	PROPN
fumecheng-12201	21	12	-	-	PROPN
fumecheng-12201	21	13	huan	huan	PROPN
fumecheng-12201	21	14	he	he	PROPN
fumecheng-12201	21	15	,	,	PUNCT
fumecheng-12201	21	16	inspired	inspire	VERB
fumecheng-12201	21	17	by	by	ADP
fumecheng-12201	21	18	ancient	ancient	ADJ
fumecheng-12201	21	19	chinese	chinese	ADJ
fumecheng-12201	21	20	algorithms	algorithm	NOUN
fumecheng-12201	21	21	[	[	X
fumecheng-12201	21	22	10	10	NUM
fumecheng-12201	21	23	-	-	SYM
fumecheng-12201	21	24	12	12	NUM
fumecheng-12201	21	25	]	]	PUNCT
fumecheng-12201	21	26	,	,	PUNCT
fumecheng-12201	21	27	proposed	propose	VERB
fumecheng-12201	21	28	a	a	DET
fumecheng-12201	21	29	simple	simple	ADJ
fumecheng-12201	21	30	method	method	NOUN
fumecheng-12201	21	31	for	for	ADP
fumecheng-12201	21	32	conserving	conserve	VERB
fumecheng-12201	21	33	nonlinear	nonlinear	ADJ
fumecheng-12201	21	34	vibrators	vibrator	NOUN
fumecheng-12201	21	35	,	,	PUNCT
fumecheng-12201	21	36	and	and	CCONJ
fumecheng-12201	21	37	a	a	DET
fumecheng-12201	21	38	frequency	frequency	NOUN
fumecheng-12201	21	39	-	-	PUNCT
fumecheng-12201	21	40	amplitude	amplitude	NOUN
fumecheng-12201	21	41	formulation	formulation	NOUN
fumecheng-12201	21	42	was	be	AUX
fumecheng-12201	21	43	proposed	propose	VERB
fumecheng-12201	21	44	,	,	PUNCT
fumecheng-12201	21	45	which	which	PRON
fumecheng-12201	21	46	is	be	AUX
fumecheng-12201	21	47	called	call	VERB
fumecheng-12201	21	48	he	he	PRON
fumecheng-12201	21	49	’s	’s	PART
fumecheng-12201	21	50	frequency	frequency	NOUN
fumecheng-12201	21	51	formulation	formulation	NOUN
fumecheng-12201	21	52	in	in	ADP
fumecheng-12201	21	53	literature	literature	NOUN
fumecheng-12201	21	54	[	[	X
fumecheng-12201	21	55	13	13	NUM
fumecheng-12201	21	56	-	-	SYM
fumecheng-12201	21	57	15	15	NUM
fumecheng-12201	21	58	]	]	PUNCT
fumecheng-12201	21	59	.	.	PUNCT
fumecheng-12201	22	1	the	the	DET
fumecheng-12201	22	2	ancient	ancient	ADJ
fumecheng-12201	22	3	chinese	chinese	ADJ
fumecheng-12201	22	4	mathematics	mathematic	NOUN
fumecheng-12201	22	5	was	be	AUX
fumecheng-12201	22	6	also	also	ADV
fumecheng-12201	22	7	further	far	ADV
fumecheng-12201	22	8	extended	extend	VERB
fumecheng-12201	22	9	to	to	PART
fumecheng-12201	22	10	solve	solve	VERB
fumecheng-12201	22	11	nonlinear	nonlinear	ADJ
fumecheng-12201	22	12	differential	differential	ADJ
fumecheng-12201	22	13	equations	equation	NOUN
fumecheng-12201	22	14	numerically	numerically	ADV
fumecheng-12201	23	1	[	[	X
fumecheng-12201	23	2	16	16	NUM
fumecheng-12201	23	3	]	]	PUNCT
fumecheng-12201	23	4	,	,	PUNCT
fumecheng-12201	23	5	and	and	CCONJ
fumecheng-12201	23	6	in	in	ADP
fumecheng-12201	23	7	literature	literature	NOUN
fumecheng-12201	23	8	the	the	DET
fumecheng-12201	23	9	method	method	NOUN
fumecheng-12201	23	10	is	be	AUX
fumecheng-12201	23	11	called	call	VERB
fumecheng-12201	23	12	as	as	ADP
fumecheng-12201	23	13	chun	chun	PROPN
fumecheng-12201	23	14	-	-	PUNCT
fumecheng-12201	23	15	hui	hui	PROPN
fumecheng-12201	24	1	he	he	PRON
fumecheng-12201	24	2	’s	’	VERB
fumecheng-12201	24	3	iteration	iteration	NOUN
fumecheng-12201	24	4	method	method	NOUN
fumecheng-12201	24	5	[	[	X
fumecheng-12201	24	6	17,18	17,18	NUM
fumecheng-12201	24	7	]	]	PUNCT
fumecheng-12201	24	8	.	.	PUNCT
fumecheng-12201	25	1	he	he	PRON
fumecheng-12201	25	2	’s	’	VERB
fumecheng-12201	25	3	frequency	frequency	NOUN
fumecheng-12201	25	4	formulation	formulation	NOUN
fumecheng-12201	25	5	[	[	X
fumecheng-12201	25	6	10	10	NUM
fumecheng-12201	25	7	-	-	SYM
fumecheng-12201	25	8	12	12	NUM
fumecheng-12201	25	9	]	]	PUNCT
fumecheng-12201	25	10	not	not	PART
fumecheng-12201	25	11	only	only	ADV
fumecheng-12201	25	12	can	can	AUX
fumecheng-12201	25	13	quickly	quickly	ADV
fumecheng-12201	25	14	unveil	unveil	VERB
fumecheng-12201	25	15	the	the	DET
fumecheng-12201	25	16	relationship	relationship	NOUN
fumecheng-12201	25	17	between	between	ADP
fumecheng-12201	25	18	the	the	DET
fumecheng-12201	25	19	frequency	frequency	NOUN
fumecheng-12201	25	20	and	and	CCONJ
fumecheng-12201	25	21	amplitude	amplitude	NOUN
fumecheng-12201	25	22	of	of	ADP
fumecheng-12201	25	23	various	various	ADJ
fumecheng-12201	25	24	vibrators	vibrator	NOUN
fumecheng-12201	25	25	but	but	CCONJ
fumecheng-12201	25	26	also	also	ADV
fumecheng-12201	25	27	ensures	ensure	VERB
fumecheng-12201	25	28	high	high	ADJ
fumecheng-12201	25	29	accuracy	accuracy	NOUN
fumecheng-12201	25	30	.	.	PUNCT
fumecheng-12201	26	1	elías	elías	NOUN
fumecheng-12201	26	2	-	-	PUNCT
fumecheng-12201	26	3	zúñiga	zúñiga	PROPN
fumecheng-12201	26	4	,	,	PUNCT
fumecheng-12201	26	5	et	et	PROPN
fumecheng-12201	26	6	al	al	PROPN
fumecheng-12201	26	7	.	.	PUNCT
fumecheng-12201	27	1	[	[	X
fumecheng-12201	27	2	19	19	NUM
fumecheng-12201	27	3	]	]	PUNCT
fumecheng-12201	27	4	extended	extend	VERB
fumecheng-12201	27	5	the	the	DET
fumecheng-12201	27	6	formulation	formulation	NOUN
fumecheng-12201	27	7	by	by	ADP
fumecheng-12201	27	8	coupling	couple	VERB
fumecheng-12201	27	9	jacobi	jacobi	PROPN
fumecheng-12201	27	10	elliptic	elliptic	ADJ
fumecheng-12201	27	11	function	function	NOUN
fumecheng-12201	27	12	,	,	PUNCT
fumecheng-12201	27	13	ma	ma	PROPN
fumecheng-12201	28	1	[	[	X
fumecheng-12201	28	2	20	20	NUM
fumecheng-12201	28	3	]	]	PUNCT
fumecheng-12201	28	4	suggested	suggest	VERB
fumecheng-12201	28	5	a	a	DET
fumecheng-12201	28	6	hamiltonian	hamiltonian	NOUN
fumecheng-12201	28	7	-	-	PUNCT
fumecheng-12201	28	8	based	base	VERB
fumecheng-12201	28	9	modification	modification	NOUN
fumecheng-12201	28	10	,	,	PUNCT
fumecheng-12201	28	11	alyousef	alyousef	PROPN
fumecheng-12201	28	12	,	,	PUNCT
fumecheng-12201	28	13	et	et	PROPN
fumecheng-12201	28	14	al	al	PROPN
fumecheng-12201	28	15	.	.	PUNCT
fumecheng-12201	29	1	[	[	X
fumecheng-12201	29	2	21	21	NUM
fumecheng-12201	29	3	]	]	PUNCT
fumecheng-12201	29	4	used	use	VERB
fumecheng-12201	29	5	the	the	DET
fumecheng-12201	29	6	formulation	formulation	NOUN
fumecheng-12201	29	7	to	to	PART
fumecheng-12201	29	8	solve	solve	VERB
fumecheng-12201	29	9	a	a	DET
fumecheng-12201	29	10	complex	complex	ADJ
fumecheng-12201	29	11	nonlinear	nonlinear	ADJ
fumecheng-12201	29	12	system	system	NOUN
fumecheng-12201	29	13	with	with	ADP
fumecheng-12201	29	14	great	great	ADJ
fumecheng-12201	29	15	success	success	NOUN
fumecheng-12201	29	16	.	.	PUNCT
fumecheng-12201	30	1	he	he	PRON
fumecheng-12201	30	2	and	and	CCONJ
fumecheng-12201	30	3	liu	liu	PROPN
fumecheng-12201	31	1	[	[	X
fumecheng-12201	31	2	22	22	NUM
fumecheng-12201	31	3	]	]	PUNCT
fumecheng-12201	31	4	gave	give	VERB
fumecheng-12201	31	5	a	a	DET
fumecheng-12201	31	6	mathematical	mathematical	ADJ
fumecheng-12201	31	7	proof	proof	NOUN
fumecheng-12201	31	8	of	of	ADP
fumecheng-12201	31	9	the	the	DET
fumecheng-12201	31	10	formulation	formulation	NOUN
fumecheng-12201	31	11	and	and	CCONJ
fumecheng-12201	31	12	suggested	suggest	VERB
fumecheng-12201	31	13	a	a	DET
fumecheng-12201	31	14	powerful	powerful	ADJ
fumecheng-12201	31	15	modification	modification	NOUN
fumecheng-12201	31	16	.	.	PUNCT
fumecheng-12201	32	1	all	all	PRON
fumecheng-12201	32	2	of	of	ADP
fumecheng-12201	32	3	the	the	DET
fumecheng-12201	32	4	above	above	ADJ
fumecheng-12201	32	5	studies	study	NOUN
fumecheng-12201	32	6	considered	consider	VERB
fumecheng-12201	32	7	simple	simple	ADJ
fumecheng-12201	32	8	initial	initial	ADJ
fumecheng-12201	32	9	conditions	condition	NOUN
fumecheng-12201	32	10	,	,	PUNCT
fumecheng-12201	32	11	and	and	CCONJ
fumecheng-12201	32	12	there	there	PRON
fumecheng-12201	32	13	is	be	VERB
fumecheng-12201	32	14	much	much	ADJ
fumecheng-12201	32	15	space	space	NOUN
fumecheng-12201	32	16	to	to	PART
fumecheng-12201	32	17	extend	extend	VERB
fumecheng-12201	32	18	the	the	DET
fumecheng-12201	32	19	formulation	formulation	NOUN
fumecheng-12201	32	20	to	to	ADP
fumecheng-12201	32	21	generalized	generalize	VERB
fumecheng-12201	32	22	initial	initial	ADJ
fumecheng-12201	32	23	condition	condition	NOUN
fumecheng-12201	32	24	.	.	PUNCT
fumecheng-12201	33	1	this	this	DET
fumecheng-12201	33	2	paper	paper	NOUN
fumecheng-12201	33	3	considers	consider	VERB
fumecheng-12201	33	4	a	a	DET
fumecheng-12201	33	5	damped	damped	ADJ
fumecheng-12201	33	6	duffing	duffing	NOUN
fumecheng-12201	33	7	oscillator	oscillator	NOUN
fumecheng-12201	33	8	with	with	ADP
fumecheng-12201	33	9	generalized	generalized	ADJ
fumecheng-12201	33	10	initial	initial	ADJ
fumecheng-12201	33	11	conditions	condition	NOUN
fumecheng-12201	33	12	to	to	PART
fumecheng-12201	33	13	show	show	VERB
fumecheng-12201	33	14	the	the	DET
fumecheng-12201	33	15	effectiveness	effectiveness	NOUN
fumecheng-12201	33	16	and	and	CCONJ
fumecheng-12201	33	17	simplicity	simplicity	NOUN
fumecheng-12201	33	18	of	of	ADP
fumecheng-12201	33	19	he	he	PRON
fumecheng-12201	33	20	’s	’s	PART
fumecheng-12201	33	21	frequency	frequency	NOUN
fumecheng-12201	33	22	formulation	formulation	NOUN
fumecheng-12201	33	23	.	.	PUNCT
fumecheng-12201	34	1	this	this	DET
fumecheng-12201	34	2	paper	paper	NOUN
fumecheng-12201	34	3	is	be	AUX
fumecheng-12201	34	4	divided	divide	VERB
fumecheng-12201	34	5	into	into	ADP
fumecheng-12201	34	6	three	three	NUM
fumecheng-12201	34	7	sections	section	NOUN
fumecheng-12201	34	8	.	.	PUNCT
fumecheng-12201	35	1	the	the	DET
fumecheng-12201	35	2	first	first	ADJ
fumecheng-12201	35	3	section	section	NOUN
fumecheng-12201	35	4	considers	consider	VERB
fumecheng-12201	35	5	an	an	DET
fumecheng-12201	35	6	undamped	undamped	ADJ
fumecheng-12201	35	7	duffing	duffing	NOUN
fumecheng-12201	35	8	oscillator	oscillator	NOUN
fumecheng-12201	35	9	with	with	ADP
fumecheng-12201	35	10	generalized	generalized	ADJ
fumecheng-12201	35	11	initial	initial	ADJ
fumecheng-12201	35	12	conditions	condition	NOUN
fumecheng-12201	35	13	and	and	CCONJ
fumecheng-12201	35	14	applies	apply	VERB
fumecheng-12201	35	15	he	he	PRON
fumecheng-12201	35	16	's	's	PART
fumecheng-12201	35	17	frequency	frequency	NOUN
fumecheng-12201	35	18	formulation	formulation	NOUN
fumecheng-12201	35	19	to	to	PART
fumecheng-12201	35	20	solve	solve	VERB
fumecheng-12201	35	21	the	the	DET
fumecheng-12201	35	22	approximate	approximate	ADJ
fumecheng-12201	35	23	frequency	frequency	NOUN
fumecheng-12201	35	24	,	,	PUNCT
fumecheng-12201	35	25	which	which	PRON
fumecheng-12201	35	26	is	be	AUX
fumecheng-12201	35	27	then	then	ADV
fumecheng-12201	35	28	compared	compare	VERB
fumecheng-12201	35	29	with	with	ADP
fumecheng-12201	35	30	the	the	DET
fumecheng-12201	35	31	rk4	rk4	PROPN
fumecheng-12201	35	32	numerical	numerical	ADJ
fumecheng-12201	35	33	solution	solution	NOUN
fumecheng-12201	35	34	.	.	PUNCT
fumecheng-12201	36	1	in	in	ADP
fumecheng-12201	36	2	the	the	DET
fumecheng-12201	36	3	second	second	ADJ
fumecheng-12201	36	4	part	part	NOUN
fumecheng-12201	36	5	,	,	PUNCT
fumecheng-12201	36	6	he	he	PRON
fumecheng-12201	36	7	's	's	PART
fumecheng-12201	36	8	frequency	frequency	NOUN
fumecheng-12201	36	9	formulation	formulation	NOUN
fumecheng-12201	36	10	is	be	AUX
fumecheng-12201	36	11	applied	apply	VERB
fumecheng-12201	36	12	to	to	ADP
fumecheng-12201	36	13	a	a	DET
fumecheng-12201	36	14	linear	linear	ADJ
fumecheng-12201	36	15	damped	damp	VERB
fumecheng-12201	36	16	oscillator	oscillator	NOUN
fumecheng-12201	36	17	with	with	ADP
fumecheng-12201	36	18	generalized	generalized	ADJ
fumecheng-12201	36	19	initial	initial	ADJ
fumecheng-12201	36	20	condition	condition	NOUN
fumecheng-12201	36	21	.	.	PUNCT
fumecheng-12201	37	1	in	in	ADP
fumecheng-12201	37	2	the	the	DET
fumecheng-12201	37	3	third	third	ADJ
fumecheng-12201	37	4	part	part	NOUN
fumecheng-12201	37	5	,	,	PUNCT
fumecheng-12201	37	6	a	a	DET
fumecheng-12201	37	7	nonlinear	nonlinear	ADJ
fumecheng-12201	37	8	duffing	duffing	NOUN
fumecheng-12201	37	9	oscillator	oscillator	NOUN
fumecheng-12201	37	10	with	with	ADP
fumecheng-12201	37	11	damping	damp	VERB
fumecheng-12201	37	12	is	be	AUX
fumecheng-12201	37	13	considered	consider	VERB
fumecheng-12201	37	14	to	to	PART
fumecheng-12201	37	15	show	show	VERB
fumecheng-12201	37	16	reliability	reliability	NOUN
fumecheng-12201	37	17	of	of	ADP
fumecheng-12201	37	18	he	he	PRON
fumecheng-12201	37	19	’s	’s	PART
fumecheng-12201	37	20	frequency	frequency	NOUN
fumecheng-12201	37	21	formulation	formulation	NOUN
fumecheng-12201	37	22	.	.	PUNCT
fumecheng-12201	38	1	2	2	X
fumecheng-12201	38	2	.	.	NUM
fumecheng-12201	38	3	undamped	undampe	VERB
fumecheng-12201	38	4	duffing	duffing	NOUN
fumecheng-12201	38	5	equation	equation	NOUN
fumecheng-12201	38	6	we	we	PRON
fumecheng-12201	38	7	consider	consider	VERB
fumecheng-12201	38	8	a	a	DET
fumecheng-12201	38	9	duffing	duffing	NOUN
fumecheng-12201	38	10	equation	equation	NOUN
fumecheng-12201	38	11	3	3	NUM
fumecheng-12201	38	12	0u	0u	ADJ
fumecheng-12201	38	13	u	u	NOUN
fumecheng-12201	38	14	u	u	PROPN
fumecheng-12201	38	15	+	+	PROPN
fumecheng-12201	38	16	+	+	CCONJ
fumecheng-12201	38	17	=	=	ADJ
fumecheng-12201	38	18			NOUN
fumecheng-12201	38	19	(	(	PUNCT
fumecheng-12201	38	20	1	1	NUM
fumecheng-12201	38	21	)	)	PUNCT
fumecheng-12201	38	22	with	with	ADP
fumecheng-12201	38	23	the	the	DET
fumecheng-12201	38	24	generalized	generalized	ADJ
fumecheng-12201	38	25	initial	initial	ADJ
fumecheng-12201	38	26	conditions	condition	NOUN
fumecheng-12201	38	27	(	(	PUNCT
fumecheng-12201	38	28	0	0	NUM
fumecheng-12201	38	29	)	)	PUNCT
fumecheng-12201	38	30	,	,	PUNCT
fumecheng-12201	38	31	(	(	PUNCT
fumecheng-12201	38	32	0)u	0)u	ADP
fumecheng-12201	38	33	a	a	DET
fumecheng-12201	38	34	u	u	NOUN
fumecheng-12201	38	35	b	b	NOUN
fumecheng-12201	38	36	=	=	PUNCT
fumecheng-12201	38	37	=	=	SYM
fumecheng-12201	38	38	(	(	PUNCT
fumecheng-12201	38	39	2	2	NUM
fumecheng-12201	38	40	)	)	PUNCT
fumecheng-12201	38	41	where	where	SCONJ
fumecheng-12201	38	42	a	a	DET
fumecheng-12201	38	43	,	,	PUNCT
fumecheng-12201	38	44	b	b	NOUN
fumecheng-12201	38	45	and	and	CCONJ
fumecheng-12201	38	46	ε	ε	PROPN
fumecheng-12201	38	47	are	be	AUX
fumecheng-12201	38	48	constants	constant	NOUN
fumecheng-12201	38	49	.	.	PUNCT
fumecheng-12201	39	1	there	there	PRON
fumecheng-12201	39	2	is	be	VERB
fumecheng-12201	39	3	much	much	ADJ
fumecheng-12201	39	4	literature	literature	NOUN
fumecheng-12201	39	5	to	to	PART
fumecheng-12201	39	6	study	study	VERB
fumecheng-12201	39	7	the	the	DET
fumecheng-12201	39	8	above	above	ADJ
fumecheng-12201	39	9	problem	problem	NOUN
fumecheng-12201	39	10	in	in	ADP
fumecheng-12201	39	11	case	case	NOUN
fumecheng-12201	39	12	of	of	ADP
fumecheng-12201	39	13	small	small	ADJ
fumecheng-12201	39	14	ε	ε	PROPN
fumecheng-12201	39	15	or	or	CCONJ
fumecheng-12201	39	16	a=0	a=0	PROPN
fumecheng-12201	39	17	/	/	SYM
fumecheng-12201	39	18	b=0	b=0	NOUN
fumecheng-12201	39	19	by	by	ADP
fumecheng-12201	39	20	various	various	ADJ
fumecheng-12201	39	21	methods	method	NOUN
fumecheng-12201	39	22	,	,	PUNCT
fumecheng-12201	39	23	for	for	ADP
fumecheng-12201	39	24	examples	example	NOUN
fumecheng-12201	39	25	,	,	PUNCT
fumecheng-12201	39	26	the	the	DET
fumecheng-12201	39	27	homotopy	homotopy	NOUN
fumecheng-12201	39	28	perturbation	perturbation	NOUN
fumecheng-12201	39	29	method	method	NOUN
fumecheng-12201	39	30	[	[	X
fumecheng-12201	39	31	23	23	NUM
fumecheng-12201	39	32	]	]	PUNCT
fumecheng-12201	39	33	,	,	PUNCT
fumecheng-12201	39	34	the	the	DET
fumecheng-12201	39	35	energy	energy	NOUN
fumecheng-12201	39	36	conservation	conservation	NOUN
fumecheng-12201	39	37	principle	principle	NOUN
fumecheng-12201	39	38	[	[	X
fumecheng-12201	39	39	24	24	NUM
fumecheng-12201	39	40	]	]	PUNCT
fumecheng-12201	39	41	and	and	CCONJ
fumecheng-12201	39	42	the	the	DET
fumecheng-12201	39	43	variational	variational	ADJ
fumecheng-12201	39	44	iteration	iteration	NOUN
fumecheng-12201	39	45	method	method	NOUN
fumecheng-12201	39	46	[	[	X
fumecheng-12201	39	47	25	25	NUM
fumecheng-12201	39	48	]	]	PUNCT
fumecheng-12201	39	49	.	.	PUNCT
fumecheng-12201	40	1	in	in	ADP
fumecheng-12201	40	2	this	this	DET
fumecheng-12201	40	3	section	section	NOUN
fumecheng-12201	40	4	,	,	PUNCT
fumecheng-12201	40	5	we	we	PRON
fumecheng-12201	40	6	will	will	AUX
fumecheng-12201	40	7	use	use	VERB
fumecheng-12201	40	8	he	he	PRON
fumecheng-12201	40	9	's	's	PART
fumecheng-12201	40	10	frequency	frequency	NOUN
fumecheng-12201	40	11	formulation	formulation	NOUN
fumecheng-12201	40	12	to	to	PART
fumecheng-12201	40	13	find	find	VERB
fumecheng-12201	40	14	the	the	DET
fumecheng-12201	40	15	solution	solution	NOUN
fumecheng-12201	40	16	to	to	ADP
fumecheng-12201	40	17	eq	eq	PROPN
fumecheng-12201	40	18	.	.	PUNCT
fumecheng-12201	41	1	(	(	PUNCT
fumecheng-12201	41	2	1	1	NUM
fumecheng-12201	41	3	)	)	PUNCT
fumecheng-12201	41	4	.	.	PUNCT
fumecheng-12201	42	1	assuming	assume	VERB
fumecheng-12201	42	2	that	that	SCONJ
fumecheng-12201	42	3	the	the	DET
fumecheng-12201	42	4	solution	solution	NOUN
fumecheng-12201	42	5	of	of	ADP
fumecheng-12201	42	6	eq	eq	PROPN
fumecheng-12201	42	7	.	.	PUNCT
fumecheng-12201	43	1	(	(	PUNCT
fumecheng-12201	43	2	1	1	X
fumecheng-12201	43	3	)	)	PUNCT
fumecheng-12201	43	4	has	have	VERB
fumecheng-12201	43	5	the	the	DET
fumecheng-12201	43	6	following	follow	VERB
fumecheng-12201	43	7	form	form	NOUN
fumecheng-12201	43	8	:	:	PUNCT
fumecheng-12201	43	9	cos	cos	PROPN
fumecheng-12201	43	10	(	(	PUNCT
fumecheng-12201	43	11	)	)	PUNCT
fumecheng-12201	43	12	u	u	NOUN
fumecheng-12201	43	13	a	a	DET
fumecheng-12201	43	14	t=	t=	ADJ
fumecheng-12201	43	15	+	+	ADJ
fumecheng-12201	43	16			X
fumecheng-12201	43	17			X
fumecheng-12201	43	18	(	(	PUNCT
fumecheng-12201	43	19	3	3	NUM
fumecheng-12201	43	20	)	)	PUNCT
fumecheng-12201	43	21	where	where	SCONJ
fumecheng-12201	43	22	ɑ	ɑ	PROPN
fumecheng-12201	43	23	and	and	CCONJ
fumecheng-12201	43	24	σ	σ	PROPN
fumecheng-12201	43	25	are	be	AUX
fumecheng-12201	43	26	constants	constant	NOUN
fumecheng-12201	43	27	,	,	PUNCT
fumecheng-12201	43	28	ω	ω	PROPN
fumecheng-12201	43	29	is	be	AUX
fumecheng-12201	43	30	the	the	DET
fumecheng-12201	43	31	frequency	frequency	NOUN
fumecheng-12201	43	32	to	to	PART
fumecheng-12201	43	33	be	be	AUX
fumecheng-12201	43	34	determined	determine	VERB
fumecheng-12201	43	35	.	.	PUNCT
fumecheng-12201	44	1	the	the	DET
fumecheng-12201	44	2	initial	initial	ADJ
fumecheng-12201	44	3	conditions	condition	NOUN
fumecheng-12201	44	4	lead	lead	VERB
fumecheng-12201	44	5	to	to	ADP
fumecheng-12201	44	6	the	the	DET
fumecheng-12201	44	7	following	follow	VERB
fumecheng-12201	44	8	relations	relation	NOUN
fumecheng-12201	44	9	:	:	PUNCT
fumecheng-12201	44	10	application	application	NOUN
fumecheng-12201	44	11	of	of	ADP
fumecheng-12201	44	12	he	he	PRON
fumecheng-12201	44	13	’s	’s	PART
fumecheng-12201	44	14	frequency	frequency	NOUN
fumecheng-12201	44	15	formula	formula	NOUN
fumecheng-12201	44	16	to	to	PART
fumecheng-12201	44	17	nonlinear	nonlinear	ADJ
fumecheng-12201	44	18	oscillators	oscillator	NOUN
fumecheng-12201	44	19	with	with	ADP
fumecheng-12201	44	20	generalized	generalized	ADJ
fumecheng-12201	44	21	initial	initial	ADJ
fumecheng-12201	44	22	condition	condition	NOUN
fumecheng-12201	44	23	703	703	NUM
fumecheng-12201	44	24	(	(	PUNCT
fumecheng-12201	44	25	0	0	NUM
fumecheng-12201	44	26	)	)	PUNCT
fumecheng-12201	44	27	sin	sin	NOUN
fumecheng-12201	44	28	(	(	PUNCT
fumecheng-12201	44	29	0	0	NUM
fumecheng-12201	44	30	)	)	PUNCT
fumecheng-12201	44	31	cos	cos	ADP
fumecheng-12201	44	32	u	u	PROPN
fumecheng-12201	44	33	a	a	DET
fumecheng-12201	44	34	a	a	DET
fumecheng-12201	44	35	u	u	NOUN
fumecheng-12201	44	36	a	a	DET
fumecheng-12201	44	37	b	b	NOUN
fumecheng-12201	44	38			NOUN
fumecheng-12201	44	39	=	=	SYM
fumecheng-12201	44	40	−	−	PROPN
fumecheng-12201	45	1	=	=	SYM
fumecheng-12201	45	2	=	=	PUNCT
fumecheng-12201	45	3	=	=	PUNCT
fumecheng-12201	45	4			X
fumecheng-12201	45	5			X
fumecheng-12201	45	6			X
fumecheng-12201	45	7	(	(	PUNCT
fumecheng-12201	45	8	4	4	X
fumecheng-12201	45	9	)	)	PUNCT
fumecheng-12201	45	10	substituting	substitute	VERB
fumecheng-12201	45	11	eq	eq	NOUN
fumecheng-12201	45	12	.	.	PUNCT
fumecheng-12201	46	1	(	(	PUNCT
fumecheng-12201	46	2	3	3	X
fumecheng-12201	46	3	)	)	PUNCT
fumecheng-12201	46	4	into	into	ADP
fumecheng-12201	46	5	eq	eq	NOUN
fumecheng-12201	46	6	.	.	PUNCT
fumecheng-12201	47	1	(	(	PUNCT
fumecheng-12201	47	2	1	1	X
fumecheng-12201	47	3	)	)	PUNCT
fumecheng-12201	47	4	gives	give	VERB
fumecheng-12201	47	5	the	the	DET
fumecheng-12201	47	6	residual	residual	ADJ
fumecheng-12201	47	7	equation	equation	NOUN
fumecheng-12201	47	8	as	as	ADP
fumecheng-12201	47	9	2	2	NUM
fumecheng-12201	47	10	3	3	NUM
fumecheng-12201	47	11	3	3	NUM
fumecheng-12201	47	12	(	(	PUNCT
fumecheng-12201	47	13	)	)	PUNCT
fumecheng-12201	47	14	cos	cos	PROPN
fumecheng-12201	47	15	(	(	PUNCT
fumecheng-12201	47	16	)	)	PUNCT
fumecheng-12201	47	17	cos	cos	PROPN
fumecheng-12201	47	18	(	(	PUNCT
fumecheng-12201	47	19	)	)	PUNCT
fumecheng-12201	47	20	cos	cos	PROPN
fumecheng-12201	47	21	(	(	PUNCT
fumecheng-12201	47	22	)	)	PUNCT
fumecheng-12201	47	23	r	r	NOUN
fumecheng-12201	47	24	t	t	PROPN
fumecheng-12201	47	25	a	a	DET
fumecheng-12201	47	26	t	t	NOUN
fumecheng-12201	47	27	a	a	DET
fumecheng-12201	47	28	t	t	NOUN
fumecheng-12201	47	29	a	a	DET
fumecheng-12201	47	30	t=	t=	ADJ
fumecheng-12201	47	31	−	−	PROPN
fumecheng-12201	48	1	+	+	CCONJ
fumecheng-12201	49	1	+	+	PUNCT
fumecheng-12201	49	2	+	+	PUNCT
fumecheng-12201	49	3	+	+	X
fumecheng-12201	49	4	+	+	ADJ
fumecheng-12201	49	5			X
fumecheng-12201	49	6			X
fumecheng-12201	49	7			PROPN
fumecheng-12201	49	8			X
fumecheng-12201	49	9			PROPN
fumecheng-12201	49	10			PROPN
fumecheng-12201	49	11			X
fumecheng-12201	49	12			X
fumecheng-12201	49	13	(	(	PUNCT
fumecheng-12201	49	14	5	5	NUM
fumecheng-12201	49	15	)	)	PUNCT
fumecheng-12201	49	16	therefore	therefore	ADV
fumecheng-12201	49	17	,	,	PUNCT
fumecheng-12201	49	18	the	the	DET
fumecheng-12201	49	19	average	average	ADJ
fumecheng-12201	49	20	residual	residual	ADJ
fumecheng-12201	49	21	equation	equation	NOUN
fumecheng-12201	49	22	is	be	AUX
fumecheng-12201	49	23	defined	define	VERB
fumecheng-12201	49	24	as	as	ADP
fumecheng-12201	49	25	2	2	NUM
fumecheng-12201	49	26	0	0	NUM
fumecheng-12201	49	27	2	2	NUM
fumecheng-12201	49	28	cos	cos	PROPN
fumecheng-12201	49	29	(	(	PUNCT
fumecheng-12201	49	30	)	)	PUNCT
fumecheng-12201	49	31	dt	dt	PROPN
fumecheng-12201	50	1	t	t	NOUN
fumecheng-12201	50	2	r	r	NOUN
fumecheng-12201	50	3	r	r	NOUN
fumecheng-12201	50	4	t	t	NOUN
fumecheng-12201	50	5	t	t	NOUN
fumecheng-12201	50	6			X
fumecheng-12201	50	7	=	=	NOUN
fumecheng-12201	51	1	+	+	NOUN
fumecheng-12201	51	2			X
fumecheng-12201	51	3	(	(	PUNCT
fumecheng-12201	51	4	6	6	NUM
fumecheng-12201	51	5	)	)	PUNCT
fumecheng-12201	52	1	where	where	SCONJ
fumecheng-12201	52	2	t=2π	t=2π	PROPN
fumecheng-12201	52	3	/	/	SYM
fumecheng-12201	52	4	ω	ω	PROPN
fumecheng-12201	52	5	.	.	PUNCT
fumecheng-12201	52	6	by	by	ADP
fumecheng-12201	52	7	choosing	choose	VERB
fumecheng-12201	52	8	two	two	NUM
fumecheng-12201	52	9	arbitrary	arbitrary	ADJ
fumecheng-12201	52	10	frequencies	frequency	NOUN
fumecheng-12201	52	11	ω1	ω1	PROPN
fumecheng-12201	52	12	and	and	CCONJ
fumecheng-12201	52	13	ω2	ω2	ADJ
fumecheng-12201	52	14	,	,	PUNCT
fumecheng-12201	52	15	we	we	PRON
fumecheng-12201	52	16	obtain	obtain	VERB
fumecheng-12201	52	17	two	two	NUM
fumecheng-12201	52	18	residual	residual	ADJ
fumecheng-12201	52	19	equations	equation	NOUN
fumecheng-12201	52	20	,	,	PUNCT
fumecheng-12201	52	21	which	which	PRON
fumecheng-12201	52	22	are	be	AUX
fumecheng-12201	52	23	2	2	NUM
fumecheng-12201	52	24	3	3	NUM
fumecheng-12201	52	25	3	3	NUM
fumecheng-12201	52	26	1	1	NUM
fumecheng-12201	52	27	1	1	NUM
fumecheng-12201	52	28	1	1	NUM
fumecheng-12201	52	29	1	1	NUM
fumecheng-12201	52	30	1	1	NUM
fumecheng-12201	52	31	2	2	NUM
fumecheng-12201	52	32	3	3	NUM
fumecheng-12201	52	33	3	3	NUM
fumecheng-12201	52	34	2	2	NUM
fumecheng-12201	52	35	2	2	NUM
fumecheng-12201	52	36	2	2	NUM
fumecheng-12201	52	37	2	2	NUM
fumecheng-12201	52	38	2	2	NUM
fumecheng-12201	52	39	(	(	PUNCT
fumecheng-12201	52	40	)	)	PUNCT
fumecheng-12201	52	41	cos	cos	PROPN
fumecheng-12201	52	42	(	(	PUNCT
fumecheng-12201	52	43	)	)	PUNCT
fumecheng-12201	52	44	cos	cos	PROPN
fumecheng-12201	52	45	(	(	PUNCT
fumecheng-12201	52	46	)	)	PUNCT
fumecheng-12201	52	47	cos	cos	PROPN
fumecheng-12201	52	48	(	(	PUNCT
fumecheng-12201	52	49	)	)	PUNCT
fumecheng-12201	52	50	(	(	PUNCT
fumecheng-12201	52	51	)	)	PUNCT
fumecheng-12201	52	52	cos	cos	PROPN
fumecheng-12201	52	53	(	(	PUNCT
fumecheng-12201	52	54	)	)	PUNCT
fumecheng-12201	52	55	cos	cos	PROPN
fumecheng-12201	52	56	(	(	PUNCT
fumecheng-12201	52	57	)	)	PUNCT
fumecheng-12201	52	58	cos	cos	PROPN
fumecheng-12201	52	59	(	(	PUNCT
fumecheng-12201	52	60	)	)	PUNCT
fumecheng-12201	52	61	r	r	NOUN
fumecheng-12201	52	62	t	t	PROPN
fumecheng-12201	52	63	a	a	DET
fumecheng-12201	52	64	t	t	NOUN
fumecheng-12201	52	65	a	a	DET
fumecheng-12201	52	66	t	t	NOUN
fumecheng-12201	52	67	a	a	DET
fumecheng-12201	52	68	t	t	NOUN
fumecheng-12201	52	69	r	r	NOUN
fumecheng-12201	52	70	t	t	PROPN
fumecheng-12201	52	71	a	a	DET
fumecheng-12201	52	72	t	t	NOUN
fumecheng-12201	52	73	a	a	DET
fumecheng-12201	52	74	t	t	NOUN
fumecheng-12201	52	75	a	a	DET
fumecheng-12201	52	76	t	t	NOUN
fumecheng-12201	52	77	=	=	SYM
fumecheng-12201	52	78	−	−	PROPN
fumecheng-12201	53	1	+	+	CCONJ
fumecheng-12201	53	2	+	+	PUNCT
fumecheng-12201	54	1	+	+	PUNCT
fumecheng-12201	54	2	+	+	PUNCT
fumecheng-12201	54	3	+	+	NUM
fumecheng-12201	54	4	=	=	SYM
fumecheng-12201	54	5	−	−	PROPN
fumecheng-12201	55	1	+	+	CCONJ
fumecheng-12201	55	2	+	+	PUNCT
fumecheng-12201	55	3	+	+	PUNCT
fumecheng-12201	55	4	+	+	PUNCT
fumecheng-12201	55	5	+	+	CCONJ
fumecheng-12201	55	6			X
fumecheng-12201	55	7			X
fumecheng-12201	55	8			PROPN
fumecheng-12201	55	9			X
fumecheng-12201	55	10			PROPN
fumecheng-12201	55	11			PROPN
fumecheng-12201	55	12			X
fumecheng-12201	55	13			PROPN
fumecheng-12201	55	14			X
fumecheng-12201	55	15			X
fumecheng-12201	55	16			PROPN
fumecheng-12201	55	17			X
fumecheng-12201	55	18			PROPN
fumecheng-12201	55	19			PROPN
fumecheng-12201	55	20			X
fumecheng-12201	55	21			X
fumecheng-12201	55	22	(	(	PUNCT
fumecheng-12201	55	23	7	7	NUM
fumecheng-12201	55	24	)	)	PUNCT
fumecheng-12201	55	25	therefore	therefore	ADV
fumecheng-12201	55	26	,	,	PUNCT
fumecheng-12201	55	27	the	the	DET
fumecheng-12201	55	28	average	average	ADJ
fumecheng-12201	55	29	residual	residual	ADJ
fumecheng-12201	55	30	equations	equation	NOUN
fumecheng-12201	55	31	as	as	ADP
fumecheng-12201	55	32	2	2	NUM
fumecheng-12201	55	33	32	32	NUM
fumecheng-12201	55	34	1	1	NUM
fumecheng-12201	55	35	1	1	NUM
fumecheng-12201	55	36	1	1	NUM
fumecheng-12201	55	37	10	10	NUM
fumecheng-12201	55	38	2	2	NUM
fumecheng-12201	55	39	32	32	NUM
fumecheng-12201	55	40	2	2	NUM
fumecheng-12201	55	41	2	2	NUM
fumecheng-12201	55	42	2	2	NUM
fumecheng-12201	55	43	20	20	NUM
fumecheng-12201	55	44	2	2	NUM
fumecheng-12201	55	45	3	3	NUM
fumecheng-12201	55	46	cos	cos	PROPN
fumecheng-12201	55	47	(	(	PUNCT
fumecheng-12201	55	48	)	)	PUNCT
fumecheng-12201	55	49	dt	dt	X
fumecheng-12201	55	50	2	2	NUM
fumecheng-12201	55	51	2	2	NUM
fumecheng-12201	55	52	8	8	NUM
fumecheng-12201	55	53	2	2	NUM
fumecheng-12201	55	54	3	3	NUM
fumecheng-12201	55	55	cos	cos	PROPN
fumecheng-12201	55	56	(	(	PUNCT
fumecheng-12201	55	57	)	)	PUNCT
fumecheng-12201	55	58	dt	dt	X
fumecheng-12201	55	59	2	2	NUM
fumecheng-12201	55	60	2	2	NUM
fumecheng-12201	55	61	8	8	NUM
fumecheng-12201	55	62	t	t	NOUN
fumecheng-12201	55	63	t	t	NOUN
fumecheng-12201	55	64	a	a	DET
fumecheng-12201	55	65	a	a	DET
fumecheng-12201	55	66	r	r	NOUN
fumecheng-12201	55	67	r	r	NOUN
fumecheng-12201	55	68	t	t	NOUN
fumecheng-12201	55	69	a	a	DET
fumecheng-12201	55	70	t	t	NOUN
fumecheng-12201	55	71	a	a	DET
fumecheng-12201	55	72	a	a	DET
fumecheng-12201	55	73	r	r	NOUN
fumecheng-12201	55	74	r	r	NOUN
fumecheng-12201	55	75	t	t	NOUN
fumecheng-12201	55	76	a	a	DET
fumecheng-12201	55	77	t	t	NOUN
fumecheng-12201	55	78	=	=	PUNCT
fumecheng-12201	56	1	+	+	PUNCT
fumecheng-12201	56	2	=	=	SYM
fumecheng-12201	57	1	−	−	PROPN
fumecheng-12201	58	1	+	+	NOUN
fumecheng-12201	58	2	+	+	PUNCT
fumecheng-12201	58	3	=	=	SYM
fumecheng-12201	58	4	+	+	NUM
fumecheng-12201	58	5	=	=	SYM
fumecheng-12201	59	1	−	−	PROPN
fumecheng-12201	60	1	+	+	CCONJ
fumecheng-12201	61	1	+	+	NUM
fumecheng-12201	61	2			NOUN
fumecheng-12201	61	3			X
fumecheng-12201	61	4			PROPN
fumecheng-12201	61	5			NUM
fumecheng-12201	61	6			PROPN
fumecheng-12201	61	7			PROPN
fumecheng-12201	61	8			X
fumecheng-12201	61	9			PROPN
fumecheng-12201	61	10			PROPN
fumecheng-12201	61	11			PROPN
fumecheng-12201	61	12	(	(	PUNCT
fumecheng-12201	61	13	8)	8)	NUM
fumecheng-12201	61	14	we	we	PRON
fumecheng-12201	61	15	choose	choose	VERB
fumecheng-12201	61	16	the	the	DET
fumecheng-12201	61	17	location	location	NOUN
fumecheng-12201	61	18	point	point	NOUN
fumecheng-12201	61	19	as	as	ADP
fumecheng-12201	61	20	cos(ω1t+σ)=cos(ω2t+σ)=√3/2	cos(ω1t+σ)=cos(ω2t+σ)=√3/2	ADJ
fumecheng-12201	61	21	,	,	PUNCT
fumecheng-12201	61	22	eq	eq	NOUN
fumecheng-12201	61	23	.	.	PUNCT
fumecheng-12201	62	1	(	(	PUNCT
fumecheng-12201	62	2	8)	8)	NUM
fumecheng-12201	62	3	becomes	become	VERB
fumecheng-12201	62	4	2	2	NUM
fumecheng-12201	62	5	3	3	NUM
fumecheng-12201	62	6	1	1	NUM
fumecheng-12201	62	7	1	1	NUM
fumecheng-12201	62	8	2	2	NUM
fumecheng-12201	62	9	3	3	NUM
fumecheng-12201	62	10	2	2	NUM
fumecheng-12201	62	11	2	2	NUM
fumecheng-12201	62	12	3	3	NUM
fumecheng-12201	62	13	3	3	NUM
fumecheng-12201	62	14	2	2	NUM
fumecheng-12201	62	15	2	2	NUM
fumecheng-12201	62	16	3	3	NUM
fumecheng-12201	62	17	3	3	NUM
fumecheng-12201	62	18	2	2	NUM
fumecheng-12201	62	19	2	2	NUM
fumecheng-12201	62	20	r	r	NOUN
fumecheng-12201	62	21	a	a	PRON
fumecheng-12201	62	22	a	a	DET
fumecheng-12201	62	23	a	a	DET
fumecheng-12201	62	24	r	r	NOUN
fumecheng-12201	62	25	a	a	PRON
fumecheng-12201	62	26	a	a	DET
fumecheng-12201	62	27	a	a	PRON
fumecheng-12201	62	28	=	=	SYM
fumecheng-12201	62	29	−	−	PROPN
fumecheng-12201	63	1	+	+	CCONJ
fumecheng-12201	63	2	+	+	NUM
fumecheng-12201	63	3	=	=	SYM
fumecheng-12201	63	4	−	−	PROPN
fumecheng-12201	64	1	+	+	CCONJ
fumecheng-12201	64	2	+	+	CCONJ
fumecheng-12201	64	3			PROPN
fumecheng-12201	64	4			PROPN
fumecheng-12201	64	5			PROPN
fumecheng-12201	64	6			PROPN
fumecheng-12201	64	7	(	(	PUNCT
fumecheng-12201	64	8	9	9	NUM
fumecheng-12201	64	9	)	)	PUNCT
fumecheng-12201	64	10	according	accord	VERB
fumecheng-12201	64	11	to	to	ADP
fumecheng-12201	64	12	he	he	PRON
fumecheng-12201	64	13	’s	’s	PART
fumecheng-12201	64	14	frequency	frequency	NOUN
fumecheng-12201	64	15	-	-	PUNCT
fumecheng-12201	64	16	amplitude	amplitude	NOUN
fumecheng-12201	64	17	formulation	formulation	NOUN
fumecheng-12201	64	18	,	,	PUNCT
fumecheng-12201	64	19	we	we	PRON
fumecheng-12201	64	20	have	have	VERB
fumecheng-12201	64	21	3	3	NUM
fumecheng-12201	64	22	3	3	NUM
fumecheng-12201	64	23	2	2	NUM
fumecheng-12201	64	24	2	2	NUM
fumecheng-12201	64	25	2	2	NUM
fumecheng-12201	64	26	2	2	NUM
fumecheng-12201	64	27	2	2	NUM
fumecheng-12201	64	28	1	1	NUM
fumecheng-12201	64	29	2	2	NUM
fumecheng-12201	64	30	22	22	NUM
fumecheng-12201	64	31	1	1	NUM
fumecheng-12201	64	32	1	1	NUM
fumecheng-12201	64	33	2	2	NUM
fumecheng-12201	64	34	1	1	NUM
fumecheng-12201	64	35	2	2	NUM
fumecheng-12201	64	36	2	2	NUM
fumecheng-12201	64	37	2	2	NUM
fumecheng-12201	64	38	1	1	NUM
fumecheng-12201	64	39	2	2	NUM
fumecheng-12201	64	40	3	3	NUM
fumecheng-12201	64	41	3	3	NUM
fumecheng-12201	64	42	(	(	PUNCT
fumecheng-12201	64	43	(	(	PUNCT
fumecheng-12201	64	44	)	)	PUNCT
fumecheng-12201	64	45	)	)	PUNCT
fumecheng-12201	64	46	(	(	PUNCT
fumecheng-12201	64	47	)	)	PUNCT
fumecheng-12201	64	48	32	32	NUM
fumecheng-12201	64	49	2	2	NUM
fumecheng-12201	64	50	1	1	NUM
fumecheng-12201	64	51	43	43	NUM
fumecheng-12201	64	52	(	(	PUNCT
fumecheng-12201	64	53	)	)	PUNCT
fumecheng-12201	64	54	2	2	NUM
fumecheng-12201	64	55	a	a	PRON
fumecheng-12201	64	56	a	a	DET
fumecheng-12201	64	57	r	r	NOUN
fumecheng-12201	64	58	r	r	NOUN
fumecheng-12201	64	59	a	a	DET
fumecheng-12201	64	60	r	r	NOUN
fumecheng-12201	64	61	r	r	NOUN
fumecheng-12201	64	62	a	a	NOUN
fumecheng-12201	64	63	+	+	NOUN
fumecheng-12201	64	64	−	−	NOUN
fumecheng-12201	64	65	−	−	NOUN
fumecheng-12201	64	66	=	=	SYM
fumecheng-12201	64	67	=	=	PUNCT
fumecheng-12201	64	68	=	=	PUNCT
fumecheng-12201	65	1	+	+	NUM
fumecheng-12201	65	2	−	−	PROPN
fumecheng-12201	65	3	−	−	NOUN
fumecheng-12201	66	1	−	−	PROPN
fumecheng-12201	66	2			PROPN
fumecheng-12201	66	3			X
fumecheng-12201	66	4			X
fumecheng-12201	66	5			X
fumecheng-12201	66	6			X
fumecheng-12201	66	7			PROPN
fumecheng-12201	66	8			PROPN
fumecheng-12201	66	9			X
fumecheng-12201	66	10			X
fumecheng-12201	66	11	(	(	PUNCT
fumecheng-12201	66	12	10	10	NUM
fumecheng-12201	66	13	)	)	PUNCT
fumecheng-12201	66	14	the	the	DET
fumecheng-12201	66	15	result	result	NOUN
fumecheng-12201	66	16	depends	depend	VERB
fumecheng-12201	66	17	upon	upon	SCONJ
fumecheng-12201	66	18	the	the	DET
fumecheng-12201	66	19	location	location	NOUN
fumecheng-12201	66	20	point	point	NOUN
fumecheng-12201	66	21	,	,	PUNCT
fumecheng-12201	66	22	to	to	PART
fumecheng-12201	66	23	overcome	overcome	VERB
fumecheng-12201	66	24	the	the	DET
fumecheng-12201	66	25	shortcoming	shortcoming	NOUN
fumecheng-12201	66	26	,	,	PUNCT
fumecheng-12201	66	27	we	we	PRON
fumecheng-12201	66	28	use	use	VERB
fumecheng-12201	66	29	the	the	DET
fumecheng-12201	66	30	following	follow	VERB
fumecheng-12201	66	31	formulation	formulation	NOUN
fumecheng-12201	66	32	2	2	NUM
fumecheng-12201	66	33	2	2	NUM
fumecheng-12201	66	34	2	2	NUM
fumecheng-12201	66	35	2	2	NUM
fumecheng-12201	66	36	1	1	NUM
fumecheng-12201	66	37	1	1	NUM
fumecheng-12201	66	38	2	2	NUM
fumecheng-12201	66	39	1	1	NUM
fumecheng-12201	66	40	2	2	NUM
fumecheng-12201	66	41	3	3	NUM
fumecheng-12201	66	42	2	2	NUM
fumecheng-12201	66	43	2	2	NUM
fumecheng-12201	66	44	2	2	NUM
fumecheng-12201	66	45	1	1	NUM
fumecheng-12201	66	46	2	2	NUM
fumecheng-12201	66	47	2	2	NUM
fumecheng-12201	66	48	2	2	NUM
fumecheng-12201	66	49	1	1	NUM
fumecheng-12201	66	50	2	2	NUM
fumecheng-12201	66	51	3	3	NUM
fumecheng-12201	66	52	(	(	PUNCT
fumecheng-12201	66	53	)	)	PUNCT
fumecheng-12201	66	54	(	(	PUNCT
fumecheng-12201	66	55	)	)	PUNCT
fumecheng-12201	66	56	32	32	NUM
fumecheng-12201	66	57	8	8	NUM
fumecheng-12201	66	58	1	1	NUM
fumecheng-12201	66	59	4	4	NUM
fumecheng-12201	66	60	(	(	PUNCT
fumecheng-12201	66	61	)	)	PUNCT
fumecheng-12201	66	62	2	2	NUM
fumecheng-12201	66	63	r	r	NOUN
fumecheng-12201	66	64	r	r	NOUN
fumecheng-12201	66	65	r	r	NOUN
fumecheng-12201	66	66	r	r	NOUN
fumecheng-12201	66	67	a	a	PRON
fumecheng-12201	66	68	a	a	PRON
fumecheng-12201	66	69	a	a	PRON
fumecheng-12201	66	70	a	a	DET
fumecheng-12201	66	71	−	−	NOUN
fumecheng-12201	66	72	=	=	SYM
fumecheng-12201	66	73	−	−	PROPN
fumecheng-12201	67	1	+	+	CCONJ
fumecheng-12201	67	2	−	−	PROPN
fumecheng-12201	67	3	=	=	SYM
fumecheng-12201	68	1	=	=	PUNCT
fumecheng-12201	69	1	+	+	NUM
fumecheng-12201	69	2	−	−	PROPN
fumecheng-12201	69	3	−	−	NOUN
fumecheng-12201	69	4			X
fumecheng-12201	70	1			X
fumecheng-12201	70	2			PROPN
fumecheng-12201	70	3			PROPN
fumecheng-12201	70	4			X
fumecheng-12201	70	5			PROPN
fumecheng-12201	70	6			PROPN
fumecheng-12201	70	7			X
fumecheng-12201	70	8			X
fumecheng-12201	70	9	(	(	PUNCT
fumecheng-12201	70	10	11	11	NUM
fumecheng-12201	70	11	)	)	PUNCT
fumecheng-12201	70	12	704	704	NUM
fumecheng-12201	70	13	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	70	14	,	,	PUNCT
fumecheng-12201	70	15	q.r.song	q.r.song	PROPN
fumecheng-12201	70	16	,	,	PUNCT
fumecheng-12201	70	17	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	70	18	,	,	PUNCT
fumecheng-12201	70	19	f.wang	f.wang	NOUN
fumecheng-12201	70	20	from	from	ADP
fumecheng-12201	70	21	eqs	eqs	PROPN
fumecheng-12201	70	22	.	.	PUNCT
fumecheng-12201	71	1	(	(	PUNCT
fumecheng-12201	71	2	4	4	NUM
fumecheng-12201	71	3	)	)	PUNCT
fumecheng-12201	71	4	and	and	CCONJ
fumecheng-12201	71	5	(	(	PUNCT
fumecheng-12201	71	6	11	11	NUM
fumecheng-12201	71	7	)	)	PUNCT
fumecheng-12201	71	8	,	,	PUNCT
fumecheng-12201	71	9	ɑ	ɑ	PROPN
fumecheng-12201	71	10	,	,	PUNCT
fumecheng-12201	71	11	σ	σ	PROPN
fumecheng-12201	71	12	and	and	CCONJ
fumecheng-12201	71	13	ω	ω	PROPN
fumecheng-12201	71	14	can	can	AUX
fumecheng-12201	71	15	be	be	AUX
fumecheng-12201	71	16	determined	determine	VERB
fumecheng-12201	71	17	for	for	ADP
fumecheng-12201	71	18	given	give	VERB
fumecheng-12201	71	19	a	a	PRON
fumecheng-12201	71	20	and	and	CCONJ
fumecheng-12201	71	21	b.	b.	PROPN
fumecheng-12201	71	22	when	when	SCONJ
fumecheng-12201	71	23	a=0	a=0	PROPN
fumecheng-12201	71	24	or	or	CCONJ
fumecheng-12201	71	25	b=0	b=0	PROPN
fumecheng-12201	71	26	,	,	PUNCT
fumecheng-12201	71	27	our	our	PRON
fumecheng-12201	71	28	result	result	NOUN
fumecheng-12201	71	29	is	be	AUX
fumecheng-12201	71	30	the	the	DET
fumecheng-12201	71	31	same	same	ADJ
fumecheng-12201	71	32	as	as	ADP
fumecheng-12201	71	33	those	those	PRON
fumecheng-12201	71	34	obtained	obtain	VERB
fumecheng-12201	71	35	by	by	ADP
fumecheng-12201	71	36	the	the	DET
fumecheng-12201	71	37	homotopy	homotopy	NOUN
fumecheng-12201	71	38	perturbation	perturbation	NOUN
fumecheng-12201	71	39	method	method	NOUN
fumecheng-12201	71	40	or	or	CCONJ
fumecheng-12201	71	41	the	the	DET
fumecheng-12201	71	42	variational	variational	ADJ
fumecheng-12201	71	43	iteration	iteration	NOUN
fumecheng-12201	71	44	method	method	NOUN
fumecheng-12201	71	45	.	.	PUNCT
fumecheng-12201	72	1	we	we	PRON
fumecheng-12201	72	2	compare	compare	VERB
fumecheng-12201	72	3	the	the	DET
fumecheng-12201	72	4	approximate	approximate	ADJ
fumecheng-12201	72	5	solution	solution	NOUN
fumecheng-12201	72	6	based	base	VERB
fumecheng-12201	72	7	on	on	ADP
fumecheng-12201	72	8	he	he	PRON
fumecheng-12201	72	9	’s	’s	PART
fumecheng-12201	72	10	frequency	frequency	NOUN
fumecheng-12201	72	11	formulation	formulation	NOUN
fumecheng-12201	72	12	with	with	ADP
fumecheng-12201	72	13	the	the	DET
fumecheng-12201	72	14	exact	exact	ADJ
fumecheng-12201	72	15	solution	solution	NOUN
fumecheng-12201	72	16	of	of	ADP
fumecheng-12201	72	17	the	the	DET
fumecheng-12201	72	18	runge	runge	NOUN
fumecheng-12201	72	19	-	-	PUNCT
fumecheng-12201	72	20	kutta	kutta	NOUN
fumecheng-12201	72	21	method	method	NOUN
fumecheng-12201	72	22	,	,	PUNCT
fumecheng-12201	72	23	as	as	SCONJ
fumecheng-12201	72	24	shown	show	VERB
fumecheng-12201	72	25	in	in	ADP
fumecheng-12201	72	26	fig	fig	NOUN
fumecheng-12201	72	27	.	.	PUNCT
fumecheng-12201	73	1	1	1	NUM
fumecheng-12201	73	2	.	.	X
fumecheng-12201	73	3	from	from	ADP
fumecheng-12201	73	4	the	the	DET
fumecheng-12201	73	5	figure	figure	NOUN
fumecheng-12201	73	6	,	,	PUNCT
fumecheng-12201	73	7	we	we	PRON
fumecheng-12201	73	8	can	can	AUX
fumecheng-12201	73	9	see	see	VERB
fumecheng-12201	73	10	that	that	SCONJ
fumecheng-12201	73	11	the	the	DET
fumecheng-12201	73	12	two	two	NUM
fumecheng-12201	73	13	curves	curve	NOUN
fumecheng-12201	73	14	fit	fit	ADJ
fumecheng-12201	73	15	well	well	ADV
fumecheng-12201	73	16	,	,	PUNCT
fumecheng-12201	73	17	reflecting	reflect	VERB
fumecheng-12201	73	18	the	the	DET
fumecheng-12201	73	19	consistency	consistency	NOUN
fumecheng-12201	73	20	between	between	ADP
fumecheng-12201	73	21	the	the	DET
fumecheng-12201	73	22	exact	exact	ADJ
fumecheng-12201	73	23	solution	solution	NOUN
fumecheng-12201	73	24	and	and	CCONJ
fumecheng-12201	73	25	the	the	DET
fumecheng-12201	73	26	approximate	approximate	ADJ
fumecheng-12201	73	27	solution	solution	NOUN
fumecheng-12201	73	28	.	.	PUNCT
fumecheng-12201	74	1	(	(	PUNCT
fumecheng-12201	74	2	a	a	DET
fumecheng-12201	74	3	,	,	PUNCT
fumecheng-12201	74	4	b)=(0.01,0.01	b)=(0.01,0.01	PROPN
fumecheng-12201	74	5	)	)	PUNCT
fumecheng-12201	74	6	(	(	PUNCT
fumecheng-12201	74	7	a	a	DET
fumecheng-12201	74	8	,	,	PUNCT
fumecheng-12201	74	9	b)=(0.1,0.1	b)=(0.1,0.1	PROPN
fumecheng-12201	74	10	)	)	PUNCT
fumecheng-12201	74	11	(	(	PUNCT
fumecheng-12201	74	12	a	a	PRON
fumecheng-12201	74	13	,	,	PUNCT
fumecheng-12201	74	14	b)=(1.6,1	b)=(1.6,1	VERB
fumecheng-12201	74	15	)	)	PUNCT
fumecheng-12201	74	16	(	(	PUNCT
fumecheng-12201	74	17	a	a	PRON
fumecheng-12201	74	18	,	,	PUNCT
fumecheng-12201	74	19	b)=(5.5,2	b)=(5.5,2	NOUN
fumecheng-12201	74	20	)	)	PUNCT
fumecheng-12201	74	21	fig	fig	NOUN
fumecheng-12201	74	22	.	.	PUNCT
fumecheng-12201	75	1	1	1	NUM
fumecheng-12201	76	1	the	the	DET
fumecheng-12201	76	2	comparison	comparison	NOUN
fumecheng-12201	76	3	between	between	ADP
fumecheng-12201	76	4	the	the	DET
fumecheng-12201	76	5	exact	exact	ADJ
fumecheng-12201	76	6	solution	solution	NOUN
fumecheng-12201	76	7	and	and	CCONJ
fumecheng-12201	76	8	the	the	DET
fumecheng-12201	76	9	approximate	approximate	ADJ
fumecheng-12201	76	10	one	one	NUM
fumecheng-12201	76	11	based	base	VERB
fumecheng-12201	76	12	on	on	ADP
fumecheng-12201	76	13	he	he	PRON
fumecheng-12201	76	14	’s	’s	PART
fumecheng-12201	76	15	frequency	frequency	NOUN
fumecheng-12201	76	16	formulation	formulation	NOUN
fumecheng-12201	76	17	for	for	ADP
fumecheng-12201	76	18	different	different	ADJ
fumecheng-12201	76	19	values	value	NOUN
fumecheng-12201	76	20	of	of	ADP
fumecheng-12201	76	21	(	(	PUNCT
fumecheng-12201	76	22	a	a	PRON
fumecheng-12201	76	23	,	,	PUNCT
fumecheng-12201	76	24	b	b	NOUN
fumecheng-12201	76	25	)	)	PUNCT
fumecheng-12201	76	26	3	3	NUM
fumecheng-12201	76	27	.	.	PUNCT
fumecheng-12201	76	28	linear	linear	PROPN
fumecheng-12201	76	29	oscillator	oscillator	NOUN
fumecheng-12201	76	30	with	with	ADP
fumecheng-12201	76	31	damping	damp	VERB
fumecheng-12201	76	32	in	in	ADP
fumecheng-12201	76	33	the	the	DET
fumecheng-12201	76	34	previous	previous	ADJ
fumecheng-12201	76	35	section	section	NOUN
fumecheng-12201	76	36	,	,	PUNCT
fumecheng-12201	76	37	we	we	PRON
fumecheng-12201	76	38	discussed	discuss	VERB
fumecheng-12201	76	39	the	the	DET
fumecheng-12201	76	40	frequency	frequency	NOUN
fumecheng-12201	76	41	formulation	formulation	NOUN
fumecheng-12201	76	42	for	for	ADP
fumecheng-12201	76	43	a	a	DET
fumecheng-12201	76	44	classical	classical	ADJ
fumecheng-12201	76	45	duffing	duffing	NOUN
fumecheng-12201	76	46	oscillator	oscillator	NOUN
fumecheng-12201	76	47	with	with	ADP
fumecheng-12201	76	48	general	general	ADJ
fumecheng-12201	76	49	initial	initial	ADJ
fumecheng-12201	76	50	conditions	condition	NOUN
fumecheng-12201	76	51	,	,	PUNCT
fumecheng-12201	76	52	but	but	CCONJ
fumecheng-12201	76	53	in	in	ADP
fumecheng-12201	76	54	reality	reality	NOUN
fumecheng-12201	76	55	,	,	PUNCT
fumecheng-12201	76	56	perfect	perfect	ADJ
fumecheng-12201	76	57	simple	simple	ADJ
fumecheng-12201	76	58	harmonic	harmonic	ADJ
fumecheng-12201	76	59	motion	motion	NOUN
fumecheng-12201	76	60	is	be	AUX
fumecheng-12201	76	61	almost	almost	ADV
fumecheng-12201	76	62	non	non	ADJ
fumecheng-12201	76	63	-	-	ADJ
fumecheng-12201	76	64	existent	existent	ADJ
fumecheng-12201	76	65	.	.	PUNCT
fumecheng-12201	77	1	in	in	ADP
fumecheng-12201	77	2	reality	reality	NOUN
fumecheng-12201	77	3	,	,	PUNCT
fumecheng-12201	77	4	the	the	DET
fumecheng-12201	77	5	amplitude	amplitude	NOUN
fumecheng-12201	77	6	of	of	ADP
fumecheng-12201	77	7	the	the	DET
fumecheng-12201	77	8	duffing	duffing	NOUN
fumecheng-12201	77	9	oscillator	oscillator	NOUN
fumecheng-12201	77	10	described	describe	VERB
fumecheng-12201	77	11	above	above	ADV
fumecheng-12201	77	12	will	will	AUX
fumecheng-12201	77	13	decrease	decrease	VERB
fumecheng-12201	77	14	due	due	ADP
fumecheng-12201	77	15	to	to	ADP
fumecheng-12201	77	16	air	air	NOUN
fumecheng-12201	77	17	damping	damp	VERB
fumecheng-12201	77	18	and	and	CCONJ
fumecheng-12201	77	19	other	other	ADJ
fumecheng-12201	77	20	effects	effect	NOUN
fumecheng-12201	77	21	,	,	PUNCT
fumecheng-12201	77	22	eventually	eventually	ADV
fumecheng-12201	77	23	reaching	reach	VERB
fumecheng-12201	77	24	an	an	DET
fumecheng-12201	77	25	equilibrium	equilibrium	NOUN
fumecheng-12201	77	26	state	state	NOUN
fumecheng-12201	77	27	.	.	PUNCT
fumecheng-12201	78	1	there	there	PRON
fumecheng-12201	78	2	are	be	VERB
fumecheng-12201	78	3	many	many	ADJ
fumecheng-12201	78	4	types	type	NOUN
fumecheng-12201	78	5	of	of	ADP
fumecheng-12201	78	6	damping	damp	VERB
fumecheng-12201	78	7	in	in	ADP
fumecheng-12201	78	8	engineering	engineering	NOUN
fumecheng-12201	78	9	,	,	PUNCT
fumecheng-12201	78	10	and	and	CCONJ
fumecheng-12201	78	11	the	the	DET
fumecheng-12201	78	12	most	most	ADV
fumecheng-12201	78	13	commonly	commonly	ADV
fumecheng-12201	78	14	used	use	VERB
fumecheng-12201	78	15	damping	damp	VERB
fumecheng-12201	78	16	is	be	AUX
fumecheng-12201	78	17	viscous	viscous	ADJ
fumecheng-12201	78	18	damping	damping	NOUN
fumecheng-12201	78	19	.	.	PUNCT
fumecheng-12201	79	1	therefore	therefore	ADV
fumecheng-12201	79	2	,	,	PUNCT
fumecheng-12201	79	3	in	in	ADP
fumecheng-12201	79	4	this	this	DET
fumecheng-12201	79	5	section	section	NOUN
fumecheng-12201	79	6	,	,	PUNCT
fumecheng-12201	79	7	the	the	DET
fumecheng-12201	79	8	linear	linear	ADJ
fumecheng-12201	79	9	oscillator	oscillator	NOUN
fumecheng-12201	79	10	with	with	ADP
fumecheng-12201	79	11	viscous	viscous	ADJ
fumecheng-12201	79	12	damping	damping	NOUN
fumecheng-12201	79	13	is	be	AUX
fumecheng-12201	79	14	considered	consider	VERB
fumecheng-12201	79	15	first	first	ADJ
fumecheng-12201	79	16	.	.	PUNCT
fumecheng-12201	80	1	application	application	NOUN
fumecheng-12201	80	2	of	of	ADP
fumecheng-12201	80	3	he	he	PRON
fumecheng-12201	80	4	’s	’s	PART
fumecheng-12201	80	5	frequency	frequency	NOUN
fumecheng-12201	80	6	formula	formula	NOUN
fumecheng-12201	80	7	to	to	PART
fumecheng-12201	80	8	nonlinear	nonlinear	ADJ
fumecheng-12201	80	9	oscillators	oscillator	NOUN
fumecheng-12201	80	10	with	with	ADP
fumecheng-12201	80	11	generalized	generalized	ADJ
fumecheng-12201	80	12	initial	initial	ADJ
fumecheng-12201	80	13	condition	condition	NOUN
fumecheng-12201	80	14	705	705	NUM
fumecheng-12201	80	15	introducing	introduce	VERB
fumecheng-12201	80	16	viscous	viscous	ADJ
fumecheng-12201	80	17	damping	damp	VERB
fumecheng-12201	80	18	into	into	ADP
fumecheng-12201	80	19	a	a	DET
fumecheng-12201	80	20	linear	linear	ADJ
fumecheng-12201	80	21	oscillator	oscillator	NOUN
fumecheng-12201	80	22	,	,	PUNCT
fumecheng-12201	80	23	the	the	DET
fumecheng-12201	80	24	equation	equation	NOUN
fumecheng-12201	80	25	of	of	ADP
fumecheng-12201	80	26	vibration	vibration	NOUN
fumecheng-12201	80	27	is	be	AUX
fumecheng-12201	80	28	:	:	PUNCT
fumecheng-12201	80	29	2	2	NUM
fumecheng-12201	80	30	0	0	NUM
fumecheng-12201	80	31	,	,	PUNCT
fumecheng-12201	80	32	(	(	PUNCT
fumecheng-12201	80	33	0	0	NUM
fumecheng-12201	80	34	)	)	PUNCT
fumecheng-12201	80	35	,	,	PUNCT
fumecheng-12201	80	36	(	(	PUNCT
fumecheng-12201	80	37	0)u	0)u	NUM
fumecheng-12201	80	38	u	u	NOUN
fumecheng-12201	80	39	u	u	NOUN
fumecheng-12201	80	40	u	u	NOUN
fumecheng-12201	80	41	b	b	PROPN
fumecheng-12201	80	42	u	u	X
fumecheng-12201	80	43	a+	a+	X
fumecheng-12201	81	1	+	+	NOUN
fumecheng-12201	81	2	=	=	SYM
fumecheng-12201	81	3	=	=	SYM
fumecheng-12201	81	4	=	=	SYM
fumecheng-12201	81	5			NUM
fumecheng-12201	81	6	(	(	PUNCT
fumecheng-12201	81	7	12	12	NUM
fumecheng-12201	81	8	)	)	PUNCT
fumecheng-12201	81	9	where	where	SCONJ
fumecheng-12201	81	10	2η	2η	PROPN
fumecheng-12201	81	11	is	be	AUX
fumecheng-12201	81	12	the	the	DET
fumecheng-12201	81	13	damping	damp	VERB
fumecheng-12201	81	14	coefficient	coefficient	NOUN
fumecheng-12201	81	15	.	.	PUNCT
fumecheng-12201	82	1	the	the	DET
fumecheng-12201	82	2	magnitude	magnitude	NOUN
fumecheng-12201	82	3	of	of	ADP
fumecheng-12201	82	4	damping	damp	VERB
fumecheng-12201	82	5	is	be	AUX
fumecheng-12201	82	6	proportional	proportional	ADJ
fumecheng-12201	82	7	to	to	ADP
fumecheng-12201	82	8	the	the	DET
fumecheng-12201	82	9	vibration	vibration	NOUN
fumecheng-12201	82	10	rate	rate	NOUN
fumecheng-12201	82	11	,	,	PUNCT
fumecheng-12201	82	12	and	and	CCONJ
fumecheng-12201	82	13	the	the	DET
fumecheng-12201	82	14	direction	direction	NOUN
fumecheng-12201	82	15	is	be	AUX
fumecheng-12201	82	16	opposite	opposite	ADJ
fumecheng-12201	82	17	to	to	ADP
fumecheng-12201	82	18	the	the	DET
fumecheng-12201	82	19	speed	speed	NOUN
fumecheng-12201	82	20	direction	direction	NOUN
fumecheng-12201	82	21	.	.	PUNCT
fumecheng-12201	83	1	based	base	VERB
fumecheng-12201	83	2	on	on	ADP
fumecheng-12201	83	3	he	he	PRON
fumecheng-12201	83	4	's	's	PART
fumecheng-12201	83	5	frequency	frequency	NOUN
fumecheng-12201	83	6	formula	formula	NOUN
fumecheng-12201	83	7	,	,	PUNCT
fumecheng-12201	83	8	the	the	DET
fumecheng-12201	83	9	approximate	approximate	ADJ
fumecheng-12201	83	10	solution	solution	NOUN
fumecheng-12201	83	11	is	be	AUX
fumecheng-12201	83	12	found	find	VERB
fumecheng-12201	83	13	in	in	ADP
fumecheng-12201	83	14	the	the	DET
fumecheng-12201	83	15	following	follow	VERB
fumecheng-12201	83	16	form	form	NOUN
fumecheng-12201	83	17	:	:	PUNCT
fumecheng-12201	83	18	(	(	PUNCT
fumecheng-12201	83	19	)	)	PUNCT
fumecheng-12201	83	20	cos	cos	PROPN
fumecheng-12201	83	21	(	(	PUNCT
fumecheng-12201	83	22	)	)	PUNCT
fumecheng-12201	83	23	tu	tu	PROPN
fumecheng-12201	83	24	t	t	PROPN
fumecheng-12201	83	25	ae	ae	PROPN
fumecheng-12201	83	26	t−	t−	PROPN
fumecheng-12201	83	27	=	=	PROPN
fumecheng-12201	84	1	+	+	PROPN
fumecheng-12201	84	2			NUM
fumecheng-12201	84	3			X
fumecheng-12201	84	4			X
fumecheng-12201	84	5	(	(	PUNCT
fumecheng-12201	84	6	13	13	NUM
fumecheng-12201	84	7	)	)	PUNCT
fumecheng-12201	84	8	where	where	SCONJ
fumecheng-12201	84	9	ω′	ω′	PROPN
fumecheng-12201	84	10	is	be	AUX
fumecheng-12201	84	11	the	the	DET
fumecheng-12201	84	12	frequency	frequency	NOUN
fumecheng-12201	84	13	to	to	PART
fumecheng-12201	84	14	be	be	AUX
fumecheng-12201	84	15	solved	solve	VERB
fumecheng-12201	84	16	later	later	ADV
fumecheng-12201	84	17	.	.	PUNCT
fumecheng-12201	85	1	based	base	VERB
fumecheng-12201	85	2	on	on	ADP
fumecheng-12201	85	3	he	he	PRON
fumecheng-12201	85	4	's	's	PART
fumecheng-12201	85	5	frequency	frequency	NOUN
fumecheng-12201	85	6	formulation	formulation	NOUN
fumecheng-12201	85	7	,	,	PUNCT
fumecheng-12201	85	8	an	an	DET
fumecheng-12201	85	9	attempt	attempt	NOUN
fumecheng-12201	85	10	is	be	AUX
fumecheng-12201	85	11	made	make	VERB
fumecheng-12201	85	12	to	to	PART
fumecheng-12201	85	13	start	start	VERB
fumecheng-12201	85	14	from	from	ADP
fumecheng-12201	85	15	two	two	NUM
fumecheng-12201	85	16	arbitrary	arbitrary	ADJ
fumecheng-12201	85	17	values	value	NOUN
fumecheng-12201	85	18	of	of	ADP
fumecheng-12201	85	19	ω1′and	ω1′and	NUM
fumecheng-12201	85	20	ω2′	ω2′	NOUN
fumecheng-12201	85	21	,	,	PUNCT
fumecheng-12201	85	22	to	to	PART
fumecheng-12201	85	23	obtain	obtain	VERB
fumecheng-12201	85	24	the	the	DET
fumecheng-12201	85	25	following	following	ADJ
fumecheng-12201	85	26	residual	residual	ADJ
fumecheng-12201	85	27	equations	equation	NOUN
fumecheng-12201	85	28	:	:	PUNCT
fumecheng-12201	85	29	2	2	NUM
fumecheng-12201	85	30	2	2	NUM
fumecheng-12201	85	31	1	1	NUM
fumecheng-12201	85	32	1	1	NUM
fumecheng-12201	85	33	1	1	NUM
fumecheng-12201	85	34	1	1	NUM
fumecheng-12201	85	35	1	1	NUM
fumecheng-12201	85	36	2	2	NUM
fumecheng-12201	85	37	1	1	NUM
fumecheng-12201	85	38	1	1	NUM
fumecheng-12201	85	39	1	1	NUM
fumecheng-12201	85	40	1	1	NUM
fumecheng-12201	85	41	2	2	NUM
fumecheng-12201	85	42	1	1	NUM
fumecheng-12201	85	43	1	1	NUM
fumecheng-12201	85	44	(	(	PUNCT
fumecheng-12201	85	45	)	)	PUNCT
fumecheng-12201	85	46	(	(	PUNCT
fumecheng-12201	85	47	)	)	PUNCT
fumecheng-12201	85	48	cos	cos	PROPN
fumecheng-12201	85	49	(	(	PUNCT
fumecheng-12201	85	50	)	)	PUNCT
fumecheng-12201	85	51	2	2	NUM
fumecheng-12201	85	52	sin	sin	NOUN
fumecheng-12201	85	53	(	(	PUNCT
fumecheng-12201	85	54	)	)	PUNCT
fumecheng-12201	85	55	2	2	NUM
fumecheng-12201	85	56	cos	cos	PROPN
fumecheng-12201	85	57	(	(	PUNCT
fumecheng-12201	85	58	)	)	PUNCT
fumecheng-12201	85	59	sin	sin	NOUN
fumecheng-12201	85	60	(	(	PUNCT
fumecheng-12201	85	61	)	)	PUNCT
fumecheng-12201	85	62	cos	cos	PROPN
fumecheng-12201	85	63	(	(	PUNCT
fumecheng-12201	85	64	)	)	PUNCT
fumecheng-12201	85	65	(	(	PUNCT
fumecheng-12201	85	66	1	1	X
fumecheng-12201	85	67	)	)	PUNCT
fumecheng-12201	85	68	cos	cos	PROPN
fumecheng-12201	85	69	(	(	PUNCT
fumecheng-12201	85	70	)	)	PUNCT
fumecheng-12201	86	1	t	t	PROPN
fumecheng-12201	86	2	t	t	PROPN
fumecheng-12201	86	3	t	t	PROPN
fumecheng-12201	86	4	t	t	PROPN
fumecheng-12201	86	5	t	t	PROPN
fumecheng-12201	86	6	t	t	PROPN
fumecheng-12201	86	7	r	r	NOUN
fumecheng-12201	86	8	t	t	PROPN
fumecheng-12201	86	9	ae	ae	PROPN
fumecheng-12201	86	10	t	t	PROPN
fumecheng-12201	86	11	a	a	DET
fumecheng-12201	86	12	e	e	NOUN
fumecheng-12201	86	13	t	t	NOUN
fumecheng-12201	86	14	a	a	DET
fumecheng-12201	86	15	e	e	NOUN
fumecheng-12201	86	16	t	t	NOUN
fumecheng-12201	86	17	a	a	DET
fumecheng-12201	86	18	e	e	NOUN
fumecheng-12201	86	19	t	t	NOUN
fumecheng-12201	86	20	ae	ae	PROPN
fumecheng-12201	86	21	t	t	PROPN
fumecheng-12201	86	22	ae	ae	PROPN
fumecheng-12201	86	23	t	t	PROPN
fumecheng-12201	86	24	−	−	PROPN
fumecheng-12201	87	1	−	−	PROPN
fumecheng-12201	87	2	−	−	PROPN
fumecheng-12201	87	3	−	−	PROPN
fumecheng-12201	87	4	−	−	NOUN
fumecheng-12201	87	5	−	−	PROPN
fumecheng-12201	88	1			PROPN
fumecheng-12201	88	2			ADV
fumecheng-12201	89	1			ADV
fumecheng-12201	89	2	=	=	INTJ
fumecheng-12201	89	3	−	−	PROPN
fumecheng-12201	90	1	+	+	CCONJ
fumecheng-12201	90	2	+	+	PUNCT
fumecheng-12201	91	1	+	+	CCONJ
fumecheng-12201	91	2			ADJ
fumecheng-12201	91	3			ADV
fumecheng-12201	91	4			ADJ
fumecheng-12201	91	5	−	−	PUNCT
fumecheng-12201	91	6	+	+	CCONJ
fumecheng-12201	91	7	−	−	X
fumecheng-12201	91	8	+	+	CCONJ
fumecheng-12201	92	1	+	+	PUNCT
fumecheng-12201	93	1	+	+	NUM
fumecheng-12201	93	2			ADJ
fumecheng-12201	93	3	=	=	INTJ
fumecheng-12201	93	4	−	−	PROPN
fumecheng-12201	94	1	−	−	PROPN
fumecheng-12201	94	2	+	+	CCONJ
fumecheng-12201	94	3			NUM
fumecheng-12201	94	4			NUM
fumecheng-12201	94	5			NUM
fumecheng-12201	94	6			NUM
fumecheng-12201	94	7			NUM
fumecheng-12201	94	8			NUM
fumecheng-12201	94	9			NUM
fumecheng-12201	94	10			X
fumecheng-12201	94	11			X
fumecheng-12201	94	12			PROPN
fumecheng-12201	94	13			NOUN
fumecheng-12201	94	14			X
fumecheng-12201	94	15			PROPN
fumecheng-12201	94	16			NUM
fumecheng-12201	94	17			X
fumecheng-12201	94	18			X
fumecheng-12201	94	19			X
fumecheng-12201	94	20			X
fumecheng-12201	94	21			X
fumecheng-12201	94	22			X
fumecheng-12201	94	23			X
fumecheng-12201	94	24			NUM
fumecheng-12201	94	25			X
fumecheng-12201	94	26			X
fumecheng-12201	94	27			X
fumecheng-12201	94	28	(	(	PUNCT
fumecheng-12201	94	29	14	14	NUM
fumecheng-12201	94	30	)	)	SYM
fumecheng-12201	94	31	2	2	NUM
fumecheng-12201	94	32	2	2	NUM
fumecheng-12201	94	33	2	2	NUM
fumecheng-12201	94	34	2	2	NUM
fumecheng-12201	94	35	2	2	NUM
fumecheng-12201	94	36	2	2	NUM
fumecheng-12201	94	37	2	2	NUM
fumecheng-12201	94	38	2	2	NUM
fumecheng-12201	94	39	2	2	NUM
fumecheng-12201	94	40	2	2	NUM
fumecheng-12201	94	41	2	2	NUM
fumecheng-12201	94	42	2	2	NUM
fumecheng-12201	94	43	2	2	NUM
fumecheng-12201	94	44	2	2	NUM
fumecheng-12201	94	45	2	2	NUM
fumecheng-12201	94	46	(	(	PUNCT
fumecheng-12201	94	47	)	)	PUNCT
fumecheng-12201	94	48	(	(	PUNCT
fumecheng-12201	94	49	)	)	PUNCT
fumecheng-12201	94	50	cos	cos	PROPN
fumecheng-12201	94	51	(	(	PUNCT
fumecheng-12201	94	52	)	)	PUNCT
fumecheng-12201	94	53	2	2	NUM
fumecheng-12201	94	54	sin	sin	NOUN
fumecheng-12201	94	55	(	(	PUNCT
fumecheng-12201	94	56	)	)	PUNCT
fumecheng-12201	94	57	2	2	NUM
fumecheng-12201	94	58	cos	cos	PROPN
fumecheng-12201	94	59	(	(	PUNCT
fumecheng-12201	94	60	)	)	PUNCT
fumecheng-12201	94	61	sin	sin	NOUN
fumecheng-12201	94	62	(	(	PUNCT
fumecheng-12201	94	63	)	)	PUNCT
fumecheng-12201	94	64	cos	cos	PROPN
fumecheng-12201	94	65	(	(	PUNCT
fumecheng-12201	94	66	)	)	PUNCT
fumecheng-12201	94	67	(	(	PUNCT
fumecheng-12201	94	68	1	1	X
fumecheng-12201	94	69	)	)	PUNCT
fumecheng-12201	94	70	cos	cos	PROPN
fumecheng-12201	94	71	(	(	PUNCT
fumecheng-12201	94	72	)	)	PUNCT
fumecheng-12201	94	73	t	t	PROPN
fumecheng-12201	94	74	t	t	PROPN
fumecheng-12201	94	75	t	t	PROPN
fumecheng-12201	94	76	t	t	PROPN
fumecheng-12201	94	77	t	t	PROPN
fumecheng-12201	94	78	t	t	PROPN
fumecheng-12201	94	79	r	r	NOUN
fumecheng-12201	94	80	t	t	PROPN
fumecheng-12201	94	81	ae	ae	PROPN
fumecheng-12201	94	82	t	t	PROPN
fumecheng-12201	94	83	a	a	DET
fumecheng-12201	94	84	e	e	NOUN
fumecheng-12201	94	85	t	t	NOUN
fumecheng-12201	94	86	a	a	DET
fumecheng-12201	94	87	e	e	NOUN
fumecheng-12201	94	88	t	t	NOUN
fumecheng-12201	94	89	a	a	DET
fumecheng-12201	94	90	e	e	NOUN
fumecheng-12201	94	91	t	t	NOUN
fumecheng-12201	94	92	ae	ae	PROPN
fumecheng-12201	94	93	t	t	PROPN
fumecheng-12201	94	94	ae	ae	PROPN
fumecheng-12201	94	95	t	t	PROPN
fumecheng-12201	94	96	−	−	PROPN
fumecheng-12201	95	1	−	−	PROPN
fumecheng-12201	95	2	−	−	PROPN
fumecheng-12201	95	3	−	−	PROPN
fumecheng-12201	95	4	−	−	NOUN
fumecheng-12201	95	5	−	−	PROPN
fumecheng-12201	96	1			PROPN
fumecheng-12201	96	2			ADV
fumecheng-12201	97	1			ADV
fumecheng-12201	97	2	=	=	INTJ
fumecheng-12201	97	3	−	−	PROPN
fumecheng-12201	98	1	+	+	CCONJ
fumecheng-12201	98	2	+	+	PUNCT
fumecheng-12201	99	1	+	+	CCONJ
fumecheng-12201	99	2			ADJ
fumecheng-12201	99	3			ADV
fumecheng-12201	99	4			ADJ
fumecheng-12201	99	5	−	−	PUNCT
fumecheng-12201	99	6	+	+	CCONJ
fumecheng-12201	99	7	−	−	X
fumecheng-12201	99	8	+	+	CCONJ
fumecheng-12201	100	1	+	+	PUNCT
fumecheng-12201	101	1	+	+	NUM
fumecheng-12201	101	2			ADJ
fumecheng-12201	101	3	=	=	INTJ
fumecheng-12201	101	4	−	−	PROPN
fumecheng-12201	102	1	−	−	PROPN
fumecheng-12201	102	2	+	+	CCONJ
fumecheng-12201	102	3			NUM
fumecheng-12201	102	4			NUM
fumecheng-12201	102	5			NUM
fumecheng-12201	102	6			NUM
fumecheng-12201	102	7			NUM
fumecheng-12201	102	8			NUM
fumecheng-12201	102	9			NUM
fumecheng-12201	102	10			X
fumecheng-12201	102	11			X
fumecheng-12201	102	12			PROPN
fumecheng-12201	102	13			NOUN
fumecheng-12201	102	14			X
fumecheng-12201	102	15			PROPN
fumecheng-12201	102	16			NUM
fumecheng-12201	102	17			X
fumecheng-12201	102	18			X
fumecheng-12201	102	19			X
fumecheng-12201	102	20			X
fumecheng-12201	102	21			X
fumecheng-12201	102	22			X
fumecheng-12201	102	23			X
fumecheng-12201	102	24			NUM
fumecheng-12201	102	25			X
fumecheng-12201	102	26			X
fumecheng-12201	102	27			X
fumecheng-12201	102	28	(	(	PUNCT
fumecheng-12201	102	29	15	15	NUM
fumecheng-12201	102	30	)	)	PUNCT
fumecheng-12201	102	31	the	the	DET
fumecheng-12201	102	32	residual	residual	ADJ
fumecheng-12201	102	33	integrals	integral	NOUN
fumecheng-12201	102	34	are	be	AUX
fumecheng-12201	102	35	given	give	VERB
fumecheng-12201	102	36	below	below	ADP
fumecheng-12201	102	37	2	2	NUM
fumecheng-12201	102	38	1	1	NUM
fumecheng-12201	102	39	1	1	NUM
fumecheng-12201	102	40	10	10	NUM
fumecheng-12201	102	41	2	2	NUM
fumecheng-12201	102	42	22	22	NUM
fumecheng-12201	102	43	1	1	NUM
fumecheng-12201	102	44	10	10	NUM
fumecheng-12201	102	45	2	2	NUM
fumecheng-12201	102	46	2	2	NUM
fumecheng-12201	102	47	1	1	NUM
fumecheng-12201	102	48	2	2	NUM
fumecheng-12201	102	49	(	(	PUNCT
fumecheng-12201	102	50	)	)	PUNCT
fumecheng-12201	102	51	cos	cos	PROPN
fumecheng-12201	102	52	(	(	PUNCT
fumecheng-12201	102	53	)	)	PUNCT
fumecheng-12201	102	54	d	d	SYM
fumecheng-12201	102	55	2	2	NUM
fumecheng-12201	102	56	(	(	PUNCT
fumecheng-12201	102	57	1	1	NUM
fumecheng-12201	102	58	)	)	PUNCT
fumecheng-12201	102	59	cos	cos	PROPN
fumecheng-12201	102	60	(	(	PUNCT
fumecheng-12201	102	61	)	)	PUNCT
fumecheng-12201	102	62	d	d	NOUN
fumecheng-12201	102	63	6	6	NUM
fumecheng-12201	102	64	4	4	NUM
fumecheng-12201	102	65	(	(	PUNCT
fumecheng-12201	102	66	1	1	NUM
fumecheng-12201	102	67	)	)	SYM
fumecheng-12201	102	68	5	5	NUM
fumecheng-12201	102	69	t	t	NOUN
fumecheng-12201	102	70	t	t	NOUN
fumecheng-12201	102	71	t	t	NOUN
fumecheng-12201	102	72	r	r	NOUN
fumecheng-12201	102	73	r	r	NOUN
fumecheng-12201	102	74	t	t	NOUN
fumecheng-12201	102	75	t	t	NOUN
fumecheng-12201	102	76	t	t	NOUN
fumecheng-12201	102	77	t	t	PROPN
fumecheng-12201	102	78	=	=	SYM
fumecheng-12201	102	79	ae	ae	PROPN
fumecheng-12201	102	80	t	t	PROPN
fumecheng-12201	102	81	t	t	PROPN
fumecheng-12201	102	82	t	t	PROPN
fumecheng-12201	102	83	e	e	PROPN
fumecheng-12201	102	84	a	a	PRON
fumecheng-12201	102	85			NUM
fumecheng-12201	102	86			X
fumecheng-12201	102	87			X
fumecheng-12201	102	88			NUM
fumecheng-12201	102	89			X
fumecheng-12201	102	90			X
fumecheng-12201	102	91			PROPN
fumecheng-12201	102	92			NUM
fumecheng-12201	102	93			X
fumecheng-12201	102	94	−	−	PROPN
fumecheng-12201	102	95			PROPN
fumecheng-12201	102	96	−	−	PROPN
fumecheng-12201	102	97	=	=	PROPN
fumecheng-12201	102	98	+	+	CCONJ
fumecheng-12201	102	99			ADJ
fumecheng-12201	102	100	−	−	VERB
fumecheng-12201	103	1	−	−	PROPN
fumecheng-12201	103	2	+	+	CCONJ
fumecheng-12201	103	3	−	−	PROPN
fumecheng-12201	104	1	=	=	INTJ
fumecheng-12201	104	2	−	−	PROPN
fumecheng-12201	105	1	−	−	PROPN
fumecheng-12201	105	2			PROPN
fumecheng-12201	105	3			X
fumecheng-12201	105	4			X
fumecheng-12201	105	5	(	(	PUNCT
fumecheng-12201	105	6	16	16	NUM
fumecheng-12201	105	7	)	)	SYM
fumecheng-12201	105	8	2	2	NUM
fumecheng-12201	105	9	2	2	NUM
fumecheng-12201	105	10	2	2	NUM
fumecheng-12201	105	11	20	20	NUM
fumecheng-12201	105	12	2	2	NUM
fumecheng-12201	105	13	22	22	NUM
fumecheng-12201	105	14	2	2	NUM
fumecheng-12201	105	15	20	20	NUM
fumecheng-12201	105	16	2	2	NUM
fumecheng-12201	105	17	2	2	NUM
fumecheng-12201	105	18	2	2	NUM
fumecheng-12201	105	19	2	2	NUM
fumecheng-12201	105	20	(	(	PUNCT
fumecheng-12201	105	21	)	)	PUNCT
fumecheng-12201	105	22	cos	cos	PROPN
fumecheng-12201	105	23	(	(	PUNCT
fumecheng-12201	105	24	)	)	PUNCT
fumecheng-12201	105	25	d	d	SYM
fumecheng-12201	105	26	2	2	NUM
fumecheng-12201	105	27	(	(	PUNCT
fumecheng-12201	105	28	1	1	NUM
fumecheng-12201	105	29	)	)	PUNCT
fumecheng-12201	105	30	cos	cos	PROPN
fumecheng-12201	105	31	(	(	PUNCT
fumecheng-12201	105	32	)	)	PUNCT
fumecheng-12201	105	33	d	d	NOUN
fumecheng-12201	105	34	6	6	NUM
fumecheng-12201	105	35	4	4	NUM
fumecheng-12201	105	36	(	(	PUNCT
fumecheng-12201	105	37	1	1	NUM
fumecheng-12201	105	38	)	)	SYM
fumecheng-12201	105	39	5	5	NUM
fumecheng-12201	105	40	t	t	NOUN
fumecheng-12201	105	41	t	t	NOUN
fumecheng-12201	105	42	t	t	NOUN
fumecheng-12201	105	43	r	r	NOUN
fumecheng-12201	105	44	r	r	NOUN
fumecheng-12201	105	45	t	t	NOUN
fumecheng-12201	105	46	t	t	NOUN
fumecheng-12201	105	47	t	t	NOUN
fumecheng-12201	105	48	t	t	PROPN
fumecheng-12201	106	1	=	=	SYM
fumecheng-12201	106	2	ae	ae	PROPN
fumecheng-12201	106	3	t	t	PROPN
fumecheng-12201	106	4	t	t	PROPN
fumecheng-12201	106	5	t	t	PROPN
fumecheng-12201	106	6	e	e	PROPN
fumecheng-12201	106	7	a	a	PRON
fumecheng-12201	106	8			NUM
fumecheng-12201	106	9			X
fumecheng-12201	106	10			X
fumecheng-12201	106	11			NUM
fumecheng-12201	106	12			X
fumecheng-12201	106	13			X
fumecheng-12201	106	14			PROPN
fumecheng-12201	106	15			NUM
fumecheng-12201	106	16			X
fumecheng-12201	106	17	−	−	PROPN
fumecheng-12201	106	18			PROPN
fumecheng-12201	106	19	−	−	PROPN
fumecheng-12201	106	20	=	=	PROPN
fumecheng-12201	107	1	+	+	CCONJ
fumecheng-12201	107	2			ADJ
fumecheng-12201	107	3	−	−	VERB
fumecheng-12201	107	4	−	−	PROPN
fumecheng-12201	107	5	+	+	CCONJ
fumecheng-12201	107	6	−	−	PROPN
fumecheng-12201	108	1	=	=	INTJ
fumecheng-12201	108	2	−	−	PROPN
fumecheng-12201	109	1	−	−	PROPN
fumecheng-12201	109	2			PROPN
fumecheng-12201	109	3			X
fumecheng-12201	109	4			X
fumecheng-12201	109	5	(	(	PUNCT
fumecheng-12201	109	6	17	17	NUM
fumecheng-12201	109	7	)	)	PUNCT
fumecheng-12201	109	8	where	where	SCONJ
fumecheng-12201	109	9	t=2π	t=2π	PROPN
fumecheng-12201	109	10	/	/	SYM
fumecheng-12201	109	11	η	η	PROPN
fumecheng-12201	109	12	,	,	PUNCT
fumecheng-12201	109	13	then	then	ADV
fumecheng-12201	109	14	the	the	DET
fumecheng-12201	109	15	frequency	frequency	NOUN
fumecheng-12201	109	16	equation	equation	NOUN
fumecheng-12201	109	17	is	be	AUX
fumecheng-12201	109	18	706	706	NUM
fumecheng-12201	109	19	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	109	20	,	,	PUNCT
fumecheng-12201	109	21	q.r.song	q.r.song	PROPN
fumecheng-12201	109	22	,	,	PUNCT
fumecheng-12201	109	23	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	109	24	,	,	PUNCT
fumecheng-12201	109	25	f.wang	f.wang	NOUN
fumecheng-12201	109	26	2	2	NUM
fumecheng-12201	109	27	2	2	NUM
fumecheng-12201	109	28	1	1	NUM
fumecheng-12201	109	29	1	1	NUM
fumecheng-12201	109	30	2	2	NUM
fumecheng-12201	109	31	1	1	NUM
fumecheng-12201	109	32	2	2	NUM
fumecheng-12201	109	33	2	2	NUM
fumecheng-12201	109	34	2	2	NUM
fumecheng-12201	109	35	2	2	NUM
fumecheng-12201	109	36	2	2	NUM
fumecheng-12201	109	37	2	2	NUM
fumecheng-12201	109	38	1	1	NUM
fumecheng-12201	109	39	2	2	NUM
fumecheng-12201	109	40	2	2	NUM
fumecheng-12201	109	41	2	2	NUM
fumecheng-12201	109	42	2	2	NUM
fumecheng-12201	109	43	1	1	NUM
fumecheng-12201	109	44	2	2	NUM
fumecheng-12201	109	45	6	6	NUM
fumecheng-12201	109	46	4	4	NUM
fumecheng-12201	109	47	(	(	PUNCT
fumecheng-12201	109	48	)	)	PUNCT
fumecheng-12201	109	49	(	(	PUNCT
fumecheng-12201	109	50	1	1	X
fumecheng-12201	109	51	)	)	PUNCT
fumecheng-12201	109	52	5	5	NUM
fumecheng-12201	109	53	6	6	NUM
fumecheng-12201	109	54	4	4	NUM
fumecheng-12201	109	55	(	(	PUNCT
fumecheng-12201	109	56	)	)	PUNCT
fumecheng-12201	109	57	5	5	NUM
fumecheng-12201	109	58	1	1	NUM
fumecheng-12201	110	1	r	r	NOUN
fumecheng-12201	110	2	r	r	NOUN
fumecheng-12201	110	3	r	r	NOUN
fumecheng-12201	110	4	r	r	NOUN
fumecheng-12201	110	5	e	e	NOUN
fumecheng-12201	110	6	a	a	X
fumecheng-12201	110	7	e	e	NOUN
fumecheng-12201	110	8	a	a	DET
fumecheng-12201	110	9			ADJ
fumecheng-12201	110	10	−	−	PROPN
fumecheng-12201	110	11			NOUN
fumecheng-12201	110	12	−	−	NOUN
fumecheng-12201	110	13			ADJ
fumecheng-12201	110	14	−	−	VERB
fumecheng-12201	111	1			PROPN
fumecheng-12201	111	2	=	=	SYM
fumecheng-12201	111	3	−	−	NOUN
fumecheng-12201	112	1	−	−	PROPN
fumecheng-12201	112	2			ADJ
fumecheng-12201	112	3	−	−	NOUN
fumecheng-12201	112	4	−	−	PUNCT
fumecheng-12201	112	5	=	=	NOUN
fumecheng-12201	112	6	−	−	PROPN
fumecheng-12201	112	7			CCONJ
fumecheng-12201	112	8	−	−	PUNCT
fumecheng-12201	112	9			PROPN
fumecheng-12201	112	10	=	=	SYM
fumecheng-12201	112	11	−	−	PROPN
fumecheng-12201	113	1			X
fumecheng-12201	114	1			X
fumecheng-12201	115	1			X
fumecheng-12201	115	2			X
fumecheng-12201	115	3			X
fumecheng-12201	115	4			NUM
fumecheng-12201	115	5			X
fumecheng-12201	115	6			X
fumecheng-12201	115	7			PUNCT
fumecheng-12201	115	8	(	(	PUNCT
fumecheng-12201	115	9	18	18	NUM
fumecheng-12201	115	10	)	)	SYM
fumecheng-12201	115	11	4	4	NUM
fumecheng-12201	115	12	.	.	PUNCT
fumecheng-12201	115	13	nonlinear	nonlinear	ADJ
fumecheng-12201	115	14	duffing	duffing	NOUN
fumecheng-12201	115	15	oscillator	oscillator	NOUN
fumecheng-12201	115	16	with	with	ADP
fumecheng-12201	115	17	damping	damp	VERB
fumecheng-12201	115	18	viscous	viscous	ADJ
fumecheng-12201	115	19	damping	damp	VERB
fumecheng-12201	115	20	is	be	AUX
fumecheng-12201	115	21	introduced	introduce	VERB
fumecheng-12201	115	22	in	in	ADP
fumecheng-12201	115	23	a	a	DET
fumecheng-12201	115	24	nonlinear	nonlinear	ADJ
fumecheng-12201	115	25	duffing	duffing	NOUN
fumecheng-12201	115	26	oscillator	oscillator	NOUN
fumecheng-12201	115	27	,	,	PUNCT
fumecheng-12201	115	28	its	its	PRON
fumecheng-12201	115	29	vibration	vibration	NOUN
fumecheng-12201	115	30	equation	equation	NOUN
fumecheng-12201	115	31	is	be	AUX
fumecheng-12201	115	32	:	:	PUNCT
fumecheng-12201	115	33	32	32	NUM
fumecheng-12201	115	34	0	0	NUM
fumecheng-12201	115	35	,	,	PUNCT
fumecheng-12201	115	36	(	(	PUNCT
fumecheng-12201	115	37	0	0	NUM
fumecheng-12201	115	38	)	)	PUNCT
fumecheng-12201	115	39	,	,	PUNCT
fumecheng-12201	115	40	(	(	PUNCT
fumecheng-12201	115	41	0)u	0)u	NUM
fumecheng-12201	115	42	u	u	NOUN
fumecheng-12201	115	43	u	u	NOUN
fumecheng-12201	115	44	u	u	NOUN
fumecheng-12201	115	45	u	u	NOUN
fumecheng-12201	115	46	b	b	PROPN
fumecheng-12201	115	47	u	u	X
fumecheng-12201	115	48	a+	a+	X
fumecheng-12201	116	1	+	+	PROPN
fumecheng-12201	116	2	+	+	PUNCT
fumecheng-12201	116	3	=	=	SYM
fumecheng-12201	116	4	=	=	SYM
fumecheng-12201	116	5	=	=	SYM
fumecheng-12201	116	6			NUM
fumecheng-12201	116	7			PROPN
fumecheng-12201	116	8	(	(	PUNCT
fumecheng-12201	116	9	19	19	NUM
fumecheng-12201	116	10	)	)	PUNCT
fumecheng-12201	116	11	in	in	ADP
fumecheng-12201	116	12	the	the	DET
fumecheng-12201	116	13	first	first	ADJ
fumecheng-12201	116	14	section	section	NOUN
fumecheng-12201	116	15	,	,	PUNCT
fumecheng-12201	116	16	the	the	DET
fumecheng-12201	116	17	frequency	frequency	NOUN
fumecheng-12201	116	18	formula	formula	NOUN
fumecheng-12201	116	19	of	of	ADP
fumecheng-12201	116	20	the	the	DET
fumecheng-12201	116	21	nonlinear	nonlinear	ADJ
fumecheng-12201	116	22	oscillator	oscillator	NOUN
fumecheng-12201	116	23	ü+u+εu3=0	ü+u+εu3=0	PROPN
fumecheng-12201	116	24	is	be	AUX
fumecheng-12201	116	25	given	give	VERB
fumecheng-12201	116	26	by	by	ADP
fumecheng-12201	116	27	2	2	NUM
fumecheng-12201	116	28	23	23	NUM
fumecheng-12201	116	29	1	1	NUM
fumecheng-12201	116	30	4	4	NUM
fumecheng-12201	116	31	a=	a=	NOUN
fumecheng-12201	116	32	+	+	ADJ
fumecheng-12201	116	33			PROPN
fumecheng-12201	116	34			PROPN
fumecheng-12201	116	35	(	(	PUNCT
fumecheng-12201	116	36	20	20	NUM
fumecheng-12201	116	37	)	)	PUNCT
fumecheng-12201	116	38	therefore	therefore	ADV
fumecheng-12201	116	39	,	,	PUNCT
fumecheng-12201	116	40	the	the	DET
fumecheng-12201	116	41	damped	damped	ADJ
fumecheng-12201	116	42	nonlinear	nonlinear	PROPN
fumecheng-12201	116	43	oscillator	oscillator	NOUN
fumecheng-12201	116	44	can	can	AUX
fumecheng-12201	116	45	be	be	AUX
fumecheng-12201	116	46	equivalent	equivalent	ADJ
fumecheng-12201	116	47	to	to	ADP
fumecheng-12201	116	48	22	22	NUM
fumecheng-12201	116	49	0	0	NUM
fumecheng-12201	116	50	,	,	PUNCT
fumecheng-12201	116	51	(	(	PUNCT
fumecheng-12201	116	52	0	0	NUM
fumecheng-12201	116	53	)	)	PUNCT
fumecheng-12201	116	54	,	,	PUNCT
fumecheng-12201	116	55	(	(	PUNCT
fumecheng-12201	116	56	0)u	0)u	NUM
fumecheng-12201	116	57	u	u	NOUN
fumecheng-12201	116	58	u	u	NOUN
fumecheng-12201	116	59	u	u	NOUN
fumecheng-12201	116	60	b	b	PROPN
fumecheng-12201	116	61	u	u	X
fumecheng-12201	116	62	a+	a+	X
fumecheng-12201	116	63	+	+	NOUN
fumecheng-12201	116	64	=	=	SYM
fumecheng-12201	116	65	=	=	SYM
fumecheng-12201	116	66	=	=	SYM
fumecheng-12201	116	67			NUM
fumecheng-12201	116	68			X
fumecheng-12201	116	69	(	(	PUNCT
fumecheng-12201	116	70	21	21	NUM
fumecheng-12201	116	71	)	)	PUNCT
fumecheng-12201	116	72	similarly	similarly	ADV
fumecheng-12201	116	73	,	,	PUNCT
fumecheng-12201	116	74	there	there	PRON
fumecheng-12201	116	75	are	be	VERB
fumecheng-12201	116	76	approximate	approximate	ADJ
fumecheng-12201	116	77	solutions	solution	NOUN
fumecheng-12201	116	78	of	of	ADP
fumecheng-12201	116	79	the	the	DET
fumecheng-12201	116	80	following	follow	VERB
fumecheng-12201	116	81	form	form	NOUN
fumecheng-12201	116	82	(	(	PUNCT
fumecheng-12201	116	83	)	)	PUNCT
fumecheng-12201	116	84	cos	cos	PROPN
fumecheng-12201	116	85	(	(	PUNCT
fumecheng-12201	116	86	)	)	PUNCT
fumecheng-12201	116	87	tu	tu	PROPN
fumecheng-12201	116	88	t	t	PROPN
fumecheng-12201	116	89	ae	ae	PROPN
fumecheng-12201	116	90	t−	t−	PROPN
fumecheng-12201	116	91	=	=	PROPN
fumecheng-12201	116	92	+	+	PROPN
fumecheng-12201	116	93			NUM
fumecheng-12201	116	94			X
fumecheng-12201	116	95			X
fumecheng-12201	116	96	(	(	PUNCT
fumecheng-12201	116	97	22	22	NUM
fumecheng-12201	116	98	)	)	PUNCT
fumecheng-12201	116	99	where	where	SCONJ
fumecheng-12201	116	100	ω′	ω′	PROPN
fumecheng-12201	116	101	is	be	AUX
fumecheng-12201	116	102	the	the	DET
fumecheng-12201	116	103	frequency	frequency	NOUN
fumecheng-12201	116	104	to	to	PART
fumecheng-12201	116	105	be	be	AUX
fumecheng-12201	116	106	solved	solve	VERB
fumecheng-12201	116	107	later	later	ADV
fumecheng-12201	116	108	.	.	PUNCT
fumecheng-12201	117	1	we	we	PRON
fumecheng-12201	117	2	try	try	VERB
fumecheng-12201	117	3	to	to	PART
fumecheng-12201	117	4	get	get	VERB
fumecheng-12201	117	5	the	the	DET
fumecheng-12201	117	6	following	follow	VERB
fumecheng-12201	117	7	residual	residual	ADJ
fumecheng-12201	117	8	equations	equation	NOUN
fumecheng-12201	117	9	starting	start	VERB
fumecheng-12201	117	10	from	from	ADP
fumecheng-12201	117	11	two	two	NUM
fumecheng-12201	117	12	arbitrary	arbitrary	ADJ
fumecheng-12201	117	13	ω1′and	ω1′and	NUM
fumecheng-12201	117	14	ω2′	ω2′	NOUN
fumecheng-12201	117	15	:	:	PUNCT
fumecheng-12201	117	16	2	2	NUM
fumecheng-12201	117	17	2	2	NUM
fumecheng-12201	117	18	1	1	NUM
fumecheng-12201	117	19	1	1	NUM
fumecheng-12201	117	20	1	1	NUM
fumecheng-12201	117	21	1	1	NUM
fumecheng-12201	117	22	1	1	NUM
fumecheng-12201	117	23	2	2	NUM
fumecheng-12201	117	24	2	2	NUM
fumecheng-12201	117	25	1	1	NUM
fumecheng-12201	117	26	1	1	NUM
fumecheng-12201	117	27	1	1	NUM
fumecheng-12201	117	28	1	1	NUM
fumecheng-12201	117	29	2	2	NUM
fumecheng-12201	117	30	2	2	NUM
fumecheng-12201	117	31	1	1	NUM
fumecheng-12201	117	32	1	1	NUM
fumecheng-12201	117	33	2	2	NUM
fumecheng-12201	117	34	2	2	NUM
fumecheng-12201	117	35	2	2	NUM
fumecheng-12201	117	36	2	2	NUM
fumecheng-12201	117	37	2	2	NUM
fumecheng-12201	117	38	2	2	NUM
fumecheng-12201	117	39	(	(	PUNCT
fumecheng-12201	117	40	)	)	PUNCT
fumecheng-12201	117	41	(	(	PUNCT
fumecheng-12201	117	42	)	)	PUNCT
fumecheng-12201	117	43	cos	cos	PROPN
fumecheng-12201	117	44	(	(	PUNCT
fumecheng-12201	117	45	)	)	PUNCT
fumecheng-12201	117	46	2	2	NUM
fumecheng-12201	117	47	sin	sin	NOUN
fumecheng-12201	117	48	(	(	PUNCT
fumecheng-12201	117	49	)	)	PUNCT
fumecheng-12201	117	50	3	3	NUM
fumecheng-12201	117	51	2	2	NUM
fumecheng-12201	117	52	cos	cos	PROPN
fumecheng-12201	117	53	(	(	PUNCT
fumecheng-12201	117	54	)	)	PUNCT
fumecheng-12201	117	55	sin	sin	NOUN
fumecheng-12201	117	56	(	(	PUNCT
fumecheng-12201	117	57	)	)	PUNCT
fumecheng-12201	117	58	(	(	PUNCT
fumecheng-12201	117	59	1	1	X
fumecheng-12201	117	60	)	)	PUNCT
fumecheng-12201	117	61	cos	cos	PROPN
fumecheng-12201	117	62	(	(	PUNCT
fumecheng-12201	117	63	)	)	PUNCT
fumecheng-12201	117	64	4	4	NUM
fumecheng-12201	117	65	3	3	NUM
fumecheng-12201	117	66	(	(	PUNCT
fumecheng-12201	117	67	1	1	NUM
fumecheng-12201	117	68	)	)	PUNCT
fumecheng-12201	117	69	cos	cos	PROPN
fumecheng-12201	117	70	(	(	PUNCT
fumecheng-12201	117	71	)	)	PUNCT
fumecheng-12201	117	72	4	4	NUM
fumecheng-12201	117	73	(	(	PUNCT
fumecheng-12201	117	74	)	)	PUNCT
fumecheng-12201	117	75	(	(	PUNCT
fumecheng-12201	117	76	)	)	PUNCT
fumecheng-12201	117	77	cos	cos	PROPN
fumecheng-12201	117	78	(	(	PUNCT
fumecheng-12201	117	79	)	)	PUNCT
fumecheng-12201	117	80	2	2	NUM
fumecheng-12201	117	81	sin	sin	NOUN
fumecheng-12201	117	82	(	(	PUNCT
fumecheng-12201	117	83	t	t	PROPN
fumecheng-12201	117	84	t	t	PROPN
fumecheng-12201	117	85	t	t	PROPN
fumecheng-12201	117	86	t	t	PROPN
fumecheng-12201	117	87	t	t	PROPN
fumecheng-12201	117	88	t	t	PROPN
fumecheng-12201	117	89	t	t	PROPN
fumecheng-12201	117	90	t	t	PROPN
fumecheng-12201	117	91	r	r	NOUN
fumecheng-12201	117	92	t	t	PROPN
fumecheng-12201	118	1	ae	ae	PROPN
fumecheng-12201	118	2	t	t	PROPN
fumecheng-12201	118	3	a	a	DET
fumecheng-12201	118	4	e	e	NOUN
fumecheng-12201	118	5	t	t	NOUN
fumecheng-12201	118	6	a	a	DET
fumecheng-12201	118	7	e	e	NOUN
fumecheng-12201	118	8	t	t	NOUN
fumecheng-12201	118	9	a	a	DET
fumecheng-12201	118	10	e	e	NOUN
fumecheng-12201	118	11	t	t	PROPN
fumecheng-12201	118	12	ae	ae	PROPN
fumecheng-12201	118	13	a	a	DET
fumecheng-12201	118	14	t	t	X
fumecheng-12201	118	15	ae	ae	PROPN
fumecheng-12201	118	16	a	a	DET
fumecheng-12201	118	17	t	t	NOUN
fumecheng-12201	118	18	r	r	NOUN
fumecheng-12201	118	19	t	t	NOUN
fumecheng-12201	118	20	ae	ae	PROPN
fumecheng-12201	118	21	t	t	PROPN
fumecheng-12201	118	22	a	a	DET
fumecheng-12201	118	23	e	e	NOUN
fumecheng-12201	118	24	−	−	PROPN
fumecheng-12201	118	25	−	−	PROPN
fumecheng-12201	118	26	−	−	PROPN
fumecheng-12201	118	27	−	−	PROPN
fumecheng-12201	118	28	−	−	PROPN
fumecheng-12201	118	29	−	−	PROPN
fumecheng-12201	119	1	−	−	NOUN
fumecheng-12201	119	2	−	−	PROPN
fumecheng-12201	120	1			PROPN
fumecheng-12201	120	2			ADV
fumecheng-12201	121	1			ADV
fumecheng-12201	121	2	=	=	INTJ
fumecheng-12201	121	3	−	−	PROPN
fumecheng-12201	122	1	+	+	CCONJ
fumecheng-12201	122	2	+	+	PUNCT
fumecheng-12201	123	1	+	+	CCONJ
fumecheng-12201	123	2			ADJ
fumecheng-12201	123	3			ADV
fumecheng-12201	123	4			ADJ
fumecheng-12201	123	5	−	−	PUNCT
fumecheng-12201	123	6	+	+	CCONJ
fumecheng-12201	123	7	−	−	X
fumecheng-12201	124	1	+	+	X
fumecheng-12201	125	1	+	+	PUNCT
fumecheng-12201	126	1	+	+	PUNCT
fumecheng-12201	126	2	+	+	NUM
fumecheng-12201	126	3			ADJ
fumecheng-12201	126	4	=	=	ADJ
fumecheng-12201	126	5	+	+	CCONJ
fumecheng-12201	126	6	−	−	ADP
fumecheng-12201	126	7	−	−	PROPN
fumecheng-12201	127	1	+	+	CCONJ
fumecheng-12201	127	2			PROPN
fumecheng-12201	127	3			ADV
fumecheng-12201	128	1			ADV
fumecheng-12201	128	2	=	=	INTJ
fumecheng-12201	128	3	−	−	X
fumecheng-12201	129	1	+	+	CCONJ
fumecheng-12201	129	2	+	+	CCONJ
fumecheng-12201	129	3			NUM
fumecheng-12201	129	4			NUM
fumecheng-12201	129	5			NUM
fumecheng-12201	129	6			NUM
fumecheng-12201	129	7			NUM
fumecheng-12201	129	8			NUM
fumecheng-12201	129	9			NUM
fumecheng-12201	129	10			NUM
fumecheng-12201	129	11			NUM
fumecheng-12201	129	12			X
fumecheng-12201	129	13			X
fumecheng-12201	129	14			PROPN
fumecheng-12201	129	15			NOUN
fumecheng-12201	129	16			X
fumecheng-12201	129	17			PROPN
fumecheng-12201	129	18			NUM
fumecheng-12201	129	19			X
fumecheng-12201	129	20			X
fumecheng-12201	129	21			X
fumecheng-12201	129	22			X
fumecheng-12201	129	23			PROPN
fumecheng-12201	129	24			PROPN
fumecheng-12201	129	25			X
fumecheng-12201	129	26			PROPN
fumecheng-12201	129	27			PROPN
fumecheng-12201	129	28			NUM
fumecheng-12201	129	29			X
fumecheng-12201	129	30			X
fumecheng-12201	129	31			PROPN
fumecheng-12201	129	32			NUM
fumecheng-12201	129	33			X
fumecheng-12201	129	34			X
fumecheng-12201	129	35			PROPN
fumecheng-12201	129	36			NOUN
fumecheng-12201	129	37	2	2	ADJ
fumecheng-12201	129	38	2	2	NUM
fumecheng-12201	129	39	2	2	NUM
fumecheng-12201	129	40	2	2	NUM
fumecheng-12201	129	41	2	2	NUM
fumecheng-12201	129	42	2	2	NUM
fumecheng-12201	129	43	2	2	NUM
fumecheng-12201	129	44	2	2	NUM
fumecheng-12201	129	45	2	2	NUM
fumecheng-12201	129	46	2	2	NUM
fumecheng-12201	129	47	2	2	NUM
fumecheng-12201	129	48	)	)	PUNCT
fumecheng-12201	129	49	3	3	NUM
fumecheng-12201	129	50	2	2	NUM
fumecheng-12201	129	51	cos	cos	PROPN
fumecheng-12201	129	52	(	(	PUNCT
fumecheng-12201	129	53	)	)	PUNCT
fumecheng-12201	129	54	sin	sin	NOUN
fumecheng-12201	129	55	(	(	PUNCT
fumecheng-12201	129	56	)	)	PUNCT
fumecheng-12201	129	57	(	(	PUNCT
fumecheng-12201	129	58	1	1	X
fumecheng-12201	129	59	)	)	PUNCT
fumecheng-12201	129	60	cos	cos	PROPN
fumecheng-12201	129	61	(	(	PUNCT
fumecheng-12201	129	62	)	)	PUNCT
fumecheng-12201	129	63	4	4	NUM
fumecheng-12201	129	64	3	3	NUM
fumecheng-12201	129	65	(	(	PUNCT
fumecheng-12201	129	66	1	1	NUM
fumecheng-12201	129	67	)	)	PUNCT
fumecheng-12201	129	68	cos	cos	PROPN
fumecheng-12201	129	69	(	(	PUNCT
fumecheng-12201	129	70	)	)	PUNCT
fumecheng-12201	129	71	4	4	NUM
fumecheng-12201	130	1	t	t	NOUN
fumecheng-12201	130	2	t	t	NOUN
fumecheng-12201	130	3	t	t	PROPN
fumecheng-12201	130	4	t	t	PROPN
fumecheng-12201	130	5	t	t	PROPN
fumecheng-12201	130	6	a	a	DET
fumecheng-12201	130	7	e	e	NOUN
fumecheng-12201	130	8	t	t	NOUN
fumecheng-12201	130	9	a	a	DET
fumecheng-12201	130	10	e	e	NOUN
fumecheng-12201	130	11	t	t	PROPN
fumecheng-12201	130	12	ae	ae	PROPN
fumecheng-12201	130	13	a	a	DET
fumecheng-12201	130	14	t	t	X
fumecheng-12201	130	15	ae	ae	PROPN
fumecheng-12201	130	16	a	a	DET
fumecheng-12201	130	17	t	t	NOUN
fumecheng-12201	130	18	−	−	PROPN
fumecheng-12201	130	19	−	−	PROPN
fumecheng-12201	130	20	−	−	PROPN
fumecheng-12201	131	1	−	−	PROPN
fumecheng-12201	132	1	+	+	CCONJ
fumecheng-12201	132	2			PROPN
fumecheng-12201	132	3			ADV
fumecheng-12201	132	4			ADV
fumecheng-12201	132	5	−	−	PUNCT
fumecheng-12201	133	1	+	+	CCONJ
fumecheng-12201	133	2	−	−	X
fumecheng-12201	133	3	+	+	X
fumecheng-12201	134	1	+	+	PUNCT
fumecheng-12201	134	2	+	+	PUNCT
fumecheng-12201	134	3	+	+	NUM
fumecheng-12201	134	4			ADJ
fumecheng-12201	134	5	=	=	ADJ
fumecheng-12201	134	6	+	+	CCONJ
fumecheng-12201	134	7	−	−	ADP
fumecheng-12201	134	8	−	−	NOUN
fumecheng-12201	134	9	+	+	CCONJ
fumecheng-12201	134	10			NUM
fumecheng-12201	134	11			NUM
fumecheng-12201	134	12			NUM
fumecheng-12201	134	13			NUM
fumecheng-12201	134	14			X
fumecheng-12201	134	15			NUM
fumecheng-12201	134	16			X
fumecheng-12201	134	17			X
fumecheng-12201	134	18			X
fumecheng-12201	134	19			X
fumecheng-12201	134	20			PROPN
fumecheng-12201	134	21			PROPN
fumecheng-12201	134	22			X
fumecheng-12201	134	23			PROPN
fumecheng-12201	134	24			PROPN
fumecheng-12201	134	25			NUM
fumecheng-12201	134	26			X
fumecheng-12201	134	27			X
fumecheng-12201	134	28			X
fumecheng-12201	134	29	(	(	PUNCT
fumecheng-12201	134	30	23	23	NUM
fumecheng-12201	134	31	)	)	PUNCT
fumecheng-12201	134	32	the	the	DET
fumecheng-12201	134	33	residual	residual	ADJ
fumecheng-12201	134	34	integrals	integral	NOUN
fumecheng-12201	134	35	are	be	AUX
fumecheng-12201	134	36	application	application	NOUN
fumecheng-12201	134	37	of	of	ADP
fumecheng-12201	134	38	he	he	PRON
fumecheng-12201	134	39	’s	’s	PART
fumecheng-12201	134	40	frequency	frequency	NOUN
fumecheng-12201	134	41	formula	formula	NOUN
fumecheng-12201	134	42	to	to	PART
fumecheng-12201	134	43	nonlinear	nonlinear	ADJ
fumecheng-12201	134	44	oscillators	oscillator	NOUN
fumecheng-12201	134	45	with	with	ADP
fumecheng-12201	134	46	generalized	generalized	ADJ
fumecheng-12201	134	47	initial	initial	ADJ
fumecheng-12201	134	48	condition	condition	NOUN
fumecheng-12201	134	49	707	707	NUM
fumecheng-12201	134	50	2	2	NUM
fumecheng-12201	134	51	1	1	NUM
fumecheng-12201	134	52	1	1	NUM
fumecheng-12201	134	53	10	10	NUM
fumecheng-12201	134	54	2	2	NUM
fumecheng-12201	134	55	2	2	NUM
fumecheng-12201	134	56	22	22	NUM
fumecheng-12201	134	57	1	1	NUM
fumecheng-12201	134	58	10	10	NUM
fumecheng-12201	134	59	2	2	NUM
fumecheng-12201	134	60	2	2	NUM
fumecheng-12201	134	61	2	2	NUM
fumecheng-12201	134	62	1	1	NUM
fumecheng-12201	134	63	2	2	NUM
fumecheng-12201	134	64	(	(	PUNCT
fumecheng-12201	134	65	)	)	PUNCT
fumecheng-12201	134	66	cos	cos	PROPN
fumecheng-12201	134	67	(	(	PUNCT
fumecheng-12201	134	68	)	)	PUNCT
fumecheng-12201	134	69	d	d	SYM
fumecheng-12201	134	70	2	2	NUM
fumecheng-12201	134	71	3	3	NUM
fumecheng-12201	134	72	(	(	PUNCT
fumecheng-12201	134	73	1	1	NUM
fumecheng-12201	134	74	)	)	PUNCT
fumecheng-12201	134	75	cos	cos	PROPN
fumecheng-12201	134	76	(	(	PUNCT
fumecheng-12201	134	77	)	)	PUNCT
fumecheng-12201	134	78	d	d	SYM
fumecheng-12201	134	79	4	4	NUM
fumecheng-12201	134	80	3	3	NUM
fumecheng-12201	134	81	6	6	NUM
fumecheng-12201	134	82	4	4	NUM
fumecheng-12201	134	83	(	(	PUNCT
fumecheng-12201	134	84	1	1	NUM
fumecheng-12201	134	85	)	)	PUNCT
fumecheng-12201	134	86	4	4	NUM
fumecheng-12201	134	87	5	5	NUM
fumecheng-12201	134	88	t	t	NOUN
fumecheng-12201	134	89	t	t	NOUN
fumecheng-12201	134	90	t	t	NOUN
fumecheng-12201	134	91	r	r	NOUN
fumecheng-12201	134	92	r	r	NOUN
fumecheng-12201	134	93	t	t	NOUN
fumecheng-12201	134	94	t	t	NOUN
fumecheng-12201	134	95	t	t	NOUN
fumecheng-12201	134	96	t	t	PROPN
fumecheng-12201	134	97	=	=	SYM
fumecheng-12201	134	98	ae	ae	PROPN
fumecheng-12201	134	99	a	a	DET
fumecheng-12201	134	100	t	t	NOUN
fumecheng-12201	134	101	t	t	NOUN
fumecheng-12201	134	102	t	t	PROPN
fumecheng-12201	134	103	e	e	PROPN
fumecheng-12201	134	104	a	a	DET
fumecheng-12201	134	105	a	a	DET
fumecheng-12201	134	106	−	−	NOUN
fumecheng-12201	134	107			NOUN
fumecheng-12201	134	108	−	−	PROPN
fumecheng-12201	134	109	=	=	PROPN
fumecheng-12201	135	1	+	+	CCONJ
fumecheng-12201	135	2			ADJ
fumecheng-12201	135	3	+	+	NOUN
fumecheng-12201	135	4	−	−	PROPN
fumecheng-12201	135	5	−	−	PROPN
fumecheng-12201	136	1	+	+	CCONJ
fumecheng-12201	136	2	−	−	PROPN
fumecheng-12201	136	3	=	=	PROPN
fumecheng-12201	136	4	+	+	CCONJ
fumecheng-12201	137	1	−	−	PROPN
fumecheng-12201	138	1	−	−	PROPN
fumecheng-12201	139	1			NOUN
fumecheng-12201	139	2			X
fumecheng-12201	139	3			PUNCT
fumecheng-12201	139	4			NUM
fumecheng-12201	140	1			PROPN
fumecheng-12201	140	2			PROPN
fumecheng-12201	140	3			PROPN
fumecheng-12201	140	4			NUM
fumecheng-12201	140	5			X
fumecheng-12201	140	6			X
fumecheng-12201	140	7			PROPN
fumecheng-12201	140	8			PROPN
fumecheng-12201	140	9			NUM
fumecheng-12201	140	10			X
fumecheng-12201	140	11	(	(	PUNCT
fumecheng-12201	140	12	24	24	NUM
fumecheng-12201	140	13	)	)	SYM
fumecheng-12201	140	14	2	2	NUM
fumecheng-12201	140	15	2	2	NUM
fumecheng-12201	140	16	2	2	NUM
fumecheng-12201	140	17	20	20	NUM
fumecheng-12201	140	18	2	2	NUM
fumecheng-12201	140	19	2	2	NUM
fumecheng-12201	140	20	22	22	NUM
fumecheng-12201	140	21	2	2	NUM
fumecheng-12201	140	22	20	20	NUM
fumecheng-12201	140	23	2	2	NUM
fumecheng-12201	140	24	2	2	NUM
fumecheng-12201	140	25	2	2	NUM
fumecheng-12201	140	26	2	2	NUM
fumecheng-12201	140	27	2	2	NUM
fumecheng-12201	140	28	(	(	PUNCT
fumecheng-12201	140	29	)	)	PUNCT
fumecheng-12201	140	30	cos	cos	PROPN
fumecheng-12201	140	31	(	(	PUNCT
fumecheng-12201	140	32	)	)	PUNCT
fumecheng-12201	140	33	d	d	SYM
fumecheng-12201	140	34	2	2	NUM
fumecheng-12201	140	35	3	3	NUM
fumecheng-12201	140	36	(	(	PUNCT
fumecheng-12201	140	37	1	1	NUM
fumecheng-12201	140	38	)	)	PUNCT
fumecheng-12201	140	39	cos	cos	PROPN
fumecheng-12201	140	40	(	(	PUNCT
fumecheng-12201	140	41	)	)	PUNCT
fumecheng-12201	140	42	d	d	SYM
fumecheng-12201	140	43	4	4	NUM
fumecheng-12201	140	44	3	3	NUM
fumecheng-12201	140	45	6	6	NUM
fumecheng-12201	140	46	4	4	NUM
fumecheng-12201	140	47	(	(	PUNCT
fumecheng-12201	140	48	1	1	NUM
fumecheng-12201	140	49	)	)	PUNCT
fumecheng-12201	140	50	4	4	NUM
fumecheng-12201	140	51	5	5	NUM
fumecheng-12201	140	52	t	t	NOUN
fumecheng-12201	140	53	t	t	NOUN
fumecheng-12201	140	54	t	t	NOUN
fumecheng-12201	140	55	r	r	NOUN
fumecheng-12201	140	56	r	r	NOUN
fumecheng-12201	140	57	t	t	NOUN
fumecheng-12201	140	58	t	t	NOUN
fumecheng-12201	140	59	t	t	NOUN
fumecheng-12201	140	60	t	t	PROPN
fumecheng-12201	140	61	=	=	SYM
fumecheng-12201	140	62	ae	ae	PROPN
fumecheng-12201	140	63	a	a	DET
fumecheng-12201	140	64	t	t	NOUN
fumecheng-12201	140	65	t	t	NOUN
fumecheng-12201	140	66	t	t	PROPN
fumecheng-12201	140	67	e	e	PROPN
fumecheng-12201	140	68	a	a	DET
fumecheng-12201	140	69	a	a	DET
fumecheng-12201	140	70	−	−	NOUN
fumecheng-12201	140	71			NOUN
fumecheng-12201	140	72	−	−	PROPN
fumecheng-12201	140	73	=	=	PROPN
fumecheng-12201	141	1	+	+	CCONJ
fumecheng-12201	141	2			ADJ
fumecheng-12201	141	3	+	+	NOUN
fumecheng-12201	141	4	−	−	PROPN
fumecheng-12201	141	5	−	−	PROPN
fumecheng-12201	142	1	+	+	CCONJ
fumecheng-12201	142	2	−	−	PROPN
fumecheng-12201	142	3	=	=	PROPN
fumecheng-12201	142	4	+	+	CCONJ
fumecheng-12201	143	1	−	−	PROPN
fumecheng-12201	144	1	−	−	PROPN
fumecheng-12201	145	1			NOUN
fumecheng-12201	145	2			X
fumecheng-12201	145	3			PUNCT
fumecheng-12201	145	4			NUM
fumecheng-12201	145	5			PROPN
fumecheng-12201	145	6			PROPN
fumecheng-12201	145	7			PROPN
fumecheng-12201	145	8			NUM
fumecheng-12201	145	9			X
fumecheng-12201	145	10			X
fumecheng-12201	145	11			PROPN
fumecheng-12201	145	12			PROPN
fumecheng-12201	145	13			NUM
fumecheng-12201	145	14			X
fumecheng-12201	145	15	(	(	PUNCT
fumecheng-12201	145	16	25	25	NUM
fumecheng-12201	145	17	)	)	PUNCT
fumecheng-12201	145	18	so	so	ADV
fumecheng-12201	145	19	a	a	DET
fumecheng-12201	145	20	frequency	frequency	NOUN
fumecheng-12201	145	21	formulation	formulation	NOUN
fumecheng-12201	145	22	is	be	AUX
fumecheng-12201	145	23	obtained	obtain	VERB
fumecheng-12201	145	24	,	,	PUNCT
fumecheng-12201	145	25	which	which	PRON
fumecheng-12201	145	26	is	be	AUX
fumecheng-12201	145	27	2	2	NUM
fumecheng-12201	145	28	2	2	NUM
fumecheng-12201	145	29	2	2	NUM
fumecheng-12201	145	30	2	2	NUM
fumecheng-12201	145	31	2	2	NUM
fumecheng-12201	145	32	2	2	NUM
fumecheng-12201	145	33	1	1	NUM
fumecheng-12201	145	34	2	2	NUM
fumecheng-12201	145	35	2	2	NUM
fumecheng-12201	145	36	22	22	NUM
fumecheng-12201	145	37	1	1	NUM
fumecheng-12201	145	38	1	1	NUM
fumecheng-12201	145	39	2	2	NUM
fumecheng-12201	145	40	1	1	NUM
fumecheng-12201	145	41	2	2	NUM
fumecheng-12201	145	42	2	2	NUM
fumecheng-12201	145	43	2	2	NUM
fumecheng-12201	145	44	2	2	NUM
fumecheng-12201	145	45	2	2	NUM
fumecheng-12201	145	46	1	1	NUM
fumecheng-12201	145	47	3	3	NUM
fumecheng-12201	145	48	6	6	NUM
fumecheng-12201	145	49	4	4	NUM
fumecheng-12201	145	50	(	(	PUNCT
fumecheng-12201	145	51	)	)	PUNCT
fumecheng-12201	145	52	(	(	PUNCT
fumecheng-12201	145	53	1	1	X
fumecheng-12201	145	54	)	)	PUNCT
fumecheng-12201	145	55	34	34	NUM
fumecheng-12201	145	56	5	5	NUM
fumecheng-12201	145	57	1	1	NUM
fumecheng-12201	145	58	4	4	NUM
fumecheng-12201	145	59	6	6	NUM
fumecheng-12201	145	60	4	4	NUM
fumecheng-12201	145	61	(	(	PUNCT
fumecheng-12201	145	62	)	)	PUNCT
fumecheng-12201	145	63	5	5	NUM
fumecheng-12201	145	64	e	e	NOUN
fumecheng-12201	145	65	a	a	DET
fumecheng-12201	145	66	a	a	DET
fumecheng-12201	145	67	r	r	NOUN
fumecheng-12201	145	68	r	r	NOUN
fumecheng-12201	145	69	a	a	DET
fumecheng-12201	145	70	r	r	NOUN
fumecheng-12201	145	71	r	r	NOUN
fumecheng-12201	145	72	e	e	NOUN
fumecheng-12201	145	73	a	a	DET
fumecheng-12201	145	74			ADJ
fumecheng-12201	145	75	−	−	PROPN
fumecheng-12201	145	76			NOUN
fumecheng-12201	145	77	−	−	NOUN
fumecheng-12201	145	78	−	−	PROPN
fumecheng-12201	145	79			ADV
fumecheng-12201	145	80	−	−	PUNCT
fumecheng-12201	146	1	+	+	CCONJ
fumecheng-12201	146	2	−	−	NUM
fumecheng-12201	146	3			ADV
fumecheng-12201	146	4	−	−	PUNCT
fumecheng-12201	146	5			ADP
fumecheng-12201	146	6	=	=	PUNCT
fumecheng-12201	146	7	=	=	PUNCT
fumecheng-12201	146	8	=	=	PUNCT
fumecheng-12201	147	1	+	+	NUM
fumecheng-12201	147	2	−	−	PROPN
fumecheng-12201	148	1	−	−	NOUN
fumecheng-12201	148	2	−	−	PROPN
fumecheng-12201	148	3			ADJ
fumecheng-12201	148	4	−	−	PUNCT
fumecheng-12201	148	5			X
fumecheng-12201	148	6			X
fumecheng-12201	148	7			PROPN
fumecheng-12201	148	8			PROPN
fumecheng-12201	148	9			NUM
fumecheng-12201	148	10			X
fumecheng-12201	148	11			X
fumecheng-12201	148	12			PROPN
fumecheng-12201	148	13			PROPN
fumecheng-12201	148	14			NUM
fumecheng-12201	148	15			X
fumecheng-12201	148	16			X
fumecheng-12201	148	17	(	(	PUNCT
fumecheng-12201	148	18	26	26	NUM
fumecheng-12201	148	19	)	)	PUNCT
fumecheng-12201	148	20	in	in	ADP
fumecheng-12201	148	21	addition	addition	NOUN
fumecheng-12201	148	22	,	,	PUNCT
fumecheng-12201	148	23	the	the	DET
fumecheng-12201	148	24	frequency	frequency	NOUN
fumecheng-12201	148	25	equation	equation	NOUN
fumecheng-12201	148	26	of	of	ADP
fumecheng-12201	148	27	eq	eq	PROPN
fumecheng-12201	148	28	.	.	PUNCT
fumecheng-12201	149	1	(	(	PUNCT
fumecheng-12201	149	2	20	20	NUM
fumecheng-12201	149	3	)	)	PUNCT
fumecheng-12201	149	4	can	can	AUX
fumecheng-12201	149	5	be	be	AUX
fumecheng-12201	149	6	found	find	VERB
fumecheng-12201	149	7	by	by	ADP
fumecheng-12201	149	8	(	(	PUNCT
fumecheng-12201	149	9	)	)	PUNCT
fumecheng-12201	149	10	cos	cos	PROPN
fumecheng-12201	149	11	(	(	PUNCT
fumecheng-12201	149	12	)	)	PUNCT
fumecheng-12201	149	13	tu	tu	PROPN
fumecheng-12201	149	14	t	t	PROPN
fumecheng-12201	149	15	ae	ae	PROPN
fumecheng-12201	149	16	t−	t−	PROPN
fumecheng-12201	149	17	=	=	PROPN
fumecheng-12201	150	1	+	+	AUX
fumecheng-12201	150	2			NUM
fumecheng-12201	150	3			X
fumecheng-12201	150	4			X
fumecheng-12201	150	5	(	(	PUNCT
fumecheng-12201	150	6	27	27	NUM
fumecheng-12201	150	7	)	)	PUNCT
fumecheng-12201	150	8	(	(	PUNCT
fumecheng-12201	150	9	0	0	NUM
fumecheng-12201	150	10	)	)	PUNCT
fumecheng-12201	150	11	cos	cos	AUX
fumecheng-12201	150	12	sinu	sinu	VERB
fumecheng-12201	150	13	a	a	DET
fumecheng-12201	150	14	a	a	DET
fumecheng-12201	150	15	a	a	X
fumecheng-12201	150	16			X
fumecheng-12201	150	17			PROPN
fumecheng-12201	150	18			PROPN
fumecheng-12201	150	19	=	=	PROPN
fumecheng-12201	151	1	−	−	PROPN
fumecheng-12201	152	1	−	−	PROPN
fumecheng-12201	152	2	=	=	SYM
fumecheng-12201	152	3	(	(	PUNCT
fumecheng-12201	152	4	28	28	NUM
fumecheng-12201	152	5	)	)	PUNCT
fumecheng-12201	152	6	(	(	PUNCT
fumecheng-12201	152	7	0	0	X
fumecheng-12201	152	8	)	)	PUNCT
fumecheng-12201	152	9	cosu	cosu	VERB
fumecheng-12201	152	10	a	a	DET
fumecheng-12201	152	11	b=	b=	NOUN
fumecheng-12201	152	12	=	=	SYM
fumecheng-12201	152	13	(	(	PUNCT
fumecheng-12201	152	14	29	29	NUM
fumecheng-12201	152	15	)	)	PUNCT
fumecheng-12201	152	16	combining	combine	VERB
fumecheng-12201	152	17	eq	eq	NOUN
fumecheng-12201	152	18	.	.	PUNCT
fumecheng-12201	153	1	(	(	PUNCT
fumecheng-12201	153	2	28	28	NUM
fumecheng-12201	153	3	)	)	PUNCT
fumecheng-12201	153	4	and	and	CCONJ
fumecheng-12201	153	5	eq	eq	NOUN
fumecheng-12201	153	6	.	.	PUNCT
fumecheng-12201	154	1	(	(	PUNCT
fumecheng-12201	154	2	29	29	NUM
fumecheng-12201	154	3	)	)	PUNCT
fumecheng-12201	154	4	yields	yield	VERB
fumecheng-12201	154	5	2	2	NUM
fumecheng-12201	154	6	2	2	NUM
fumecheng-12201	154	7	2	2	NUM
fumecheng-12201	154	8	2	2	NUM
fumecheng-12201	154	9	(	(	PUNCT
fumecheng-12201	154	10	cos	cos	PROPN
fumecheng-12201	154	11	)	)	PUNCT
fumecheng-12201	154	12	a	a	DET
fumecheng-12201	154	13	a	a	DET
fumecheng-12201	154	14	a	a	DET
fumecheng-12201	154	15	b	b	NOUN
fumecheng-12201	154	16	+	+	CCONJ
fumecheng-12201	154	17			ADJ
fumecheng-12201	154	18	=	=	SYM
fumecheng-12201	154	19	−	−	PROPN
fumecheng-12201	154	20			NUM
fumecheng-12201	154	21			X
fumecheng-12201	154	22			X
fumecheng-12201	154	23	(	(	PUNCT
fumecheng-12201	154	24	30	30	NUM
fumecheng-12201	154	25	)	)	PUNCT
fumecheng-12201	154	26	in	in	ADP
fumecheng-12201	154	27	the	the	DET
fumecheng-12201	154	28	following	following	NOUN
fumecheng-12201	154	29	,	,	PUNCT
fumecheng-12201	154	30	we	we	PRON
fumecheng-12201	154	31	will	will	AUX
fumecheng-12201	154	32	use	use	VERB
fumecheng-12201	154	33	numerical	numerical	ADJ
fumecheng-12201	154	34	simulation	simulation	NOUN
fumecheng-12201	154	35	to	to	PART
fumecheng-12201	154	36	analyze	analyze	VERB
fumecheng-12201	154	37	the	the	DET
fumecheng-12201	154	38	impact	impact	NOUN
fumecheng-12201	154	39	of	of	ADP
fumecheng-12201	154	40	the	the	DET
fumecheng-12201	154	41	variation	variation	NOUN
fumecheng-12201	154	42	of	of	ADP
fumecheng-12201	154	43	the	the	DET
fumecheng-12201	154	44	damping	damp	VERB
fumecheng-12201	154	45	term	term	NOUN
fumecheng-12201	154	46	on	on	ADP
fumecheng-12201	154	47	nonlinear	nonlinear	ADJ
fumecheng-12201	154	48	oscillators	oscillator	NOUN
fumecheng-12201	154	49	with	with	ADP
fumecheng-12201	154	50	generalized	generalized	ADJ
fumecheng-12201	154	51	initial	initial	ADJ
fumecheng-12201	154	52	conditions	condition	NOUN
fumecheng-12201	154	53	.	.	PUNCT
fumecheng-12201	155	1	in	in	ADP
fumecheng-12201	155	2	order	order	NOUN
fumecheng-12201	155	3	to	to	PART
fumecheng-12201	155	4	better	well	ADV
fumecheng-12201	155	5	align	align	VERB
fumecheng-12201	155	6	with	with	ADP
fumecheng-12201	155	7	the	the	DET
fumecheng-12201	155	8	actual	actual	ADJ
fumecheng-12201	155	9	operating	operating	NOUN
fumecheng-12201	155	10	conditions	condition	NOUN
fumecheng-12201	155	11	of	of	ADP
fumecheng-12201	155	12	the	the	DET
fumecheng-12201	155	13	machinery	machinery	NOUN
fumecheng-12201	155	14	,	,	PUNCT
fumecheng-12201	155	15	we	we	PRON
fumecheng-12201	155	16	make	make	VERB
fumecheng-12201	155	17	the	the	DET
fumecheng-12201	155	18	values	value	NOUN
fumecheng-12201	155	19	of	of	ADP
fumecheng-12201	155	20	a	a	DET
fumecheng-12201	155	21	and	and	CCONJ
fumecheng-12201	155	22	b	b	NOUN
fumecheng-12201	155	23	vary	vary	NOUN
fumecheng-12201	155	24	from	from	ADP
fumecheng-12201	155	25	small	small	ADJ
fumecheng-12201	155	26	to	to	ADP
fumecheng-12201	155	27	large	large	ADJ
fumecheng-12201	155	28	.	.	PUNCT
fumecheng-12201	156	1	fig	fig	NOUN
fumecheng-12201	156	2	.	.	PUNCT
fumecheng-12201	157	1	2	2	NUM
fumecheng-12201	157	2	-	-	PUNCT
fumecheng-12201	157	3	fig	fig	NOUN
fumecheng-12201	157	4	.	.	PUNCT
fumecheng-12201	157	5	4	4	NUM
fumecheng-12201	157	6	show	show	VERB
fumecheng-12201	157	7	the	the	DET
fumecheng-12201	157	8	fitting	fitting	ADJ
fumecheng-12201	157	9	results	result	NOUN
fumecheng-12201	157	10	of	of	ADP
fumecheng-12201	157	11	the	the	DET
fumecheng-12201	157	12	exact	exact	ADJ
fumecheng-12201	157	13	and	and	CCONJ
fumecheng-12201	157	14	approximate	approximate	ADJ
fumecheng-12201	157	15	solutions	solution	NOUN
fumecheng-12201	157	16	when	when	SCONJ
fumecheng-12201	157	17	the	the	DET
fumecheng-12201	157	18	damping	damp	VERB
fumecheng-12201	157	19	η	η	PROPN
fumecheng-12201	157	20	is	be	AUX
fumecheng-12201	157	21	varied	varied	ADJ
fumecheng-12201	157	22	,	,	PUNCT
fumecheng-12201	157	23	respectively	respectively	ADV
fumecheng-12201	157	24	.	.	PUNCT
fumecheng-12201	158	1	708	708	NUM
fumecheng-12201	158	2	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	158	3	,	,	PUNCT
fumecheng-12201	158	4	q.r.song	q.r.song	PROPN
fumecheng-12201	158	5	,	,	PUNCT
fumecheng-12201	158	6	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	158	7	,	,	PUNCT
fumecheng-12201	158	8	f.wang	f.wang	NOUN
fumecheng-12201	158	9	in	in	ADP
fumecheng-12201	158	10	fig	fig	NOUN
fumecheng-12201	158	11	.	.	PUNCT
fumecheng-12201	159	1	2	2	NUM
fumecheng-12201	159	2	,	,	PUNCT
fumecheng-12201	159	3	we	we	PRON
fumecheng-12201	159	4	choose	choose	VERB
fumecheng-12201	159	5	η=0.01	η=0.01	NOUN
fumecheng-12201	159	6	and	and	CCONJ
fumecheng-12201	159	7	let	let	VERB
fumecheng-12201	159	8	(	(	PUNCT
fumecheng-12201	159	9	a	a	DET
fumecheng-12201	159	10	,	,	PUNCT
fumecheng-12201	159	11	b	b	NOUN
fumecheng-12201	159	12	)	)	PUNCT
fumecheng-12201	159	13	vary	vary	VERB
fumecheng-12201	159	14	from	from	ADP
fumecheng-12201	159	15	0.2	0.2	NUM
fumecheng-12201	159	16	to	to	ADP
fumecheng-12201	159	17	1000	1000	NUM
fumecheng-12201	159	18	,	,	PUNCT
fumecheng-12201	159	19	where	where	SCONJ
fumecheng-12201	159	20	the	the	DET
fumecheng-12201	159	21	blue	blue	ADJ
fumecheng-12201	159	22	curve	curve	NOUN
fumecheng-12201	159	23	denotes	denote	VERB
fumecheng-12201	159	24	the	the	DET
fumecheng-12201	159	25	exact	exact	ADJ
fumecheng-12201	159	26	solution	solution	NOUN
fumecheng-12201	159	27	and	and	CCONJ
fumecheng-12201	159	28	the	the	DET
fumecheng-12201	159	29	red	red	ADJ
fumecheng-12201	159	30	denotes	denote	NOUN
fumecheng-12201	159	31	the	the	DET
fumecheng-12201	159	32	approximate	approximate	ADJ
fumecheng-12201	159	33	solution	solution	NOUN
fumecheng-12201	159	34	based	base	VERB
fumecheng-12201	159	35	on	on	ADP
fumecheng-12201	159	36	he	he	PRON
fumecheng-12201	159	37	’s	’s	PART
fumecheng-12201	159	38	frequency	frequency	NOUN
fumecheng-12201	159	39	formulation	formulation	NOUN
fumecheng-12201	159	40	.	.	PUNCT
fumecheng-12201	160	1	the	the	DET
fumecheng-12201	160	2	two	two	NUM
fumecheng-12201	160	3	curves	curve	NOUN
fumecheng-12201	160	4	are	be	AUX
fumecheng-12201	160	5	highly	highly	ADV
fumecheng-12201	160	6	fitted	fit	VERB
fumecheng-12201	160	7	as	as	SCONJ
fumecheng-12201	160	8	can	can	AUX
fumecheng-12201	160	9	be	be	AUX
fumecheng-12201	160	10	seen	see	VERB
fumecheng-12201	160	11	in	in	ADP
fumecheng-12201	160	12	the	the	DET
fumecheng-12201	160	13	figure	figure	NOUN
fumecheng-12201	160	14	.	.	PUNCT
fumecheng-12201	161	1	(	(	PUNCT
fumecheng-12201	161	2	a	a	DET
fumecheng-12201	161	3	,	,	PUNCT
fumecheng-12201	161	4	b)=(0.2,0.2	b)=(0.2,0.2	PROPN
fumecheng-12201	161	5	)	)	PUNCT
fumecheng-12201	161	6	(	(	PUNCT
fumecheng-12201	161	7	a	a	DET
fumecheng-12201	161	8	,	,	PUNCT
fumecheng-12201	161	9	b)=(10,10	b)=(10,10	PROPN
fumecheng-12201	161	10	)	)	PUNCT
fumecheng-12201	161	11	(	(	PUNCT
fumecheng-12201	161	12	a	a	PRON
fumecheng-12201	161	13	,	,	PUNCT
fumecheng-12201	161	14	b)=(99,100	b)=(99,100	PROPN
fumecheng-12201	161	15	)	)	PUNCT
fumecheng-12201	161	16	(	(	PUNCT
fumecheng-12201	161	17	a	a	PRON
fumecheng-12201	161	18	,	,	PUNCT
fumecheng-12201	161	19	b)=(1000,1000	b)=(1000,1000	ADJ
fumecheng-12201	161	20	)	)	PUNCT
fumecheng-12201	161	21	fig	fig	NOUN
fumecheng-12201	161	22	.	.	NOUN
fumecheng-12201	162	1	2	2	NUM
fumecheng-12201	162	2	when	when	SCONJ
fumecheng-12201	162	3	η=0.01	η=0.01	NOUN
fumecheng-12201	162	4	,	,	PUNCT
fumecheng-12201	162	5	the	the	DET
fumecheng-12201	162	6	comparison	comparison	NOUN
fumecheng-12201	162	7	between	between	ADP
fumecheng-12201	162	8	the	the	DET
fumecheng-12201	162	9	exact	exact	ADJ
fumecheng-12201	162	10	solution	solution	NOUN
fumecheng-12201	162	11	and	and	CCONJ
fumecheng-12201	162	12	the	the	DET
fumecheng-12201	162	13	approximate	approximate	ADJ
fumecheng-12201	162	14	one	one	NUM
fumecheng-12201	162	15	based	base	VERB
fumecheng-12201	162	16	on	on	ADP
fumecheng-12201	162	17	he	he	PRON
fumecheng-12201	162	18	’s	’s	PART
fumecheng-12201	162	19	frequency	frequency	NOUN
fumecheng-12201	162	20	formulation	formulation	NOUN
fumecheng-12201	162	21	for	for	ADP
fumecheng-12201	162	22	taking	take	VERB
fumecheng-12201	162	23	different	different	ADJ
fumecheng-12201	162	24	values	value	NOUN
fumecheng-12201	162	25	of	of	ADP
fumecheng-12201	162	26	(	(	PUNCT
fumecheng-12201	162	27	a	a	DET
fumecheng-12201	162	28	,	,	PUNCT
fumecheng-12201	162	29	b	b	NOUN
fumecheng-12201	162	30	)	)	PUNCT
fumecheng-12201	162	31	when	when	SCONJ
fumecheng-12201	162	32	η=0.1	η=0.1	NOUN
fumecheng-12201	162	33	,	,	PUNCT
fumecheng-12201	162	34	considering	consider	VERB
fumecheng-12201	162	35	that	that	SCONJ
fumecheng-12201	162	36	the	the	DET
fumecheng-12201	162	37	nonlinear	nonlinear	ADJ
fumecheng-12201	162	38	vibrations	vibration	NOUN
fumecheng-12201	162	39	in	in	ADP
fumecheng-12201	162	40	the	the	DET
fumecheng-12201	162	41	actual	actual	ADJ
fumecheng-12201	162	42	working	work	VERB
fumecheng-12201	162	43	conditions	condition	NOUN
fumecheng-12201	162	44	are	be	AUX
fumecheng-12201	162	45	all	all	PRON
fumecheng-12201	162	46	large	large	ADJ
fumecheng-12201	162	47	parameters	parameter	NOUN
fumecheng-12201	162	48	,	,	PUNCT
fumecheng-12201	162	49	as	as	SCONJ
fumecheng-12201	162	50	we	we	PRON
fumecheng-12201	162	51	take	take	VERB
fumecheng-12201	162	52	(	(	PUNCT
fumecheng-12201	162	53	a	a	DET
fumecheng-12201	162	54	,	,	PUNCT
fumecheng-12201	162	55	b	b	NOUN
fumecheng-12201	162	56	)	)	PUNCT
fumecheng-12201	162	57	from	from	ADP
fumecheng-12201	162	58	1	1	NUM
fumecheng-12201	162	59	to	to	ADP
fumecheng-12201	162	60	1000	1000	NUM
fumecheng-12201	162	61	,	,	PUNCT
fumecheng-12201	162	62	respectively	respectively	ADV
fumecheng-12201	162	63	.	.	PUNCT
fumecheng-12201	163	1	the	the	DET
fumecheng-12201	163	2	resulting	result	VERB
fumecheng-12201	163	3	figure	figure	NOUN
fumecheng-12201	163	4	is	be	AUX
fumecheng-12201	163	5	shown	show	VERB
fumecheng-12201	163	6	in	in	ADP
fumecheng-12201	163	7	fig	fig	NOUN
fumecheng-12201	163	8	.	.	PUNCT
fumecheng-12201	164	1	3	3	X
fumecheng-12201	164	2	.	.	X
fumecheng-12201	164	3	from	from	ADP
fumecheng-12201	164	4	the	the	DET
fumecheng-12201	164	5	figure	figure	NOUN
fumecheng-12201	164	6	,	,	PUNCT
fumecheng-12201	164	7	we	we	PRON
fumecheng-12201	164	8	can	can	AUX
fumecheng-12201	164	9	not	not	PART
fumecheng-12201	164	10	only	only	ADV
fumecheng-12201	164	11	see	see	VERB
fumecheng-12201	164	12	that	that	SCONJ
fumecheng-12201	164	13	the	the	DET
fumecheng-12201	164	14	increase	increase	NOUN
fumecheng-12201	164	15	of	of	ADP
fumecheng-12201	164	16	damping	damp	VERB
fumecheng-12201	164	17	makes	make	VERB
fumecheng-12201	164	18	the	the	DET
fumecheng-12201	164	19	system	system	NOUN
fumecheng-12201	164	20	amplitude	amplitude	NOUN
fumecheng-12201	164	21	gradually	gradually	ADV
fumecheng-12201	164	22	decrease	decrease	VERB
fumecheng-12201	164	23	,	,	PUNCT
fumecheng-12201	164	24	but	but	CCONJ
fumecheng-12201	164	25	also	also	ADV
fumecheng-12201	164	26	find	find	VERB
fumecheng-12201	164	27	that	that	SCONJ
fumecheng-12201	164	28	the	the	DET
fumecheng-12201	164	29	exact	exact	ADJ
fumecheng-12201	164	30	and	and	CCONJ
fumecheng-12201	164	31	approximate	approximate	ADJ
fumecheng-12201	164	32	solutions	solution	NOUN
fumecheng-12201	164	33	are	be	AUX
fumecheng-12201	164	34	in	in	ADP
fumecheng-12201	164	35	good	good	ADJ
fumecheng-12201	164	36	agreement	agreement	NOUN
fumecheng-12201	164	37	.	.	PUNCT
fumecheng-12201	165	1	in	in	ADP
fumecheng-12201	165	2	addition	addition	NOUN
fumecheng-12201	165	3	,	,	PUNCT
fumecheng-12201	165	4	compared	compare	VERB
fumecheng-12201	165	5	to	to	ADP
fumecheng-12201	165	6	fig	fig	NOUN
fumecheng-12201	165	7	.	.	PUNCT
fumecheng-12201	166	1	2	2	NUM
fumecheng-12201	166	2	,	,	PUNCT
fumecheng-12201	166	3	the	the	DET
fumecheng-12201	166	4	magnitude	magnitude	NOUN
fumecheng-12201	166	5	of	of	ADP
fumecheng-12201	166	6	the	the	DET
fumecheng-12201	166	7	system	system	NOUN
fumecheng-12201	166	8	amplitude	amplitude	NOUN
fumecheng-12201	166	9	reduction	reduction	NOUN
fumecheng-12201	166	10	is	be	AUX
fumecheng-12201	166	11	more	more	ADV
fumecheng-12201	166	12	pronounced	pronounced	ADJ
fumecheng-12201	166	13	when	when	SCONJ
fumecheng-12201	166	14	the	the	DET
fumecheng-12201	166	15	damping	damp	VERB
fumecheng-12201	166	16	is	be	AUX
fumecheng-12201	166	17	increased	increase	VERB
fumecheng-12201	166	18	from	from	ADP
fumecheng-12201	166	19	0.01	0.01	NUM
fumecheng-12201	166	20	to	to	ADP
fumecheng-12201	166	21	0.1	0.1	NUM
fumecheng-12201	166	22	.	.	PUNCT
fumecheng-12201	167	1	application	application	NOUN
fumecheng-12201	167	2	of	of	ADP
fumecheng-12201	167	3	he	he	PRON
fumecheng-12201	167	4	’s	’s	PART
fumecheng-12201	167	5	frequency	frequency	NOUN
fumecheng-12201	167	6	formula	formula	NOUN
fumecheng-12201	167	7	to	to	PART
fumecheng-12201	167	8	nonlinear	nonlinear	ADJ
fumecheng-12201	167	9	oscillators	oscillator	NOUN
fumecheng-12201	167	10	with	with	ADP
fumecheng-12201	167	11	generalized	generalized	ADJ
fumecheng-12201	167	12	initial	initial	ADJ
fumecheng-12201	167	13	condition	condition	NOUN
fumecheng-12201	167	14	709	709	NUM
fumecheng-12201	167	15	(	(	PUNCT
fumecheng-12201	167	16	a	a	DET
fumecheng-12201	167	17	,	,	PUNCT
fumecheng-12201	167	18	b)=(1,1	b)=(1,1	NOUN
fumecheng-12201	167	19	)	)	PUNCT
fumecheng-12201	167	20	(	(	PUNCT
fumecheng-12201	167	21	a	a	DET
fumecheng-12201	167	22	,	,	PUNCT
fumecheng-12201	167	23	b)=(10,10	b)=(10,10	PROPN
fumecheng-12201	167	24	)	)	PUNCT
fumecheng-12201	167	25	(	(	PUNCT
fumecheng-12201	167	26	a	a	PRON
fumecheng-12201	167	27	,	,	PUNCT
fumecheng-12201	167	28	b)=(99,100	b)=(99,100	PROPN
fumecheng-12201	167	29	)	)	PUNCT
fumecheng-12201	167	30	(	(	PUNCT
fumecheng-12201	167	31	a	a	PRON
fumecheng-12201	167	32	,	,	PUNCT
fumecheng-12201	167	33	b)=(1000,1000	b)=(1000,1000	ADJ
fumecheng-12201	167	34	)	)	PUNCT
fumecheng-12201	167	35	fig	fig	NOUN
fumecheng-12201	167	36	.	.	PUNCT
fumecheng-12201	168	1	3	3	NUM
fumecheng-12201	168	2	when	when	SCONJ
fumecheng-12201	168	3	η=0.1	η=0.1	NOUN
fumecheng-12201	168	4	,	,	PUNCT
fumecheng-12201	168	5	the	the	DET
fumecheng-12201	168	6	comparison	comparison	NOUN
fumecheng-12201	168	7	between	between	ADP
fumecheng-12201	168	8	the	the	DET
fumecheng-12201	168	9	exact	exact	ADJ
fumecheng-12201	168	10	solution	solution	NOUN
fumecheng-12201	168	11	and	and	CCONJ
fumecheng-12201	168	12	the	the	DET
fumecheng-12201	168	13	approximate	approximate	ADJ
fumecheng-12201	168	14	one	one	NUM
fumecheng-12201	168	15	based	base	VERB
fumecheng-12201	168	16	on	on	ADP
fumecheng-12201	168	17	he	he	PRON
fumecheng-12201	168	18	’s	’s	PART
fumecheng-12201	168	19	frequency	frequency	NOUN
fumecheng-12201	168	20	formulation	formulation	NOUN
fumecheng-12201	168	21	for	for	ADP
fumecheng-12201	168	22	taking	take	VERB
fumecheng-12201	168	23	different	different	ADJ
fumecheng-12201	168	24	values	value	NOUN
fumecheng-12201	168	25	of	of	ADP
fumecheng-12201	168	26	(	(	PUNCT
fumecheng-12201	168	27	a	a	DET
fumecheng-12201	168	28	,	,	PUNCT
fumecheng-12201	168	29	b	b	NOUN
fumecheng-12201	168	30	)	)	PUNCT
fumecheng-12201	168	31	to	to	PART
fumecheng-12201	168	32	further	far	ADV
fumecheng-12201	168	33	verify	verify	VERB
fumecheng-12201	168	34	the	the	DET
fumecheng-12201	168	35	conclusion	conclusion	NOUN
fumecheng-12201	168	36	,	,	PUNCT
fumecheng-12201	168	37	we	we	PRON
fumecheng-12201	168	38	increase	increase	VERB
fumecheng-12201	168	39	the	the	DET
fumecheng-12201	168	40	damping	damp	VERB
fumecheng-12201	168	41	so	so	SCONJ
fumecheng-12201	168	42	that	that	SCONJ
fumecheng-12201	168	43	η=0.15	η=0.15	NOUN
fumecheng-12201	168	44	and	and	CCONJ
fumecheng-12201	168	45	(	(	PUNCT
fumecheng-12201	168	46	a	a	DET
fumecheng-12201	168	47	,	,	PUNCT
fumecheng-12201	168	48	b	b	NOUN
fumecheng-12201	168	49	)	)	PUNCT
fumecheng-12201	168	50	is	be	AUX
fumecheng-12201	168	51	varied	varied	ADJ
fumecheng-12201	168	52	from	from	ADP
fumecheng-12201	168	53	25	25	NUM
fumecheng-12201	168	54	to	to	ADP
fumecheng-12201	168	55	2500	2500	NUM
fumecheng-12201	168	56	.	.	PUNCT
fumecheng-12201	169	1	the	the	DET
fumecheng-12201	169	2	image	image	NOUN
fumecheng-12201	169	3	is	be	AUX
fumecheng-12201	169	4	displayed	display	VERB
fumecheng-12201	169	5	in	in	ADP
fumecheng-12201	169	6	fig	fig	NOUN
fumecheng-12201	169	7	.	.	PUNCT
fumecheng-12201	170	1	4	4	X
fumecheng-12201	170	2	.	.	X
fumecheng-12201	170	3	the	the	DET
fumecheng-12201	170	4	numerical	numerical	PROPN
fumecheng-12201	170	5	simulation	simulation	PROPN
fumecheng-12201	170	6	shows	show	VERB
fumecheng-12201	170	7	that	that	SCONJ
fumecheng-12201	170	8	even	even	ADV
fumecheng-12201	170	9	if	if	SCONJ
fumecheng-12201	170	10	we	we	PRON
fumecheng-12201	170	11	increase	increase	VERB
fumecheng-12201	170	12	the	the	DET
fumecheng-12201	170	13	damping	damping	NOUN
fumecheng-12201	170	14	and	and	CCONJ
fumecheng-12201	170	15	the	the	DET
fumecheng-12201	170	16	initial	initial	ADJ
fumecheng-12201	170	17	values	value	NOUN
fumecheng-12201	170	18	,	,	PUNCT
fumecheng-12201	170	19	the	the	DET
fumecheng-12201	170	20	approximate	approximate	ADJ
fumecheng-12201	170	21	solution	solution	NOUN
fumecheng-12201	170	22	based	base	VERB
fumecheng-12201	170	23	on	on	ADP
fumecheng-12201	170	24	he	he	PRON
fumecheng-12201	170	25	’s	’s	PART
fumecheng-12201	170	26	frequency	frequency	NOUN
fumecheng-12201	170	27	formulation	formulation	NOUN
fumecheng-12201	170	28	still	still	ADV
fumecheng-12201	170	29	agrees	agree	VERB
fumecheng-12201	170	30	with	with	ADP
fumecheng-12201	170	31	the	the	DET
fumecheng-12201	170	32	exact	exact	ADJ
fumecheng-12201	170	33	solution	solution	NOUN
fumecheng-12201	170	34	from	from	ADP
fumecheng-12201	170	35	the	the	DET
fumecheng-12201	170	36	runge	runge	NOUN
fumecheng-12201	170	37	-	-	PUNCT
fumecheng-12201	170	38	kutta	kutta	NOUN
fumecheng-12201	170	39	method	method	NOUN
fumecheng-12201	170	40	.	.	PUNCT
fumecheng-12201	171	1	in	in	ADP
fumecheng-12201	171	2	addition	addition	NOUN
fumecheng-12201	171	3	,	,	PUNCT
fumecheng-12201	171	4	combined	combine	VERB
fumecheng-12201	171	5	with	with	ADP
fumecheng-12201	171	6	fig	fig	NOUN
fumecheng-12201	171	7	.	.	PUNCT
fumecheng-12201	172	1	2	2	NUM
fumecheng-12201	172	2	,	,	PUNCT
fumecheng-12201	172	3	fig	fig	NOUN
fumecheng-12201	172	4	.	.	NOUN
fumecheng-12201	172	5	3	3	NUM
fumecheng-12201	172	6	and	and	CCONJ
fumecheng-12201	172	7	fig	fig	NOUN
fumecheng-12201	172	8	.	.	PUNCT
fumecheng-12201	173	1	4	4	NUM
fumecheng-12201	173	2	,	,	PUNCT
fumecheng-12201	173	3	we	we	PRON
fumecheng-12201	173	4	can	can	AUX
fumecheng-12201	173	5	observe	observe	VERB
fumecheng-12201	173	6	that	that	SCONJ
fumecheng-12201	173	7	a	a	DET
fumecheng-12201	173	8	small	small	ADJ
fumecheng-12201	173	9	change	change	NOUN
fumecheng-12201	173	10	in	in	ADP
fumecheng-12201	173	11	the	the	DET
fumecheng-12201	173	12	damping	damp	VERB
fumecheng-12201	173	13	term	term	NOUN
fumecheng-12201	173	14	can	can	AUX
fumecheng-12201	173	15	make	make	VERB
fumecheng-12201	173	16	the	the	DET
fumecheng-12201	173	17	amplitude	amplitude	NOUN
fumecheng-12201	173	18	oscillation	oscillation	NOUN
fumecheng-12201	173	19	of	of	ADP
fumecheng-12201	173	20	the	the	DET
fumecheng-12201	173	21	oscillator	oscillator	NOUN
fumecheng-12201	173	22	solution	solution	NOUN
fumecheng-12201	173	23	curve	curve	VERB
fumecheng-12201	173	24	more	more	ADV
fumecheng-12201	173	25	significant	significant	ADJ
fumecheng-12201	173	26	,	,	PUNCT
fumecheng-12201	173	27	and	and	CCONJ
fumecheng-12201	173	28	the	the	DET
fumecheng-12201	173	29	solution	solution	NOUN
fumecheng-12201	173	30	curve	curve	NOUN
fumecheng-12201	173	31	will	will	AUX
fumecheng-12201	173	32	gradually	gradually	ADV
fumecheng-12201	173	33	approach	approach	VERB
fumecheng-12201	173	34	equilibrium	equilibrium	NOUN
fumecheng-12201	173	35	over	over	ADP
fumecheng-12201	173	36	time	time	NOUN
fumecheng-12201	173	37	.	.	PUNCT
fumecheng-12201	174	1	710	710	NUM
fumecheng-12201	174	2	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	174	3	,	,	PUNCT
fumecheng-12201	174	4	q.r.song	q.r.song	PROPN
fumecheng-12201	174	5	,	,	PUNCT
fumecheng-12201	174	6	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	174	7	,	,	PUNCT
fumecheng-12201	174	8	f.wang	f.wang	X
fumecheng-12201	174	9	(	(	PUNCT
fumecheng-12201	174	10	a	a	PRON
fumecheng-12201	174	11	,	,	PUNCT
fumecheng-12201	174	12	b)=(25,30	b)=(25,30	PROPN
fumecheng-12201	174	13	)	)	PUNCT
fumecheng-12201	174	14	(	(	PUNCT
fumecheng-12201	174	15	a	a	PRON
fumecheng-12201	174	16	,	,	PUNCT
fumecheng-12201	174	17	b)=(100,120	b)=(100,120	NOUN
fumecheng-12201	174	18	)	)	PUNCT
fumecheng-12201	174	19	(	(	PUNCT
fumecheng-12201	174	20	a	a	PRON
fumecheng-12201	174	21	,	,	PUNCT
fumecheng-12201	174	22	b)=(1100,1300	b)=(1100,1300	PROPN
fumecheng-12201	174	23	)	)	PUNCT
fumecheng-12201	174	24	(	(	PUNCT
fumecheng-12201	174	25	a	a	PRON
fumecheng-12201	174	26	,	,	PUNCT
fumecheng-12201	174	27	b)=(2500,3000	b)=(2500,3000	NUM
fumecheng-12201	174	28	)	)	PUNCT
fumecheng-12201	174	29	fig	fig	NOUN
fumecheng-12201	174	30	.	.	PUNCT
fumecheng-12201	174	31	4	4	NUM
fumecheng-12201	175	1	when	when	SCONJ
fumecheng-12201	175	2	η=0.15	η=0.15	NOUN
fumecheng-12201	175	3	,	,	PUNCT
fumecheng-12201	175	4	the	the	DET
fumecheng-12201	175	5	comparison	comparison	NOUN
fumecheng-12201	175	6	between	between	ADP
fumecheng-12201	175	7	the	the	DET
fumecheng-12201	175	8	exact	exact	ADJ
fumecheng-12201	175	9	solution	solution	NOUN
fumecheng-12201	175	10	and	and	CCONJ
fumecheng-12201	175	11	the	the	DET
fumecheng-12201	175	12	approximate	approximate	ADJ
fumecheng-12201	175	13	one	one	NUM
fumecheng-12201	175	14	based	base	VERB
fumecheng-12201	175	15	on	on	ADP
fumecheng-12201	175	16	he	he	PRON
fumecheng-12201	175	17	’s	’s	PART
fumecheng-12201	175	18	frequency	frequency	NOUN
fumecheng-12201	175	19	formulation	formulation	NOUN
fumecheng-12201	175	20	for	for	ADP
fumecheng-12201	175	21	taking	take	VERB
fumecheng-12201	175	22	different	different	ADJ
fumecheng-12201	175	23	values	value	NOUN
fumecheng-12201	175	24	of	of	ADP
fumecheng-12201	175	25	(	(	PUNCT
fumecheng-12201	175	26	a	a	DET
fumecheng-12201	175	27	,	,	PUNCT
fumecheng-12201	175	28	b	b	NOUN
fumecheng-12201	175	29	)	)	PUNCT
fumecheng-12201	175	30	5	5	NUM
fumecheng-12201	175	31	.	.	X
fumecheng-12201	175	32	conclusion	conclusion	NOUN
fumecheng-12201	175	33	this	this	DET
fumecheng-12201	175	34	article	article	NOUN
fumecheng-12201	175	35	mainly	mainly	ADV
fumecheng-12201	175	36	utilizes	utilize	VERB
fumecheng-12201	175	37	the	the	DET
fumecheng-12201	175	38	he	he	PRON
fumecheng-12201	175	39	’s	’s	PART
fumecheng-12201	175	40	frequency	frequency	NOUN
fumecheng-12201	175	41	formula	formula	NOUN
fumecheng-12201	175	42	to	to	PART
fumecheng-12201	175	43	solve	solve	VERB
fumecheng-12201	175	44	the	the	DET
fumecheng-12201	175	45	solution	solution	NOUN
fumecheng-12201	175	46	of	of	ADP
fumecheng-12201	175	47	the	the	DET
fumecheng-12201	175	48	nonlinear	nonlinear	ADJ
fumecheng-12201	175	49	duffing	duffing	NOUN
fumecheng-12201	175	50	oscillator	oscillator	NOUN
fumecheng-12201	175	51	with	with	ADP
fumecheng-12201	175	52	generalized	generalized	ADJ
fumecheng-12201	175	53	initial	initial	ADJ
fumecheng-12201	175	54	conditions	condition	NOUN
fumecheng-12201	175	55	,	,	PUNCT
fumecheng-12201	175	56	and	and	CCONJ
fumecheng-12201	175	57	compares	compare	VERB
fumecheng-12201	175	58	it	it	PRON
fumecheng-12201	175	59	with	with	ADP
fumecheng-12201	175	60	the	the	DET
fumecheng-12201	175	61	exact	exact	ADJ
fumecheng-12201	175	62	solution	solution	NOUN
fumecheng-12201	175	63	of	of	ADP
fumecheng-12201	175	64	the	the	DET
fumecheng-12201	175	65	runge	runge	NOUN
fumecheng-12201	175	66	-	-	PUNCT
fumecheng-12201	175	67	kutta	kutta	NOUN
fumecheng-12201	175	68	method	method	NOUN
fumecheng-12201	175	69	.	.	PUNCT
fumecheng-12201	176	1	we	we	PRON
fumecheng-12201	176	2	summarize	summarize	VERB
fumecheng-12201	176	3	this	this	DET
fumecheng-12201	176	4	article	article	NOUN
fumecheng-12201	176	5	in	in	ADP
fumecheng-12201	176	6	the	the	DET
fumecheng-12201	176	7	following	follow	VERB
fumecheng-12201	176	8	two	two	NUM
fumecheng-12201	176	9	aspects	aspect	NOUN
fumecheng-12201	176	10	:	:	PUNCT
fumecheng-12201	176	11	(	(	PUNCT
fumecheng-12201	176	12	1	1	X
fumecheng-12201	176	13	)	)	PUNCT
fumecheng-12201	176	14	for	for	ADP
fumecheng-12201	176	15	the	the	DET
fumecheng-12201	176	16	undamped	undampe	VERB
fumecheng-12201	176	17	nonlinear	nonlinear	PROPN
fumecheng-12201	176	18	duffing	duffing	PROPN
fumecheng-12201	176	19	oscillator	oscillator	NOUN
fumecheng-12201	176	20	,	,	PUNCT
fumecheng-12201	176	21	this	this	DET
fumecheng-12201	176	22	paper	paper	NOUN
fumecheng-12201	176	23	first	first	ADV
fumecheng-12201	176	24	utilizes	utilize	VERB
fumecheng-12201	176	25	he	he	PRON
fumecheng-12201	176	26	’s	’	VERB
fumecheng-12201	176	27	frequency	frequency	NOUN
fumecheng-12201	176	28	formula	formula	NOUN
fumecheng-12201	176	29	to	to	PART
fumecheng-12201	176	30	calculate	calculate	VERB
fumecheng-12201	176	31	the	the	DET
fumecheng-12201	176	32	approximate	approximate	ADJ
fumecheng-12201	176	33	frequency	frequency	NOUN
fumecheng-12201	176	34	and	and	CCONJ
fumecheng-12201	176	35	derive	derive	VERB
fumecheng-12201	176	36	the	the	DET
fumecheng-12201	176	37	corresponding	corresponding	ADJ
fumecheng-12201	176	38	approximate	approximate	ADJ
fumecheng-12201	176	39	solution	solution	NOUN
fumecheng-12201	176	40	.	.	PUNCT
fumecheng-12201	177	1	subsequently	subsequently	ADV
fumecheng-12201	177	2	,	,	PUNCT
fumecheng-12201	177	3	we	we	PRON
fumecheng-12201	177	4	compare	compare	VERB
fumecheng-12201	177	5	the	the	DET
fumecheng-12201	177	6	approximate	approximate	ADJ
fumecheng-12201	177	7	solution	solution	NOUN
fumecheng-12201	177	8	with	with	ADP
fumecheng-12201	177	9	the	the	DET
fumecheng-12201	177	10	runge	runge	NOUN
fumecheng-12201	177	11	-	-	PUNCT
fumecheng-12201	177	12	kutta	kutta	NOUN
fumecheng-12201	177	13	exact	exact	ADJ
fumecheng-12201	177	14	solution	solution	NOUN
fumecheng-12201	177	15	through	through	ADP
fumecheng-12201	177	16	numerical	numerical	ADJ
fumecheng-12201	177	17	simulation	simulation	NOUN
fumecheng-12201	177	18	and	and	CCONJ
fumecheng-12201	177	19	find	find	VERB
fumecheng-12201	177	20	consistent	consistent	ADJ
fumecheng-12201	177	21	results	result	NOUN
fumecheng-12201	177	22	between	between	ADP
fumecheng-12201	177	23	them	they	PRON
fumecheng-12201	177	24	.	.	PUNCT
fumecheng-12201	178	1	it	it	PRON
fumecheng-12201	178	2	is	be	AUX
fumecheng-12201	178	3	worth	worth	ADJ
fumecheng-12201	178	4	noting	note	VERB
fumecheng-12201	178	5	that	that	SCONJ
fumecheng-12201	178	6	this	this	DET
fumecheng-12201	178	7	study	study	NOUN
fumecheng-12201	178	8	focuses	focus	VERB
fumecheng-12201	178	9	on	on	ADP
fumecheng-12201	178	10	generalized	generalized	ADJ
fumecheng-12201	178	11	initial	initial	ADJ
fumecheng-12201	178	12	conditions	condition	NOUN
fumecheng-12201	178	13	,	,	PUNCT
fumecheng-12201	178	14	and	and	CCONJ
fumecheng-12201	178	15	when	when	SCONJ
fumecheng-12201	178	16	we	we	PRON
fumecheng-12201	178	17	set	set	VERB
fumecheng-12201	178	18	the	the	DET
fumecheng-12201	178	19	initial	initial	ADJ
fumecheng-12201	178	20	condition	condition	NOUN
fumecheng-12201	178	21	a	a	DET
fumecheng-12201	178	22	to	to	ADP
fumecheng-12201	178	23	0	0	NUM
fumecheng-12201	178	24	or	or	CCONJ
fumecheng-12201	178	25	b	b	NOUN
fumecheng-12201	178	26	to	to	PART
fumecheng-12201	178	27	0	0	NUM
fumecheng-12201	178	28	,	,	PUNCT
fumecheng-12201	178	29	our	our	PRON
fumecheng-12201	178	30	results	result	NOUN
fumecheng-12201	178	31	are	be	AUX
fumecheng-12201	178	32	in	in	ADP
fumecheng-12201	178	33	complete	complete	ADJ
fumecheng-12201	178	34	agreement	agreement	NOUN
fumecheng-12201	178	35	with	with	ADP
fumecheng-12201	178	36	those	those	PRON
fumecheng-12201	178	37	obtained	obtain	VERB
fumecheng-12201	178	38	by	by	ADP
fumecheng-12201	178	39	the	the	DET
fumecheng-12201	178	40	homotopy	homotopy	NOUN
fumecheng-12201	178	41	perturbation	perturbation	NOUN
fumecheng-12201	178	42	method	method	NOUN
fumecheng-12201	178	43	or	or	CCONJ
fumecheng-12201	178	44	the	the	DET
fumecheng-12201	178	45	variational	variational	ADJ
fumecheng-12201	178	46	iteration	iteration	NOUN
fumecheng-12201	178	47	method	method	NOUN
fumecheng-12201	178	48	.	.	PUNCT
fumecheng-12201	179	1	(	(	PUNCT
fumecheng-12201	179	2	2	2	X
fumecheng-12201	179	3	)	)	PUNCT
fumecheng-12201	179	4	in	in	ADP
fumecheng-12201	179	5	this	this	DET
fumecheng-12201	179	6	paper	paper	NOUN
fumecheng-12201	179	7	,	,	PUNCT
fumecheng-12201	179	8	we	we	PRON
fumecheng-12201	179	9	investigate	investigate	VERB
fumecheng-12201	179	10	the	the	DET
fumecheng-12201	179	11	duffing	duffing	NOUN
fumecheng-12201	179	12	oscillator	oscillator	NOUN
fumecheng-12201	179	13	with	with	ADP
fumecheng-12201	179	14	viscous	viscous	ADJ
fumecheng-12201	179	15	damping	damping	NOUN
fumecheng-12201	179	16	.	.	PUNCT
fumecheng-12201	180	1	we	we	PRON
fumecheng-12201	180	2	divided	divide	VERB
fumecheng-12201	180	3	the	the	DET
fumecheng-12201	180	4	duffing	duffing	NOUN
fumecheng-12201	180	5	oscillator	oscillator	NOUN
fumecheng-12201	180	6	into	into	ADP
fumecheng-12201	180	7	linear	linear	ADJ
fumecheng-12201	180	8	and	and	CCONJ
fumecheng-12201	180	9	nonlinear	nonlinear	ADJ
fumecheng-12201	180	10	types	type	NOUN
fumecheng-12201	180	11	,	,	PUNCT
fumecheng-12201	180	12	and	and	CCONJ
fumecheng-12201	180	13	used	use	VERB
fumecheng-12201	180	14	he	he	PRON
fumecheng-12201	180	15	's	's	PART
fumecheng-12201	180	16	frequency	frequency	NOUN
fumecheng-12201	180	17	formula	formula	NOUN
fumecheng-12201	180	18	to	to	PART
fumecheng-12201	180	19	find	find	VERB
fumecheng-12201	180	20	approximate	approximate	ADJ
fumecheng-12201	180	21	solutions	solution	NOUN
fumecheng-12201	180	22	in	in	ADP
fumecheng-12201	180	23	both	both	DET
fumecheng-12201	180	24	cases	case	NOUN
fumecheng-12201	180	25	,	,	PUNCT
fumecheng-12201	180	26	followed	follow	VERB
fumecheng-12201	180	27	by	by	ADP
fumecheng-12201	180	28	numerical	numerical	ADJ
fumecheng-12201	180	29	simulations	simulation	NOUN
fumecheng-12201	180	30	.	.	PUNCT
fumecheng-12201	181	1	application	application	NOUN
fumecheng-12201	181	2	of	of	ADP
fumecheng-12201	181	3	he	he	PRON
fumecheng-12201	181	4	’s	’s	PART
fumecheng-12201	181	5	frequency	frequency	NOUN
fumecheng-12201	181	6	formula	formula	NOUN
fumecheng-12201	181	7	to	to	PART
fumecheng-12201	181	8	nonlinear	nonlinear	ADJ
fumecheng-12201	181	9	oscillators	oscillator	NOUN
fumecheng-12201	181	10	with	with	ADP
fumecheng-12201	181	11	generalized	generalized	ADJ
fumecheng-12201	181	12	initial	initial	ADJ
fumecheng-12201	181	13	condition	condition	NOUN
fumecheng-12201	181	14	711	711	NUM
fumecheng-12201	181	15	the	the	DET
fumecheng-12201	181	16	experimental	experimental	ADJ
fumecheng-12201	181	17	results	result	NOUN
fumecheng-12201	181	18	show	show	VERB
fumecheng-12201	181	19	that	that	SCONJ
fumecheng-12201	181	20	,	,	PUNCT
fumecheng-12201	181	21	even	even	ADV
fumecheng-12201	181	22	when	when	SCONJ
fumecheng-12201	181	23	we	we	PRON
fumecheng-12201	181	24	increase	increase	VERB
fumecheng-12201	181	25	the	the	DET
fumecheng-12201	181	26	damping	damping	NOUN
fumecheng-12201	181	27	and	and	CCONJ
fumecheng-12201	181	28	the	the	DET
fumecheng-12201	181	29	initial	initial	ADJ
fumecheng-12201	181	30	conditions	condition	NOUN
fumecheng-12201	181	31	a	a	PRON
fumecheng-12201	181	32	and	and	CCONJ
fumecheng-12201	181	33	b	b	NOUN
fumecheng-12201	181	34	in	in	ADP
fumecheng-12201	181	35	the	the	DET
fumecheng-12201	181	36	nonlinear	nonlinear	ADJ
fumecheng-12201	181	37	duffing	duffing	PROPN
fumecheng-12201	181	38	oscillator	oscillator	NOUN
fumecheng-12201	181	39	,	,	PUNCT
fumecheng-12201	181	40	the	the	DET
fumecheng-12201	181	41	approximate	approximate	ADJ
fumecheng-12201	181	42	solution	solution	NOUN
fumecheng-12201	181	43	obtained	obtain	VERB
fumecheng-12201	181	44	using	use	VERB
fumecheng-12201	181	45	he	he	PRON
fumecheng-12201	181	46	's	's	PART
fumecheng-12201	181	47	frequency	frequency	NOUN
fumecheng-12201	181	48	formula	formula	NOUN
fumecheng-12201	181	49	still	still	ADV
fumecheng-12201	181	50	matches	match	VERB
fumecheng-12201	181	51	the	the	DET
fumecheng-12201	181	52	exact	exact	ADJ
fumecheng-12201	181	53	solution	solution	NOUN
fumecheng-12201	181	54	obtained	obtain	VERB
fumecheng-12201	181	55	by	by	ADP
fumecheng-12201	181	56	the	the	DET
fumecheng-12201	181	57	runge	runge	NOUN
fumecheng-12201	181	58	-	-	PUNCT
fumecheng-12201	181	59	kutta	kutta	NOUN
fumecheng-12201	181	60	method	method	NOUN
fumecheng-12201	181	61	very	very	ADV
fumecheng-12201	181	62	closely	closely	ADV
fumecheng-12201	181	63	.	.	PUNCT
fumecheng-12201	182	1	this	this	PRON
fumecheng-12201	182	2	fully	fully	ADV
fumecheng-12201	182	3	demonstrates	demonstrate	VERB
fumecheng-12201	182	4	that	that	SCONJ
fumecheng-12201	182	5	he	he	PRON
fumecheng-12201	182	6	's	's	PART
fumecheng-12201	182	7	frequency	frequency	NOUN
fumecheng-12201	182	8	formula	formula	NOUN
fumecheng-12201	182	9	is	be	AUX
fumecheng-12201	182	10	equally	equally	ADV
fumecheng-12201	182	11	applicable	applicable	ADJ
fumecheng-12201	182	12	to	to	AUX
fumecheng-12201	182	13	nonlinear	nonlinear	VERB
fumecheng-12201	182	14	damped	damped	ADJ
fumecheng-12201	182	15	oscillators	oscillator	NOUN
fumecheng-12201	182	16	with	with	ADP
fumecheng-12201	182	17	general	general	ADJ
fumecheng-12201	182	18	initial	initial	ADJ
fumecheng-12201	182	19	conditions	condition	NOUN
fumecheng-12201	182	20	.	.	PUNCT
fumecheng-12201	183	1	the	the	DET
fumecheng-12201	183	2	he	he	PRON
fumecheng-12201	183	3	's	's	PART
fumecheng-12201	183	4	frequency	frequency	NOUN
fumecheng-12201	183	5	formula	formula	NOUN
fumecheng-12201	183	6	method	method	NOUN
fumecheng-12201	183	7	is	be	AUX
fumecheng-12201	183	8	both	both	PRON
fumecheng-12201	183	9	simple	simple	ADJ
fumecheng-12201	183	10	and	and	CCONJ
fumecheng-12201	183	11	fast	fast	ADJ
fumecheng-12201	183	12	,	,	PUNCT
fumecheng-12201	183	13	and	and	CCONJ
fumecheng-12201	183	14	we	we	PRON
fumecheng-12201	183	15	also	also	ADV
fumecheng-12201	183	16	observed	observe	VERB
fumecheng-12201	183	17	a	a	DET
fumecheng-12201	183	18	gradual	gradual	ADJ
fumecheng-12201	183	19	decrease	decrease	NOUN
fumecheng-12201	183	20	in	in	ADP
fumecheng-12201	183	21	the	the	DET
fumecheng-12201	183	22	amplitude	amplitude	NOUN
fumecheng-12201	183	23	of	of	ADP
fumecheng-12201	183	24	the	the	DET
fumecheng-12201	183	25	duffing	duffing	NOUN
fumecheng-12201	183	26	oscillator	oscillator	NOUN
fumecheng-12201	183	27	's	's	PART
fumecheng-12201	183	28	solution	solution	NOUN
fumecheng-12201	183	29	,	,	PUNCT
fumecheng-12201	183	30	eventually	eventually	ADV
fumecheng-12201	183	31	reaching	reach	VERB
fumecheng-12201	183	32	equilibrium	equilibrium	NOUN
fumecheng-12201	183	33	as	as	SCONJ
fumecheng-12201	183	34	the	the	DET
fumecheng-12201	183	35	damping	damp	VERB
fumecheng-12201	183	36	increased	increase	VERB
fumecheng-12201	183	37	.	.	PUNCT
fumecheng-12201	184	1	these	these	DET
fumecheng-12201	184	2	results	result	NOUN
fumecheng-12201	184	3	are	be	AUX
fumecheng-12201	184	4	of	of	ADP
fumecheng-12201	184	5	great	great	ADJ
fumecheng-12201	184	6	significance	significance	NOUN
fumecheng-12201	184	7	for	for	ADP
fumecheng-12201	184	8	a	a	DET
fumecheng-12201	184	9	deeper	deep	ADJ
fumecheng-12201	184	10	understanding	understanding	NOUN
fumecheng-12201	184	11	and	and	CCONJ
fumecheng-12201	184	12	application	application	NOUN
fumecheng-12201	184	13	of	of	ADP
fumecheng-12201	184	14	the	the	DET
fumecheng-12201	184	15	dynamical	dynamical	ADJ
fumecheng-12201	184	16	behavior	behavior	NOUN
fumecheng-12201	184	17	of	of	ADP
fumecheng-12201	184	18	duffing	duffe	VERB
fumecheng-12201	184	19	oscillators	oscillator	NOUN
fumecheng-12201	184	20	.	.	PUNCT
fumecheng-12201	185	1	in	in	ADP
fumecheng-12201	185	2	conclusion	conclusion	NOUN
fumecheng-12201	185	3	,	,	PUNCT
fumecheng-12201	185	4	this	this	DET
fumecheng-12201	185	5	frequency	frequency	NOUN
fumecheng-12201	185	6	formula	formula	NOUN
fumecheng-12201	185	7	possesses	possess	VERB
fumecheng-12201	185	8	simple	simple	ADJ
fumecheng-12201	185	9	yet	yet	CCONJ
fumecheng-12201	185	10	profound	profound	ADJ
fumecheng-12201	185	11	mathematical	mathematical	ADJ
fumecheng-12201	185	12	properties	property	NOUN
fumecheng-12201	185	13	and	and	CCONJ
fumecheng-12201	185	14	holds	hold	VERB
fumecheng-12201	185	15	significant	significant	ADJ
fumecheng-12201	185	16	practical	practical	ADJ
fumecheng-12201	185	17	value	value	NOUN
fumecheng-12201	185	18	.	.	PUNCT
fumecheng-12201	186	1	it	it	PRON
fumecheng-12201	186	2	provides	provide	VERB
fumecheng-12201	186	3	engineers	engineer	NOUN
fumecheng-12201	186	4	with	with	ADP
fumecheng-12201	186	5	an	an	DET
fumecheng-12201	186	6	efficient	efficient	ADJ
fumecheng-12201	186	7	and	and	CCONJ
fumecheng-12201	186	8	reliable	reliable	ADJ
fumecheng-12201	186	9	approach	approach	NOUN
fumecheng-12201	186	10	to	to	ADP
fumecheng-12201	186	11	studying	study	VERB
fumecheng-12201	186	12	nonlinear	nonlinear	ADJ
fumecheng-12201	186	13	vibration	vibration	NOUN
fumecheng-12201	186	14	systems	system	NOUN
fumecheng-12201	186	15	.	.	PUNCT
fumecheng-12201	187	1	in	in	ADP
fumecheng-12201	187	2	future	future	ADJ
fumecheng-12201	187	3	research	research	NOUN
fumecheng-12201	187	4	,	,	PUNCT
fumecheng-12201	187	5	we	we	PRON
fumecheng-12201	187	6	aim	aim	VERB
fumecheng-12201	187	7	to	to	PART
fumecheng-12201	187	8	further	far	ADV
fumecheng-12201	187	9	explore	explore	VERB
fumecheng-12201	187	10	the	the	DET
fumecheng-12201	187	11	application	application	NOUN
fumecheng-12201	187	12	of	of	ADP
fumecheng-12201	187	13	this	this	DET
fumecheng-12201	187	14	frequency	frequency	NOUN
fumecheng-12201	187	15	formula	formula	NOUN
fumecheng-12201	187	16	to	to	ADP
fumecheng-12201	187	17	fractional	fractional	ADJ
fumecheng-12201	187	18	-	-	PUNCT
fumecheng-12201	187	19	order	order	NOUN
fumecheng-12201	187	20	nonlinear	nonlinear	ADJ
fumecheng-12201	187	21	systems	system	NOUN
fumecheng-12201	187	22	with	with	ADP
fumecheng-12201	187	23	generalized	generalized	ADJ
fumecheng-12201	187	24	initial	initial	ADJ
fumecheng-12201	187	25	conditions	condition	NOUN
fumecheng-12201	187	26	,	,	PUNCT
fumecheng-12201	187	27	and	and	CCONJ
fumecheng-12201	187	28	thoroughly	thoroughly	ADV
fumecheng-12201	187	29	examine	examine	VERB
fumecheng-12201	187	30	its	its	PRON
fumecheng-12201	187	31	effectiveness	effectiveness	NOUN
fumecheng-12201	187	32	.	.	PUNCT
fumecheng-12201	188	1	by	by	ADP
fumecheng-12201	188	2	applying	apply	VERB
fumecheng-12201	188	3	this	this	DET
fumecheng-12201	188	4	formula	formula	NOUN
fumecheng-12201	188	5	in	in	ADP
fumecheng-12201	188	6	broader	broad	ADJ
fumecheng-12201	188	7	domains	domain	NOUN
fumecheng-12201	188	8	,	,	PUNCT
fumecheng-12201	188	9	we	we	PRON
fumecheng-12201	188	10	can	can	AUX
fumecheng-12201	188	11	enhance	enhance	VERB
fumecheng-12201	188	12	our	our	PRON
fumecheng-12201	188	13	understanding	understanding	NOUN
fumecheng-12201	188	14	and	and	CCONJ
fumecheng-12201	188	15	analysis	analysis	NOUN
fumecheng-12201	188	16	of	of	ADP
fumecheng-12201	188	17	complex	complex	ADJ
fumecheng-12201	188	18	vibration	vibration	NOUN
fumecheng-12201	188	19	systems	system	NOUN
fumecheng-12201	188	20	,	,	PUNCT
fumecheng-12201	188	21	offering	offer	VERB
fumecheng-12201	188	22	more	more	ADV
fumecheng-12201	188	23	reliable	reliable	ADJ
fumecheng-12201	188	24	and	and	CCONJ
fumecheng-12201	188	25	accurate	accurate	ADJ
fumecheng-12201	188	26	solutions	solution	NOUN
fumecheng-12201	188	27	for	for	ADP
fumecheng-12201	188	28	engineering	engineering	NOUN
fumecheng-12201	188	29	practices	practice	NOUN
fumecheng-12201	188	30	and	and	CCONJ
fumecheng-12201	188	31	scientific	scientific	ADJ
fumecheng-12201	188	32	investigations	investigation	NOUN
fumecheng-12201	188	33	.	.	PUNCT
fumecheng-12201	189	1	acknowledgement	acknowledgement	NOUN
fumecheng-12201	189	2	:	:	PUNCT
fumecheng-12201	189	3	the	the	DET
fumecheng-12201	189	4	paper	paper	NOUN
fumecheng-12201	189	5	was	be	AUX
fumecheng-12201	189	6	supported	support	VERB
fumecheng-12201	189	7	by	by	ADP
fumecheng-12201	189	8	the	the	DET
fumecheng-12201	189	9	national	national	ADJ
fumecheng-12201	189	10	natural	natural	PROPN
fumecheng-12201	189	11	science	science	PROPN
fumecheng-12201	189	12	foundation	foundation	PROPN
fumecheng-12201	189	13	of	of	ADP
fumecheng-12201	189	14	china	china	PROPN
fumecheng-12201	189	15	(	(	PUNCT
fumecheng-12201	189	16	61863022	61863022	NUM
fumecheng-12201	189	17	)	)	PUNCT
fumecheng-12201	189	18	and	and	CCONJ
fumecheng-12201	189	19	the	the	DET
fumecheng-12201	189	20	key	key	ADJ
fumecheng-12201	189	21	project	project	NOUN
fumecheng-12201	189	22	of	of	ADP
fumecheng-12201	189	23	gansu	gansu	PROPN
fumecheng-12201	189	24	natural	natural	PROPN
fumecheng-12201	189	25	science	science	PROPN
fumecheng-12201	189	26	foundation	foundation	PROPN
fumecheng-12201	189	27	(	(	PUNCT
fumecheng-12201	189	28	23jrra882	23jrra882	NUM
fumecheng-12201	189	29	)	)	PUNCT
fumecheng-12201	189	30	.	.	PUNCT
fumecheng-12201	190	1	references	reference	NOUN
fumecheng-12201	190	2	1	1	NUM
fumecheng-12201	190	3	.	.	PUNCT
fumecheng-12201	190	4	yan	yan	PROPN
fumecheng-12201	190	5	,	,	PUNCT
fumecheng-12201	190	6	w.	w.	PROPN
fumecheng-12201	190	7	,	,	PUNCT
fumecheng-12201	190	8	noel	noel	PROPN
fumecheng-12201	190	9	,	,	PUNCT
fumecheng-12201	190	10	g.	g.	PROPN
fumecheng-12201	190	11	,	,	PUNCT
fumecheng-12201	190	12	loke	loke	ADV
fumecheng-12201	190	13	,	,	PUNCT
fumecheng-12201	190	14	g.	g.	PROPN
fumecheng-12201	190	15	,	,	PUNCT
fumecheng-12201	190	16	et	et	PROPN
fumecheng-12201	190	17	al	al	PROPN
fumecheng-12201	190	18	.	.	PROPN
fumecheng-12201	190	19	,	,	PUNCT
fumecheng-12201	190	20	2022	2022	NUM
fumecheng-12201	190	21	,	,	PUNCT
fumecheng-12201	190	22	single	single	ADJ
fumecheng-12201	190	23	fibre	fibre	NOUN
fumecheng-12201	190	24	enables	enable	VERB
fumecheng-12201	190	25	acoustic	acoustic	ADJ
fumecheng-12201	190	26	fabrics	fabric	NOUN
fumecheng-12201	190	27	via	via	ADP
fumecheng-12201	190	28	nanometre	nanometre	NOUN
fumecheng-12201	190	29	-	-	PUNCT
fumecheng-12201	190	30	scale	scale	NOUN
fumecheng-12201	190	31	vibrations	vibration	NOUN
fumecheng-12201	190	32	,	,	PUNCT
fumecheng-12201	190	33	nature	nature	NOUN
fumecheng-12201	190	34	,	,	PUNCT
fumecheng-12201	190	35	603(7902	603(7902	NUM
fumecheng-12201	190	36	)	)	PUNCT
fumecheng-12201	190	37	,	,	PUNCT
fumecheng-12201	190	38	pp	pp	PROPN
fumecheng-12201	190	39	.	.	PUNCT
fumecheng-12201	191	1	616	616	NUM
fumecheng-12201	191	2	-	-	SYM
fumecheng-12201	191	3	623	623	NUM
fumecheng-12201	191	4	.	.	PUNCT
fumecheng-12201	192	1	2	2	NUM
fumecheng-12201	192	2	.	.	X
fumecheng-12201	192	3	chen	chen	PROPN
fumecheng-12201	192	4	,	,	PUNCT
fumecheng-12201	192	5	z.	z.	PROPN
fumecheng-12201	192	6	,	,	PUNCT
fumecheng-12201	192	7	jiang	jiang	PROPN
fumecheng-12201	192	8	,	,	PUNCT
fumecheng-12201	192	9	y.	y.	PROPN
fumecheng-12201	192	10	,	,	PUNCT
fumecheng-12201	192	11	shao	shao	PROPN
fumecheng-12201	192	12	,	,	PUNCT
fumecheng-12201	192	13	y.t	y.t	PROPN
fumecheng-12201	192	14	.	.	PROPN
fumecheng-12201	192	15	,	,	PUNCT
fumecheng-12201	192	16	et	et	PROPN
fumecheng-12201	192	17	al	al	PROPN
fumecheng-12201	192	18	.	.	PROPN
fumecheng-12201	192	19	,	,	PUNCT
fumecheng-12201	192	20	2021	2021	NUM
fumecheng-12201	192	21	,	,	PUNCT
fumecheng-12201	192	22	electron	electron	NOUN
fumecheng-12201	192	23	ptychography	ptychography	NOUN
fumecheng-12201	192	24	achieves	achieve	VERB
fumecheng-12201	192	25	atomic	atomic	ADJ
fumecheng-12201	192	26	-	-	PUNCT
fumecheng-12201	192	27	resolution	resolution	NOUN
fumecheng-12201	192	28	limits	limit	NOUN
fumecheng-12201	192	29	set	set	VERB
fumecheng-12201	192	30	by	by	ADP
fumecheng-12201	192	31	lattice	lattice	NOUN
fumecheng-12201	192	32	vibrations	vibration	NOUN
fumecheng-12201	192	33	,	,	PUNCT
fumecheng-12201	192	34	science	science	NOUN
fumecheng-12201	192	35	,	,	PUNCT
fumecheng-12201	192	36	372(6544	372(6544	NUM
fumecheng-12201	192	37	)	)	PUNCT
fumecheng-12201	192	38	,	,	PUNCT
fumecheng-12201	192	39	pp	pp	PROPN
fumecheng-12201	192	40	.	.	PUNCT
fumecheng-12201	193	1	826	826	NUM
fumecheng-12201	193	2	-	-	SYM
fumecheng-12201	193	3	831	831	NUM
fumecheng-12201	193	4	.	.	PUNCT
fumecheng-12201	194	1	3	3	X
fumecheng-12201	194	2	.	.	X
fumecheng-12201	194	3	skrzypacz	skrzypacz	NOUN
fumecheng-12201	194	4	,	,	PUNCT
fumecheng-12201	194	5	p.	p.	PROPN
fumecheng-12201	194	6	,	,	PUNCT
fumecheng-12201	194	7	ellis	ellis	PROPN
fumecheng-12201	194	8	,	,	PUNCT
fumecheng-12201	194	9	g.	g.	PROPN
fumecheng-12201	194	10	,	,	PUNCT
fumecheng-12201	194	11	he	he	PRON
fumecheng-12201	194	12	,	,	PUNCT
fumecheng-12201	194	13	j.h	j.h	PROPN
fumecheng-12201	194	14	.	.	PROPN
fumecheng-12201	194	15	,	,	PUNCT
fumecheng-12201	194	16	he	he	PRON
fumecheng-12201	194	17	,	,	PUNCT
fumecheng-12201	194	18	c.h	c.h	PROPN
fumecheng-12201	194	19	.	.	PROPN
fumecheng-12201	194	20	,	,	PUNCT
fumecheng-12201	194	21	2022	2022	NUM
fumecheng-12201	194	22	,	,	PUNCT
fumecheng-12201	194	23	dynamic	dynamic	ADJ
fumecheng-12201	194	24	pull	pull	NOUN
fumecheng-12201	194	25	-	-	PUNCT
fumecheng-12201	194	26	in	in	NOUN
fumecheng-12201	194	27	and	and	CCONJ
fumecheng-12201	194	28	oscillations	oscillation	NOUN
fumecheng-12201	194	29	of	of	ADP
fumecheng-12201	194	30	current	current	ADJ
fumecheng-12201	194	31	-	-	PUNCT
fumecheng-12201	194	32	carrying	carry	VERB
fumecheng-12201	194	33	filaments	filament	NOUN
fumecheng-12201	194	34	in	in	ADP
fumecheng-12201	194	35	magnetic	magnetic	ADJ
fumecheng-12201	194	36	micro	micro	ADJ
fumecheng-12201	194	37	-	-	ADJ
fumecheng-12201	194	38	electro	electro	ADJ
fumecheng-12201	194	39	-	-	PUNCT
fumecheng-12201	194	40	mechanical	mechanical	ADJ
fumecheng-12201	194	41	system	system	NOUN
fumecheng-12201	194	42	,	,	PUNCT
fumecheng-12201	194	43	communications	communication	NOUN
fumecheng-12201	194	44	in	in	ADP
fumecheng-12201	194	45	nonlinear	nonlinear	ADJ
fumecheng-12201	194	46	science	science	NOUN
fumecheng-12201	194	47	and	and	CCONJ
fumecheng-12201	194	48	numerical	numerical	PROPN
fumecheng-12201	194	49	simulation	simulation	PROPN
fumecheng-12201	194	50	,	,	PUNCT
fumecheng-12201	194	51	109	109	NUM
fumecheng-12201	194	52	,	,	PUNCT
fumecheng-12201	194	53	106350	106350	NUM
fumecheng-12201	194	54	.	.	PUNCT
fumecheng-12201	195	1	4	4	X
fumecheng-12201	195	2	.	.	X
fumecheng-12201	195	3	aditya	aditya	PROPN
fumecheng-12201	195	4	,	,	PUNCT
fumecheng-12201	195	5	a.	a.	PROPN
fumecheng-12201	195	6	,	,	PUNCT
fumecheng-12201	195	7	rufus	rufus	PROPN
fumecheng-12201	195	8	,	,	PUNCT
fumecheng-12201	195	9	e.	e.	PROPN
fumecheng-12201	195	10	,	,	PUNCT
fumecheng-12201	195	11	2023	2023	NUM
fumecheng-12201	195	12	,	,	PUNCT
fumecheng-12201	195	13	the	the	DET
fumecheng-12201	195	14	review	review	NOUN
fumecheng-12201	195	15	of	of	ADP
fumecheng-12201	195	16	micro	micro	ADJ
fumecheng-12201	195	17	-	-	ADJ
fumecheng-12201	195	18	electromechanical	electromechanical	ADJ
fumecheng-12201	195	19	systems	system	NOUN
fumecheng-12201	195	20	-	-	PUNCT
fumecheng-12201	195	21	based	base	VERB
fumecheng-12201	195	22	biosensor	biosensor	NOUN
fumecheng-12201	195	23	:	:	PUNCT
fumecheng-12201	195	24	a	a	DET
fumecheng-12201	195	25	cellular	cellular	ADJ
fumecheng-12201	195	26	base	base	NOUN
fumecheng-12201	195	27	perspective	perspective	NOUN
fumecheng-12201	195	28	,	,	PUNCT
fumecheng-12201	195	29	sensors	sensor	NOUN
fumecheng-12201	195	30	for	for	ADP
fumecheng-12201	195	31	next	next	ADJ
fumecheng-12201	195	32	-	-	PUNCT
fumecheng-12201	195	33	generation	generation	NOUN
fumecheng-12201	195	34	electronic	electronic	ADJ
fumecheng-12201	195	35	systems	system	NOUN
fumecheng-12201	195	36	and	and	CCONJ
fumecheng-12201	195	37	technologies	technology	NOUN
fumecheng-12201	195	38	,	,	PUNCT
fumecheng-12201	195	39	crc	crc	NOUN
fumecheng-12201	195	40	press	press	NOUN
fumecheng-12201	195	41	,	,	PUNCT
fumecheng-12201	195	42	pp	pp	PROPN
fumecheng-12201	195	43	.	.	PUNCT
fumecheng-12201	196	1	25	25	NUM
fumecheng-12201	196	2	-	-	SYM
fumecheng-12201	196	3	54	54	NUM
fumecheng-12201	196	4	.	.	PUNCT
fumecheng-12201	197	1	5	5	NUM
fumecheng-12201	197	2	.	.	X
fumecheng-12201	197	3	zaouali	zaouali	VERB
fumecheng-12201	197	4	,	,	PUNCT
fumecheng-12201	197	5	e.	e.	PROPN
fumecheng-12201	197	6	,	,	PUNCT
fumecheng-12201	197	7	najar	najar	PROPN
fumecheng-12201	197	8	,	,	PUNCT
fumecheng-12201	197	9	f.	f.	PROPN
fumecheng-12201	197	10	,	,	PUNCT
fumecheng-12201	197	11	kacem	kacem	PROPN
fumecheng-12201	197	12	,	,	PUNCT
fumecheng-12201	197	13	n.	n.	NOUN
fumecheng-12201	197	14	,	,	PUNCT
fumecheng-12201	197	15	foltete	foltete	PROPN
fumecheng-12201	197	16	,	,	PUNCT
fumecheng-12201	197	17	e.	e.	PROPN
fumecheng-12201	197	18	,	,	PUNCT
fumecheng-12201	197	19	2022	2022	NUM
fumecheng-12201	197	20	,	,	PUNCT
fumecheng-12201	197	21	pendulum	pendulum	NOUN
fumecheng-12201	197	22	-	-	PUNCT
fumecheng-12201	197	23	based	base	VERB
fumecheng-12201	197	24	embedded	embed	VERB
fumecheng-12201	197	25	energy	energy	NOUN
fumecheng-12201	197	26	harvester	harvester	NOUN
fumecheng-12201	197	27	for	for	ADP
fumecheng-12201	197	28	rotating	rotate	VERB
fumecheng-12201	197	29	systems	system	NOUN
fumecheng-12201	197	30	,	,	PUNCT
fumecheng-12201	197	31	mechanical	mechanical	ADJ
fumecheng-12201	197	32	systems	system	NOUN
fumecheng-12201	197	33	and	and	CCONJ
fumecheng-12201	197	34	signal	signal	NOUN
fumecheng-12201	197	35	processing	processing	NOUN
fumecheng-12201	197	36	,	,	PUNCT
fumecheng-12201	197	37	180	180	NUM
fumecheng-12201	197	38	,	,	PUNCT
fumecheng-12201	197	39	109415	109415	NUM
fumecheng-12201	197	40	.	.	PUNCT
fumecheng-12201	198	1	6	6	X
fumecheng-12201	198	2	.	.	X
fumecheng-12201	198	3	maadani	maadani	PROPN
fumecheng-12201	198	4	,	,	PUNCT
fumecheng-12201	198	5	m.	m.	NOUN
fumecheng-12201	198	6	,	,	PUNCT
fumecheng-12201	198	7	butcher	butcher	NOUN
fumecheng-12201	198	8	,	,	PUNCT
fumecheng-12201	198	9	e.a	e.a	PROPN
fumecheng-12201	198	10	.	.	PROPN
fumecheng-12201	198	11	,	,	PUNCT
fumecheng-12201	198	12	2022	2022	NUM
fumecheng-12201	198	13	,	,	PUNCT
fumecheng-12201	198	14	6	6	NUM
fumecheng-12201	198	15	-	-	PUNCT
fumecheng-12201	198	16	dof	dof	NOUN
fumecheng-12201	198	17	consensus	consensus	NOUN
fumecheng-12201	198	18	control	control	NOUN
fumecheng-12201	198	19	of	of	ADP
fumecheng-12201	198	20	multi	multi	ADJ
fumecheng-12201	198	21	-	-	ADJ
fumecheng-12201	198	22	agent	agent	ADJ
fumecheng-12201	198	23	rigid	rigid	ADJ
fumecheng-12201	198	24	body	body	NOUN
fumecheng-12201	198	25	systems	system	NOUN
fumecheng-12201	198	26	using	use	VERB
fumecheng-12201	198	27	rotation	rotation	NOUN
fumecheng-12201	198	28	matrices	matrix	NOUN
fumecheng-12201	198	29	,	,	PUNCT
fumecheng-12201	198	30	international	international	ADJ
fumecheng-12201	198	31	journal	journal	NOUN
fumecheng-12201	198	32	of	of	ADP
fumecheng-12201	198	33	control	control	NOUN
fumecheng-12201	198	34	,	,	PUNCT
fumecheng-12201	198	35	95(10	95(10	NUM
fumecheng-12201	198	36	)	)	PUNCT
fumecheng-12201	198	37	,	,	PUNCT
fumecheng-12201	198	38	pp	pp	ADJ
fumecheng-12201	198	39	.	.	PUNCT
fumecheng-12201	199	1	2667	2667	NUM
fumecheng-12201	199	2	-	-	SYM
fumecheng-12201	199	3	2681	2681	NUM
fumecheng-12201	199	4	.	.	PUNCT
fumecheng-12201	200	1	7	7	X
fumecheng-12201	200	2	.	.	X
fumecheng-12201	200	3	ramadoss	ramadoss	PROPN
fumecheng-12201	200	4	,	,	PUNCT
fumecheng-12201	200	5	j.	j.	PROPN
fumecheng-12201	200	6	,	,	PUNCT
fumecheng-12201	200	7	kengne	kengne	PROPN
fumecheng-12201	200	8	,	,	PUNCT
fumecheng-12201	200	9	j.	j.	PROPN
fumecheng-12201	200	10	,	,	PUNCT
fumecheng-12201	200	11	tanekou	tanekou	PROPN
fumecheng-12201	200	12	,	,	PUNCT
fumecheng-12201	200	13	s.t	s.t	PROPN
fumecheng-12201	200	14	.	.	PROPN
fumecheng-12201	200	15	,	,	PUNCT
fumecheng-12201	200	16	rajagopal	rajagopal	PROPN
fumecheng-12201	200	17	,	,	PUNCT
fumecheng-12201	200	18	k.	k.	PROPN
fumecheng-12201	200	19	,	,	PUNCT
fumecheng-12201	200	20	kenmoe	kenmoe	PROPN
fumecheng-12201	200	21	,	,	PUNCT
fumecheng-12201	200	22	g.d	g.d	PROPN
fumecheng-12201	200	23	.	.	PROPN
fumecheng-12201	200	24	,	,	PUNCT
fumecheng-12201	200	25	2022	2022	NUM
fumecheng-12201	200	26	,	,	PUNCT
fumecheng-12201	200	27	reversal	reversal	NOUN
fumecheng-12201	200	28	of	of	ADP
fumecheng-12201	200	29	period	period	NOUN
fumecheng-12201	200	30	doubling	double	VERB
fumecheng-12201	200	31	,	,	PUNCT
fumecheng-12201	200	32	multistability	multistability	NOUN
fumecheng-12201	200	33	and	and	CCONJ
fumecheng-12201	200	34	symmetry	symmetry	NOUN
fumecheng-12201	200	35	breaking	break	VERB
fumecheng-12201	200	36	aspects	aspect	NOUN
fumecheng-12201	200	37	for	for	ADP
fumecheng-12201	200	38	a	a	DET
fumecheng-12201	200	39	system	system	NOUN
fumecheng-12201	200	40	composed	compose	VERB
fumecheng-12201	200	41	of	of	ADP
fumecheng-12201	200	42	a	a	DET
fumecheng-12201	200	43	van	van	PROPN
fumecheng-12201	200	44	der	der	ADJ
fumecheng-12201	200	45	pol	pol	PROPN
fumecheng-12201	200	46	oscillator	oscillator	NOUN
fumecheng-12201	200	47	coupled	couple	VERB
fumecheng-12201	200	48	to	to	ADP
fumecheng-12201	200	49	a	a	DET
fumecheng-12201	200	50	duffing	duffing	NOUN
fumecheng-12201	200	51	oscillator	oscillator	NOUN
fumecheng-12201	200	52	,	,	PUNCT
fumecheng-12201	200	53	chaos	chaos	NOUN
fumecheng-12201	200	54	,	,	PUNCT
fumecheng-12201	200	55	solitons	soliton	NOUN
fumecheng-12201	200	56	and	and	CCONJ
fumecheng-12201	200	57	fractals	fractal	NOUN
fumecheng-12201	200	58	,	,	PUNCT
fumecheng-12201	200	59	159	159	NUM
fumecheng-12201	200	60	,	,	PUNCT
fumecheng-12201	200	61	112157	112157	NUM
fumecheng-12201	200	62	.	.	PUNCT
fumecheng-12201	201	1	8	8	NUM
fumecheng-12201	201	2	.	.	PUNCT
fumecheng-12201	201	3	amur	amur	NOUN
fumecheng-12201	201	4	,	,	PUNCT
fumecheng-12201	201	5	a.a	a.a	PROPN
fumecheng-12201	201	6	.	.	PROPN
fumecheng-12201	201	7	,	,	PUNCT
fumecheng-12201	201	8	memon	memon	PROPN
fumecheng-12201	201	9	,	,	PUNCT
fumecheng-12201	201	10	k.n	k.n	PROPN
fumecheng-12201	201	11	.	.	PROPN
fumecheng-12201	201	12	,	,	PUNCT
fumecheng-12201	201	13	shah	shah	PROPN
fumecheng-12201	201	14	,	,	PUNCT
fumecheng-12201	201	15	s.f	s.f	PROPN
fumecheng-12201	201	16	.	.	PROPN
fumecheng-12201	201	17	,	,	PUNCT
fumecheng-12201	201	18	et	et	PROPN
fumecheng-12201	201	19	al	al	PROPN
fumecheng-12201	201	20	.	.	PROPN
fumecheng-12201	201	21	,	,	PUNCT
fumecheng-12201	201	22	2023	2023	NUM
fumecheng-12201	201	23	,	,	PUNCT
fumecheng-12201	201	24	the	the	DET
fumecheng-12201	201	25	hydrodyanamics	hydrodyanamic	NOUN
fumecheng-12201	201	26	of	of	ADP
fumecheng-12201	201	27	gravity	gravity	NOUN
fumecheng-12201	201	28	-	-	PUNCT
fumecheng-12201	201	29	driven	drive	VERB
fumecheng-12201	201	30	vessel	vessel	NOUN
fumecheng-12201	201	31	drainage	drainage	NOUN
fumecheng-12201	201	32	of	of	ADP
fumecheng-12201	201	33	third	third	ADJ
fumecheng-12201	201	34	order	order	NOUN
fumecheng-12201	201	35	fluid	fluid	NOUN
fumecheng-12201	201	36	using	use	VERB
fumecheng-12201	201	37	perturbation	perturbation	NOUN
fumecheng-12201	201	38	method	method	NOUN
fumecheng-12201	201	39	,	,	PUNCT
fumecheng-12201	201	40	heliyon	heliyon	NOUN
fumecheng-12201	201	41	,	,	PUNCT
fumecheng-12201	201	42	9(10	9(10	NUM
fumecheng-12201	201	43	)	)	PUNCT
fumecheng-12201	201	44	,	,	PUNCT
fumecheng-12201	201	45	e20196	e20196	PROPN
fumecheng-12201	201	46	.	.	PUNCT
fumecheng-12201	202	1	9	9	X
fumecheng-12201	202	2	.	.	X
fumecheng-12201	202	3	qi	qi	PROPN
fumecheng-12201	202	4	,	,	PUNCT
fumecheng-12201	202	5	k.y	k.y	PROPN
fumecheng-12201	202	6	.	.	PROPN
fumecheng-12201	202	7	,	,	PUNCT
fumecheng-12201	202	8	yao	yao	PROPN
fumecheng-12201	202	9	,	,	PUNCT
fumecheng-12201	202	10	x.k	x.k	PROPN
fumecheng-12201	202	11	.	.	PROPN
fumecheng-12201	202	12	,	,	PUNCT
fumecheng-12201	202	13	zhao	zhao	PROPN
fumecheng-12201	202	14	,	,	PUNCT
fumecheng-12201	202	15	l.c	l.c	PROPN
fumecheng-12201	202	16	.	.	PROPN
fumecheng-12201	202	17	,	,	PUNCT
fumecheng-12201	202	18	yang	yang	PROPN
fumecheng-12201	202	19	,	,	PUNCT
fumecheng-12201	202	20	z.y	z.y	PROPN
fumecheng-12201	202	21	.	.	PROPN
fumecheng-12201	202	22	,	,	PUNCT
fumecheng-12201	202	23	2023	2023	NUM
fumecheng-12201	202	24	,	,	PUNCT
fumecheng-12201	202	25	solitonic	solitonic	ADJ
fumecheng-12201	202	26	attractors	attractor	NOUN
fumecheng-12201	202	27	in	in	ADP
fumecheng-12201	202	28	the	the	DET
fumecheng-12201	202	29	coupled	couple	VERB
fumecheng-12201	202	30	nonlinear	nonlinear	ADJ
fumecheng-12201	202	31	schrodinger	schrodinger	PROPN
fumecheng-12201	202	32	equations	equation	NOUN
fumecheng-12201	202	33	with	with	ADP
fumecheng-12201	202	34	weak	weak	ADJ
fumecheng-12201	202	35	dissipations	dissipation	NOUN
fumecheng-12201	202	36	,	,	PUNCT
fumecheng-12201	202	37	communications	communication	NOUN
fumecheng-12201	202	38	in	in	ADP
fumecheng-12201	202	39	theoretical	theoretical	ADJ
fumecheng-12201	202	40	physics	physics	NOUN
fumecheng-12201	202	41	,	,	PUNCT
fumecheng-12201	202	42	75(6	75(6	NUM
fumecheng-12201	202	43	)	)	PUNCT
fumecheng-12201	202	44	,	,	PUNCT
fumecheng-12201	202	45	065003	065003	NUM
fumecheng-12201	202	46	.	.	PUNCT
fumecheng-12201	203	1	10	10	NUM
fumecheng-12201	203	2	.	.	X
fumecheng-12201	203	3	qie	qie	PROPN
fumecheng-12201	203	4	,	,	PUNCT
fumecheng-12201	203	5	n.	n.	NOUN
fumecheng-12201	203	6	,	,	PUNCT
fumecheng-12201	203	7	houa	houa	PROPN
fumecheng-12201	203	8	,	,	PUNCT
fumecheng-12201	203	9	w.f	w.f	PROPN
fumecheng-12201	203	10	.	.	PROPN
fumecheng-12201	203	11	,	,	PUNCT
fumecheng-12201	203	12	he	he	PRON
fumecheng-12201	203	13	,	,	PUNCT
fumecheng-12201	203	14	j.h	j.h	PROPN
fumecheng-12201	203	15	.	.	PROPN
fumecheng-12201	203	16	,	,	PUNCT
fumecheng-12201	203	17	2021	2021	NUM
fumecheng-12201	203	18	,	,	PUNCT
fumecheng-12201	203	19	the	the	DET
fumecheng-12201	203	20	fastest	fast	ADJ
fumecheng-12201	203	21	insight	insight	NOUN
fumecheng-12201	203	22	into	into	ADP
fumecheng-12201	203	23	the	the	DET
fumecheng-12201	203	24	large	large	ADJ
fumecheng-12201	203	25	amplitude	amplitude	NOUN
fumecheng-12201	203	26	vibration	vibration	NOUN
fumecheng-12201	203	27	of	of	ADP
fumecheng-12201	203	28	a	a	DET
fumecheng-12201	203	29	string	string	NOUN
fumecheng-12201	203	30	,	,	PUNCT
fumecheng-12201	203	31	reports	report	NOUN
fumecheng-12201	203	32	in	in	ADP
fumecheng-12201	203	33	mechanical	mechanical	ADJ
fumecheng-12201	203	34	engineering	engineering	NOUN
fumecheng-12201	203	35	,	,	PUNCT
fumecheng-12201	203	36	2(1	2(1	NUM
fumecheng-12201	203	37	)	)	PUNCT
fumecheng-12201	203	38	,	,	PUNCT
fumecheng-12201	203	39	pp	pp	ADP
fumecheng-12201	203	40	.	.	PUNCT
fumecheng-12201	204	1	1	1	NUM
fumecheng-12201	204	2	-	-	SYM
fumecheng-12201	204	3	5	5	NUM
fumecheng-12201	204	4	.	.	NOUN
fumecheng-12201	204	5	11	11	NUM
fumecheng-12201	204	6	.	.	PUNCT
fumecheng-12201	205	1	he	he	PRON
fumecheng-12201	205	2	,	,	PUNCT
fumecheng-12201	205	3	j.h	j.h	PROPN
fumecheng-12201	205	4	.	.	PROPN
fumecheng-12201	205	5	,	,	PUNCT
fumecheng-12201	205	6	2019	2019	NUM
fumecheng-12201	205	7	,	,	PUNCT
fumecheng-12201	205	8	the	the	DET
fumecheng-12201	205	9	simplest	simple	ADJ
fumecheng-12201	205	10	approach	approach	NOUN
fumecheng-12201	205	11	to	to	ADP
fumecheng-12201	205	12	nonlinear	nonlinear	ADJ
fumecheng-12201	205	13	oscillators	oscillator	NOUN
fumecheng-12201	205	14	,	,	PUNCT
fumecheng-12201	205	15	results	result	NOUN
fumecheng-12201	205	16	in	in	ADP
fumecheng-12201	205	17	physics	physics	NOUN
fumecheng-12201	205	18	,	,	PUNCT
fumecheng-12201	205	19	15(2019	15(2019	NUM
fumecheng-12201	205	20	)	)	PUNCT
fumecheng-12201	205	21	,	,	PUNCT
fumecheng-12201	205	22	102546	102546	NUM
fumecheng-12201	205	23	.	.	PUNCT
fumecheng-12201	206	1	12	12	NUM
fumecheng-12201	206	2	.	.	PUNCT
fumecheng-12201	207	1	he	he	PRON
fumecheng-12201	207	2	,	,	PUNCT
fumecheng-12201	207	3	j.h	j.h	PROPN
fumecheng-12201	207	4	.	.	PROPN
fumecheng-12201	207	5	,	,	PUNCT
fumecheng-12201	207	6	yang	yang	PROPN
fumecheng-12201	207	7	,	,	PUNCT
fumecheng-12201	207	8	q.	q.	PROPN
fumecheng-12201	207	9	,	,	PUNCT
fumecheng-12201	207	10	he	he	PRON
fumecheng-12201	207	11	,	,	PUNCT
fumecheng-12201	207	12	c.h	c.h	PROPN
fumecheng-12201	207	13	.	.	PROPN
fumecheng-12201	207	14	,	,	PUNCT
fumecheng-12201	207	15	khan	khan	PROPN
fumecheng-12201	207	16	,	,	PUNCT
fumecheng-12201	207	17	y.	y.	PROPN
fumecheng-12201	207	18	,	,	PUNCT
fumecheng-12201	207	19	2021	2021	NUM
fumecheng-12201	207	20	,	,	PUNCT
fumecheng-12201	207	21	a	a	DET
fumecheng-12201	207	22	simple	simple	ADJ
fumecheng-12201	207	23	frequency	frequency	NOUN
fumecheng-12201	207	24	formulation	formulation	NOUN
fumecheng-12201	207	25	for	for	ADP
fumecheng-12201	207	26	the	the	DET
fumecheng-12201	207	27	tangent	tangent	NOUN
fumecheng-12201	207	28	oscillator	oscillator	NOUN
fumecheng-12201	207	29	,	,	PUNCT
fumecheng-12201	207	30	axioms	axiom	NOUN
fumecheng-12201	207	31	,	,	PUNCT
fumecheng-12201	207	32	10(4	10(4	NUM
fumecheng-12201	207	33	)	)	PUNCT
fumecheng-12201	207	34	,	,	PUNCT
fumecheng-12201	207	35	320	320	NUM
fumecheng-12201	207	36	.	.	NOUN
fumecheng-12201	207	37	13	13	NUM
fumecheng-12201	207	38	.	.	PUNCT
fumecheng-12201	207	39	elias	elias	PROPN
fumecheng-12201	207	40	-	-	PUNCT
fumecheng-12201	207	41	zuniga	zuniga	PROPN
fumecheng-12201	207	42	,	,	PUNCT
fumecheng-12201	207	43	a.	a.	NOUN
fumecheng-12201	207	44	,	,	PUNCT
fumecheng-12201	207	45	palacios	palacio	NOUN
fumecheng-12201	207	46	-	-	PUNCT
fumecheng-12201	207	47	pineda	pineda	PROPN
fumecheng-12201	207	48	,	,	PUNCT
fumecheng-12201	207	49	l.m	l.m	PROPN
fumecheng-12201	207	50	.	.	PROPN
fumecheng-12201	207	51	,	,	PUNCT
fumecheng-12201	207	52	jimenez	jimenez	PROPN
fumecheng-12201	207	53	-	-	PUNCT
fumecheng-12201	207	54	cedeno	cedeno	PROPN
fumecheng-12201	207	55	,	,	PUNCT
fumecheng-12201	207	56	i.h	i.h	PROPN
fumecheng-12201	207	57	.	.	PROPN
fumecheng-12201	207	58	,	,	PUNCT
fumecheng-12201	207	59	martinez	martinez	PROPN
fumecheng-12201	207	60	-	-	PUNCT
fumecheng-12201	207	61	romero	romero	PROPN
fumecheng-12201	207	62	,	,	PUNCT
fumecheng-12201	207	63	o.	o.	PROPN
fumecheng-12201	207	64	,	,	PUNCT
fumecheng-12201	207	65	trejo	trejo	PROPN
fumecheng-12201	207	66	,	,	PUNCT
fumecheng-12201	207	67	d.o	d.o	PROPN
fumecheng-12201	207	68	.	.	PROPN
fumecheng-12201	207	69	,	,	PUNCT
fumecheng-12201	207	70	2021	2021	NUM
fumecheng-12201	207	71	,	,	PUNCT
fumecheng-12201	207	72	equivalent	equivalent	ADJ
fumecheng-12201	207	73	power	power	NOUN
fumecheng-12201	207	74	-	-	PUNCT
fumecheng-12201	207	75	form	form	NOUN
fumecheng-12201	207	76	representation	representation	NOUN
fumecheng-12201	207	77	of	of	ADP
fumecheng-12201	207	78	the	the	DET
fumecheng-12201	207	79	fractal	fractal	ADJ
fumecheng-12201	207	80	toda	toda	PROPN
fumecheng-12201	207	81	oscillator	oscillator	PROPN
fumecheng-12201	207	82	,	,	PUNCT
fumecheng-12201	207	83	fractals	fractal	NOUN
fumecheng-12201	207	84	,	,	PUNCT
fumecheng-12201	207	85	29(02	29(02	NUM
fumecheng-12201	207	86	)	)	PUNCT
fumecheng-12201	207	87	,	,	PUNCT
fumecheng-12201	207	88	2150034	2150034	NUM
fumecheng-12201	207	89	.	.	PUNCT
fumecheng-12201	208	1	14	14	NUM
fumecheng-12201	208	2	.	.	X
fumecheng-12201	209	1	tian	tian	ADJ
fumecheng-12201	209	2	,	,	PUNCT
fumecheng-12201	209	3	y.	y.	NOUN
fumecheng-12201	209	4	,	,	PUNCT
fumecheng-12201	209	5	2022	2022	NUM
fumecheng-12201	209	6	,	,	PUNCT
fumecheng-12201	209	7	frequency	frequency	NOUN
fumecheng-12201	209	8	formula	formula	NOUN
fumecheng-12201	209	9	for	for	ADP
fumecheng-12201	209	10	a	a	DET
fumecheng-12201	209	11	class	class	NOUN
fumecheng-12201	209	12	of	of	ADP
fumecheng-12201	209	13	fractal	fractal	ADJ
fumecheng-12201	209	14	vibration	vibration	NOUN
fumecheng-12201	209	15	system	system	NOUN
fumecheng-12201	209	16	,	,	PUNCT
fumecheng-12201	209	17	reports	report	NOUN
fumecheng-12201	209	18	in	in	ADP
fumecheng-12201	209	19	mechanical	mechanical	ADJ
fumecheng-12201	209	20	engineering	engineering	NOUN
fumecheng-12201	209	21	,	,	PUNCT
fumecheng-12201	209	22	3(1	3(1	NUM
fumecheng-12201	209	23	)	)	PUNCT
fumecheng-12201	209	24	,	,	PUNCT
fumecheng-12201	209	25	pp	pp	ADP
fumecheng-12201	209	26	.	.	PUNCT
fumecheng-12201	210	1	55	55	NUM
fumecheng-12201	210	2	-	-	SYM
fumecheng-12201	210	3	61	61	NUM
fumecheng-12201	210	4	.	.	PUNCT
fumecheng-12201	211	1	712	712	NUM
fumecheng-12201	211	2	j.g.zhang	j.g.zhang	PROPN
fumecheng-12201	211	3	,	,	PUNCT
fumecheng-12201	211	4	q.r.song	q.r.song	PROPN
fumecheng-12201	211	5	,	,	PUNCT
fumecheng-12201	211	6	j.q.zhang	j.q.zhang	PROPN
fumecheng-12201	211	7	,	,	PUNCT
fumecheng-12201	211	8	f.wang	f.wang	PROPN
fumecheng-12201	211	9	15	15	NUM
fumecheng-12201	211	10	.	.	PUNCT
fumecheng-12201	212	1	feng	feng	PROPN
fumecheng-12201	212	2	,	,	PUNCT
fumecheng-12201	212	3	g.q	g.q	PROPN
fumecheng-12201	212	4	.	.	PROPN
fumecheng-12201	212	5	,	,	PUNCT
fumecheng-12201	212	6	2021	2021	NUM
fumecheng-12201	212	7	,	,	PUNCT
fumecheng-12201	212	8	he	he	PRON
fumecheng-12201	212	9	’s	’	VERB
fumecheng-12201	212	10	frequency	frequency	NOUN
fumecheng-12201	212	11	formula	formula	NOUN
fumecheng-12201	212	12	to	to	ADP
fumecheng-12201	212	13	fractal	fractal	ADJ
fumecheng-12201	212	14	undamped	undampe	VERB
fumecheng-12201	212	15	duffing	duffing	NOUN
fumecheng-12201	212	16	equation	equation	NOUN
fumecheng-12201	212	17	,	,	PUNCT
fumecheng-12201	212	18	journal	journal	NOUN
fumecheng-12201	212	19	of	of	ADP
fumecheng-12201	212	20	low	low	ADJ
fumecheng-12201	212	21	frequency	frequency	NOUN
fumecheng-12201	212	22	noise	noise	NOUN
fumecheng-12201	212	23	,	,	PUNCT
fumecheng-12201	212	24	vibration	vibration	NOUN
fumecheng-12201	212	25	and	and	CCONJ
fumecheng-12201	212	26	active	active	ADJ
fumecheng-12201	212	27	control	control	NOUN
fumecheng-12201	212	28	,	,	PUNCT
fumecheng-12201	212	29	40(4	40(4	NUM
fumecheng-12201	212	30	)	)	PUNCT
fumecheng-12201	212	31	,	,	PUNCT
fumecheng-12201	212	32	pp	pp	ADP
fumecheng-12201	212	33	.	.	PUNCT
fumecheng-12201	213	1	1671–1676	1671–1676	NUM
fumecheng-12201	213	2	.	.	PUNCT
fumecheng-12201	214	1	16	16	NUM
fumecheng-12201	214	2	.	.	PUNCT
fumecheng-12201	215	1	he	he	PRON
fumecheng-12201	215	2	,	,	PUNCT
fumecheng-12201	215	3	c.h	c.h	PROPN
fumecheng-12201	215	4	.	.	PROPN
fumecheng-12201	215	5	,	,	PUNCT
fumecheng-12201	215	6	2016	2016	NUM
fumecheng-12201	215	7	,	,	PUNCT
fumecheng-12201	215	8	an	an	DET
fumecheng-12201	215	9	introduction	introduction	NOUN
fumecheng-12201	215	10	to	to	ADP
fumecheng-12201	215	11	an	an	DET
fumecheng-12201	215	12	ancient	ancient	ADJ
fumecheng-12201	215	13	chinese	chinese	ADJ
fumecheng-12201	215	14	algorithm	algorithm	NOUN
fumecheng-12201	215	15	and	and	CCONJ
fumecheng-12201	215	16	its	its	PRON
fumecheng-12201	215	17	modification	modification	NOUN
fumecheng-12201	215	18	,	,	PUNCT
fumecheng-12201	215	19	international	international	ADJ
fumecheng-12201	215	20	journal	journal	NOUN
fumecheng-12201	215	21	of	of	ADP
fumecheng-12201	215	22	numerical	numerical	ADJ
fumecheng-12201	215	23	methods	method	NOUN
fumecheng-12201	215	24	for	for	ADP
fumecheng-12201	215	25	heat	heat	NOUN
fumecheng-12201	215	26	and	and	CCONJ
fumecheng-12201	215	27	fluid	fluid	ADJ
fumecheng-12201	215	28	flow	flow	NOUN
fumecheng-12201	215	29	,	,	PUNCT
fumecheng-12201	215	30	26(8	26(8	NUM
fumecheng-12201	215	31	)	)	PUNCT
fumecheng-12201	215	32	,	,	PUNCT
fumecheng-12201	215	33	pp	pp	PROPN
fumecheng-12201	215	34	.	.	PUNCT
fumecheng-12201	215	35	2486	2486	NUM
fumecheng-12201	215	36	-	-	SYM
fumecheng-12201	215	37	2491	2491	NUM
fumecheng-12201	215	38	.	.	PUNCT
fumecheng-12201	216	1	17	17	NUM
fumecheng-12201	216	2	.	.	PUNCT
fumecheng-12201	217	1	khan	khan	PROPN
fumecheng-12201	217	2	,	,	PUNCT
fumecheng-12201	217	3	w.a	w.a	PROPN
fumecheng-12201	217	4	.	.	PROPN
fumecheng-12201	217	5	,	,	PUNCT
fumecheng-12201	217	6	2022	2022	NUM
fumecheng-12201	217	7	,	,	PUNCT
fumecheng-12201	217	8	numerical	numerical	PROPN
fumecheng-12201	217	9	simulation	simulation	NOUN
fumecheng-12201	217	10	of	of	ADP
fumecheng-12201	217	11	chun	chun	PROPN
fumecheng-12201	217	12	-	-	PUNCT
fumecheng-12201	217	13	hui	hui	PROPN
fumecheng-12201	218	1	he	he	PRON
fumecheng-12201	218	2	's	be	AUX
fumecheng-12201	218	3	iteration	iteration	NOUN
fumecheng-12201	218	4	method	method	NOUN
fumecheng-12201	218	5	with	with	ADP
fumecheng-12201	218	6	applications	application	NOUN
fumecheng-12201	218	7	in	in	ADP
fumecheng-12201	218	8	engineering	engineering	NOUN
fumecheng-12201	218	9	,	,	PUNCT
fumecheng-12201	218	10	international	international	ADJ
fumecheng-12201	218	11	journal	journal	NOUN
fumecheng-12201	218	12	of	of	ADP
fumecheng-12201	218	13	numerical	numerical	ADJ
fumecheng-12201	218	14	methods	method	NOUN
fumecheng-12201	218	15	for	for	ADP
fumecheng-12201	218	16	heat	heat	NOUN
fumecheng-12201	218	17	and	and	CCONJ
fumecheng-12201	218	18	fluid	fluid	ADJ
fumecheng-12201	218	19	flow	flow	NOUN
fumecheng-12201	218	20	,	,	PUNCT
fumecheng-12201	218	21	32(3	32(3	NUM
fumecheng-12201	218	22	)	)	PUNCT
fumecheng-12201	218	23	,	,	PUNCT
fumecheng-12201	218	24	pp	pp	PROPN
fumecheng-12201	218	25	.	.	PUNCT
fumecheng-12201	219	1	944	944	NUM
fumecheng-12201	219	2	-	-	SYM
fumecheng-12201	219	3	955	955	NUM
fumecheng-12201	219	4	.	.	PUNCT
fumecheng-12201	220	1	18	18	NUM
fumecheng-12201	220	2	.	.	PUNCT
fumecheng-12201	221	1	khan	khan	PROPN
fumecheng-12201	221	2	,	,	PUNCT
fumecheng-12201	221	3	w.a	w.a	PROPN
fumecheng-12201	221	4	.	.	PROPN
fumecheng-12201	221	5	,	,	PUNCT
fumecheng-12201	221	6	arif	arif	PROPN
fumecheng-12201	221	7	,	,	PUNCT
fumecheng-12201	221	8	m.	m.	NOUN
fumecheng-12201	221	9	,	,	PUNCT
fumecheng-12201	221	10	mohammed	mohammed	PROPN
fumecheng-12201	221	11	,	,	PUNCT
fumecheng-12201	221	12	m.	m.	NOUN
fumecheng-12201	221	13	,	,	PUNCT
fumecheng-12201	221	14	et	et	PROPN
fumecheng-12201	221	15	al	al	PROPN
fumecheng-12201	221	16	.	.	PROPN
fumecheng-12201	221	17	,	,	PUNCT
fumecheng-12201	221	18	2022	2022	NUM
fumecheng-12201	221	19	,	,	PUNCT
fumecheng-12201	221	20	numerical	numerical	ADJ
fumecheng-12201	221	21	and	and	CCONJ
fumecheng-12201	221	22	theoretical	theoretical	ADJ
fumecheng-12201	221	23	investigation	investigation	NOUN
fumecheng-12201	221	24	to	to	PART
fumecheng-12201	221	25	estimate	estimate	VERB
fumecheng-12201	221	26	darcy	darcy	PROPN
fumecheng-12201	221	27	friction	friction	NOUN
fumecheng-12201	221	28	factor	factor	NOUN
fumecheng-12201	221	29	in	in	ADP
fumecheng-12201	221	30	water	water	NOUN
fumecheng-12201	221	31	network	network	NOUN
fumecheng-12201	221	32	problem	problem	NOUN
fumecheng-12201	221	33	based	base	VERB
fumecheng-12201	221	34	on	on	ADP
fumecheng-12201	221	35	modified	modified	ADJ
fumecheng-12201	221	36	chun	chun	PROPN
fumecheng-12201	221	37	-	-	PUNCT
fumecheng-12201	221	38	hui	hui	PROPN
fumecheng-12201	222	1	he	he	PRON
fumecheng-12201	222	2	's	be	AUX
fumecheng-12201	222	3	algorithm	algorithm	NOUN
fumecheng-12201	222	4	and	and	CCONJ
fumecheng-12201	222	5	applications	application	NOUN
fumecheng-12201	222	6	,	,	PUNCT
fumecheng-12201	222	7	mathematical	mathematical	ADJ
fumecheng-12201	222	8	problems	problem	NOUN
fumecheng-12201	222	9	in	in	ADP
fumecheng-12201	222	10	engineering	engineering	NOUN
fumecheng-12201	222	11	,	,	PUNCT
fumecheng-12201	222	12	2022	2022	NUM
fumecheng-12201	222	13	,	,	PUNCT
fumecheng-12201	222	14	8116282	8116282	NUM
fumecheng-12201	222	15	,	,	PUNCT
fumecheng-12201	222	16	doi	doi	NOUN
fumecheng-12201	222	17	:	:	PUNCT
fumecheng-12201	222	18	10.1155/2022/8116282	10.1155/2022/8116282	NUM
fumecheng-12201	222	19	.	.	PUNCT
fumecheng-12201	223	1	19	19	NUM
fumecheng-12201	223	2	.	.	PUNCT
fumecheng-12201	223	3	elías	elías	PROPN
fumecheng-12201	223	4	-	-	PUNCT
fumecheng-12201	223	5	zúñiga	zúñiga	PROPN
fumecheng-12201	223	6	,	,	PUNCT
fumecheng-12201	223	7	a.	a.	NOUN
fumecheng-12201	223	8	,	,	PUNCT
fumecheng-12201	223	9	palacios	palacio	NOUN
fumecheng-12201	223	10	-	-	PUNCT
fumecheng-12201	223	11	pineda	pineda	PROPN
fumecheng-12201	223	12	,	,	PUNCT
fumecheng-12201	223	13	l.m	l.m	PROPN
fumecheng-12201	223	14	.	.	PROPN
fumecheng-12201	223	15	,	,	PUNCT
fumecheng-12201	223	16	jiménez	jiménez	PROPN
fumecheng-12201	223	17	-	-	PUNCT
fumecheng-12201	223	18	cedeño	cedeño	PROPN
fumecheng-12201	223	19	,	,	PUNCT
fumecheng-12201	223	20	i.h	i.h	PROPN
fumecheng-12201	223	21	.	.	PROPN
fumecheng-12201	223	22	,	,	PUNCT
fumecheng-12201	223	23	martínez	martínez	PROPN
fumecheng-12201	223	24	-	-	PUNCT
fumecheng-12201	223	25	romero	romero	PROPN
fumecheng-12201	223	26	,	,	PUNCT
fumecheng-12201	223	27	o.	o.	PROPN
fumecheng-12201	223	28	,	,	PUNCT
fumecheng-12201	223	29	trejo	trejo	PROPN
fumecheng-12201	223	30	,	,	PUNCT
fumecheng-12201	223	31	d.o	d.o	PROPN
fumecheng-12201	223	32	.	.	PROPN
fumecheng-12201	223	33	,	,	PUNCT
fumecheng-12201	223	34	2020	2020	NUM
fumecheng-12201	223	35	,	,	PUNCT
fumecheng-12201	223	36	he	he	PRON
fumecheng-12201	223	37	’s	’	VERB
fumecheng-12201	223	38	frequency	frequency	NOUN
fumecheng-12201	223	39	–	–	PUNCT
fumecheng-12201	223	40	amplitude	amplitude	NOUN
fumecheng-12201	223	41	formulation	formulation	NOUN
fumecheng-12201	223	42	for	for	ADP
fumecheng-12201	223	43	nonlinear	nonlinear	ADJ
fumecheng-12201	223	44	oscillators	oscillator	NOUN
fumecheng-12201	223	45	using	use	VERB
fumecheng-12201	223	46	jacobi	jacobi	PROPN
fumecheng-12201	223	47	elliptic	elliptic	ADJ
fumecheng-12201	223	48	functions	function	NOUN
fumecheng-12201	223	49	,	,	PUNCT
fumecheng-12201	223	50	journal	journal	NOUN
fumecheng-12201	223	51	of	of	ADP
fumecheng-12201	223	52	low	low	ADJ
fumecheng-12201	223	53	frequency	frequency	NOUN
fumecheng-12201	223	54	noise	noise	NOUN
fumecheng-12201	223	55	,	,	PUNCT
fumecheng-12201	223	56	vibration	vibration	NOUN
fumecheng-12201	223	57	and	and	CCONJ
fumecheng-12201	223	58	active	active	ADJ
fumecheng-12201	223	59	control	control	NOUN
fumecheng-12201	223	60	,	,	PUNCT
fumecheng-12201	223	61	39(4	39(4	NOUN
fumecheng-12201	223	62	)	)	PUNCT
fumecheng-12201	223	63	,	,	PUNCT
fumecheng-12201	223	64	pp	pp	PROPN
fumecheng-12201	223	65	.	.	PUNCT
fumecheng-12201	224	1	1216	1216	NUM
fumecheng-12201	224	2	-	-	SYM
fumecheng-12201	224	3	1223	1223	NUM
fumecheng-12201	224	4	.	.	PUNCT
fumecheng-12201	225	1	20	20	NUM
fumecheng-12201	225	2	.	.	X
fumecheng-12201	226	1	ma	ma	PROPN
fumecheng-12201	226	2	,	,	PUNCT
fumecheng-12201	226	3	h.j	h.j	PROPN
fumecheng-12201	226	4	.	.	PROPN
fumecheng-12201	226	5	,	,	PUNCT
fumecheng-12201	226	6	2022	2022	NUM
fumecheng-12201	226	7	,	,	PUNCT
fumecheng-12201	226	8	simplified	simplified	ADJ
fumecheng-12201	226	9	hamiltonian	hamiltonian	ADJ
fumecheng-12201	226	10	-	-	PUNCT
fumecheng-12201	226	11	based	base	VERB
fumecheng-12201	226	12	frequency	frequency	NOUN
fumecheng-12201	226	13	-	-	PUNCT
fumecheng-12201	226	14	amplitude	amplitude	NOUN
fumecheng-12201	226	15	formulation	formulation	NOUN
fumecheng-12201	226	16	for	for	ADP
fumecheng-12201	226	17	nonlinear	nonlinear	ADJ
fumecheng-12201	226	18	vibration	vibration	NOUN
fumecheng-12201	226	19	systems	system	NOUN
fumecheng-12201	226	20	,	,	PUNCT
fumecheng-12201	226	21	facta	facta	PROPN
fumecheng-12201	226	22	universitatis	universitatis	PROPN
fumecheng-12201	226	23	series	series	PROPN
fumecheng-12201	226	24	mechanical	mechanical	ADJ
fumecheng-12201	226	25	engineering	engineering	NOUN
fumecheng-12201	226	26	,	,	PUNCT
fumecheng-12201	226	27	20(2	20(2	NUM
fumecheng-12201	226	28	)	)	PUNCT
fumecheng-12201	226	29	,	,	PUNCT
fumecheng-12201	226	30	pp	pp	PROPN
fumecheng-12201	226	31	.	.	PUNCT
fumecheng-12201	227	1	445	445	NUM
fumecheng-12201	227	2	-	-	SYM
fumecheng-12201	227	3	455	455	NUM
fumecheng-12201	227	4	.	.	PUNCT
fumecheng-12201	228	1	21	21	NUM
fumecheng-12201	228	2	.	.	PUNCT
fumecheng-12201	229	1	alyousef	alyousef	PROPN
fumecheng-12201	229	2	,	,	PUNCT
fumecheng-12201	229	3	h.a	h.a	PROPN
fumecheng-12201	229	4	.	.	PROPN
fumecheng-12201	229	5	,	,	PUNCT
fumecheng-12201	229	6	salas	salas	PROPN
fumecheng-12201	229	7	,	,	PUNCT
fumecheng-12201	229	8	a.h	a.h	PROPN
fumecheng-12201	229	9	.	.	PROPN
fumecheng-12201	229	10	,	,	PUNCT
fumecheng-12201	229	11	alharthi	alharthi	PROPN
fumecheng-12201	229	12	,	,	PUNCT
fumecheng-12201	229	13	m.r	m.r	PROPN
fumecheng-12201	229	14	.	.	PROPN
fumecheng-12201	229	15	,	,	PUNCT
fumecheng-12201	229	16	el	el	PROPN
fumecheng-12201	229	17	-	-	PUNCT
fumecheng-12201	229	18	tantawy	tantawy	NOUN
fumecheng-12201	229	19	,	,	PUNCT
fumecheng-12201	229	20	s.a	s.a	PROPN
fumecheng-12201	229	21	.	.	PROPN
fumecheng-12201	229	22	,	,	PUNCT
fumecheng-12201	229	23	2022	2022	NUM
fumecheng-12201	229	24	,	,	PUNCT
fumecheng-12201	229	25	galerkin	galerkin	ADJ
fumecheng-12201	229	26	method	method	NOUN
fumecheng-12201	229	27	,	,	PUNCT
fumecheng-12201	229	28	ansatz	ansatz	ADJ
fumecheng-12201	229	29	method	method	NOUN
fumecheng-12201	229	30	,	,	PUNCT
fumecheng-12201	229	31	and	and	CCONJ
fumecheng-12201	229	32	he	he	PRON
fumecheng-12201	229	33	’s	’	VERB
fumecheng-12201	229	34	frequency	frequency	NOUN
fumecheng-12201	229	35	formulation	formulation	NOUN
fumecheng-12201	229	36	for	for	ADP
fumecheng-12201	229	37	modeling	model	VERB
fumecheng-12201	229	38	the	the	DET
fumecheng-12201	229	39	forced	force	VERB
fumecheng-12201	229	40	damped	damp	VERB
fumecheng-12201	229	41	parametric	parametric	ADJ
fumecheng-12201	229	42	driven	drive	VERB
fumecheng-12201	229	43	pendulum	pendulum	NOUN
fumecheng-12201	229	44	oscillators	oscillator	NOUN
fumecheng-12201	229	45	,	,	PUNCT
fumecheng-12201	229	46	journal	journal	NOUN
fumecheng-12201	229	47	of	of	ADP
fumecheng-12201	229	48	low	low	ADJ
fumecheng-12201	229	49	frequency	frequency	NOUN
fumecheng-12201	229	50	noise	noise	NOUN
fumecheng-12201	229	51	,	,	PUNCT
fumecheng-12201	229	52	vibration	vibration	NOUN
fumecheng-12201	229	53	and	and	CCONJ
fumecheng-12201	229	54	active	active	ADJ
fumecheng-12201	229	55	control	control	NOUN
fumecheng-12201	229	56	,	,	PUNCT
fumecheng-12201	229	57	41(4	41(4	NUM
fumecheng-12201	229	58	)	)	PUNCT
fumecheng-12201	229	59	,	,	PUNCT
fumecheng-12201	229	60	pp	pp	ADJ
fumecheng-12201	229	61	.	.	PUNCT
fumecheng-12201	230	1	1426	1426	NUM
fumecheng-12201	230	2	-	-	SYM
fumecheng-12201	230	3	1445	1445	NUM
fumecheng-12201	230	4	.	.	PUNCT
fumecheng-12201	231	1	22	22	NUM
fumecheng-12201	231	2	.	.	PUNCT
fumecheng-12201	232	1	he	he	PRON
fumecheng-12201	232	2	,	,	PUNCT
fumecheng-12201	232	3	c.h	c.h	PROPN
fumecheng-12201	232	4	.	.	PROPN
fumecheng-12201	232	5	,	,	PUNCT
fumecheng-12201	232	6	liu	liu	PROPN
fumecheng-12201	232	7	,	,	PUNCT
fumecheng-12201	232	8	c.	c.	PROPN
fumecheng-12201	232	9	,	,	PUNCT
fumecheng-12201	232	10	2022	2022	NUM
fumecheng-12201	232	11	,	,	PUNCT
fumecheng-12201	232	12	a	a	DET
fumecheng-12201	232	13	modified	modify	VERB
fumecheng-12201	232	14	frequency	frequency	NOUN
fumecheng-12201	232	15	-	-	PUNCT
fumecheng-12201	232	16	amplitude	amplitude	NOUN
fumecheng-12201	232	17	formulation	formulation	NOUN
fumecheng-12201	232	18	for	for	ADP
fumecheng-12201	232	19	fractal	fractal	ADJ
fumecheng-12201	232	20	vibration	vibration	NOUN
fumecheng-12201	232	21	systems	system	NOUN
fumecheng-12201	232	22	,	,	PUNCT
fumecheng-12201	232	23	fractals	fractal	NOUN
fumecheng-12201	232	24	,	,	PUNCT
fumecheng-12201	232	25	30(3	30(3	NUM
fumecheng-12201	232	26	)	)	PUNCT
fumecheng-12201	232	27	,	,	PUNCT
fumecheng-12201	232	28	2250046	2250046	NUM
fumecheng-12201	232	29	.	.	PUNCT
fumecheng-12201	233	1	23	23	NUM
fumecheng-12201	233	2	.	.	PUNCT
fumecheng-12201	234	1	moatimid	moatimid	PROPN
fumecheng-12201	234	2	,	,	PUNCT
fumecheng-12201	234	3	g.m	g.m	PROPN
fumecheng-12201	234	4	.	.	PROPN
fumecheng-12201	234	5	,	,	PUNCT
fumecheng-12201	234	6	amer	amer	PROPN
fumecheng-12201	234	7	,	,	PUNCT
fumecheng-12201	234	8	t.s	t.s	PROPN
fumecheng-12201	234	9	.	.	PROPN
fumecheng-12201	234	10	,	,	PUNCT
fumecheng-12201	234	11	amer	amer	PROPN
fumecheng-12201	234	12	,	,	PUNCT
fumecheng-12201	234	13	w.s	w.s	PROPN
fumecheng-12201	234	14	.	.	PROPN
fumecheng-12201	234	15	,	,	PUNCT
fumecheng-12201	234	16	2023	2023	NUM
fumecheng-12201	234	17	,	,	PUNCT
fumecheng-12201	234	18	dynamical	dynamical	ADJ
fumecheng-12201	234	19	analysis	analysis	NOUN
fumecheng-12201	234	20	of	of	ADP
fumecheng-12201	234	21	a	a	DET
fumecheng-12201	234	22	damped	damped	ADJ
fumecheng-12201	234	23	harmonic	harmonic	NOUN
fumecheng-12201	234	24	forced	force	VERB
fumecheng-12201	234	25	duffing	duffe	VERB
fumecheng-12201	234	26	oscillator	oscillator	NOUN
fumecheng-12201	234	27	with	with	ADP
fumecheng-12201	234	28	time	time	NOUN
fumecheng-12201	234	29	delay	delay	NOUN
fumecheng-12201	234	30	,	,	PUNCT
fumecheng-12201	234	31	scientific	scientific	ADJ
fumecheng-12201	234	32	reports	report	NOUN
fumecheng-12201	234	33	,	,	PUNCT
fumecheng-12201	234	34	13(1	13(1	NUM
fumecheng-12201	234	35	)	)	PUNCT
fumecheng-12201	234	36	,	,	PUNCT
fumecheng-12201	234	37	6507	6507	NUM
fumecheng-12201	234	38	.	.	PUNCT
fumecheng-12201	235	1	24	24	NUM
fumecheng-12201	235	2	.	.	PUNCT
fumecheng-12201	235	3	mirzabeigy	mirzabeigy	PROPN
fumecheng-12201	235	4	,	,	PUNCT
fumecheng-12201	235	5	a.	a.	NOUN
fumecheng-12201	235	6	,	,	PUNCT
fumecheng-12201	235	7	2022	2022	NUM
fumecheng-12201	235	8	,	,	PUNCT
fumecheng-12201	235	9	a	a	DET
fumecheng-12201	235	10	simple	simple	ADJ
fumecheng-12201	235	11	approach	approach	NOUN
fumecheng-12201	235	12	for	for	ADP
fumecheng-12201	235	13	dealing	deal	VERB
fumecheng-12201	235	14	with	with	ADP
fumecheng-12201	235	15	autonomous	autonomous	ADJ
fumecheng-12201	235	16	conservative	conservative	ADJ
fumecheng-12201	235	17	oscillator	oscillator	NOUN
fumecheng-12201	235	18	under	under	ADP
fumecheng-12201	235	19	initial	initial	ADJ
fumecheng-12201	235	20	velocity	velocity	NOUN
fumecheng-12201	235	21	,	,	PUNCT
fumecheng-12201	235	22	journal	journal	NOUN
fumecheng-12201	235	23	of	of	ADP
fumecheng-12201	235	24	applied	applied	ADJ
fumecheng-12201	235	25	and	and	CCONJ
fumecheng-12201	235	26	computational	computational	ADJ
fumecheng-12201	235	27	mechanics	mechanic	NOUN
fumecheng-12201	235	28	,	,	PUNCT
fumecheng-12201	235	29	8(3	8(3	NUM
fumecheng-12201	235	30	)	)	PUNCT
fumecheng-12201	235	31	,	,	PUNCT
fumecheng-12201	235	32	pp	pp	ADP
fumecheng-12201	235	33	.	.	PUNCT
fumecheng-12201	236	1	918	918	NUM
fumecheng-12201	236	2	-	-	SYM
fumecheng-12201	236	3	924	924	NUM
fumecheng-12201	236	4	.	.	NOUN
fumecheng-12201	237	1	25	25	NUM
fumecheng-12201	237	2	.	.	PUNCT
fumecheng-12201	237	3	özaltun	özaltun	PROPN
fumecheng-12201	237	4	,	,	PUNCT
fumecheng-12201	237	5	g.	g.	PROPN
fumecheng-12201	237	6	,	,	PUNCT
fumecheng-12201	237	7	gümgüm	gümgüm	NOUN
fumecheng-12201	237	8	,	,	PUNCT
fumecheng-12201	237	9	s.	s.	PROPN
fumecheng-12201	237	10	,	,	PUNCT
fumecheng-12201	237	11	2023	2023	NUM
fumecheng-12201	237	12	,	,	PUNCT
fumecheng-12201	237	13	numerical	numerical	ADJ
fumecheng-12201	237	14	solutions	solution	NOUN
fumecheng-12201	237	15	of	of	ADP
fumecheng-12201	237	16	troesch	troesch	NOUN
fumecheng-12201	237	17	and	and	CCONJ
fumecheng-12201	237	18	duffing	duffe	VERB
fumecheng-12201	237	19	equations	equation	NOUN
fumecheng-12201	237	20	by	by	ADP
fumecheng-12201	237	21	taylor	taylor	PROPN
fumecheng-12201	237	22	wavelets	wavelet	NOUN
fumecheng-12201	237	23	,	,	PUNCT
fumecheng-12201	237	24	hacettepe	hacettepe	ADJ
fumecheng-12201	237	25	journal	journal	NOUN
fumecheng-12201	237	26	of	of	ADP
fumecheng-12201	237	27	mathematics	mathematic	NOUN
fumecheng-12201	237	28	and	and	CCONJ
fumecheng-12201	237	29	statistics	statistic	NOUN
fumecheng-12201	237	30	,	,	PUNCT
fumecheng-12201	237	31	52(2	52(2	NUM
fumecheng-12201	237	32	)	)	PUNCT
fumecheng-12201	237	33	,	,	PUNCT
fumecheng-12201	237	34	pp	pp	ADP
fumecheng-12201	237	35	.	.	PUNCT
fumecheng-12201	238	1	292	292	NUM
fumecheng-12201	238	2	-	-	SYM
fumecheng-12201	238	3	302	302	NUM
fumecheng-12201	238	4	.	.	PUNCT
fumecheng-12201	238	5	26	26	NUM
fumecheng-12201	238	6	.	.	PUNCT
fumecheng-12201	239	1	he	he	PRON
fumecheng-12201	239	2	,	,	PUNCT
fumecheng-12201	239	3	j.h	j.h	PROPN
fumecheng-12201	239	4	.	.	PROPN
fumecheng-12201	239	5	,	,	PUNCT
fumecheng-12201	239	6	jiao	jiao	PROPN
fumecheng-12201	239	7	,	,	PUNCT
fumecheng-12201	239	8	m.l	m.l	PROPN
fumecheng-12201	239	9	.	.	PROPN
fumecheng-12201	239	10	,	,	PUNCT
fumecheng-12201	239	11	he	he	PRON
fumecheng-12201	239	12	,	,	PUNCT
fumecheng-12201	239	13	c.h	c.h	PROPN
fumecheng-12201	239	14	.	.	PROPN
fumecheng-12201	239	15	,	,	PUNCT
fumecheng-12201	239	16	2022	2022	NUM
fumecheng-12201	239	17	,	,	PUNCT
fumecheng-12201	239	18	homotopy	homotopy	VERB
fumecheng-12201	239	19	perturbation	perturbation	NOUN
fumecheng-12201	239	20	method	method	NOUN
fumecheng-12201	239	21	for	for	ADP
fumecheng-12201	239	22	fractal	fractal	ADJ
fumecheng-12201	239	23	duffing	duffing	NOUN
fumecheng-12201	239	24	oscillator	oscillator	NOUN
fumecheng-12201	239	25	with	with	ADP
fumecheng-12201	239	26	arbitrary	arbitrary	ADJ
fumecheng-12201	239	27	conditions	condition	NOUN
fumecheng-12201	239	28	,	,	PUNCT
fumecheng-12201	239	29	fractals	fractal	NOUN
fumecheng-12201	239	30	,	,	PUNCT
fumecheng-12201	239	31	30(09	30(09	NUM
fumecheng-12201	239	32	)	)	PUNCT
fumecheng-12201	239	33	,	,	PUNCT
fumecheng-12201	239	34	2250165	2250165	NUM
fumecheng-12201	239	35	.	.	PUNCT