id	sid	tid	token	lemma	pos
american_scientific_journal-3866	1	1	125	125	NUM
american_scientific_journal-3866	1	2	american	american	ADJ
american_scientific_journal-3866	1	3	scientific	scientific	ADJ
american_scientific_journal-3866	1	4	research	research	NOUN
american_scientific_journal-3866	1	5	journal	journal	NOUN
american_scientific_journal-3866	1	6	for	for	ADP
american_scientific_journal-3866	1	7	engineering	engineering	NOUN
american_scientific_journal-3866	1	8	,	,	PUNCT
american_scientific_journal-3866	1	9	technology	technology	NOUN
american_scientific_journal-3866	1	10	,	,	PUNCT
american_scientific_journal-3866	1	11	and	and	CCONJ
american_scientific_journal-3866	1	12	sciences	science	NOUN
american_scientific_journal-3866	1	13	(	(	PUNCT
american_scientific_journal-3866	1	14	asrjets	asrjet	NOUN
american_scientific_journal-3866	1	15	)	)	PUNCT
american_scientific_journal-3866	1	16	issn	issn	PROPN
american_scientific_journal-3866	1	17	(	(	PUNCT
american_scientific_journal-3866	1	18	print	print	NOUN
american_scientific_journal-3866	1	19	)	)	PUNCT
american_scientific_journal-3866	1	20	2313	2313	NUM
american_scientific_journal-3866	1	21	-	-	SYM
american_scientific_journal-3866	1	22	4410	4410	NUM
american_scientific_journal-3866	1	23	,	,	PUNCT
american_scientific_journal-3866	1	24	issn	issn	PROPN
american_scientific_journal-3866	1	25	(	(	PUNCT
american_scientific_journal-3866	1	26	online	online	ADJ
american_scientific_journal-3866	1	27	)	)	PUNCT
american_scientific_journal-3866	1	28	2313	2313	NUM
american_scientific_journal-3866	1	29	-	-	SYM
american_scientific_journal-3866	1	30	4402	4402	NUM
american_scientific_journal-3866	1	31	©	©	PROPN
american_scientific_journal-3866	1	32	global	global	ADJ
american_scientific_journal-3866	1	33	society	society	NOUN
american_scientific_journal-3866	1	34	of	of	ADP
american_scientific_journal-3866	1	35	scientific	scientific	ADJ
american_scientific_journal-3866	1	36	research	research	NOUN
american_scientific_journal-3866	1	37	and	and	CCONJ
american_scientific_journal-3866	1	38	researchers	researcher	NOUN
american_scientific_journal-3866	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	ADJ
american_scientific_journal-3866	1	40	period	period	NOUN
american_scientific_journal-3866	1	41	of	of	ADP
american_scientific_journal-3866	1	42	the	the	DET
american_scientific_journal-3866	1	43	simple	simple	ADJ
american_scientific_journal-3866	1	44	pendulum	pendulum	NOUN
american_scientific_journal-3866	1	45	without	without	ADP
american_scientific_journal-3866	1	46	differential	differential	ADJ
american_scientific_journal-3866	1	47	equations	equation	NOUN
american_scientific_journal-3866	1	48	alejandra	alejandra	PROPN
american_scientific_journal-3866	1	49	lira	lira	PROPN
american_scientific_journal-3866	1	50	vázqueza	vázqueza	PROPN
american_scientific_journal-3866	1	51	*	*	PUNCT
american_scientific_journal-3866	1	52	,	,	PUNCT
american_scientific_journal-3866	1	53	gulmaro	gulmaro	NOUN
american_scientific_journal-3866	1	54	corona	corona	NOUN
american_scientific_journal-3866	1	55	-	-	PUNCT
american_scientific_journal-3866	1	56	coronab	coronab	PROPN
american_scientific_journal-3866	1	57	auniversidad	auniversidad	PROPN
american_scientific_journal-3866	1	58	nacional	nacional	PROPN
american_scientific_journal-3866	1	59	autónoma	autónoma	PROPN
american_scientific_journal-3866	1	60	de	de	PROPN
american_scientific_journal-3866	1	61	méxico	méxico	PROPN
american_scientific_journal-3866	1	62	.	.	PUNCT
american_scientific_journal-3866	2	1	cch	cch	NOUN
american_scientific_journal-3866	2	2	-	-	PUNCT
american_scientific_journal-3866	2	3	azcapotzalco	azcapotzalco	NOUN
american_scientific_journal-3866	2	4	.	.	PUNCT
american_scientific_journal-3866	3	1	área	área	PROPN
american_scientific_journal-3866	3	2	de	de	PROPN
american_scientific_journal-3866	3	3	matemáticas	matemáticas	PROPN
american_scientific_journal-3866	3	4	.	.	PUNCT
american_scientific_journal-3866	4	1	avenida	avenida	PROPN
american_scientific_journal-3866	4	2	aquiles	aquiles	PROPN
american_scientific_journal-3866	4	3	serdán	serdán	ADP
american_scientific_journal-3866	4	4	2060	2060	NUM
american_scientific_journal-3866	4	5	,	,	PUNCT
american_scientific_journal-3866	4	6	azcapotzalco	azcapotzalco	VERB
american_scientific_journal-3866	4	7	,	,	PUNCT
american_scientific_journal-3866	4	8	ex	ex	PROPN
american_scientific_journal-3866	4	9	-	-	PROPN
american_scientific_journal-3866	4	10	hacienda	hacienda	PROPN
american_scientific_journal-3866	4	11	el	el	PROPN
american_scientific_journal-3866	4	12	rosario	rosario	PROPN
american_scientific_journal-3866	4	13	,	,	PUNCT
american_scientific_journal-3866	4	14	cdmx	cdmx	PROPN
american_scientific_journal-3866	4	15	.	.	PUNCT
american_scientific_journal-3866	5	1	c.p	c.p	PROPN
american_scientific_journal-3866	5	2	.	.	PROPN
american_scientific_journal-3866	5	3	02020	02020	NUM
american_scientific_journal-3866	5	4	,	,	PUNCT
american_scientific_journal-3866	5	5	méxico	méxico	PROPN
american_scientific_journal-3866	5	6	buniversidad	buniversidad	PROPN
american_scientific_journal-3866	5	7	autónoma	autónoma	PROPN
american_scientific_journal-3866	5	8	metropolitana	metropolitana	PROPN
american_scientific_journal-3866	5	9	,	,	PUNCT
american_scientific_journal-3866	5	10	unidad	unidad	PROPN
american_scientific_journal-3866	5	11	azcapotzalco	azcapotzalco	NOUN
american_scientific_journal-3866	5	12	,	,	PUNCT
american_scientific_journal-3866	5	13	departamento	departamento	PROPN
american_scientific_journal-3866	5	14	de	de	PROPN
american_scientific_journal-3866	5	15	ciencias	ciencias	PROPN
american_scientific_journal-3866	5	16	básicas	básicas	PROPN
american_scientific_journal-3866	5	17	e	e	PROPN
american_scientific_journal-3866	5	18	ingeniería	ingeniería	PROPN
american_scientific_journal-3866	5	19	,	,	PUNCT
american_scientific_journal-3866	5	20	área	área	PROPN
american_scientific_journal-3866	5	21	de	de	PROPN
american_scientific_journal-3866	5	22	matemáticas	matemáticas	NOUN
american_scientific_journal-3866	5	23	.	.	PUNCT
american_scientific_journal-3866	6	1	av	av	X
american_scientific_journal-3866	6	2	.	.	PUNCT
american_scientific_journal-3866	7	1	san	san	PROPN
american_scientific_journal-3866	7	2	pablo	pablo	PROPN
american_scientific_journal-3866	7	3	,	,	PUNCT
american_scientific_journal-3866	7	4	colonia	colonia	PROPN
american_scientific_journal-3866	7	5	reynosa	reynosa	PROPN
american_scientific_journal-3866	7	6	tamaulipas	tamaulipas	PROPN
american_scientific_journal-3866	7	7	,	,	PUNCT
american_scientific_journal-3866	7	8	delegación	delegación	NOUN
american_scientific_journal-3866	7	9	azcapotzalco	azcapotzalco	NOUN
american_scientific_journal-3866	7	10	,	,	PUNCT
american_scientific_journal-3866	7	11	cdmx	cdmx	NOUN
american_scientific_journal-3866	7	12	,	,	PUNCT
american_scientific_journal-3866	7	13	c.p	c.p	PROPN
american_scientific_journal-3866	7	14	.	.	PROPN
american_scientific_journal-3866	7	15	02200	02200	NUM
american_scientific_journal-3866	7	16	,	,	PUNCT
american_scientific_journal-3866	7	17	méxico	méxico	PROPN
american_scientific_journal-3866	7	18	aemail	aemail	NOUN
american_scientific_journal-3866	7	19	:	:	PUNCT
american_scientific_journal-3866	7	20	alv@unam.mx	alv@unam.mx	ADJ
american_scientific_journal-3866	7	21	bemail	bemail	NOUN
american_scientific_journal-3866	7	22	:	:	PUNCT
american_scientific_journal-3866	7	23	ccg@correo.azc.uam.mx	ccg@correo.azc.uam.mx	ADJ
american_scientific_journal-3866	7	24	abstract	abstract	NOUN
american_scientific_journal-3866	7	25	the	the	DET
american_scientific_journal-3866	7	26	purpose	purpose	NOUN
american_scientific_journal-3866	7	27	of	of	ADP
american_scientific_journal-3866	7	28	this	this	DET
american_scientific_journal-3866	7	29	research	research	NOUN
american_scientific_journal-3866	7	30	is	be	AUX
american_scientific_journal-3866	7	31	to	to	PART
american_scientific_journal-3866	7	32	learn	learn	VERB
american_scientific_journal-3866	7	33	that	that	SCONJ
american_scientific_journal-3866	7	34	the	the	DET
american_scientific_journal-3866	7	35	topics	topic	NOUN
american_scientific_journal-3866	7	36	of	of	ADP
american_scientific_journal-3866	7	37	physics	physics	NOUN
american_scientific_journal-3866	7	38	,	,	PUNCT
american_scientific_journal-3866	7	39	such	such	ADJ
american_scientific_journal-3866	7	40	as	as	ADP
american_scientific_journal-3866	7	41	the	the	DET
american_scientific_journal-3866	7	42	period	period	NOUN
american_scientific_journal-3866	7	43	of	of	ADP
american_scientific_journal-3866	7	44	a	a	DET
american_scientific_journal-3866	7	45	simple	simple	ADJ
american_scientific_journal-3866	7	46	pendulum	pendulum	NOUN
american_scientific_journal-3866	7	47	,	,	PUNCT
american_scientific_journal-3866	7	48	only	only	ADV
american_scientific_journal-3866	7	49	require	require	VERB
american_scientific_journal-3866	7	50	the	the	DET
american_scientific_journal-3866	7	51	use	use	NOUN
american_scientific_journal-3866	7	52	of	of	ADP
american_scientific_journal-3866	7	53	simple	simple	ADJ
american_scientific_journal-3866	7	54	concepts	concept	NOUN
american_scientific_journal-3866	7	55	of	of	ADP
american_scientific_journal-3866	7	56	energy	energy	NOUN
american_scientific_journal-3866	7	57	and	and	CCONJ
american_scientific_journal-3866	7	58	trigonometric	trigonometric	ADJ
american_scientific_journal-3866	7	59	relationships	relationship	NOUN
american_scientific_journal-3866	7	60	to	to	PART
american_scientific_journal-3866	7	61	determine	determine	VERB
american_scientific_journal-3866	7	62	the	the	DET
american_scientific_journal-3866	7	63	theoretical	theoretical	ADJ
american_scientific_journal-3866	7	64	mathematical	mathematical	ADJ
american_scientific_journal-3866	7	65	model	model	NOUN
american_scientific_journal-3866	7	66	that	that	PRON
american_scientific_journal-3866	7	67	allows	allow	VERB
american_scientific_journal-3866	7	68	to	to	PART
american_scientific_journal-3866	7	69	calculate	calculate	VERB
american_scientific_journal-3866	7	70	this	this	DET
american_scientific_journal-3866	7	71	period	period	NOUN
american_scientific_journal-3866	7	72	,	,	PUNCT
american_scientific_journal-3866	7	73	at	at	ADP
american_scientific_journal-3866	7	74	the	the	DET
american_scientific_journal-3866	7	75	baccalaureate	baccalaureate	NOUN
american_scientific_journal-3866	7	76	level	level	NOUN
american_scientific_journal-3866	7	77	.	.	PUNCT
american_scientific_journal-3866	8	1	two	two	NUM
american_scientific_journal-3866	8	2	of	of	ADP
american_scientific_journal-3866	8	3	the	the	DET
american_scientific_journal-3866	8	4	difficulties	difficulty	NOUN
american_scientific_journal-3866	8	5	that	that	PRON
american_scientific_journal-3866	8	6	are	be	AUX
american_scientific_journal-3866	8	7	presented	present	VERB
american_scientific_journal-3866	8	8	to	to	ADP
american_scientific_journal-3866	8	9	students	student	NOUN
american_scientific_journal-3866	8	10	of	of	ADP
american_scientific_journal-3866	8	11	high	high	ADJ
american_scientific_journal-3866	8	12	school	school	NOUN
american_scientific_journal-3866	8	13	physics	physics	NOUN
american_scientific_journal-3866	8	14	is	be	AUX
american_scientific_journal-3866	8	15	to	to	PART
american_scientific_journal-3866	8	16	deal	deal	VERB
american_scientific_journal-3866	8	17	with	with	ADP
american_scientific_journal-3866	8	18	complex	complex	ADJ
american_scientific_journal-3866	8	19	equations	equation	NOUN
american_scientific_journal-3866	8	20	for	for	ADP
american_scientific_journal-3866	8	21	the	the	DET
american_scientific_journal-3866	8	22	determination	determination	NOUN
american_scientific_journal-3866	8	23	of	of	ADP
american_scientific_journal-3866	8	24	the	the	DET
american_scientific_journal-3866	8	25	period	period	NOUN
american_scientific_journal-3866	8	26	of	of	ADP
american_scientific_journal-3866	8	27	a	a	DET
american_scientific_journal-3866	8	28	pendulum	pendulum	NOUN
american_scientific_journal-3866	8	29	and	and	CCONJ
american_scientific_journal-3866	8	30	the	the	DET
american_scientific_journal-3866	8	31	hard	hard	ADJ
american_scientific_journal-3866	8	32	task	task	NOUN
american_scientific_journal-3866	8	33	of	of	ADP
american_scientific_journal-3866	8	34	understanding	understanding	NOUN
american_scientific_journal-3866	8	35	which	which	PRON
american_scientific_journal-3866	8	36	are	be	AUX
american_scientific_journal-3866	8	37	the	the	DET
american_scientific_journal-3866	8	38	important	important	ADJ
american_scientific_journal-3866	8	39	variables	variable	NOUN
american_scientific_journal-3866	8	40	in	in	ADP
american_scientific_journal-3866	8	41	the	the	DET
american_scientific_journal-3866	8	42	mathematical	mathematical	ADJ
american_scientific_journal-3866	8	43	model	model	NOUN
american_scientific_journal-3866	8	44	that	that	PRON
american_scientific_journal-3866	8	45	determines	determine	VERB
american_scientific_journal-3866	8	46	the	the	DET
american_scientific_journal-3866	8	47	value	value	NOUN
american_scientific_journal-3866	8	48	of	of	ADP
american_scientific_journal-3866	8	49	said	say	VERB
american_scientific_journal-3866	8	50	period	period	NOUN
american_scientific_journal-3866	8	51	,	,	PUNCT
american_scientific_journal-3866	8	52	that	that	PRON
american_scientific_journal-3866	8	53	is	be	AUX
american_scientific_journal-3866	8	54	why	why	SCONJ
american_scientific_journal-3866	8	55	we	we	PRON
american_scientific_journal-3866	8	56	decided	decide	VERB
american_scientific_journal-3866	8	57	to	to	PART
american_scientific_journal-3866	8	58	develop	develop	VERB
american_scientific_journal-3866	8	59	this	this	DET
american_scientific_journal-3866	8	60	work	work	NOUN
american_scientific_journal-3866	8	61	,	,	PUNCT
american_scientific_journal-3866	8	62	so	so	SCONJ
american_scientific_journal-3866	8	63	that	that	SCONJ
american_scientific_journal-3866	8	64	it	it	PRON
american_scientific_journal-3866	8	65	serves	serve	VERB
american_scientific_journal-3866	8	66	the	the	DET
american_scientific_journal-3866	8	67	physics	physics	NOUN
american_scientific_journal-3866	8	68	teacher	teacher	NOUN
american_scientific_journal-3866	8	69	as	as	ADP
american_scientific_journal-3866	8	70	a	a	DET
american_scientific_journal-3866	8	71	strategy	strategy	NOUN
american_scientific_journal-3866	8	72	in	in	ADP
american_scientific_journal-3866	8	73	the	the	DET
american_scientific_journal-3866	8	74	classroom	classroom	NOUN
american_scientific_journal-3866	8	75	in	in	ADP
american_scientific_journal-3866	8	76	the	the	DET
american_scientific_journal-3866	8	77	development	development	NOUN
american_scientific_journal-3866	8	78	of	of	ADP
american_scientific_journal-3866	8	79	the	the	DET
american_scientific_journal-3866	8	80	simple	simple	ADJ
american_scientific_journal-3866	8	81	pendulum	pendulum	NOUN
american_scientific_journal-3866	8	82	theme	theme	NOUN
american_scientific_journal-3866	8	83	without	without	ADP
american_scientific_journal-3866	8	84	differential	differential	ADJ
american_scientific_journal-3866	8	85	equations	equation	NOUN
american_scientific_journal-3866	8	86	.	.	PUNCT
american_scientific_journal-3866	9	1	keywords	keyword	NOUN
american_scientific_journal-3866	9	2	:	:	PUNCT
american_scientific_journal-3866	9	3	period	period	NOUN
american_scientific_journal-3866	9	4	;	;	PUNCT
american_scientific_journal-3866	9	5	period	period	NOUN
american_scientific_journal-3866	9	6	of	of	ADP
american_scientific_journal-3866	9	7	the	the	DET
american_scientific_journal-3866	9	8	simple	simple	ADJ
american_scientific_journal-3866	9	9	pendulum	pendulum	NOUN
american_scientific_journal-3866	9	10	;	;	PUNCT
american_scientific_journal-3866	9	11	period	period	NOUN
american_scientific_journal-3866	9	12	without	without	ADP
american_scientific_journal-3866	9	13	differential	differential	ADJ
american_scientific_journal-3866	9	14	equations	equation	NOUN
american_scientific_journal-3866	9	15	.	.	PUNCT
american_scientific_journal-3866	10	1	1	1	X
american_scientific_journal-3866	10	2	.	.	X
american_scientific_journal-3866	10	3	introduction	introduction	NOUN
american_scientific_journal-3866	10	4	in	in	ADP
american_scientific_journal-3866	10	5	a	a	DET
american_scientific_journal-3866	10	6	pendulum	pendulum	NOUN
american_scientific_journal-3866	10	7	the	the	DET
american_scientific_journal-3866	10	8	period	period	NOUN
american_scientific_journal-3866	10	9	is	be	AUX
american_scientific_journal-3866	10	10	the	the	DET
american_scientific_journal-3866	10	11	time	time	NOUN
american_scientific_journal-3866	10	12	necessary	necessary	ADJ
american_scientific_journal-3866	10	13	to	to	PART
american_scientific_journal-3866	10	14	perform	perform	VERB
american_scientific_journal-3866	10	15	an	an	DET
american_scientific_journal-3866	10	16	oscillation	oscillation	NOUN
american_scientific_journal-3866	10	17	.	.	PUNCT
american_scientific_journal-3866	11	1	to	to	PART
american_scientific_journal-3866	11	2	determine	determine	VERB
american_scientific_journal-3866	11	3	the	the	DET
american_scientific_journal-3866	11	4	expression	expression	NOUN
american_scientific_journal-3866	11	5	to	to	PART
american_scientific_journal-3866	11	6	calculate	calculate	VERB
american_scientific_journal-3866	11	7	the	the	DET
american_scientific_journal-3866	11	8	period	period	NOUN
american_scientific_journal-3866	11	9	of	of	ADP
american_scientific_journal-3866	11	10	a	a	DET
american_scientific_journal-3866	11	11	simple	simple	ADJ
american_scientific_journal-3866	11	12	pendulum	pendulum	NOUN
american_scientific_journal-3866	11	13	at	at	ADP
american_scientific_journal-3866	11	14	any	any	DET
american_scientific_journal-3866	11	15	angle	angle	NOUN
american_scientific_journal-3866	11	16	,	,	PUNCT
american_scientific_journal-3866	11	17	we	we	PRON
american_scientific_journal-3866	11	18	only	only	ADV
american_scientific_journal-3866	11	19	have	have	VERB
american_scientific_journal-3866	11	20	to	to	PART
american_scientific_journal-3866	11	21	establish	establish	VERB
american_scientific_journal-3866	11	22	the	the	DET
american_scientific_journal-3866	11	23	relations	relation	NOUN
american_scientific_journal-3866	11	24	of	of	ADP
american_scientific_journal-3866	11	25	the	the	DET
american_scientific_journal-3866	11	26	variables	variable	NOUN
american_scientific_journal-3866	11	27	that	that	PRON
american_scientific_journal-3866	11	28	intervene	intervene	VERB
american_scientific_journal-3866	11	29	in	in	ADP
american_scientific_journal-3866	11	30	the	the	DET
american_scientific_journal-3866	11	31	pendulum	pendulum	NOUN
american_scientific_journal-3866	11	32	movement	movement	NOUN
american_scientific_journal-3866	11	33	.	.	PUNCT
american_scientific_journal-3866	12	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-3866	13	1	*	*	PUNCT
american_scientific_journal-3866	13	2	corresponding	correspond	VERB
american_scientific_journal-3866	13	3	author	author	NOUN
american_scientific_journal-3866	13	4	.	.	PUNCT
american_scientific_journal-3866	14	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-3866	14	2	american	american	PROPN
american_scientific_journal-3866	14	3	scientific	scientific	PROPN
american_scientific_journal-3866	14	4	research	research	NOUN
american_scientific_journal-3866	14	5	journal	journal	NOUN
american_scientific_journal-3866	14	6	for	for	ADP
american_scientific_journal-3866	14	7	engineering	engineering	NOUN
american_scientific_journal-3866	14	8	,	,	PUNCT
american_scientific_journal-3866	14	9	technology	technology	NOUN
american_scientific_journal-3866	14	10	,	,	PUNCT
american_scientific_journal-3866	14	11	and	and	CCONJ
american_scientific_journal-3866	14	12	sciences	science	NOUN
american_scientific_journal-3866	14	13	(	(	PUNCT
american_scientific_journal-3866	14	14	asrjets	asrjet	NOUN
american_scientific_journal-3866	14	15	)	)	PUNCT
american_scientific_journal-3866	14	16	(	(	PUNCT
american_scientific_journal-3866	14	17	2018	2018	NUM
american_scientific_journal-3866	14	18	)	)	PUNCT
american_scientific_journal-3866	14	19	volume	volume	NOUN
american_scientific_journal-3866	14	20	40	40	NUM
american_scientific_journal-3866	14	21	,	,	PUNCT
american_scientific_journal-3866	14	22	no	no	DET
american_scientific_journal-3866	14	23	1	1	NUM
american_scientific_journal-3866	14	24	,	,	PUNCT
american_scientific_journal-3866	14	25	pp	pp	ADV
american_scientific_journal-3866	14	26	125	125	NUM
american_scientific_journal-3866	14	27	-	-	SYM
american_scientific_journal-3866	14	28	131	131	NUM
american_scientific_journal-3866	14	29	126	126	NUM
american_scientific_journal-3866	14	30	some	some	DET
american_scientific_journal-3866	14	31	authors	author	NOUN
american_scientific_journal-3866	14	32	like	like	AUX
american_scientific_journal-3866	14	33	in	in	ADP
american_scientific_journal-3866	14	34	[	[	X
american_scientific_journal-3866	14	35	2	2	NUM
american_scientific_journal-3866	14	36	,	,	PUNCT
american_scientific_journal-3866	14	37	3	3	NUM
american_scientific_journal-3866	14	38	,	,	PUNCT
american_scientific_journal-3866	14	39	5	5	NUM
american_scientific_journal-3866	14	40	,	,	PUNCT
american_scientific_journal-3866	14	41	6	6	NUM
american_scientific_journal-3866	14	42	,	,	PUNCT
american_scientific_journal-3866	14	43	7	7	NUM
american_scientific_journal-3866	14	44	,	,	PUNCT
american_scientific_journal-3866	14	45	8	8	NUM
american_scientific_journal-3866	14	46	]	]	PUNCT
american_scientific_journal-3866	14	47	establish	establish	VERB
american_scientific_journal-3866	14	48	differential	differential	ADJ
american_scientific_journal-3866	14	49	equations	equation	NOUN
american_scientific_journal-3866	14	50	for	for	ADP
american_scientific_journal-3866	14	51	such	such	ADJ
american_scientific_journal-3866	14	52	movement	movement	NOUN
american_scientific_journal-3866	14	53	.	.	PUNCT
american_scientific_journal-3866	15	1	in	in	ADP
american_scientific_journal-3866	15	2	this	this	DET
american_scientific_journal-3866	15	3	work	work	NOUN
american_scientific_journal-3866	15	4	we	we	PRON
american_scientific_journal-3866	15	5	deduce	deduce	VERB
american_scientific_journal-3866	15	6	the	the	DET
american_scientific_journal-3866	15	7	expression	expression	NOUN
american_scientific_journal-3866	15	8	of	of	ADP
american_scientific_journal-3866	15	9	the	the	DET
american_scientific_journal-3866	15	10	period	period	NOUN
american_scientific_journal-3866	15	11	of	of	ADP
american_scientific_journal-3866	15	12	the	the	DET
american_scientific_journal-3866	15	13	simple	simple	ADJ
american_scientific_journal-3866	15	14	pendulum	pendulum	NOUN
american_scientific_journal-3866	15	15	,	,	PUNCT
american_scientific_journal-3866	15	16	only	only	ADV
american_scientific_journal-3866	15	17	using	use	VERB
american_scientific_journal-3866	15	18	body	body	NOUN
american_scientific_journal-3866	15	19	diagram	diagram	NOUN
american_scientific_journal-3866	15	20	of	of	ADP
american_scientific_journal-3866	15	21	the	the	DET
american_scientific_journal-3866	15	22	simple	simple	ADJ
american_scientific_journal-3866	15	23	pendulum	pendulum	NOUN
american_scientific_journal-3866	15	24	,	,	PUNCT
american_scientific_journal-3866	15	25	the	the	DET
american_scientific_journal-3866	15	26	conservation	conservation	NOUN
american_scientific_journal-3866	15	27	of	of	ADP
american_scientific_journal-3866	15	28	energy	energy	NOUN
american_scientific_journal-3866	15	29	,	,	PUNCT
american_scientific_journal-3866	15	30	the	the	DET
american_scientific_journal-3866	15	31	definition	definition	NOUN
american_scientific_journal-3866	15	32	of	of	ADP
american_scientific_journal-3866	15	33	speed	speed	NOUN
american_scientific_journal-3866	15	34	,	,	PUNCT
american_scientific_journal-3866	15	35	the	the	DET
american_scientific_journal-3866	15	36	period	period	NOUN
american_scientific_journal-3866	15	37	and	and	CCONJ
american_scientific_journal-3866	15	38	the	the	DET
american_scientific_journal-3866	15	39	trigonometric	trigonometric	ADJ
american_scientific_journal-3866	15	40	functions	function	NOUN
american_scientific_journal-3866	15	41	,	,	PUNCT
american_scientific_journal-3866	15	42	so	so	SCONJ
american_scientific_journal-3866	15	43	that	that	SCONJ
american_scientific_journal-3866	15	44	it	it	PRON
american_scientific_journal-3866	15	45	is	be	AUX
american_scientific_journal-3866	15	46	understandable	understandable	ADJ
american_scientific_journal-3866	15	47	by	by	ADP
american_scientific_journal-3866	15	48	high	high	ADJ
american_scientific_journal-3866	15	49	school	school	NOUN
american_scientific_journal-3866	15	50	students	student	NOUN
american_scientific_journal-3866	15	51	.	.	PUNCT
american_scientific_journal-3866	16	1	2	2	X
american_scientific_journal-3866	16	2	.	.	X
american_scientific_journal-3866	16	3	materials	material	NOUN
american_scientific_journal-3866	16	4	and	and	CCONJ
american_scientific_journal-3866	16	5	methods	method	NOUN
american_scientific_journal-3866	16	6	the	the	DET
american_scientific_journal-3866	16	7	period	period	NOUN
american_scientific_journal-3866	16	8	of	of	ADP
american_scientific_journal-3866	16	9	the	the	DET
american_scientific_journal-3866	16	10	simple	simple	ADJ
american_scientific_journal-3866	16	11	pendulum	pendulum	NOUN
american_scientific_journal-3866	16	12	is	be	AUX
american_scientific_journal-3866	16	13	calculated	calculate	VERB
american_scientific_journal-3866	16	14	without	without	ADP
american_scientific_journal-3866	16	15	the	the	DET
american_scientific_journal-3866	16	16	use	use	NOUN
american_scientific_journal-3866	16	17	of	of	ADP
american_scientific_journal-3866	16	18	differential	differential	ADJ
american_scientific_journal-3866	16	19	equations	equation	NOUN
american_scientific_journal-3866	16	20	,	,	PUNCT
american_scientific_journal-3866	16	21	which	which	PRON
american_scientific_journal-3866	16	22	makes	make	VERB
american_scientific_journal-3866	16	23	it	it	PRON
american_scientific_journal-3866	16	24	possible	possible	ADJ
american_scientific_journal-3866	16	25	to	to	PART
american_scientific_journal-3866	16	26	have	have	VERB
american_scientific_journal-3866	16	27	an	an	DET
american_scientific_journal-3866	16	28	explanation	explanation	NOUN
american_scientific_journal-3866	16	29	of	of	ADP
american_scientific_journal-3866	16	30	this	this	DET
american_scientific_journal-3866	16	31	topic	topic	NOUN
american_scientific_journal-3866	16	32	for	for	ADP
american_scientific_journal-3866	16	33	high	high	ADJ
american_scientific_journal-3866	16	34	school	school	NOUN
american_scientific_journal-3866	16	35	students	student	NOUN
american_scientific_journal-3866	16	36	.	.	PUNCT
american_scientific_journal-3866	17	1	only	only	ADV
american_scientific_journal-3866	17	2	the	the	DET
american_scientific_journal-3866	17	3	free	free	ADJ
american_scientific_journal-3866	17	4	body	body	NOUN
american_scientific_journal-3866	17	5	diagram	diagram	NOUN
american_scientific_journal-3866	17	6	of	of	ADP
american_scientific_journal-3866	17	7	the	the	DET
american_scientific_journal-3866	17	8	simple	simple	ADJ
american_scientific_journal-3866	17	9	pendulum	pendulum	NOUN
american_scientific_journal-3866	17	10	and	and	CCONJ
american_scientific_journal-3866	17	11	the	the	DET
american_scientific_journal-3866	17	12	trigonometric	trigonometric	ADJ
american_scientific_journal-3866	17	13	relations	relation	NOUN
american_scientific_journal-3866	17	14	of	of	ADP
american_scientific_journal-3866	17	15	a	a	DET
american_scientific_journal-3866	17	16	right	right	ADJ
american_scientific_journal-3866	17	17	triangle	triangle	NOUN
american_scientific_journal-3866	17	18	are	be	AUX
american_scientific_journal-3866	17	19	used	use	VERB
american_scientific_journal-3866	17	20	,	,	PUNCT
american_scientific_journal-3866	17	21	considering	consider	VERB
american_scientific_journal-3866	17	22	the	the	DET
american_scientific_journal-3866	17	23	law	law	NOUN
american_scientific_journal-3866	17	24	of	of	ADP
american_scientific_journal-3866	17	25	conservation	conservation	NOUN
american_scientific_journal-3866	17	26	of	of	ADP
american_scientific_journal-3866	17	27	energy	energy	NOUN
american_scientific_journal-3866	17	28	and	and	CCONJ
american_scientific_journal-3866	17	29	some	some	DET
american_scientific_journal-3866	17	30	relations	relation	NOUN
american_scientific_journal-3866	17	31	of	of	ADP
american_scientific_journal-3866	17	32	basic	basic	ADJ
american_scientific_journal-3866	17	33	mechanical	mechanical	ADJ
american_scientific_journal-3866	17	34	properties	property	NOUN
american_scientific_journal-3866	17	35	.	.	PUNCT
american_scientific_journal-3866	18	1	3	3	X
american_scientific_journal-3866	18	2	.	.	X
american_scientific_journal-3866	18	3	results	result	NOUN
american_scientific_journal-3866	18	4	if	if	SCONJ
american_scientific_journal-3866	18	5	we	we	PRON
american_scientific_journal-3866	18	6	consider	consider	VERB
american_scientific_journal-3866	18	7	the	the	DET
american_scientific_journal-3866	18	8	movement	movement	NOUN
american_scientific_journal-3866	18	9	of	of	ADP
american_scientific_journal-3866	18	10	a	a	DET
american_scientific_journal-3866	18	11	pendulum	pendulum	NOUN
american_scientific_journal-3866	18	12	,	,	PUNCT
american_scientific_journal-3866	18	13	we	we	PRON
american_scientific_journal-3866	18	14	can	can	AUX
american_scientific_journal-3866	18	15	establish	establish	VERB
american_scientific_journal-3866	18	16	the	the	DET
american_scientific_journal-3866	18	17	mathematical	mathematical	ADJ
american_scientific_journal-3866	18	18	model	model	NOUN
american_scientific_journal-3866	18	19	to	to	PART
american_scientific_journal-3866	18	20	calculate	calculate	VERB
american_scientific_journal-3866	18	21	its	its	PRON
american_scientific_journal-3866	18	22	period	period	NOUN
american_scientific_journal-3866	18	23	without	without	ADP
american_scientific_journal-3866	18	24	using	use	VERB
american_scientific_journal-3866	18	25	differential	differential	ADJ
american_scientific_journal-3866	18	26	equations	equation	NOUN
american_scientific_journal-3866	18	27	.	.	PUNCT
american_scientific_journal-3866	19	1	to	to	PART
american_scientific_journal-3866	19	2	obtain	obtain	VERB
american_scientific_journal-3866	19	3	the	the	DET
american_scientific_journal-3866	19	4	period	period	NOUN
american_scientific_journal-3866	19	5	of	of	ADP
american_scientific_journal-3866	19	6	a	a	DET
american_scientific_journal-3866	19	7	simple	simple	ADJ
american_scientific_journal-3866	19	8	pendulum	pendulum	NOUN
american_scientific_journal-3866	19	9	at	at	ADP
american_scientific_journal-3866	19	10	any	any	DET
american_scientific_journal-3866	19	11	angle	angle	NOUN
american_scientific_journal-3866	19	12	,	,	PUNCT
american_scientific_journal-3866	19	13	we	we	PRON
american_scientific_journal-3866	19	14	only	only	ADV
american_scientific_journal-3866	19	15	have	have	VERB
american_scientific_journal-3866	19	16	to	to	PART
american_scientific_journal-3866	19	17	establish	establish	VERB
american_scientific_journal-3866	19	18	the	the	DET
american_scientific_journal-3866	19	19	relationships	relationship	NOUN
american_scientific_journal-3866	19	20	of	of	ADP
american_scientific_journal-3866	19	21	the	the	DET
american_scientific_journal-3866	19	22	variables	variable	NOUN
american_scientific_journal-3866	19	23	that	that	PRON
american_scientific_journal-3866	19	24	intervene	intervene	VERB
american_scientific_journal-3866	19	25	in	in	ADP
american_scientific_journal-3866	19	26	the	the	DET
american_scientific_journal-3866	19	27	pendulum	pendulum	NOUN
american_scientific_journal-3866	19	28	movement	movement	NOUN
american_scientific_journal-3866	19	29	,	,	PUNCT
american_scientific_journal-3866	19	30	referring	refer	VERB
american_scientific_journal-3866	19	31	to	to	PART
american_scientific_journal-3866	19	32	figure	figure	VERB
american_scientific_journal-3866	19	33	1	1	NUM
american_scientific_journal-3866	19	34	.	.	PUNCT
american_scientific_journal-3866	19	35	figura	figura	PROPN
american_scientific_journal-3866	19	36	1	1	NUM
american_scientific_journal-3866	19	37	𝑠𝑠𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠	NOUN
american_scientific_journal-3866	19	38	𝜃𝜃	𝜃𝜃	INTJ
american_scientific_journal-3866	19	39	=	=	PUNCT
american_scientific_journal-3866	19	40	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3866	19	41	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-3866	19	42	(	(	PUNCT
american_scientific_journal-3866	19	43	1	1	NUM
american_scientific_journal-3866	19	44	)	)	PUNCT
american_scientific_journal-3866	20	1	cos	cos	PROPN
american_scientific_journal-3866	20	2	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-3866	20	3	=	=	X
american_scientific_journal-3866	20	4	𝑙𝑙−𝑦𝑦	𝑙𝑙−𝑦𝑦	X
american_scientific_journal-3866	20	5	𝑙𝑙	𝑙𝑙	INTJ
american_scientific_journal-3866	20	6	(	(	PUNCT
american_scientific_journal-3866	20	7	2	2	X
american_scientific_journal-3866	20	8	)	)	PUNCT
american_scientific_journal-3866	20	9	solving	solve	VERB
american_scientific_journal-3866	20	10	for	for	ADP
american_scientific_journal-3866	20	11	y	y	PROPN
american_scientific_journal-3866	20	12	,	,	PUNCT
american_scientific_journal-3866	20	13	it	it	PRON
american_scientific_journal-3866	20	14	has	have	VERB
american_scientific_journal-3866	20	15	:	:	PUNCT
american_scientific_journal-3866	20	16	(	(	PUNCT
american_scientific_journal-3866	20	17	3	3	X
american_scientific_journal-3866	20	18	)	)	PUNCT
american_scientific_journal-3866	20	19	from	from	ADP
american_scientific_journal-3866	20	20	figure	figure	NOUN
american_scientific_journal-3866	20	21	1	1	NUM
american_scientific_journal-3866	20	22	,	,	PUNCT
american_scientific_journal-3866	20	23	we	we	PRON
american_scientific_journal-3866	20	24	can	can	AUX
american_scientific_journal-3866	20	25	observe	observe	VERB
american_scientific_journal-3866	20	26	the	the	DET
american_scientific_journal-3866	20	27	formation	formation	NOUN
american_scientific_journal-3866	20	28	of	of	ADP
american_scientific_journal-3866	20	29	a	a	DET
american_scientific_journal-3866	20	30	right	right	ADJ
american_scientific_journal-3866	20	31	triangle	triangle	NOUN
american_scientific_journal-3866	20	32	with	with	ADP
american_scientific_journal-3866	20	33	sides	side	NOUN
american_scientific_journal-3866	21	1	𝑙𝑙	𝑙𝑙	INTJ
american_scientific_journal-3866	21	2	−	−	PROPN
american_scientific_journal-3866	21	3	𝑦𝑦	𝑦𝑦	PROPN
american_scientific_journal-3866	21	4	,	,	PUNCT
american_scientific_journal-3866	21	5	𝑙𝑙	𝑙𝑙	PROPN
american_scientific_journal-3866	21	6	y	y	PROPN
american_scientific_journal-3866	21	7	𝑥𝑥.	𝑥𝑥.	PROPN
american_scientific_journal-3866	21	8	american	american	PROPN
american_scientific_journal-3866	21	9	scientific	scientific	PROPN
american_scientific_journal-3866	21	10	research	research	PROPN
american_scientific_journal-3866	21	11	journal	journal	NOUN
american_scientific_journal-3866	21	12	for	for	ADP
american_scientific_journal-3866	21	13	engineering	engineering	NOUN
american_scientific_journal-3866	21	14	,	,	PUNCT
american_scientific_journal-3866	21	15	technology	technology	NOUN
american_scientific_journal-3866	21	16	,	,	PUNCT
american_scientific_journal-3866	21	17	and	and	CCONJ
american_scientific_journal-3866	21	18	sciences	science	NOUN
american_scientific_journal-3866	21	19	(	(	PUNCT
american_scientific_journal-3866	21	20	asrjets	asrjet	NOUN
american_scientific_journal-3866	21	21	)	)	PUNCT
american_scientific_journal-3866	21	22	(	(	PUNCT
american_scientific_journal-3866	21	23	2018	2018	NUM
american_scientific_journal-3866	21	24	)	)	PUNCT
american_scientific_journal-3866	21	25	volume	volume	NOUN
american_scientific_journal-3866	21	26	40	40	NUM
american_scientific_journal-3866	21	27	,	,	PUNCT
american_scientific_journal-3866	21	28	no	no	DET
american_scientific_journal-3866	21	29	1	1	NUM
american_scientific_journal-3866	21	30	,	,	PUNCT
american_scientific_journal-3866	21	31	pp	pp	ADV
american_scientific_journal-3866	21	32	125	125	NUM
american_scientific_journal-3866	21	33	-	-	SYM
american_scientific_journal-3866	21	34	131	131	NUM
american_scientific_journal-3866	21	35	127	127	NUM
american_scientific_journal-3866	21	36	where	where	SCONJ
american_scientific_journal-3866	21	37	:	:	PUNCT
american_scientific_journal-3866	21	38	𝑙𝑙	𝑙𝑙	X
american_scientific_journal-3866	21	39	:	:	PUNCT
american_scientific_journal-3866	21	40	length	length	NOUN
american_scientific_journal-3866	21	41	of	of	ADP
american_scientific_journal-3866	21	42	the	the	DET
american_scientific_journal-3866	21	43	pendulum	pendulum	NOUN
american_scientific_journal-3866	21	44	.	.	PUNCT
american_scientific_journal-3866	22	1	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3866	22	2	:	:	PUNCT
american_scientific_journal-3866	22	3	distance	distance	NOUN
american_scientific_journal-3866	22	4	traveled	travel	VERB
american_scientific_journal-3866	22	5	horizontally	horizontally	ADV
american_scientific_journal-3866	22	6	.	.	PUNCT
american_scientific_journal-3866	23	1	:	:	PUNCT
american_scientific_journal-3866	23	2	height	height	NOUN
american_scientific_journal-3866	23	3	traveled	travel	VERB
american_scientific_journal-3866	23	4	by	by	ADP
american_scientific_journal-3866	23	5	the	the	DET
american_scientific_journal-3866	23	6	particle	particle	NOUN
american_scientific_journal-3866	23	7	along	along	ADP
american_scientific_journal-3866	23	8	the	the	DET
american_scientific_journal-3866	23	9	vertical	vertical	ADJ
american_scientific_journal-3866	23	10	axis	axis	NOUN
american_scientific_journal-3866	23	11	.	.	PUNCT
american_scientific_journal-3866	24	1	:	:	PUNCT
american_scientific_journal-3866	24	2	change	change	NOUN
american_scientific_journal-3866	24	3	in	in	ADP
american_scientific_journal-3866	24	4	the	the	DET
american_scientific_journal-3866	24	5	angle	angle	NOUN
american_scientific_journal-3866	24	6	that	that	SCONJ
american_scientific_journal-3866	24	7	the	the	DET
american_scientific_journal-3866	24	8	length	length	NOUN
american_scientific_journal-3866	24	9	of	of	ADP
american_scientific_journal-3866	24	10	the	the	DET
american_scientific_journal-3866	24	11	pendulum	pendulum	NOUN
american_scientific_journal-3866	24	12	forms	form	NOUN
american_scientific_journal-3866	24	13	with	with	ADP
american_scientific_journal-3866	24	14	regarding	regard	VERB
american_scientific_journal-3866	24	15	its	its	PRON
american_scientific_journal-3866	24	16	initial	initial	ADJ
american_scientific_journal-3866	24	17	position	position	NOUN
american_scientific_journal-3866	24	18	1	1	NUM
american_scientific_journal-3866	24	19	.	.	NOUN
american_scientific_journal-3866	24	20	2	2	NUM
american_scientific_journal-3866	24	21	:	:	PUNCT
american_scientific_journal-3866	24	22	end	end	NOUN
american_scientific_journal-3866	24	23	point	point	NOUN
american_scientific_journal-3866	24	24	of	of	ADP
american_scientific_journal-3866	24	25	the	the	DET
american_scientific_journal-3866	24	26	movement	movement	NOUN
american_scientific_journal-3866	24	27	.	.	PUNCT
american_scientific_journal-3866	25	1	1	1	NUM
american_scientific_journal-3866	25	2	:	:	PUNCT
american_scientific_journal-3866	25	3	starting	start	VERB
american_scientific_journal-3866	25	4	point	point	NOUN
american_scientific_journal-3866	25	5	of	of	ADP
american_scientific_journal-3866	25	6	the	the	DET
american_scientific_journal-3866	25	7	movement	movement	NOUN
american_scientific_journal-3866	25	8	.	.	PUNCT
american_scientific_journal-3866	26	1	in	in	ADP
american_scientific_journal-3866	26	2	this	this	DET
american_scientific_journal-3866	26	3	type	type	NOUN
american_scientific_journal-3866	26	4	of	of	ADP
american_scientific_journal-3866	26	5	movement	movement	NOUN
american_scientific_journal-3866	26	6	,	,	PUNCT
american_scientific_journal-3866	26	7	the	the	DET
american_scientific_journal-3866	26	8	law	law	NOUN
american_scientific_journal-3866	26	9	of	of	ADP
american_scientific_journal-3866	26	10	conservation	conservation	NOUN
american_scientific_journal-3866	26	11	of	of	ADP
american_scientific_journal-3866	26	12	energy	energy	NOUN
american_scientific_journal-3866	26	13	is	be	AUX
american_scientific_journal-3866	26	14	applicable	applicable	ADJ
american_scientific_journal-3866	26	15	,	,	PUNCT
american_scientific_journal-3866	26	16	since	since	SCONJ
american_scientific_journal-3866	26	17	there	there	PRON
american_scientific_journal-3866	26	18	are	be	VERB
american_scientific_journal-3866	26	19	no	no	DET
american_scientific_journal-3866	26	20	external	external	ADJ
american_scientific_journal-3866	26	21	forces	force	NOUN
american_scientific_journal-3866	26	22	acting	act	VERB
american_scientific_journal-3866	26	23	on	on	ADP
american_scientific_journal-3866	26	24	the	the	DET
american_scientific_journal-3866	26	25	body	body	NOUN
american_scientific_journal-3866	26	26	,	,	PUNCT
american_scientific_journal-3866	26	27	therefore	therefore	ADV
american_scientific_journal-3866	26	28	the	the	DET
american_scientific_journal-3866	26	29	change	change	NOUN
american_scientific_journal-3866	26	30	in	in	ADP
american_scientific_journal-3866	26	31	kinetic	kinetic	ADJ
american_scientific_journal-3866	26	32	energy	energy	NOUN
american_scientific_journal-3866	26	33	is	be	AUX
american_scientific_journal-3866	26	34	equal	equal	ADJ
american_scientific_journal-3866	26	35	to	to	ADP
american_scientific_journal-3866	26	36	the	the	DET
american_scientific_journal-3866	26	37	change	change	NOUN
american_scientific_journal-3866	26	38	in	in	ADP
american_scientific_journal-3866	26	39	potential	potential	ADJ
american_scientific_journal-3866	26	40	energy	energy	NOUN
american_scientific_journal-3866	26	41	,	,	PUNCT
american_scientific_journal-3866	26	42	which	which	PRON
american_scientific_journal-3866	26	43	establishes	establish	VERB
american_scientific_journal-3866	26	44	the	the	DET
american_scientific_journal-3866	26	45	following	follow	VERB
american_scientific_journal-3866	26	46	relationships	relationship	NOUN
american_scientific_journal-3866	26	47	:	:	PUNCT
american_scientific_journal-3866	26	48	ecep	ecep	VERB
american_scientific_journal-3866	26	49	∆=∆	∆=∆	VERB
american_scientific_journal-3866	26	50	the	the	DET
american_scientific_journal-3866	26	51	change	change	NOUN
american_scientific_journal-3866	26	52	in	in	ADP
american_scientific_journal-3866	26	53	potential	potential	ADJ
american_scientific_journal-3866	26	54	energy	energy	NOUN
american_scientific_journal-3866	26	55	being	be	AUX
american_scientific_journal-3866	26	56	equal	equal	ADJ
american_scientific_journal-3866	26	57	to	to	ADP
american_scientific_journal-3866	26	58	:	:	PUNCT
american_scientific_journal-3866	26	59	)	)	PUNCT
american_scientific_journal-3866	26	60	(	(	PUNCT
american_scientific_journal-3866	26	61	0yymgep	0yymgep	NUM
american_scientific_journal-3866	26	62	−=∆	−=∆	PRON
american_scientific_journal-3866	26	63	and	and	CCONJ
american_scientific_journal-3866	26	64	the	the	DET
american_scientific_journal-3866	26	65	change	change	NOUN
american_scientific_journal-3866	26	66	in	in	ADP
american_scientific_journal-3866	26	67	kinetic	kinetic	ADJ
american_scientific_journal-3866	26	68	energy	energy	NOUN
american_scientific_journal-3866	26	69	equal	equal	ADJ
american_scientific_journal-3866	26	70	to	to	ADP
american_scientific_journal-3866	26	71	:	:	PUNCT
american_scientific_journal-3866	26	72	)	)	PUNCT
american_scientific_journal-3866	26	73	vv	vv	INTJ
american_scientific_journal-3866	26	74	(	(	PUNCT
american_scientific_journal-3866	26	75	2	2	NUM
american_scientific_journal-3866	26	76	1	1	NUM
american_scientific_journal-3866	26	77	2	2	NUM
american_scientific_journal-3866	26	78	0	0	NUM
american_scientific_journal-3866	26	79	2	2	NUM
american_scientific_journal-3866	26	80	−=∆	−=∆	DET
american_scientific_journal-3866	26	81	mec	mec	PROPN
american_scientific_journal-3866	26	82	because	because	SCONJ
american_scientific_journal-3866	26	83	00	00	PROPN
american_scientific_journal-3866	27	1	=	=	NUM
american_scientific_journal-3866	27	2	y	y	PROPN
american_scientific_journal-3866	27	3	y	y	NOUN
american_scientific_journal-3866	27	4	0v0	0v0	PUNCT
american_scientific_journal-3866	27	5	=	=	PUNCT
american_scientific_journal-3866	28	1	then	then	ADV
american_scientific_journal-3866	28	2	:	:	PUNCT
american_scientific_journal-3866	28	3	mgyep	mgyep	PROPN
american_scientific_journal-3866	28	4	=	=	NOUN
american_scientific_journal-3866	28	5	∆	∆	X
american_scientific_journal-3866	28	6	2v	2v	NOUN
american_scientific_journal-3866	28	7	2	2	NUM
american_scientific_journal-3866	28	8	1	1	NUM
american_scientific_journal-3866	28	9	mec	mec	X
american_scientific_journal-3866	28	10	=	=	NOUN
american_scientific_journal-3866	28	11	∆	∆	PROPN
american_scientific_journal-3866	28	12	so	so	ADV
american_scientific_journal-3866	28	13	by	by	ADP
american_scientific_journal-3866	28	14	matching	match	VERB
american_scientific_journal-3866	28	15	the	the	DET
american_scientific_journal-3866	28	16	change	change	NOUN
american_scientific_journal-3866	28	17	in	in	ADP
american_scientific_journal-3866	28	18	kinetic	kinetic	ADJ
american_scientific_journal-3866	28	19	energy	energy	NOUN
american_scientific_journal-3866	28	20	with	with	ADP
american_scientific_journal-3866	28	21	the	the	DET
american_scientific_journal-3866	28	22	change	change	NOUN
american_scientific_journal-3866	28	23	in	in	ADP
american_scientific_journal-3866	28	24	potential	potential	ADJ
american_scientific_journal-3866	28	25	energy	energy	NOUN
american_scientific_journal-3866	28	26	we	we	PRON
american_scientific_journal-3866	28	27	have	have	VERB
american_scientific_journal-3866	28	28	to	to	PART
american_scientific_journal-3866	28	29	:	:	PUNCT
american_scientific_journal-3866	28	30	american	american	ADJ
american_scientific_journal-3866	28	31	scientific	scientific	ADJ
american_scientific_journal-3866	28	32	research	research	PROPN
american_scientific_journal-3866	28	33	journal	journal	NOUN
american_scientific_journal-3866	28	34	for	for	ADP
american_scientific_journal-3866	28	35	engineering	engineering	NOUN
american_scientific_journal-3866	28	36	,	,	PUNCT
american_scientific_journal-3866	28	37	technology	technology	NOUN
american_scientific_journal-3866	28	38	,	,	PUNCT
american_scientific_journal-3866	28	39	and	and	CCONJ
american_scientific_journal-3866	28	40	sciences	science	NOUN
american_scientific_journal-3866	28	41	(	(	PUNCT
american_scientific_journal-3866	28	42	asrjets	asrjet	NOUN
american_scientific_journal-3866	28	43	)	)	PUNCT
american_scientific_journal-3866	28	44	(	(	PUNCT
american_scientific_journal-3866	28	45	2018	2018	NUM
american_scientific_journal-3866	28	46	)	)	PUNCT
american_scientific_journal-3866	28	47	volume	volume	NOUN
american_scientific_journal-3866	28	48	40	40	NUM
american_scientific_journal-3866	28	49	,	,	PUNCT
american_scientific_journal-3866	28	50	no	no	DET
american_scientific_journal-3866	28	51	1	1	NUM
american_scientific_journal-3866	28	52	,	,	PUNCT
american_scientific_journal-3866	28	53	pp	pp	ADV
american_scientific_journal-3866	28	54	125	125	NUM
american_scientific_journal-3866	28	55	-	-	SYM
american_scientific_journal-3866	28	56	131	131	NUM
american_scientific_journal-3866	28	57	128	128	NUM
american_scientific_journal-3866	28	58	𝑚𝑚𝑚𝑚𝑦𝑦	𝑚𝑚𝑚𝑚𝑦𝑦	ADJ
american_scientific_journal-3866	28	59	=	=	SYM
american_scientific_journal-3866	28	60	1	1	NUM
american_scientific_journal-3866	28	61	2	2	NUM
american_scientific_journal-3866	28	62	𝑚𝑚𝑣𝑣2	𝑚𝑚𝑣𝑣2	NOUN
american_scientific_journal-3866	28	63	(	(	PUNCT
american_scientific_journal-3866	28	64	4	4	NUM
american_scientific_journal-3866	28	65	)	)	PUNCT
american_scientific_journal-3866	28	66	where	where	SCONJ
american_scientific_journal-3866	28	67	:	:	PUNCT
american_scientific_journal-3866	28	68	ep∆	ep∆	NOUN
american_scientific_journal-3866	28	69	:	:	PUNCT
american_scientific_journal-3866	28	70	change	change	NOUN
american_scientific_journal-3866	28	71	in	in	ADP
american_scientific_journal-3866	28	72	potential	potential	ADJ
american_scientific_journal-3866	28	73	energy	energy	NOUN
american_scientific_journal-3866	28	74	.	.	PUNCT
american_scientific_journal-3866	29	1	ec∆	ec∆	NOUN
american_scientific_journal-3866	29	2	:	:	PUNCT
american_scientific_journal-3866	29	3	change	change	NOUN
american_scientific_journal-3866	29	4	in	in	ADP
american_scientific_journal-3866	29	5	kinetic	kinetic	ADJ
american_scientific_journal-3866	29	6	energy	energy	NOUN
american_scientific_journal-3866	29	7	.	.	PUNCT
american_scientific_journal-3866	30	1	m	m	VERB
american_scientific_journal-3866	30	2	:	:	PUNCT
american_scientific_journal-3866	30	3	mass	mass	NOUN
american_scientific_journal-3866	30	4	of	of	ADP
american_scientific_journal-3866	30	5	the	the	DET
american_scientific_journal-3866	30	6	particle	particle	NOUN
american_scientific_journal-3866	30	7	in	in	ADP
american_scientific_journal-3866	30	8	the	the	DET
american_scientific_journal-3866	30	9	pendulum	pendulum	NOUN
american_scientific_journal-3866	30	10	.	.	PUNCT
american_scientific_journal-3866	31	1	g	g	NOUN
american_scientific_journal-3866	31	2	:	:	PUNCT
american_scientific_journal-3866	31	3	acceleration	acceleration	NOUN
american_scientific_journal-3866	31	4	due	due	ADP
american_scientific_journal-3866	31	5	to	to	ADP
american_scientific_journal-3866	31	6	gravity	gravity	NOUN
american_scientific_journal-3866	31	7	.	.	PUNCT
american_scientific_journal-3866	32	1	y	y	X
american_scientific_journal-3866	32	2	:	:	PUNCT
american_scientific_journal-3866	32	3	height	height	NOUN
american_scientific_journal-3866	32	4	that	that	SCONJ
american_scientific_journal-3866	32	5	the	the	DET
american_scientific_journal-3866	32	6	particle	particle	NOUN
american_scientific_journal-3866	32	7	travels	travel	VERB
american_scientific_journal-3866	32	8	along	along	ADP
american_scientific_journal-3866	32	9	the	the	DET
american_scientific_journal-3866	32	10	vertical	vertical	ADJ
american_scientific_journal-3866	32	11	axis	axis	NOUN
american_scientific_journal-3866	32	12	.	.	PUNCT
american_scientific_journal-3866	33	1	v	v	X
american_scientific_journal-3866	33	2	:	:	PUNCT
american_scientific_journal-3866	33	3	speed	speed	NOUN
american_scientific_journal-3866	33	4	of	of	ADP
american_scientific_journal-3866	33	5	the	the	DET
american_scientific_journal-3866	33	6	particle	particle	NOUN
american_scientific_journal-3866	33	7	.	.	PUNCT
american_scientific_journal-3866	34	1	solving	solve	VERB
american_scientific_journal-3866	34	2	for	for	ADP
american_scientific_journal-3866	34	3	the	the	DET
american_scientific_journal-3866	34	4	speed	speed	NOUN
american_scientific_journal-3866	34	5	of	of	ADP
american_scientific_journal-3866	34	6	the	the	DET
american_scientific_journal-3866	34	7	equation	equation	NOUN
american_scientific_journal-3866	34	8	(	(	PUNCT
american_scientific_journal-3866	34	9	4	4	X
american_scientific_journal-3866	34	10	)	)	PUNCT
american_scientific_journal-3866	34	11	we	we	PRON
american_scientific_journal-3866	34	12	get	get	VERB
american_scientific_journal-3866	34	13	𝑣𝑣2	𝑣𝑣2	ADJ
american_scientific_journal-3866	34	14	=	=	SYM
american_scientific_journal-3866	35	1	2𝑚𝑚𝑚𝑚𝑦𝑦	2𝑚𝑚𝑚𝑚𝑦𝑦	NUM
american_scientific_journal-3866	35	2	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-3866	35	3	when	when	SCONJ
american_scientific_journal-3866	35	4	simplifying	simplify	VERB
american_scientific_journal-3866	35	5	we	we	PRON
american_scientific_journal-3866	35	6	have	have	AUX
american_scientific_journal-3866	35	7	:	:	PUNCT
american_scientific_journal-3866	35	8	𝑣𝑣2	𝑣𝑣2	PROPN
american_scientific_journal-3866	35	9	=	=	SYM
american_scientific_journal-3866	35	10	2𝑚𝑚𝑦𝑦	2𝑚𝑚𝑦𝑦	NUM
american_scientific_journal-3866	35	11	(	(	PUNCT
american_scientific_journal-3866	35	12	does	do	AUX
american_scientific_journal-3866	35	13	not	not	PART
american_scientific_journal-3866	35	14	depend	depend	VERB
american_scientific_journal-3866	35	15	on	on	ADP
american_scientific_journal-3866	35	16	the	the	DET
american_scientific_journal-3866	35	17	mass	mass	NOUN
american_scientific_journal-3866	35	18	)	)	PUNCT
american_scientific_journal-3866	35	19	𝑣𝑣	𝑣𝑣	X
american_scientific_journal-3866	35	20	=	=	SYM
american_scientific_journal-3866	35	21	�	�	PROPN
american_scientific_journal-3866	35	22	2𝑚𝑚𝑦𝑦	2𝑚𝑚𝑦𝑦	NUM
american_scientific_journal-3866	35	23	(	(	PUNCT
american_scientific_journal-3866	35	24	depends	depend	VERB
american_scientific_journal-3866	35	25	on	on	ADP
american_scientific_journal-3866	35	26	the	the	DET
american_scientific_journal-3866	35	27	height	height	NOUN
american_scientific_journal-3866	35	28	at	at	ADP
american_scientific_journal-3866	35	29	which	which	PRON
american_scientific_journal-3866	35	30	the	the	DET
american_scientific_journal-3866	35	31	pendulum	pendulum	NOUN
american_scientific_journal-3866	35	32	arrives	arrive	VERB
american_scientific_journal-3866	35	33	)	)	PUNCT
american_scientific_journal-3866	35	34	substituting	substitute	VERB
american_scientific_journal-3866	35	35	the	the	DET
american_scientific_journal-3866	35	36	relationship	relationship	NOUN
american_scientific_journal-3866	35	37	(	(	PUNCT
american_scientific_journal-3866	35	38	3	3	NUM
american_scientific_journal-3866	35	39	)	)	PUNCT
american_scientific_journal-3866	35	40	,	,	PUNCT
american_scientific_journal-3866	35	41	we	we	PRON
american_scientific_journal-3866	35	42	have	have	VERB
american_scientific_journal-3866	35	43	:	:	PUNCT
american_scientific_journal-3866	35	44	𝑣𝑣	𝑣𝑣	NUM
american_scientific_journal-3866	35	45	=	=	SYM
american_scientific_journal-3866	35	46	�	�	PROPN
american_scientific_journal-3866	35	47	2𝑚𝑚𝑙𝑙(1	2𝑚𝑚𝑙𝑙(1	NUM
american_scientific_journal-3866	35	48	−	−	NOUN
american_scientific_journal-3866	35	49	𝑐𝑐𝑐𝑐𝑠𝑠𝜃𝜃	𝑐𝑐𝑐𝑐𝑠𝑠𝜃𝜃	NOUN
american_scientific_journal-3866	35	50	)	)	PUNCT
american_scientific_journal-3866	35	51	(	(	PUNCT
american_scientific_journal-3866	35	52	5	5	NUM
american_scientific_journal-3866	35	53	)	)	PUNCT
american_scientific_journal-3866	35	54	from	from	ADP
american_scientific_journal-3866	35	55	kinematics	kinematic	NOUN
american_scientific_journal-3866	35	56	,	,	PUNCT
american_scientific_journal-3866	35	57	we	we	PRON
american_scientific_journal-3866	35	58	establish	establish	VERB
american_scientific_journal-3866	35	59	the	the	DET
american_scientific_journal-3866	35	60	formula	formula	NOUN
american_scientific_journal-3866	35	61	of	of	ADP
american_scientific_journal-3866	35	62	the	the	DET
american_scientific_journal-3866	35	63	average	average	ADJ
american_scientific_journal-3866	35	64	speed	speed	NOUN
american_scientific_journal-3866	35	65	of	of	ADP
american_scientific_journal-3866	35	66	a	a	DET
american_scientific_journal-3866	35	67	particle	particle	NOUN
american_scientific_journal-3866	35	68	:	:	PUNCT
american_scientific_journal-3866	36	1	𝑣𝑣	𝑣𝑣	X
american_scientific_journal-3866	36	2	=	=	SYM
american_scientific_journal-3866	36	3	𝑑𝑑	𝑑𝑑	PROPN
american_scientific_journal-3866	36	4	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-3866	36	5	(	(	PUNCT
american_scientific_journal-3866	36	6	6	6	NUM
american_scientific_journal-3866	36	7	)	)	PUNCT
american_scientific_journal-3866	36	8	where	where	SCONJ
american_scientific_journal-3866	36	9	:	:	PUNCT
american_scientific_journal-3866	36	10	d	d	NOUN
american_scientific_journal-3866	36	11	:	:	PUNCT
american_scientific_journal-3866	36	12	distance	distance	NOUN
american_scientific_journal-3866	36	13	traveled	travel	VERB
american_scientific_journal-3866	36	14	over	over	ADP
american_scientific_journal-3866	36	15	the	the	DET
american_scientific_journal-3866	36	16	trajectory	trajectory	NOUN
american_scientific_journal-3866	36	17	of	of	ADP
american_scientific_journal-3866	36	18	the	the	DET
american_scientific_journal-3866	36	19	pendulum	pendulum	NOUN
american_scientific_journal-3866	36	20	particle	particle	NOUN
american_scientific_journal-3866	36	21	,	,	PUNCT
american_scientific_journal-3866	36	22	the	the	DET
american_scientific_journal-3866	36	23	arc	arc	NOUN
american_scientific_journal-3866	36	24	length	length	NOUN
american_scientific_journal-3866	36	25	between	between	ADP
american_scientific_journal-3866	36	26	position	position	NOUN
american_scientific_journal-3866	36	27	1	1	NUM
american_scientific_journal-3866	36	28	and	and	CCONJ
american_scientific_journal-3866	36	29	2	2	NUM
american_scientific_journal-3866	36	30	.	.	X
american_scientific_journal-3866	37	1	t	t	NOUN
american_scientific_journal-3866	37	2	:	:	PUNCT
american_scientific_journal-3866	37	3	time	time	NOUN
american_scientific_journal-3866	37	4	the	the	DET
american_scientific_journal-3866	37	5	movement	movement	NOUN
american_scientific_journal-3866	37	6	last	last	ADJ
american_scientific_journal-3866	37	7	.	.	PUNCT
american_scientific_journal-3866	38	1	from	from	ADP
american_scientific_journal-3866	38	2	figure	figure	NOUN
american_scientific_journal-3866	38	3	1	1	NUM
american_scientific_journal-3866	38	4	,	,	PUNCT
american_scientific_journal-3866	38	5	it	it	PRON
american_scientific_journal-3866	38	6	can	can	AUX
american_scientific_journal-3866	38	7	be	be	AUX
american_scientific_journal-3866	38	8	seen	see	VERB
american_scientific_journal-3866	38	9	that	that	SCONJ
american_scientific_journal-3866	38	10	the	the	DET
american_scientific_journal-3866	38	11	trajectory	trajectory	NOUN
american_scientific_journal-3866	38	12	that	that	PRON
american_scientific_journal-3866	38	13	follows	follow	VERB
american_scientific_journal-3866	38	14	the	the	DET
american_scientific_journal-3866	38	15	particle	particle	NOUN
american_scientific_journal-3866	38	16	of	of	ADP
american_scientific_journal-3866	38	17	the	the	DET
american_scientific_journal-3866	38	18	pendulum	pendulum	NOUN
american_scientific_journal-3866	38	19	is	be	AUX
american_scientific_journal-3866	38	20	the	the	DET
american_scientific_journal-3866	38	21	length	length	NOUN
american_scientific_journal-3866	38	22	of	of	ADP
american_scientific_journal-3866	38	23	the	the	DET
american_scientific_journal-3866	38	24	arc	arc	NOUN
american_scientific_journal-3866	38	25	,	,	PUNCT
american_scientific_journal-3866	38	26	which	which	PRON
american_scientific_journal-3866	38	27	is	be	AUX
american_scientific_journal-3866	38	28	given	give	VERB
american_scientific_journal-3866	38	29	by	by	ADP
american_scientific_journal-3866	38	30	:	:	PUNCT
american_scientific_journal-3866	38	31	american	american	ADJ
american_scientific_journal-3866	38	32	scientific	scientific	ADJ
american_scientific_journal-3866	38	33	research	research	PROPN
american_scientific_journal-3866	38	34	journal	journal	NOUN
american_scientific_journal-3866	38	35	for	for	ADP
american_scientific_journal-3866	38	36	engineering	engineering	NOUN
american_scientific_journal-3866	38	37	,	,	PUNCT
american_scientific_journal-3866	38	38	technology	technology	NOUN
american_scientific_journal-3866	38	39	,	,	PUNCT
american_scientific_journal-3866	38	40	and	and	CCONJ
american_scientific_journal-3866	38	41	sciences	science	NOUN
american_scientific_journal-3866	38	42	(	(	PUNCT
american_scientific_journal-3866	38	43	asrjets	asrjet	NOUN
american_scientific_journal-3866	38	44	)	)	PUNCT
american_scientific_journal-3866	38	45	(	(	PUNCT
american_scientific_journal-3866	38	46	2018	2018	NUM
american_scientific_journal-3866	38	47	)	)	PUNCT
american_scientific_journal-3866	38	48	volume	volume	NOUN
american_scientific_journal-3866	38	49	40	40	NUM
american_scientific_journal-3866	38	50	,	,	PUNCT
american_scientific_journal-3866	38	51	no	no	DET
american_scientific_journal-3866	38	52	1	1	NUM
american_scientific_journal-3866	38	53	,	,	PUNCT
american_scientific_journal-3866	38	54	pp	pp	ADV
american_scientific_journal-3866	38	55	125	125	NUM
american_scientific_journal-3866	38	56	-	-	SYM
american_scientific_journal-3866	38	57	131	131	NUM
american_scientific_journal-3866	38	58	129	129	NUM
american_scientific_journal-3866	38	59	substituting	substitute	VERB
american_scientific_journal-3866	38	60	d	d	NOUN
american_scientific_journal-3866	38	61	in	in	ADP
american_scientific_journal-3866	38	62	equation	equation	NOUN
american_scientific_journal-3866	38	63	(	(	PUNCT
american_scientific_journal-3866	38	64	6	6	NUM
american_scientific_journal-3866	38	65	)	)	PUNCT
american_scientific_journal-3866	38	66	,	,	PUNCT
american_scientific_journal-3866	38	67	we	we	PRON
american_scientific_journal-3866	38	68	obtain	obtain	VERB
american_scientific_journal-3866	38	69	:	:	PUNCT
american_scientific_journal-3866	38	70	𝑣𝑣	𝑣𝑣	NUM
american_scientific_journal-3866	38	71	=	=	SYM
american_scientific_journal-3866	38	72	𝑙𝑙𝑙𝑙	𝑙𝑙𝑙𝑙	PROPN
american_scientific_journal-3866	38	73	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-3866	38	74	(	(	PUNCT
american_scientific_journal-3866	38	75	7	7	X
american_scientific_journal-3866	38	76	)	)	PUNCT
american_scientific_journal-3866	38	77	equaling	equal	VERB
american_scientific_journal-3866	38	78	equation	equation	NOUN
american_scientific_journal-3866	38	79	(	(	PUNCT
american_scientific_journal-3866	38	80	5	5	NUM
american_scientific_journal-3866	38	81	)	)	PUNCT
american_scientific_journal-3866	38	82	with	with	ADP
american_scientific_journal-3866	38	83	(	(	PUNCT
american_scientific_journal-3866	38	84	7	7	X
american_scientific_journal-3866	38	85	)	)	PUNCT
american_scientific_journal-3866	38	86	we	we	PRON
american_scientific_journal-3866	38	87	have	have	AUX
american_scientific_journal-3866	38	88	:	:	PUNCT
american_scientific_journal-3866	38	89	(	(	PUNCT
american_scientific_journal-3866	38	90	8)	8)	NUM
american_scientific_journal-3866	38	91	solving	solving	NOUN
american_scientific_journal-3866	38	92	for	for	ADP
american_scientific_journal-3866	38	93	t	t	NOUN
american_scientific_journal-3866	38	94	from	from	ADP
american_scientific_journal-3866	38	95	this	this	DET
american_scientific_journal-3866	38	96	equation	equation	NOUN
american_scientific_journal-3866	38	97	,	,	PUNCT
american_scientific_journal-3866	38	98	we	we	PRON
american_scientific_journal-3866	38	99	obtain	obtain	VERB
american_scientific_journal-3866	38	100	:	:	PUNCT
american_scientific_journal-3866	38	101	rearranging	rearrange	VERB
american_scientific_journal-3866	38	102	terms	term	NOUN
american_scientific_journal-3866	38	103	we	we	PRON
american_scientific_journal-3866	38	104	have	have	VERB
american_scientific_journal-3866	38	105	to	to	PART
american_scientific_journal-3866	38	106	:	:	PUNCT
american_scientific_journal-3866	38	107	(	(	PUNCT
american_scientific_journal-3866	38	108	9	9	X
american_scientific_journal-3866	38	109	)	)	PUNCT
american_scientific_journal-3866	38	110	considering	consider	VERB
american_scientific_journal-3866	38	111	the	the	DET
american_scientific_journal-3866	38	112	approximation	approximation	NOUN
american_scientific_journal-3866	38	113	for	for	ADP
american_scientific_journal-3866	38	114	cos	cos	PROPN
american_scientific_journal-3866	38	115	𝜃𝜃	𝜃𝜃	PROPN
american_scientific_journal-3866	38	116	(	(	PUNCT
american_scientific_journal-3866	38	117	for	for	ADP
american_scientific_journal-3866	38	118	small	small	ADJ
american_scientific_journal-3866	38	119	angles	angle	NOUN
american_scientific_journal-3866	38	120	)	)	PUNCT
american_scientific_journal-3866	38	121	and	and	CCONJ
american_scientific_journal-3866	38	122	substituting	substitute	VERB
american_scientific_journal-3866	38	123	in	in	ADP
american_scientific_journal-3866	38	124	equation	equation	NOUN
american_scientific_journal-3866	38	125	(	(	PUNCT
american_scientific_journal-3866	38	126	9	9	NUM
american_scientific_journal-3866	38	127	)	)	PUNCT
american_scientific_journal-3866	38	128	,	,	PUNCT
american_scientific_journal-3866	38	129	we	we	PRON
american_scientific_journal-3866	38	130	obtain	obtain	VERB
american_scientific_journal-3866	38	131	:	:	PUNCT
american_scientific_journal-3866	38	132	making	make	VERB
american_scientific_journal-3866	38	133	the	the	DET
american_scientific_journal-3866	38	134	3	3	NUM
american_scientific_journal-3866	38	135	following	follow	VERB
american_scientific_journal-3866	38	136	operations	operation	NOUN
american_scientific_journal-3866	38	137	:	:	PUNCT
american_scientific_journal-3866	38	138	simplifying	simplify	VERB
american_scientific_journal-3866	38	139	𝜃𝜃	𝜃𝜃	INTJ
american_scientific_journal-3866	38	140	we	we	PRON
american_scientific_journal-3866	38	141	obtain	obtain	VERB
american_scientific_journal-3866	38	142	:	:	PUNCT
american_scientific_journal-3866	38	143	american	american	ADJ
american_scientific_journal-3866	38	144	scientific	scientific	ADJ
american_scientific_journal-3866	38	145	research	research	PROPN
american_scientific_journal-3866	38	146	journal	journal	NOUN
american_scientific_journal-3866	38	147	for	for	ADP
american_scientific_journal-3866	38	148	engineering	engineering	NOUN
american_scientific_journal-3866	38	149	,	,	PUNCT
american_scientific_journal-3866	38	150	technology	technology	NOUN
american_scientific_journal-3866	38	151	,	,	PUNCT
american_scientific_journal-3866	38	152	and	and	CCONJ
american_scientific_journal-3866	38	153	sciences	science	NOUN
american_scientific_journal-3866	38	154	(	(	PUNCT
american_scientific_journal-3866	38	155	asrjets	asrjet	NOUN
american_scientific_journal-3866	38	156	)	)	PUNCT
american_scientific_journal-3866	38	157	(	(	PUNCT
american_scientific_journal-3866	38	158	2018	2018	NUM
american_scientific_journal-3866	38	159	)	)	PUNCT
american_scientific_journal-3866	38	160	volume	volume	NOUN
american_scientific_journal-3866	38	161	40	40	NUM
american_scientific_journal-3866	38	162	,	,	PUNCT
american_scientific_journal-3866	38	163	no	no	DET
american_scientific_journal-3866	38	164	1	1	NUM
american_scientific_journal-3866	38	165	,	,	PUNCT
american_scientific_journal-3866	38	166	pp	pp	ADV
american_scientific_journal-3866	38	167	125	125	NUM
american_scientific_journal-3866	38	168	-	-	SYM
american_scientific_journal-3866	38	169	131	131	NUM
american_scientific_journal-3866	38	170	130	130	NUM
american_scientific_journal-3866	38	171	lg	lg	NOUN
american_scientific_journal-3866	38	172	lt	lt	NOUN
american_scientific_journal-3866	38	173	=	=	X
american_scientific_journal-3866	38	174	(	(	PUNCT
american_scientific_journal-3866	38	175	10	10	NUM
american_scientific_journal-3866	38	176	)	)	PUNCT
american_scientific_journal-3866	38	177	multiplying	multiply	VERB
american_scientific_journal-3866	38	178	l	l	NOUN
american_scientific_journal-3866	38	179	by	by	ADP
american_scientific_journal-3866	38	180	the	the	DET
american_scientific_journal-3866	38	181	numerator	numerator	NOUN
american_scientific_journal-3866	38	182	and	and	CCONJ
american_scientific_journal-3866	38	183	denominator	denominator	NOUN
american_scientific_journal-3866	38	184	of	of	ADP
american_scientific_journal-3866	38	185	equation	equation	NOUN
american_scientific_journal-3866	38	186	(	(	PUNCT
american_scientific_journal-3866	38	187	10	10	NUM
american_scientific_journal-3866	38	188	)	)	PUNCT
american_scientific_journal-3866	38	189	,	,	PUNCT
american_scientific_journal-3866	38	190	we	we	PRON
american_scientific_journal-3866	38	191	have	have	VERB
american_scientific_journal-3866	38	192	:	:	PUNCT
american_scientific_journal-3866	39	1	l	l	NOUN
american_scientific_journal-3866	39	2	l	l	PUNCT
american_scientific_journal-3866	39	3	g	g	NOUN
american_scientific_journal-3866	39	4	lt	lt	NOUN
american_scientific_journal-3866	39	5	=	=	VERB
american_scientific_journal-3866	39	6	simplifying	simplify	VERB
american_scientific_journal-3866	39	7	the	the	DET
american_scientific_journal-3866	39	8	lengths	length	NOUN
american_scientific_journal-3866	39	9	,	,	PUNCT
american_scientific_journal-3866	39	10	we	we	PRON
american_scientific_journal-3866	39	11	have	have	VERB
american_scientific_journal-3866	39	12	that	that	PRON
american_scientific_journal-3866	39	13	:	:	PUNCT
american_scientific_journal-3866	39	14	g	g	NOUN
american_scientific_journal-3866	39	15	lt	lt	NOUN
american_scientific_journal-3866	39	16	=	=	X
american_scientific_journal-3866	39	17	(	(	PUNCT
american_scientific_journal-3866	39	18	11	11	NUM
american_scientific_journal-3866	39	19	)	)	PUNCT
american_scientific_journal-3866	39	20	as	as	ADP
american_scientific_journal-3866	39	21	the	the	DET
american_scientific_journal-3866	39	22	period	period	NOUN
american_scientific_journal-3866	39	23	of	of	ADP
american_scientific_journal-3866	39	24	the	the	DET
american_scientific_journal-3866	39	25	simple	simple	ADJ
american_scientific_journal-3866	39	26	pendulum	pendulum	NOUN
american_scientific_journal-3866	39	27	is	be	AUX
american_scientific_journal-3866	39	28	equal	equal	ADJ
american_scientific_journal-3866	39	29	to	to	ADP
american_scientific_journal-3866	39	30	:	:	PUNCT
american_scientific_journal-3866	39	31	where	where	SCONJ
american_scientific_journal-3866	39	32	:	:	PUNCT
american_scientific_journal-3866	39	33	t	t	X
american_scientific_journal-3866	39	34	:	:	PUNCT
american_scientific_journal-3866	39	35	pendulum	pendulum	NOUN
american_scientific_journal-3866	39	36	period	period	NOUN
american_scientific_journal-3866	39	37	.	.	PUNCT
american_scientific_journal-3866	40	1	t	t	NOUN
american_scientific_journal-3866	40	2	:	:	PUNCT
american_scientific_journal-3866	40	3	time	time	NOUN
american_scientific_journal-3866	40	4	the	the	DET
american_scientific_journal-3866	40	5	movement	movement	NOUN
american_scientific_journal-3866	40	6	lasts	last	VERB
american_scientific_journal-3866	40	7	.	.	PUNCT
american_scientific_journal-3866	41	1	then	then	ADV
american_scientific_journal-3866	41	2	the	the	DET
american_scientific_journal-3866	41	3	period	period	NOUN
american_scientific_journal-3866	41	4	of	of	ADP
american_scientific_journal-3866	41	5	a	a	DET
american_scientific_journal-3866	41	6	simple	simple	ADJ
american_scientific_journal-3866	41	7	pendulum	pendulum	NOUN
american_scientific_journal-3866	41	8	is	be	AUX
american_scientific_journal-3866	41	9	obtained	obtain	VERB
american_scientific_journal-3866	41	10	from	from	ADP
american_scientific_journal-3866	41	11	:	:	PUNCT
american_scientific_journal-3866	41	12	g	g	PROPN
american_scientific_journal-3866	41	13	lt	lt	PRON
american_scientific_journal-3866	41	14	π2=	π2=	PROPN
american_scientific_journal-3866	41	15	4	4	NUM
american_scientific_journal-3866	41	16	.	.	PUNCT
american_scientific_journal-3866	41	17	discussion	discussion	NOUN
american_scientific_journal-3866	41	18	although	although	SCONJ
american_scientific_journal-3866	41	19	in	in	ADP
american_scientific_journal-3866	41	20	reference	reference	NOUN
american_scientific_journal-3866	41	21	[	[	X
american_scientific_journal-3866	41	22	1	1	NUM
american_scientific_journal-3866	41	23	]	]	PUNCT
american_scientific_journal-3866	41	24	,	,	PUNCT
american_scientific_journal-3866	41	25	does	do	AUX
american_scientific_journal-3866	41	26	not	not	PART
american_scientific_journal-3866	41	27	use	use	VERB
american_scientific_journal-3866	41	28	differential	differential	ADJ
american_scientific_journal-3866	41	29	equations	equation	NOUN
american_scientific_journal-3866	41	30	in	in	ADP
american_scientific_journal-3866	41	31	the	the	DET
american_scientific_journal-3866	41	32	deduction	deduction	NOUN
american_scientific_journal-3866	41	33	of	of	ADP
american_scientific_journal-3866	41	34	the	the	DET
american_scientific_journal-3866	41	35	equation	equation	NOUN
american_scientific_journal-3866	41	36	to	to	PART
american_scientific_journal-3866	41	37	calculate	calculate	VERB
american_scientific_journal-3866	41	38	the	the	DET
american_scientific_journal-3866	41	39	period	period	NOUN
american_scientific_journal-3866	41	40	of	of	ADP
american_scientific_journal-3866	41	41	the	the	DET
american_scientific_journal-3866	41	42	simple	simple	ADJ
american_scientific_journal-3866	41	43	pendulum	pendulum	NOUN
american_scientific_journal-3866	41	44	and	and	CCONJ
american_scientific_journal-3866	41	45	the	the	DET
american_scientific_journal-3866	41	46	same	same	ADJ
american_scientific_journal-3866	41	47	expression	expression	NOUN
american_scientific_journal-3866	41	48	is	be	AUX
american_scientific_journal-3866	41	49	reached	reach	VERB
american_scientific_journal-3866	41	50	,	,	PUNCT
american_scientific_journal-3866	41	51	it	it	PRON
american_scientific_journal-3866	41	52	presents	present	VERB
american_scientific_journal-3866	41	53	differences	difference	NOUN
american_scientific_journal-3866	41	54	,	,	PUNCT
american_scientific_journal-3866	41	55	with	with	ADP
american_scientific_journal-3866	41	56	this	this	DET
american_scientific_journal-3866	41	57	work	work	NOUN
american_scientific_journal-3866	41	58	,	,	PUNCT
american_scientific_journal-3866	41	59	since	since	SCONJ
american_scientific_journal-3866	41	60	the	the	DET
american_scientific_journal-3866	41	61	author	author	NOUN
american_scientific_journal-3866	41	62	uses	use	VERB
american_scientific_journal-3866	41	63	the	the	DET
american_scientific_journal-3866	41	64	concept	concept	NOUN
american_scientific_journal-3866	41	65	of	of	ADP
american_scientific_journal-3866	41	66	frequency	frequency	NOUN
american_scientific_journal-3866	41	67	and	and	CCONJ
american_scientific_journal-3866	41	68	the	the	DET
american_scientific_journal-3866	41	69	relations	relation	NOUN
american_scientific_journal-3866	41	70	between	between	ADP
american_scientific_journal-3866	41	71	the	the	DET
american_scientific_journal-3866	41	72	forces	force	NOUN
american_scientific_journal-3866	41	73	present	present	ADJ
american_scientific_journal-3866	41	74	in	in	ADP
american_scientific_journal-3866	41	75	the	the	DET
american_scientific_journal-3866	41	76	pendulum	pendulum	NOUN
american_scientific_journal-3866	41	77	movement	movement	NOUN
american_scientific_journal-3866	41	78	.	.	PUNCT
american_scientific_journal-3866	42	1	on	on	ADP
american_scientific_journal-3866	42	2	the	the	DET
american_scientific_journal-3866	42	3	other	other	ADJ
american_scientific_journal-3866	42	4	hand	hand	NOUN
american_scientific_journal-3866	42	5	,	,	PUNCT
american_scientific_journal-3866	42	6	in	in	ADP
american_scientific_journal-3866	42	7	reference	reference	NOUN
american_scientific_journal-3866	42	8	[	[	X
american_scientific_journal-3866	42	9	2	2	NUM
american_scientific_journal-3866	42	10	]	]	PUNCT
american_scientific_journal-3866	42	11	,	,	PUNCT
american_scientific_journal-3866	42	12	there	there	PRON
american_scientific_journal-3866	42	13	is	be	VERB
american_scientific_journal-3866	42	14	a	a	DET
american_scientific_journal-3866	42	15	difference	difference	NOUN
american_scientific_journal-3866	42	16	with	with	ADP
american_scientific_journal-3866	42	17	this	this	DET
american_scientific_journal-3866	42	18	work	work	NOUN
american_scientific_journal-3866	42	19	because	because	SCONJ
american_scientific_journal-3866	42	20	it	it	PRON
american_scientific_journal-3866	42	21	uses	use	VERB
american_scientific_journal-3866	42	22	differential	differential	ADJ
american_scientific_journal-3866	42	23	equations	equation	NOUN
american_scientific_journal-3866	42	24	and	and	CCONJ
american_scientific_journal-3866	42	25	the	the	DET
american_scientific_journal-3866	42	26	relationship	relationship	NOUN
american_scientific_journal-3866	42	27	of	of	ADP
american_scientific_journal-3866	42	28	frequency	frequency	NOUN
american_scientific_journal-3866	42	29	with	with	ADP
american_scientific_journal-3866	42	30	period	period	NOUN
american_scientific_journal-3866	42	31	,	,	PUNCT
american_scientific_journal-3866	42	32	to	to	PART
american_scientific_journal-3866	42	33	arrive	arrive	VERB
american_scientific_journal-3866	42	34	at	at	ADP
american_scientific_journal-3866	42	35	the	the	DET
american_scientific_journal-3866	42	36	equation	equation	NOUN
american_scientific_journal-3866	42	37	of	of	ADP
american_scientific_journal-3866	42	38	the	the	DET
american_scientific_journal-3866	42	39	period	period	NOUN
american_scientific_journal-3866	42	40	of	of	ADP
american_scientific_journal-3866	42	41	the	the	DET
american_scientific_journal-3866	42	42	simple	simple	ADJ
american_scientific_journal-3866	42	43	pendulum	pendulum	NOUN
american_scientific_journal-3866	42	44	.	.	PUNCT
american_scientific_journal-3866	43	1	with	with	ADP
american_scientific_journal-3866	43	2	respect	respect	NOUN
american_scientific_journal-3866	43	3	to	to	ADP
american_scientific_journal-3866	43	4	the	the	DET
american_scientific_journal-3866	43	5	reference	reference	NOUN
american_scientific_journal-3866	43	6	[	[	X
american_scientific_journal-3866	43	7	3	3	NUM
american_scientific_journal-3866	43	8	]	]	PUNCT
american_scientific_journal-3866	43	9	,	,	PUNCT
american_scientific_journal-3866	43	10	it	it	PRON
american_scientific_journal-3866	43	11	presents	present	VERB
american_scientific_journal-3866	43	12	great	great	ADJ
american_scientific_journal-3866	43	13	differences	difference	NOUN
american_scientific_journal-3866	43	14	,	,	PUNCT
american_scientific_journal-3866	43	15	with	with	ADP
american_scientific_journal-3866	43	16	our	our	PRON
american_scientific_journal-3866	43	17	work	work	NOUN
american_scientific_journal-3866	43	18	,	,	PUNCT
american_scientific_journal-3866	43	19	since	since	SCONJ
american_scientific_journal-3866	43	20	it	it	PRON
american_scientific_journal-3866	43	21	considers	consider	VERB
american_scientific_journal-3866	43	22	differential	differential	ADJ
american_scientific_journal-3866	43	23	equations	equation	NOUN
american_scientific_journal-3866	43	24	and	and	CCONJ
american_scientific_journal-3866	43	25	the	the	DET
american_scientific_journal-3866	43	26	concept	concept	NOUN
american_scientific_journal-3866	43	27	of	of	ADP
american_scientific_journal-3866	43	28	periodic	periodic	ADJ
american_scientific_journal-3866	43	29	function	function	NOUN
american_scientific_journal-3866	43	30	,	,	PUNCT
american_scientific_journal-3866	43	31	when	when	SCONJ
american_scientific_journal-3866	43	32	increasing	increase	VERB
american_scientific_journal-3866	43	33	the	the	DET
american_scientific_journal-3866	43	34	2𝜋𝜋	2𝜋𝜋	ADJ
american_scientific_journal-3866	43	35	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	VERB
american_scientific_journal-3866	43	36	phase	phase	NOUN
american_scientific_journal-3866	43	37	in	in	ADP
american_scientific_journal-3866	43	38	a	a	DET
american_scientific_journal-3866	43	39	time	time	NOUN
american_scientific_journal-3866	43	40	t	t	NOUN
american_scientific_journal-3866	43	41	,	,	PUNCT
american_scientific_journal-3866	43	42	to	to	PART
american_scientific_journal-3866	43	43	establish	establish	VERB
american_scientific_journal-3866	43	44	the	the	DET
american_scientific_journal-3866	43	45	expression	expression	NOUN
american_scientific_journal-3866	43	46	to	to	PART
american_scientific_journal-3866	43	47	calculate	calculate	VERB
american_scientific_journal-3866	43	48	the	the	DET
american_scientific_journal-3866	43	49	period	period	NOUN
american_scientific_journal-3866	43	50	.	.	PUNCT
american_scientific_journal-3866	44	1	the	the	DET
american_scientific_journal-3866	44	2	reference	reference	NOUN
american_scientific_journal-3866	44	3	[	[	X
american_scientific_journal-3866	44	4	4	4	NUM
american_scientific_journal-3866	44	5	]	]	PUNCT
american_scientific_journal-3866	44	6	,	,	PUNCT
american_scientific_journal-3866	44	7	has	have	VERB
american_scientific_journal-3866	44	8	a	a	DET
american_scientific_journal-3866	44	9	difference	difference	NOUN
american_scientific_journal-3866	44	10	with	with	ADP
american_scientific_journal-3866	44	11	our	our	PRON
american_scientific_journal-3866	44	12	work	work	NOUN
american_scientific_journal-3866	44	13	,	,	PUNCT
american_scientific_journal-3866	44	14	because	because	SCONJ
american_scientific_journal-3866	44	15	it	it	PRON
american_scientific_journal-3866	44	16	does	do	AUX
american_scientific_journal-3866	44	17	not	not	PART
american_scientific_journal-3866	44	18	deduce	deduce	VERB
american_scientific_journal-3866	44	19	the	the	DET
american_scientific_journal-3866	44	20	expression	expression	NOUN
american_scientific_journal-3866	44	21	,	,	PUNCT
american_scientific_journal-3866	44	22	only	only	ADV
american_scientific_journal-3866	44	23	takes	take	VERB
american_scientific_journal-3866	44	24	it	it	PRON
american_scientific_journal-3866	44	25	for	for	ADP
american_scientific_journal-3866	44	26	granted	grant	VERB
american_scientific_journal-3866	44	27	.	.	PUNCT
american_scientific_journal-3866	45	1	reference	reference	NOUN
american_scientific_journal-3866	45	2	[	[	X
american_scientific_journal-3866	45	3	5	5	NUM
american_scientific_journal-3866	45	4	]	]	PUNCT
american_scientific_journal-3866	45	5	has	have	VERB
american_scientific_journal-3866	45	6	differences	difference	NOUN
american_scientific_journal-3866	45	7	because	because	SCONJ
american_scientific_journal-3866	45	8	it	it	PRON
american_scientific_journal-3866	45	9	considers	consider	VERB
american_scientific_journal-3866	45	10	differential	differential	ADJ
american_scientific_journal-3866	45	11	equations	equation	NOUN
american_scientific_journal-3866	45	12	and	and	CCONJ
american_scientific_journal-3866	45	13	the	the	DET
american_scientific_journal-3866	45	14	definition	definition	NOUN
american_scientific_journal-3866	45	15	of	of	ADP
american_scientific_journal-3866	45	16	simple	simple	ADJ
american_scientific_journal-3866	45	17	harmonic	harmonic	ADJ
american_scientific_journal-3866	45	18	motion	motion	NOUN
american_scientific_journal-3866	45	19	,	,	PUNCT
american_scientific_journal-3866	45	20	as	as	ADV
american_scientific_journal-3866	45	21	well	well	ADV
american_scientific_journal-3866	45	22	as	as	ADP
american_scientific_journal-3866	45	23	the	the	DET
american_scientific_journal-3866	45	24	definition	definition	NOUN
american_scientific_journal-3866	45	25	of	of	ADP
american_scientific_journal-3866	45	26	periodic	periodic	ADJ
american_scientific_journal-3866	45	27	american	american	ADJ
american_scientific_journal-3866	45	28	scientific	scientific	ADJ
american_scientific_journal-3866	45	29	research	research	NOUN
american_scientific_journal-3866	45	30	journal	journal	NOUN
american_scientific_journal-3866	45	31	for	for	ADP
american_scientific_journal-3866	45	32	engineering	engineering	NOUN
american_scientific_journal-3866	45	33	,	,	PUNCT
american_scientific_journal-3866	45	34	technology	technology	NOUN
american_scientific_journal-3866	45	35	,	,	PUNCT
american_scientific_journal-3866	45	36	and	and	CCONJ
american_scientific_journal-3866	45	37	sciences	science	NOUN
american_scientific_journal-3866	45	38	(	(	PUNCT
american_scientific_journal-3866	45	39	asrjets	asrjet	NOUN
american_scientific_journal-3866	45	40	)	)	PUNCT
american_scientific_journal-3866	45	41	(	(	PUNCT
american_scientific_journal-3866	45	42	2018	2018	NUM
american_scientific_journal-3866	45	43	)	)	PUNCT
american_scientific_journal-3866	45	44	volume	volume	NOUN
american_scientific_journal-3866	45	45	40	40	NUM
american_scientific_journal-3866	45	46	,	,	PUNCT
american_scientific_journal-3866	45	47	no	no	DET
american_scientific_journal-3866	45	48	1	1	NUM
american_scientific_journal-3866	45	49	,	,	PUNCT
american_scientific_journal-3866	45	50	pp	pp	ADV
american_scientific_journal-3866	45	51	125	125	NUM
american_scientific_journal-3866	45	52	-	-	SYM
american_scientific_journal-3866	45	53	131	131	NUM
american_scientific_journal-3866	45	54	131	131	NUM
american_scientific_journal-3866	45	55	function	function	NOUN
american_scientific_journal-3866	45	56	,	,	PUNCT
american_scientific_journal-3866	45	57	since	since	SCONJ
american_scientific_journal-3866	45	58	it	it	PRON
american_scientific_journal-3866	45	59	establishes	establish	VERB
american_scientific_journal-3866	45	60	that	that	SCONJ
american_scientific_journal-3866	45	61	after	after	ADP
american_scientific_journal-3866	45	62	a	a	DET
american_scientific_journal-3866	45	63	time	time	NOUN
american_scientific_journal-3866	45	64	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-3866	45	65	=	=	PUNCT
american_scientific_journal-3866	45	66	2𝜋𝜋	2𝜋𝜋	ADJ
american_scientific_journal-3866	45	67	𝑤𝑤	𝑤𝑤	NOUN
american_scientific_journal-3866	45	68	,	,	PUNCT
american_scientific_journal-3866	45	69	the	the	DET
american_scientific_journal-3866	45	70	function	function	NOUN
american_scientific_journal-3866	45	71	is	be	AUX
american_scientific_journal-3866	45	72	repeated	repeat	VERB
american_scientific_journal-3866	45	73	.	.	PUNCT
american_scientific_journal-3866	46	1	the	the	DET
american_scientific_journal-3866	46	2	references	reference	NOUN
american_scientific_journal-3866	46	3	[	[	X
american_scientific_journal-3866	46	4	6,7,8	6,7,8	NUM
american_scientific_journal-3866	46	5	]	]	PUNCT
american_scientific_journal-3866	46	6	have	have	VERB
american_scientific_journal-3866	46	7	several	several	ADJ
american_scientific_journal-3866	46	8	differences	difference	NOUN
american_scientific_journal-3866	46	9	with	with	ADP
american_scientific_journal-3866	46	10	our	our	PRON
american_scientific_journal-3866	46	11	work	work	NOUN
american_scientific_journal-3866	46	12	,	,	PUNCT
american_scientific_journal-3866	46	13	because	because	SCONJ
american_scientific_journal-3866	46	14	they	they	PRON
american_scientific_journal-3866	46	15	use	use	VERB
american_scientific_journal-3866	46	16	differential	differential	ADJ
american_scientific_journal-3866	46	17	equations	equation	NOUN
american_scientific_journal-3866	46	18	and	and	CCONJ
american_scientific_journal-3866	46	19	they	they	PRON
american_scientific_journal-3866	46	20	manage	manage	VERB
american_scientific_journal-3866	46	21	to	to	PART
american_scientific_journal-3866	46	22	establish	establish	VERB
american_scientific_journal-3866	46	23	the	the	DET
american_scientific_journal-3866	46	24	expression	expression	NOUN
american_scientific_journal-3866	46	25	to	to	PART
american_scientific_journal-3866	46	26	calculate	calculate	VERB
american_scientific_journal-3866	46	27	the	the	DET
american_scientific_journal-3866	46	28	period	period	NOUN
american_scientific_journal-3866	46	29	of	of	ADP
american_scientific_journal-3866	46	30	the	the	DET
american_scientific_journal-3866	46	31	simple	simple	ADJ
american_scientific_journal-3866	46	32	pendulum	pendulum	NOUN
american_scientific_journal-3866	46	33	considering	consider	VERB
american_scientific_journal-3866	46	34	an	an	DET
american_scientific_journal-3866	46	35	approximation	approximation	NOUN
american_scientific_journal-3866	46	36	,	,	PUNCT
american_scientific_journal-3866	46	37	also	also	ADV
american_scientific_journal-3866	46	38	consider	consider	VERB
american_scientific_journal-3866	46	39	relations	relation	NOUN
american_scientific_journal-3866	46	40	between	between	ADP
american_scientific_journal-3866	46	41	the	the	DET
american_scientific_journal-3866	46	42	force	force	NOUN
american_scientific_journal-3866	46	43	,	,	PUNCT
american_scientific_journal-3866	46	44	angular	angular	ADJ
american_scientific_journal-3866	46	45	speed	speed	NOUN
american_scientific_journal-3866	46	46	and	and	CCONJ
american_scientific_journal-3866	46	47	the	the	DET
american_scientific_journal-3866	46	48	time	time	NOUN
american_scientific_journal-3866	46	49	.	.	PUNCT
american_scientific_journal-3866	47	1	5	5	X
american_scientific_journal-3866	47	2	.	.	X
american_scientific_journal-3866	47	3	conclusions	conclusion	NOUN
american_scientific_journal-3866	47	4	although	although	SCONJ
american_scientific_journal-3866	47	5	,	,	PUNCT
american_scientific_journal-3866	47	6	there	there	PRON
american_scientific_journal-3866	47	7	are	be	VERB
american_scientific_journal-3866	47	8	other	other	ADJ
american_scientific_journal-3866	47	9	ways	way	NOUN
american_scientific_journal-3866	47	10	to	to	PART
american_scientific_journal-3866	47	11	get	get	VERB
american_scientific_journal-3866	47	12	to	to	ADP
american_scientific_journal-3866	47	13	the	the	DET
american_scientific_journal-3866	47	14	expression	expression	NOUN
american_scientific_journal-3866	47	15	of	of	ADP
american_scientific_journal-3866	47	16	the	the	DET
american_scientific_journal-3866	47	17	period	period	NOUN
american_scientific_journal-3866	47	18	of	of	ADP
american_scientific_journal-3866	47	19	the	the	DET
american_scientific_journal-3866	47	20	simple	simple	ADJ
american_scientific_journal-3866	47	21	pendulum	pendulum	NOUN
american_scientific_journal-3866	47	22	,	,	PUNCT
american_scientific_journal-3866	47	23	the	the	DET
american_scientific_journal-3866	47	24	way	way	NOUN
american_scientific_journal-3866	47	25	to	to	PART
american_scientific_journal-3866	47	26	deduce	deduce	VERB
american_scientific_journal-3866	47	27	the	the	DET
american_scientific_journal-3866	47	28	equation	equation	NOUN
american_scientific_journal-3866	47	29	of	of	ADP
american_scientific_journal-3866	47	30	the	the	DET
american_scientific_journal-3866	47	31	period	period	NOUN
american_scientific_journal-3866	47	32	of	of	ADP
american_scientific_journal-3866	47	33	the	the	DET
american_scientific_journal-3866	47	34	pendulum	pendulum	NOUN
american_scientific_journal-3866	47	35	in	in	ADP
american_scientific_journal-3866	47	36	this	this	DET
american_scientific_journal-3866	47	37	work	work	NOUN
american_scientific_journal-3866	47	38	allows	allow	VERB
american_scientific_journal-3866	47	39	teachers	teacher	NOUN
american_scientific_journal-3866	47	40	to	to	PART
american_scientific_journal-3866	47	41	induce	induce	VERB
american_scientific_journal-3866	47	42	high	high	ADJ
american_scientific_journal-3866	47	43	school	school	NOUN
american_scientific_journal-3866	47	44	students	student	NOUN
american_scientific_journal-3866	47	45	,	,	PUNCT
american_scientific_journal-3866	47	46	in	in	ADP
american_scientific_journal-3866	47	47	a	a	DET
american_scientific_journal-3866	47	48	simple	simple	ADJ
american_scientific_journal-3866	47	49	way	way	NOUN
american_scientific_journal-3866	47	50	,	,	PUNCT
american_scientific_journal-3866	47	51	using	use	VERB
american_scientific_journal-3866	47	52	trigonometry	trigonometry	NOUN
american_scientific_journal-3866	47	53	and	and	CCONJ
american_scientific_journal-3866	47	54	the	the	DET
american_scientific_journal-3866	47	55	law	law	NOUN
american_scientific_journal-3866	47	56	of	of	ADP
american_scientific_journal-3866	47	57	the	the	DET
american_scientific_journal-3866	47	58	conservation	conservation	NOUN
american_scientific_journal-3866	47	59	of	of	ADP
american_scientific_journal-3866	47	60	energy	energy	NOUN
american_scientific_journal-3866	47	61	primarily	primarily	ADV
american_scientific_journal-3866	47	62	,	,	PUNCT
american_scientific_journal-3866	47	63	to	to	PART
american_scientific_journal-3866	47	64	conclude	conclude	VERB
american_scientific_journal-3866	47	65	that	that	SCONJ
american_scientific_journal-3866	47	66	the	the	DET
american_scientific_journal-3866	47	67	period	period	NOUN
american_scientific_journal-3866	47	68	does	do	AUX
american_scientific_journal-3866	47	69	not	not	PART
american_scientific_journal-3866	47	70	depend	depend	VERB
american_scientific_journal-3866	47	71	on	on	ADP
american_scientific_journal-3866	47	72	the	the	DET
american_scientific_journal-3866	47	73	mass	mass	NOUN
american_scientific_journal-3866	47	74	or	or	CCONJ
american_scientific_journal-3866	47	75	the	the	DET
american_scientific_journal-3866	47	76	angle	angle	NOUN
american_scientific_journal-3866	47	77	or	or	CCONJ
american_scientific_journal-3866	47	78	the	the	DET
american_scientific_journal-3866	47	79	height	height	NOUN
american_scientific_journal-3866	47	80	to	to	PART
american_scientific_journal-3866	47	81	which	which	PRON
american_scientific_journal-3866	47	82	it	it	PRON
american_scientific_journal-3866	47	83	is	be	AUX
american_scientific_journal-3866	47	84	released	release	VERB
american_scientific_journal-3866	47	85	,	,	PUNCT
american_scientific_journal-3866	47	86	it	it	PRON
american_scientific_journal-3866	47	87	only	only	ADV
american_scientific_journal-3866	47	88	depends	depend	VERB
american_scientific_journal-3866	47	89	on	on	ADP
american_scientific_journal-3866	47	90	its	its	PRON
american_scientific_journal-3866	47	91	length	length	NOUN
american_scientific_journal-3866	47	92	and	and	CCONJ
american_scientific_journal-3866	47	93	the	the	DET
american_scientific_journal-3866	47	94	acceleration	acceleration	NOUN
american_scientific_journal-3866	47	95	of	of	ADP
american_scientific_journal-3866	47	96	the	the	DET
american_scientific_journal-3866	47	97	gravity	gravity	NOUN
american_scientific_journal-3866	47	98	of	of	ADP
american_scientific_journal-3866	47	99	the	the	DET
american_scientific_journal-3866	47	100	place	place	NOUN
american_scientific_journal-3866	47	101	where	where	SCONJ
american_scientific_journal-3866	47	102	the	the	DET
american_scientific_journal-3866	47	103	movement	movement	NOUN
american_scientific_journal-3866	47	104	was	be	AUX
american_scientific_journal-3866	47	105	made	make	VERB
american_scientific_journal-3866	47	106	,	,	PUNCT
american_scientific_journal-3866	47	107	without	without	ADP
american_scientific_journal-3866	47	108	using	use	VERB
american_scientific_journal-3866	47	109	differential	differential	ADJ
american_scientific_journal-3866	47	110	equations	equation	NOUN
american_scientific_journal-3866	47	111	.	.	PUNCT
american_scientific_journal-3866	48	1	therefore	therefore	ADV
american_scientific_journal-3866	48	2	,	,	PUNCT
american_scientific_journal-3866	48	3	to	to	PART
american_scientific_journal-3866	48	4	deduce	deduce	VERB
american_scientific_journal-3866	48	5	the	the	DET
american_scientific_journal-3866	48	6	expression	expression	NOUN
american_scientific_journal-3866	48	7	of	of	ADP
american_scientific_journal-3866	48	8	the	the	DET
american_scientific_journal-3866	48	9	period	period	NOUN
american_scientific_journal-3866	48	10	of	of	ADP
american_scientific_journal-3866	48	11	a	a	DET
american_scientific_journal-3866	48	12	simple	simple	ADJ
american_scientific_journal-3866	48	13	pendulum	pendulum	NOUN
american_scientific_journal-3866	48	14	,	,	PUNCT
american_scientific_journal-3866	48	15	in	in	ADP
american_scientific_journal-3866	48	16	theoretical	theoretical	ADJ
american_scientific_journal-3866	48	17	form	form	NOUN
american_scientific_journal-3866	48	18	,	,	PUNCT
american_scientific_journal-3866	48	19	without	without	ADP
american_scientific_journal-3866	48	20	differential	differential	ADJ
american_scientific_journal-3866	48	21	equations	equation	NOUN
american_scientific_journal-3866	48	22	,	,	PUNCT
american_scientific_journal-3866	48	23	we	we	PRON
american_scientific_journal-3866	48	24	must	must	AUX
american_scientific_journal-3866	48	25	consider	consider	VERB
american_scientific_journal-3866	48	26	that	that	PRON
american_scientific_journal-3866	48	27	:	:	PUNCT
american_scientific_journal-3866	48	28	1	1	X
american_scientific_journal-3866	48	29	)	)	PUNCT
american_scientific_journal-3866	48	30	the	the	DET
american_scientific_journal-3866	48	31	change	change	NOUN
american_scientific_journal-3866	48	32	in	in	ADP
american_scientific_journal-3866	48	33	kinetic	kinetic	ADJ
american_scientific_journal-3866	48	34	energy	energy	NOUN
american_scientific_journal-3866	48	35	is	be	AUX
american_scientific_journal-3866	48	36	equal	equal	ADJ
american_scientific_journal-3866	48	37	to	to	ADP
american_scientific_journal-3866	48	38	the	the	DET
american_scientific_journal-3866	48	39	change	change	NOUN
american_scientific_journal-3866	48	40	in	in	ADP
american_scientific_journal-3866	48	41	potential	potential	ADJ
american_scientific_journal-3866	48	42	energy	energy	NOUN
american_scientific_journal-3866	48	43	.	.	PUNCT
american_scientific_journal-3866	49	1	2	2	X
american_scientific_journal-3866	49	2	)	)	PUNCT
american_scientific_journal-3866	49	3	the	the	DET
american_scientific_journal-3866	49	4	height	height	NOUN
american_scientific_journal-3866	49	5	at	at	ADP
american_scientific_journal-3866	49	6	which	which	PRON
american_scientific_journal-3866	49	7	the	the	DET
american_scientific_journal-3866	49	8	pendulum	pendulum	NOUN
american_scientific_journal-3866	49	9	is	be	AUX
american_scientific_journal-3866	49	10	located	locate	VERB
american_scientific_journal-3866	49	11	is	be	AUX
american_scientific_journal-3866	49	12	determined	determine	VERB
american_scientific_journal-3866	49	13	with	with	ADP
american_scientific_journal-3866	49	14	a	a	DET
american_scientific_journal-3866	49	15	trigonometric	trigonometric	ADJ
american_scientific_journal-3866	49	16	function	function	NOUN
american_scientific_journal-3866	49	17	,	,	PUNCT
american_scientific_journal-3866	49	18	with	with	ADP
american_scientific_journal-3866	49	19	an	an	DET
american_scientific_journal-3866	49	20	approximation	approximation	NOUN
american_scientific_journal-3866	49	21	for	for	ADP
american_scientific_journal-3866	49	22	small	small	ADJ
american_scientific_journal-3866	49	23	angles	angle	NOUN
american_scientific_journal-3866	49	24	.	.	PUNCT
american_scientific_journal-3866	50	1	3	3	X
american_scientific_journal-3866	50	2	)	)	PUNCT
american_scientific_journal-3866	50	3	the	the	DET
american_scientific_journal-3866	50	4	speed	speed	NOUN
american_scientific_journal-3866	50	5	is	be	AUX
american_scientific_journal-3866	50	6	the	the	DET
american_scientific_journal-3866	50	7	quotient	quotient	NOUN
american_scientific_journal-3866	50	8	of	of	ADP
american_scientific_journal-3866	50	9	the	the	DET
american_scientific_journal-3866	50	10	length	length	NOUN
american_scientific_journal-3866	50	11	of	of	ADP
american_scientific_journal-3866	50	12	the	the	DET
american_scientific_journal-3866	50	13	arc	arc	NOUN
american_scientific_journal-3866	50	14	traveled	travel	VERB
american_scientific_journal-3866	50	15	and	and	CCONJ
american_scientific_journal-3866	50	16	the	the	DET
american_scientific_journal-3866	50	17	time	time	NOUN
american_scientific_journal-3866	50	18	of	of	ADP
american_scientific_journal-3866	50	19	movement	movement	NOUN
american_scientific_journal-3866	50	20	,	,	PUNCT
american_scientific_journal-3866	50	21	respectively	respectively	ADV
american_scientific_journal-3866	50	22	.	.	PUNCT
american_scientific_journal-3866	51	1	references	reference	NOUN
american_scientific_journal-3866	51	2	[	[	X
american_scientific_journal-3866	51	3	1	1	NUM
american_scientific_journal-3866	51	4	]	]	PUNCT
american_scientific_journal-3866	51	5	tippens	tippen	NOUN
american_scientific_journal-3866	51	6	,	,	PUNCT
american_scientific_journal-3866	51	7	paul	paul	PROPN
american_scientific_journal-3866	51	8	e.	e.	PROPN
american_scientific_journal-3866	51	9	(	(	PUNCT
american_scientific_journal-3866	51	10	1988	1988	NUM
american_scientific_journal-3866	51	11	)	)	PUNCT
american_scientific_journal-3866	51	12	.	.	PUNCT
american_scientific_journal-3866	52	1	física	física	PROPN
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american_scientific_journal-3866	52	3	y	y	PROPN
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american_scientific_journal-3866	52	5	.	.	PUNCT
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american_scientific_journal-3866	53	5	.	.	PUNCT
american_scientific_journal-3866	54	1	mc	mc	PROPN
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american_scientific_journal-3866	54	3	-	-	PUNCT
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american_scientific_journal-3866	54	5	.	.	PUNCT
american_scientific_journal-3866	55	1	[	[	X
american_scientific_journal-3866	55	2	2	2	X
american_scientific_journal-3866	55	3	]	]	PUNCT
american_scientific_journal-3866	55	4	seely	seely	ADV
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american_scientific_journal-3866	55	7	(	(	PUNCT
american_scientific_journal-3866	55	8	1959	1959	NUM
american_scientific_journal-3866	55	9	)	)	PUNCT
american_scientific_journal-3866	55	10	.	.	PUNCT
american_scientific_journal-3866	56	1	mecánica	mecánica	PROPN
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american_scientific_journal-3866	56	3	para	para	PROPN
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american_scientific_journal-3866	56	5	.	.	PUNCT
american_scientific_journal-3866	57	1	uteha	uteha	NOUN
american_scientific_journal-3866	57	2	,	,	PUNCT
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american_scientific_journal-3866	57	4	.	.	PUNCT
american_scientific_journal-3866	58	1	[	[	X
american_scientific_journal-3866	58	2	3	3	NUM
american_scientific_journal-3866	58	3	]	]	X
american_scientific_journal-3866	58	4	sears	sear	NOUN
american_scientific_journal-3866	58	5	,	,	PUNCT
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american_scientific_journal-3866	58	8	&	&	CCONJ
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american_scientific_journal-3866	58	10	,	,	PUNCT
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american_scientific_journal-3866	58	13	&	&	CCONJ
american_scientific_journal-3866	58	14	young	young	PROPN
american_scientific_journal-3866	58	15	hugh	hugh	PROPN
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american_scientific_journal-3866	58	17	(	(	PUNCT
american_scientific_journal-3866	58	18	1987	1987	NUM
american_scientific_journal-3866	58	19	)	)	PUNCT
american_scientific_journal-3866	58	20	.	.	PUNCT
american_scientific_journal-3866	59	1	university	university	NOUN
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american_scientific_journal-3866	59	3	.	.	PUNCT
american_scientific_journal-3866	60	1	seventh	seventh	PROPN
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american_scientific_journal-3866	60	3	.	.	PUNCT
american_scientific_journal-3866	61	1	adsison	adsison	PROPN
american_scientific_journal-3866	61	2	-	-	PUNCT
american_scientific_journal-3866	61	3	wesley	wesley	PROPN
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american_scientific_journal-3866	61	5	company	company	NOUN
american_scientific_journal-3866	61	6	.	.	PUNCT
american_scientific_journal-3866	62	1	[	[	X
american_scientific_journal-3866	62	2	4	4	NUM
american_scientific_journal-3866	62	3	]	]	X
american_scientific_journal-3866	62	4	hewitt	hewitt	PROPN
american_scientific_journal-3866	62	5	,	,	PUNCT
american_scientific_journal-3866	62	6	paul	paul	PROPN
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american_scientific_journal-3866	62	8	(	(	PUNCT
american_scientific_journal-3866	62	9	2000	2000	NUM
american_scientific_journal-3866	62	10	)	)	PUNCT
american_scientific_journal-3866	62	11	.	.	PUNCT
american_scientific_journal-3866	63	1	física	física	PROPN
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american_scientific_journal-3866	63	3	.	.	PUNCT
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american_scientific_journal-3866	64	2	edición	edición	PROPN
american_scientific_journal-3866	64	3	.	.	PUNCT
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american_scientific_journal-3866	64	6	,	,	PUNCT
american_scientific_journal-3866	64	7	addison	addison	PROPN
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american_scientific_journal-3866	64	10	,	,	PUNCT
american_scientific_journal-3866	64	11	[	[	X
american_scientific_journal-3866	64	12	5	5	NUM
american_scientific_journal-3866	64	13	]	]	X
american_scientific_journal-3866	64	14	resnick	resnick	PROPN
american_scientific_journal-3866	64	15	,	,	PUNCT
american_scientific_journal-3866	64	16	robert	robert	PROPN
american_scientific_journal-3866	64	17	&	&	CCONJ
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american_scientific_journal-3866	64	19	,	,	PUNCT
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american_scientific_journal-3866	64	21	(	(	PUNCT
american_scientific_journal-3866	64	22	2004	2004	NUM
american_scientific_journal-3866	64	23	)	)	PUNCT
american_scientific_journal-3866	64	24	.	.	PUNCT
american_scientific_journal-3866	65	1	física	física	PROPN
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american_scientific_journal-3866	66	2	,	,	PUNCT
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american_scientific_journal-3866	66	5	,	,	PUNCT
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american_scientific_journal-3866	67	3	-	-	SYM
american_scientific_journal-3866	67	4	24	24	NUM
american_scientific_journal-3866	67	5	-	-	PUNCT
american_scientific_journal-3866	67	6	0257	0257	NUM
american_scientific_journal-3866	67	7	-	-	PUNCT
american_scientific_journal-3866	67	8	3	3	NUM
american_scientific_journal-3866	67	9	.	.	PUNCT
american_scientific_journal-3866	68	1	[	[	X
american_scientific_journal-3866	68	2	6	6	NUM
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american_scientific_journal-3866	68	4	targ	targ	PROPN
american_scientific_journal-3866	68	5	,	,	PUNCT
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american_scientific_journal-3866	68	7	)	)	PUNCT
american_scientific_journal-3866	68	8	.	.	PUNCT
american_scientific_journal-3866	69	1	curso	curso	PROPN
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american_scientific_journal-3866	69	3	de	de	PROPN
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american_scientific_journal-3866	69	6	.	.	PUNCT
american_scientific_journal-3866	70	1	2ª.	2ª.	NUM
american_scientific_journal-3866	70	2	edición	edición	PROPN
american_scientific_journal-3866	70	3	.	.	PUNCT
american_scientific_journal-3866	71	1	editorial	editorial	PROPN
american_scientific_journal-3866	71	2	mir	mir	PROPN
american_scientific_journal-3866	71	3	,	,	PUNCT
american_scientific_journal-3866	71	4	moscú	moscú	ADJ
american_scientific_journal-3866	71	5	.	.	PUNCT
american_scientific_journal-3866	72	1	[	[	X
american_scientific_journal-3866	72	2	7	7	NUM
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american_scientific_journal-3866	72	4	gettys	gettys	PROPN
american_scientific_journal-3866	72	5	,	,	PUNCT
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american_scientific_journal-3866	72	7	:	:	PUNCT
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american_scientific_journal-3866	72	9	,	,	PUNCT
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american_scientific_journal-3866	72	11	,	,	PUNCT
american_scientific_journal-3866	72	12	s.	s.	PROPN
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american_scientific_journal-3866	72	15	.	.	PUNCT
american_scientific_journal-3866	73	1	(	(	PUNCT
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american_scientific_journal-3866	73	3	)	)	PUNCT
american_scientific_journal-3866	73	4	.	.	PUNCT
american_scientific_journal-3866	74	1	physics	physics	NOUN
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american_scientific_journal-3866	74	3	a	a	DET
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american_scientific_journal-3866	74	5	.	.	PUNCT
american_scientific_journal-3866	75	1	usa	usa	PROPN
american_scientific_journal-3866	75	2	,	,	PUNCT
american_scientific_journal-3866	75	3	mc	mc	PROPN
american_scientific_journal-3866	75	4	graw	graw	PROPN
american_scientific_journal-3866	75	5	-	-	PUNCT
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american_scientific_journal-3866	75	7	.	.	PUNCT
american_scientific_journal-3866	76	1	[	[	X
american_scientific_journal-3866	76	2	8	8	NUM
american_scientific_journal-3866	76	3	]	]	X
american_scientific_journal-3866	76	4	marion	marion	PROPN
american_scientific_journal-3866	76	5	,	,	PUNCT
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american_scientific_journal-3866	76	8	(	(	PUNCT
american_scientific_journal-3866	76	9	1996	1996	NUM
american_scientific_journal-3866	76	10	)	)	PUNCT
american_scientific_journal-3866	76	11	.	.	PUNCT
american_scientific_journal-3866	77	1	dinámica	dinámica	PROPN
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american_scientific_journal-3866	77	6	y	y	PROPN
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american_scientific_journal-3866	77	8	.	.	PUNCT
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american_scientific_journal-3866	78	2	:	:	PUNCT
american_scientific_journal-3866	79	1	ed	ed	X
american_scientific_journal-3866	79	2	.	.	PUNCT
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american_scientific_journal-3866	79	4	.	.	PUNCT
american_scientific_journal-3866	80	1	isbn	isbn	ADJ
american_scientific_journal-3866	80	2	84	84	NUM
american_scientific_journal-3866	80	3	-	-	SYM
american_scientific_journal-3866	80	4	291	291	NUM
american_scientific_journal-3866	80	5	-	-	PUNCT
american_scientific_journal-3866	80	6	4094	4094	NUM
american_scientific_journal-3866	80	7	-	-	SYM
american_scientific_journal-3866	80	8	8	8	NUM
american_scientific_journal-3866	80	9	.	.	PUNCT
american_scientific_journal-3866	81	1	https://es.wikipedia.org/wiki/especial:fuentesdelibros/9702402573	https://es.wikipedia.org/wiki/especial:fuentesdelibros/9702402573	PROPN
american_scientific_journal-3866	81	2	https://es.wikipedia.org/wiki/especial:fuentesdelibros/8429140948	https://es.wikipedia.org/wiki/especial:fuentesdelibros/8429140948	PROPN
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