id	sid	tid	token	lemma	pos
american_scientific_journal-7932	1	1	229	229	NUM
american_scientific_journal-7932	1	2	american	american	ADJ
american_scientific_journal-7932	1	3	academic	academic	ADJ
american_scientific_journal-7932	1	4	scientific	scientific	ADJ
american_scientific_journal-7932	1	5	research	research	NOUN
american_scientific_journal-7932	1	6	journal	journal	NOUN
american_scientific_journal-7932	1	7	for	for	ADP
american_scientific_journal-7932	1	8	engineering	engineering	NOUN
american_scientific_journal-7932	1	9	,	,	PUNCT
american_scientific_journal-7932	1	10	technology	technology	NOUN
american_scientific_journal-7932	1	11	,	,	PUNCT
american_scientific_journal-7932	1	12	and	and	CCONJ
american_scientific_journal-7932	1	13	sciences	sciences	PROPN
american_scientific_journal-7932	1	14	issn	issn	PROPN
american_scientific_journal-7932	1	15	(	(	PUNCT
american_scientific_journal-7932	1	16	print	print	NOUN
american_scientific_journal-7932	1	17	)	)	PUNCT
american_scientific_journal-7932	1	18	2313	2313	NUM
american_scientific_journal-7932	1	19	-	-	SYM
american_scientific_journal-7932	1	20	4410	4410	NUM
american_scientific_journal-7932	1	21	,	,	PUNCT
american_scientific_journal-7932	1	22	issn	issn	PROPN
american_scientific_journal-7932	1	23	(	(	PUNCT
american_scientific_journal-7932	1	24	online	online	ADJ
american_scientific_journal-7932	1	25	)	)	PUNCT
american_scientific_journal-7932	1	26	2313	2313	NUM
american_scientific_journal-7932	1	27	-	-	SYM
american_scientific_journal-7932	1	28	4402	4402	NUM
american_scientific_journal-7932	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7932	1	30	internal	internal	ADJ
american_scientific_journal-7932	1	31	newtonian	newtonian	ADJ
american_scientific_journal-7932	1	32	flow	flow	NOUN
american_scientific_journal-7932	1	33	due	due	ADP
american_scientific_journal-7932	1	34	to	to	ADP
american_scientific_journal-7932	1	35	a	a	DET
american_scientific_journal-7932	1	36	cylinder	cylinder	NOUN
american_scientific_journal-7932	1	37	undergoing	undergo	VERB
american_scientific_journal-7932	1	38	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	1	39	and	and	CCONJ
american_scientific_journal-7932	1	40	torsional	torsional	ADJ
american_scientific_journal-7932	1	41	oscillations	oscillation	NOUN
american_scientific_journal-7932	1	42	of	of	ADP
american_scientific_journal-7932	1	43	different	different	ADJ
american_scientific_journal-7932	1	44	frequencies	frequency	NOUN
american_scientific_journal-7932	1	45	robin	robin	PROPN
american_scientific_journal-7932	1	46	ramlal	ramlal	VERB
american_scientific_journal-7932	1	47	a	a	PROPN
american_scientific_journal-7932	1	48	*	*	X
american_scientific_journal-7932	1	49	,	,	PUNCT
american_scientific_journal-7932	1	50	karim	karim	PROPN
american_scientific_journal-7932	1	51	rahaman	rahaman	PROPN
american_scientific_journal-7932	1	52	b	b	PROPN
american_scientific_journal-7932	1	53	a	a	DET
american_scientific_journal-7932	1	54	senior	senior	ADJ
american_scientific_journal-7932	1	55	lecturer	lecturer	NOUN
american_scientific_journal-7932	1	56	in	in	ADP
american_scientific_journal-7932	1	57	mathematics	mathematics	PROPN
american_scientific_journal-7932	1	58	,	,	PUNCT
american_scientific_journal-7932	1	59	college	college	NOUN
american_scientific_journal-7932	1	60	of	of	ADP
american_scientific_journal-7932	1	61	science	science	NOUN
american_scientific_journal-7932	1	62	,	,	PUNCT
american_scientific_journal-7932	1	63	technology	technology	NOUN
american_scientific_journal-7932	1	64	and	and	CCONJ
american_scientific_journal-7932	1	65	applied	apply	VERB
american_scientific_journal-7932	1	66	arts	art	NOUN
american_scientific_journal-7932	1	67	of	of	ADP
american_scientific_journal-7932	1	68	trinidad	trinidad	PROPN
american_scientific_journal-7932	1	69	and	and	CCONJ
american_scientific_journal-7932	1	70	tobago	tobago	PROPN
american_scientific_journal-7932	1	71	costaatt	costaatt	PROPN
american_scientific_journal-7932	2	1	b	b	PROPN
american_scientific_journal-7932	2	2	senior	senior	ADJ
american_scientific_journal-7932	2	3	lecturer	lecturer	NOUN
american_scientific_journal-7932	2	4	in	in	ADP
american_scientific_journal-7932	2	5	mathematics	mathematics	PROPN
american_scientific_journal-7932	2	6	,	,	PUNCT
american_scientific_journal-7932	2	7	department	department	NOUN
american_scientific_journal-7932	2	8	of	of	ADP
american_scientific_journal-7932	2	9	mathematics	mathematics	PROPN
american_scientific_journal-7932	2	10	and	and	CCONJ
american_scientific_journal-7932	2	11	statistics	statistic	NOUN
american_scientific_journal-7932	2	12	,	,	PUNCT
american_scientific_journal-7932	2	13	the	the	DET
american_scientific_journal-7932	2	14	university	university	NOUN
american_scientific_journal-7932	2	15	of	of	ADP
american_scientific_journal-7932	2	16	the	the	DET
american_scientific_journal-7932	2	17	west	west	PROPN
american_scientific_journal-7932	2	18	indies	indies	PROPN
american_scientific_journal-7932	2	19	,	,	PUNCT
american_scientific_journal-7932	2	20	trinidad	trinidad	PROPN
american_scientific_journal-7932	2	21	and	and	CCONJ
american_scientific_journal-7932	2	22	tobago	tobago	VERB
american_scientific_journal-7932	2	23	a	a	DET
american_scientific_journal-7932	2	24	email	email	NOUN
american_scientific_journal-7932	2	25	:	:	PUNCT
american_scientific_journal-7932	3	1	robinramlal@outlook.com	robinramlal@outlook.com	X
american_scientific_journal-7932	3	2	b	b	X
american_scientific_journal-7932	3	3	email	email	NOUN
american_scientific_journal-7932	3	4	:	:	PUNCT
american_scientific_journal-7932	3	5	karim.rahaman@sta.uwi.edu	karim.rahaman@sta.uwi.edu	VERB
american_scientific_journal-7932	3	6	abstract	abstract	ADJ
american_scientific_journal-7932	3	7	the	the	DET
american_scientific_journal-7932	3	8	unsteady	unsteady	ADJ
american_scientific_journal-7932	3	9	flow	flow	NOUN
american_scientific_journal-7932	3	10	of	of	ADP
american_scientific_journal-7932	3	11	an	an	DET
american_scientific_journal-7932	3	12	incompressible	incompressible	ADJ
american_scientific_journal-7932	3	13	viscous	viscous	ADJ
american_scientific_journal-7932	3	14	fluid	fluid	NOUN
american_scientific_journal-7932	3	15	contained	contain	VERB
american_scientific_journal-7932	3	16	in	in	ADP
american_scientific_journal-7932	3	17	a	a	DET
american_scientific_journal-7932	3	18	cylinder	cylinder	NOUN
american_scientific_journal-7932	3	19	of	of	ADP
american_scientific_journal-7932	3	20	infinite	infinite	ADJ
american_scientific_journal-7932	3	21	length	length	NOUN
american_scientific_journal-7932	3	22	,	,	PUNCT
american_scientific_journal-7932	3	23	subject	subject	ADJ
american_scientific_journal-7932	3	24	to	to	ADP
american_scientific_journal-7932	3	25	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	3	26	and	and	CCONJ
american_scientific_journal-7932	3	27	torsional	torsional	ADJ
american_scientific_journal-7932	3	28	oscillations	oscillation	NOUN
american_scientific_journal-7932	3	29	of	of	ADP
american_scientific_journal-7932	3	30	different	different	ADJ
american_scientific_journal-7932	3	31	frequencies	frequency	NOUN
american_scientific_journal-7932	3	32	is	be	AUX
american_scientific_journal-7932	3	33	examined	examine	VERB
american_scientific_journal-7932	3	34	.	.	PUNCT
american_scientific_journal-7932	4	1	analytical	analytical	ADJ
american_scientific_journal-7932	4	2	expressions	expression	NOUN
american_scientific_journal-7932	4	3	for	for	ADP
american_scientific_journal-7932	4	4	the	the	DET
american_scientific_journal-7932	4	5	velocity	velocity	NOUN
american_scientific_journal-7932	4	6	field	field	NOUN
american_scientific_journal-7932	4	7	,	,	PUNCT
american_scientific_journal-7932	4	8	shear	shear	NOUN
american_scientific_journal-7932	4	9	stresses	stress	NOUN
american_scientific_journal-7932	4	10	,	,	PUNCT
american_scientific_journal-7932	4	11	drag	drag	VERB
american_scientific_journal-7932	4	12	on	on	ADP
american_scientific_journal-7932	4	13	the	the	DET
american_scientific_journal-7932	4	14	cylinder	cylinder	NOUN
american_scientific_journal-7932	4	15	,	,	PUNCT
american_scientific_journal-7932	4	16	work	work	NOUN
american_scientific_journal-7932	4	17	done	do	VERB
american_scientific_journal-7932	4	18	and	and	CCONJ
american_scientific_journal-7932	4	19	the	the	DET
american_scientific_journal-7932	4	20	drag	drag	NOUN
american_scientific_journal-7932	4	21	coefficients	coefficient	NOUN
american_scientific_journal-7932	4	22	are	be	AUX
american_scientific_journal-7932	4	23	obtained	obtain	VERB
american_scientific_journal-7932	4	24	.	.	PUNCT
american_scientific_journal-7932	5	1	keywords	keyword	NOUN
american_scientific_journal-7932	5	2	:	:	PUNCT
american_scientific_journal-7932	5	3	viscous	viscous	ADJ
american_scientific_journal-7932	5	4	;	;	PUNCT
american_scientific_journal-7932	5	5	unsteady	unsteady	ADJ
american_scientific_journal-7932	5	6	flow	flow	NOUN
american_scientific_journal-7932	5	7	;	;	PUNCT
american_scientific_journal-7932	5	8	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	5	9	;	;	PUNCT
american_scientific_journal-7932	5	10	torsional	torsional	ADJ
american_scientific_journal-7932	5	11	;	;	PUNCT
american_scientific_journal-7932	5	12	oscillation	oscillation	NOUN
american_scientific_journal-7932	5	13	;	;	PUNCT
american_scientific_journal-7932	5	14	different	different	ADJ
american_scientific_journal-7932	5	15	frequencies	frequency	NOUN
american_scientific_journal-7932	5	16	.	.	PUNCT
american_scientific_journal-7932	6	1	1	1	X
american_scientific_journal-7932	6	2	.	.	X
american_scientific_journal-7932	6	3	introduction	introduction	NOUN
american_scientific_journal-7932	6	4	as	as	ADV
american_scientific_journal-7932	6	5	early	early	ADV
american_scientific_journal-7932	6	6	as	as	ADP
american_scientific_journal-7932	6	7	1886	1886	NUM
american_scientific_journal-7932	6	8	,	,	PUNCT
american_scientific_journal-7932	6	9	an	an	DET
american_scientific_journal-7932	6	10	exact	exact	ADJ
american_scientific_journal-7932	6	11	solution	solution	NOUN
american_scientific_journal-7932	6	12	for	for	ADP
american_scientific_journal-7932	6	13	the	the	DET
american_scientific_journal-7932	6	14	velocity	velocity	NOUN
american_scientific_journal-7932	6	15	field	field	NOUN
american_scientific_journal-7932	6	16	due	due	ADP
american_scientific_journal-7932	6	17	to	to	ADP
american_scientific_journal-7932	6	18	an	an	DET
american_scientific_journal-7932	6	19	infinite	infinite	ADJ
american_scientific_journal-7932	6	20	rod	rod	NOUN
american_scientific_journal-7932	6	21	rotating	rotating	NOUN
american_scientific_journal-7932	6	22	in	in	ADP
american_scientific_journal-7932	6	23	a	a	DET
american_scientific_journal-7932	6	24	newtonian	newtonian	ADJ
american_scientific_journal-7932	6	25	fluid	fluid	NOUN
american_scientific_journal-7932	6	26	was	be	AUX
american_scientific_journal-7932	6	27	determined	determine	VERB
american_scientific_journal-7932	6	28	by	by	ADP
american_scientific_journal-7932	6	29	stokes	stoke	NOUN
american_scientific_journal-7932	6	30	[	[	X
american_scientific_journal-7932	6	31	1	1	NUM
american_scientific_journal-7932	6	32	]	]	PUNCT
american_scientific_journal-7932	6	33	.	.	PUNCT
american_scientific_journal-7932	7	1	later	later	ADV
american_scientific_journal-7932	7	2	,	,	PUNCT
american_scientific_journal-7932	7	3	casarella	casarella	PROPN
american_scientific_journal-7932	7	4	and	and	CCONJ
american_scientific_journal-7932	7	5	laura	laura	NOUN
american_scientific_journal-7932	8	1	[	[	X
american_scientific_journal-7932	8	2	2	2	NUM
american_scientific_journal-7932	8	3	]	]	PUNCT
american_scientific_journal-7932	8	4	determined	determine	VERB
american_scientific_journal-7932	8	5	analytical	analytical	ADJ
american_scientific_journal-7932	8	6	expressions	expression	NOUN
american_scientific_journal-7932	8	7	for	for	ADP
american_scientific_journal-7932	8	8	the	the	DET
american_scientific_journal-7932	8	9	velocity	velocity	NOUN
american_scientific_journal-7932	8	10	components	component	NOUN
american_scientific_journal-7932	8	11	of	of	ADP
american_scientific_journal-7932	8	12	a	a	DET
american_scientific_journal-7932	8	13	newtonian	newtonian	ADJ
american_scientific_journal-7932	8	14	fluid	fluid	NOUN
american_scientific_journal-7932	8	15	and	and	CCONJ
american_scientific_journal-7932	8	16	the	the	DET
american_scientific_journal-7932	8	17	viscous	viscous	ADJ
american_scientific_journal-7932	8	18	drag	drag	NOUN
american_scientific_journal-7932	8	19	forces	force	NOUN
american_scientific_journal-7932	8	20	acting	act	VERB
american_scientific_journal-7932	8	21	on	on	ADP
american_scientific_journal-7932	8	22	a	a	DET
american_scientific_journal-7932	8	23	cylindrical	cylindrical	ADJ
american_scientific_journal-7932	8	24	rod	rod	NOUN
american_scientific_journal-7932	8	25	-	-	PUNCT
american_scientific_journal-7932	8	26	like	like	ADJ
american_scientific_journal-7932	8	27	cable	cable	NOUN
american_scientific_journal-7932	8	28	which	which	PRON
american_scientific_journal-7932	8	29	is	be	AUX
american_scientific_journal-7932	8	30	undergoing	undergo	VERB
american_scientific_journal-7932	8	31	both	both	CCONJ
american_scientific_journal-7932	8	32	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	8	33	and	and	CCONJ
american_scientific_journal-7932	8	34	torsional	torsional	ADJ
american_scientific_journal-7932	8	35	oscillations	oscillation	NOUN
american_scientific_journal-7932	8	36	.	.	PUNCT
american_scientific_journal-7932	9	1	ramkissoon	ramkissoon	NOUN
american_scientific_journal-7932	9	2	and	and	CCONJ
american_scientific_journal-7932	9	3	majumdar	majumdar	PROPN
american_scientific_journal-7932	10	1	[	[	X
american_scientific_journal-7932	10	2	3	3	NUM
american_scientific_journal-7932	10	3	]	]	PUNCT
american_scientific_journal-7932	10	4	looked	look	VERB
american_scientific_journal-7932	10	5	at	at	ADP
american_scientific_journal-7932	10	6	the	the	DET
american_scientific_journal-7932	10	7	corresponding	corresponding	ADJ
american_scientific_journal-7932	10	8	internal	internal	ADJ
american_scientific_journal-7932	10	9	problem	problem	NOUN
american_scientific_journal-7932	10	10	to	to	ADP
american_scientific_journal-7932	10	11	that	that	PRON
american_scientific_journal-7932	10	12	done	do	VERB
american_scientific_journal-7932	10	13	in	in	ADP
american_scientific_journal-7932	10	14	[	[	X
american_scientific_journal-7932	10	15	2	2	NUM
american_scientific_journal-7932	10	16	]	]	PUNCT
american_scientific_journal-7932	10	17	,	,	PUNCT
american_scientific_journal-7932	10	18	and	and	CCONJ
american_scientific_journal-7932	10	19	determined	determine	VERB
american_scientific_journal-7932	10	20	the	the	DET
american_scientific_journal-7932	10	21	corresponding	corresponding	ADJ
american_scientific_journal-7932	10	22	results	result	NOUN
american_scientific_journal-7932	10	23	.	.	PUNCT
american_scientific_journal-7932	11	1	a	a	DET
american_scientific_journal-7932	11	2	modification	modification	NOUN
american_scientific_journal-7932	11	3	to	to	ADP
american_scientific_journal-7932	11	4	[	[	X
american_scientific_journal-7932	11	5	3	3	NUM
american_scientific_journal-7932	11	6	]	]	PUNCT
american_scientific_journal-7932	11	7	,	,	PUNCT
american_scientific_journal-7932	11	8	which	which	PRON
american_scientific_journal-7932	11	9	considered	consider	VERB
american_scientific_journal-7932	11	10	independent	independent	ADJ
american_scientific_journal-7932	11	11	amplitudes	amplitude	NOUN
american_scientific_journal-7932	11	12	of	of	ADP
american_scientific_journal-7932	11	13	the	the	DET
american_scientific_journal-7932	11	14	oscillations	oscillation	NOUN
american_scientific_journal-7932	11	15	,	,	PUNCT
american_scientific_journal-7932	11	16	was	be	AUX
american_scientific_journal-7932	11	17	looked	look	VERB
american_scientific_journal-7932	11	18	at	at	ADP
american_scientific_journal-7932	11	19	by	by	ADP
american_scientific_journal-7932	11	20	phillips	phillip	NOUN
american_scientific_journal-7932	11	21	and	and	CCONJ
american_scientific_journal-7932	11	22	rahaman	rahaman	NOUN
american_scientific_journal-7932	11	23	[	[	X
american_scientific_journal-7932	11	24	4	4	NUM
american_scientific_journal-7932	11	25	]	]	X
american_scientific_journal-7932	11	26	,	,	PUNCT
american_scientific_journal-7932	11	27	here	here	ADV
american_scientific_journal-7932	11	28	,	,	PUNCT
american_scientific_journal-7932	11	29	expressions	expression	NOUN
american_scientific_journal-7932	11	30	for	for	ADP
american_scientific_journal-7932	11	31	the	the	DET
american_scientific_journal-7932	11	32	velocity	velocity	NOUN
american_scientific_journal-7932	11	33	field	field	NOUN
american_scientific_journal-7932	11	34	,	,	PUNCT
american_scientific_journal-7932	11	35	shear	shear	NOUN
american_scientific_journal-7932	11	36	stresses	stress	NOUN
american_scientific_journal-7932	11	37	,	,	PUNCT
american_scientific_journal-7932	11	38	drag	drag	NOUN
american_scientific_journal-7932	11	39	forces	force	NOUN
american_scientific_journal-7932	11	40	,	,	PUNCT
american_scientific_journal-7932	11	41	drag	drag	VERB
american_scientific_journal-7932	11	42	coefficient	coefficient	NOUN
american_scientific_journal-7932	11	43	and	and	CCONJ
american_scientific_journal-7932	11	44	work	work	NOUN
american_scientific_journal-7932	11	45	done	do	VERB
american_scientific_journal-7932	11	46	by	by	ADP
american_scientific_journal-7932	11	47	the	the	DET
american_scientific_journal-7932	11	48	drag	drag	NOUN
american_scientific_journal-7932	11	49	forces	force	NOUN
american_scientific_journal-7932	11	50	were	be	AUX
american_scientific_journal-7932	11	51	obtained	obtain	VERB
american_scientific_journal-7932	11	52	.	.	PUNCT
american_scientific_journal-7932	12	1	due	due	ADP
american_scientific_journal-7932	12	2	to	to	ADP
american_scientific_journal-7932	12	3	much	much	ADJ
american_scientific_journal-7932	12	4	interests	interest	NOUN
american_scientific_journal-7932	12	5	in	in	ADP
american_scientific_journal-7932	12	6	the	the	DET
american_scientific_journal-7932	12	7	field	field	NOUN
american_scientific_journal-7932	12	8	of	of	ADP
american_scientific_journal-7932	12	9	non	non	ADJ
american_scientific_journal-7932	12	10	-	-	ADJ
american_scientific_journal-7932	12	11	newtonian	newtonian	ADJ
american_scientific_journal-7932	12	12	fluids	fluid	NOUN
american_scientific_journal-7932	12	13	and	and	CCONJ
american_scientific_journal-7932	12	14	the	the	DET
american_scientific_journal-7932	12	15	important	important	ADJ
american_scientific_journal-7932	12	16	applications	application	NOUN
american_scientific_journal-7932	12	17	of	of	ADP
american_scientific_journal-7932	12	18	such	such	ADJ
american_scientific_journal-7932	12	19	,	,	PUNCT
american_scientific_journal-7932	12	20	calmelet	calmelet	NOUN
american_scientific_journal-7932	12	21	-	-	PUNCT
american_scientific_journal-7932	12	22	eluhu	eluhu	PROPN
american_scientific_journal-7932	12	23	and	and	CCONJ
american_scientific_journal-7932	12	24	majumdar	majumdar	PROPN
american_scientific_journal-7932	13	1	[	[	X
american_scientific_journal-7932	13	2	5	5	NUM
american_scientific_journal-7932	13	3	]	]	PUNCT
american_scientific_journal-7932	13	4	considered	consider	VERB
american_scientific_journal-7932	13	5	the	the	DET
american_scientific_journal-7932	13	6	problem	problem	NOUN
american_scientific_journal-7932	13	7	for	for	ADP
american_scientific_journal-7932	13	8	a	a	DET
american_scientific_journal-7932	13	9	micropolar	micropolar	ADJ
american_scientific_journal-7932	13	10	fluid	fluid	NOUN
american_scientific_journal-7932	13	11	.	.	PUNCT
american_scientific_journal-7932	14	1	analytical	analytical	ADJ
american_scientific_journal-7932	14	2	expressions	expression	NOUN
american_scientific_journal-7932	14	3	of	of	ADP
american_scientific_journal-7932	14	4	the	the	DET
american_scientific_journal-7932	14	5	fluid	fluid	ADJ
american_scientific_journal-7932	14	6	velocity	velocity	NOUN
american_scientific_journal-7932	14	7	and	and	CCONJ
american_scientific_journal-7932	14	8	micro	micro	NOUN
american_scientific_journal-7932	14	9	-	-	NOUN
american_scientific_journal-7932	14	10	rotation	rotation	NOUN
american_scientific_journal-7932	14	11	were	be	AUX
american_scientific_journal-7932	14	12	obtained	obtain	VERB
american_scientific_journal-7932	14	13	,	,	PUNCT
american_scientific_journal-7932	14	14	along	along	ADP
american_scientific_journal-7932	14	15	with	with	ADP
american_scientific_journal-7932	14	16	explicit	explicit	ADJ
american_scientific_journal-7932	14	17	expressions	expression	NOUN
american_scientific_journal-7932	14	18	for	for	ADP
american_scientific_journal-7932	14	19	the	the	DET
american_scientific_journal-7932	14	20	shear	shear	NOUN
american_scientific_journal-7932	14	21	stresses	stress	NOUN
american_scientific_journal-7932	14	22	and	and	CCONJ
american_scientific_journal-7932	14	23	drag	drag	NOUN
american_scientific_journal-7932	14	24	force	force	NOUN
american_scientific_journal-7932	14	25	acting	act	VERB
american_scientific_journal-7932	14	26	at	at	ADP
american_scientific_journal-7932	14	27	the	the	DET
american_scientific_journal-7932	14	28	wall	wall	NOUN
american_scientific_journal-7932	14	29	of	of	ADP
american_scientific_journal-7932	14	30	the	the	DET
american_scientific_journal-7932	14	31	cylinder	cylinder	NOUN
american_scientific_journal-7932	14	32	.	.	PUNCT
american_scientific_journal-7932	15	1	rahaman	rahaman	NOUN
american_scientific_journal-7932	16	1	[	[	X
american_scientific_journal-7932	16	2	6	6	NUM
american_scientific_journal-7932	16	3	]	]	PUNCT
american_scientific_journal-7932	16	4	considered	consider	VERB
american_scientific_journal-7932	16	5	a	a	DET
american_scientific_journal-7932	16	6	similar	similar	ADJ
american_scientific_journal-7932	16	7	situation	situation	NOUN
american_scientific_journal-7932	16	8	using	use	VERB
american_scientific_journal-7932	16	9	an	an	DET
american_scientific_journal-7932	16	10	upper	upper	ADV
american_scientific_journal-7932	16	11	-	-	PUNCT
american_scientific_journal-7932	16	12	convected	convect	VERB
american_scientific_journal-7932	16	13	maxwell	maxwell	PROPN
american_scientific_journal-7932	16	14	fluid	fluid	NOUN
american_scientific_journal-7932	16	15	;	;	PUNCT
american_scientific_journal-7932	16	16	the	the	DET
american_scientific_journal-7932	16	17	velocity	velocity	NOUN
american_scientific_journal-7932	16	18	field	field	NOUN
american_scientific_journal-7932	16	19	,	,	PUNCT
american_scientific_journal-7932	16	20	shear	shear	NOUN
american_scientific_journal-7932	16	21	stresses	stress	NOUN
american_scientific_journal-7932	16	22	and	and	CCONJ
american_scientific_journal-7932	16	23	drag	drag	NOUN
american_scientific_journal-7932	16	24	were	be	AUX
american_scientific_journal-7932	16	25	obtained	obtain	VERB
american_scientific_journal-7932	16	26	and	and	CCONJ
american_scientific_journal-7932	16	27	comparisons	comparison	NOUN
american_scientific_journal-7932	16	28	made	make	VERB
american_scientific_journal-7932	16	29	with	with	ADP
american_scientific_journal-7932	16	30	its	its	PRON
american_scientific_journal-7932	16	31	newtonian	newtonian	ADJ
american_scientific_journal-7932	16	32	counterpart	counterpart	NOUN
american_scientific_journal-7932	16	33	.	.	PUNCT
american_scientific_journal-7932	17	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7932	18	1	*	*	PUNCT
american_scientific_journal-7932	18	2	corresponding	correspond	VERB
american_scientific_journal-7932	18	3	author	author	NOUN
american_scientific_journal-7932	18	4	.	.	PUNCT
american_scientific_journal-7932	19	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-7932	19	2	american	american	PROPN
american_scientific_journal-7932	19	3	academic	academic	PROPN
american_scientific_journal-7932	19	4	scientific	scientific	ADJ
american_scientific_journal-7932	19	5	research	research	NOUN
american_scientific_journal-7932	19	6	journal	journal	NOUN
american_scientific_journal-7932	19	7	for	for	ADP
american_scientific_journal-7932	19	8	engineering	engineering	NOUN
american_scientific_journal-7932	19	9	,	,	PUNCT
american_scientific_journal-7932	19	10	technology	technology	NOUN
american_scientific_journal-7932	19	11	,	,	PUNCT
american_scientific_journal-7932	19	12	and	and	CCONJ
american_scientific_journal-7932	19	13	sciences	science	NOUN
american_scientific_journal-7932	19	14	(	(	PUNCT
american_scientific_journal-7932	19	15	asrjets	asrjet	NOUN
american_scientific_journal-7932	19	16	)	)	PUNCT
american_scientific_journal-7932	19	17	(	(	PUNCT
american_scientific_journal-7932	19	18	2022	2022	NUM
american_scientific_journal-7932	19	19	)	)	PUNCT
american_scientific_journal-7932	19	20	volume	volume	NOUN
american_scientific_journal-7932	19	21	89	89	NUM
american_scientific_journal-7932	19	22	,	,	PUNCT
american_scientific_journal-7932	19	23	no	no	DET
american_scientific_journal-7932	19	24	1	1	NUM
american_scientific_journal-7932	19	25	,	,	PUNCT
american_scientific_journal-7932	19	26	pp229	pp229	NOUN
american_scientific_journal-7932	19	27	-	-	PUNCT
american_scientific_journal-7932	19	28	240	240	NUM
american_scientific_journal-7932	19	29	230	230	NUM
american_scientific_journal-7932	19	30	reference	reference	NOUN
american_scientific_journal-7932	19	31	[	[	X
american_scientific_journal-7932	19	32	7	7	NUM
american_scientific_journal-7932	19	33	]	]	PUNCT
american_scientific_journal-7932	19	34	considered	consider	VERB
american_scientific_journal-7932	19	35	the	the	DET
american_scientific_journal-7932	19	36	case	case	NOUN
american_scientific_journal-7932	19	37	for	for	ADP
american_scientific_journal-7932	19	38	different	different	ADJ
american_scientific_journal-7932	19	39	frequencies	frequency	NOUN
american_scientific_journal-7932	19	40	of	of	ADP
american_scientific_journal-7932	19	41	oscillations	oscillation	NOUN
american_scientific_journal-7932	19	42	with	with	ADP
american_scientific_journal-7932	19	43	an	an	DET
american_scientific_journal-7932	19	44	oldroyd	oldroyd	VERB
american_scientific_journal-7932	19	45	-	-	PUNCT
american_scientific_journal-7932	19	46	b	b	NOUN
american_scientific_journal-7932	19	47	fluid	fluid	ADJ
american_scientific_journal-7932	19	48	,	,	PUNCT
american_scientific_journal-7932	19	49	analytic	analytic	ADJ
american_scientific_journal-7932	19	50	solutions	solution	NOUN
american_scientific_journal-7932	19	51	were	be	AUX
american_scientific_journal-7932	19	52	obtained	obtain	VERB
american_scientific_journal-7932	19	53	for	for	ADP
american_scientific_journal-7932	19	54	the	the	DET
american_scientific_journal-7932	19	55	velocity	velocity	NOUN
american_scientific_journal-7932	19	56	components	component	NOUN
american_scientific_journal-7932	19	57	,	,	PUNCT
american_scientific_journal-7932	19	58	shear	shear	NOUN
american_scientific_journal-7932	19	59	stresses	stress	NOUN
american_scientific_journal-7932	19	60	and	and	CCONJ
american_scientific_journal-7932	19	61	drag	drag	VERB
american_scientific_journal-7932	19	62	on	on	ADP
american_scientific_journal-7932	19	63	the	the	DET
american_scientific_journal-7932	19	64	cylinder	cylinder	NOUN
american_scientific_journal-7932	19	65	.	.	PUNCT
american_scientific_journal-7932	20	1	different	different	ADJ
american_scientific_journal-7932	20	2	frequencies	frequency	NOUN
american_scientific_journal-7932	20	3	was	be	AUX
american_scientific_journal-7932	20	4	also	also	ADV
american_scientific_journal-7932	20	5	considered	consider	VERB
american_scientific_journal-7932	20	6	by	by	ADP
american_scientific_journal-7932	20	7	[	[	X
american_scientific_journal-7932	20	8	8	8	NUM
american_scientific_journal-7932	20	9	]	]	PUNCT
american_scientific_journal-7932	20	10	for	for	ADP
american_scientific_journal-7932	20	11	a	a	DET
american_scientific_journal-7932	20	12	micropolar	micropolar	ADJ
american_scientific_journal-7932	20	13	fluid	fluid	NOUN
american_scientific_journal-7932	20	14	,	,	PUNCT
american_scientific_journal-7932	20	15	analytical	analytical	ADJ
american_scientific_journal-7932	20	16	expressions	expression	NOUN
american_scientific_journal-7932	20	17	for	for	ADP
american_scientific_journal-7932	20	18	the	the	DET
american_scientific_journal-7932	20	19	velocity	velocity	NOUN
american_scientific_journal-7932	20	20	and	and	CCONJ
american_scientific_journal-7932	20	21	microrotation	microrotation	NOUN
american_scientific_journal-7932	20	22	components	component	NOUN
american_scientific_journal-7932	20	23	were	be	AUX
american_scientific_journal-7932	20	24	obtained	obtain	VERB
american_scientific_journal-7932	20	25	in	in	ADP
american_scientific_journal-7932	20	26	terms	term	NOUN
american_scientific_journal-7932	20	27	of	of	ADP
american_scientific_journal-7932	20	28	modified	modified	ADJ
american_scientific_journal-7932	20	29	bessel	bessel	NOUN
american_scientific_journal-7932	20	30	's	's	PART
american_scientific_journal-7932	20	31	functions	function	NOUN
american_scientific_journal-7932	20	32	,	,	PUNCT
american_scientific_journal-7932	20	33	along	along	ADP
american_scientific_journal-7932	20	34	with	with	ADP
american_scientific_journal-7932	20	35	the	the	DET
american_scientific_journal-7932	20	36	drag	drag	NOUN
american_scientific_journal-7932	20	37	force	force	NOUN
american_scientific_journal-7932	20	38	acting	act	VERB
american_scientific_journal-7932	20	39	on	on	ADP
american_scientific_journal-7932	20	40	the	the	DET
american_scientific_journal-7932	20	41	wall	wall	NOUN
american_scientific_journal-7932	20	42	of	of	ADP
american_scientific_journal-7932	20	43	the	the	DET
american_scientific_journal-7932	20	44	cylinder	cylinder	NOUN
american_scientific_journal-7932	20	45	.	.	PUNCT
american_scientific_journal-7932	21	1	the	the	DET
american_scientific_journal-7932	21	2	main	main	ADJ
american_scientific_journal-7932	21	3	objective	objective	NOUN
american_scientific_journal-7932	21	4	of	of	ADP
american_scientific_journal-7932	21	5	this	this	DET
american_scientific_journal-7932	21	6	research	research	NOUN
american_scientific_journal-7932	21	7	is	be	AUX
american_scientific_journal-7932	21	8	to	to	PART
american_scientific_journal-7932	21	9	investigate	investigate	VERB
american_scientific_journal-7932	21	10	an	an	DET
american_scientific_journal-7932	21	11	extension	extension	NOUN
american_scientific_journal-7932	21	12	to	to	ADP
american_scientific_journal-7932	21	13	that	that	PRON
american_scientific_journal-7932	21	14	done	do	VERB
american_scientific_journal-7932	21	15	by	by	ADP
american_scientific_journal-7932	21	16	[	[	X
american_scientific_journal-7932	21	17	3	3	NUM
american_scientific_journal-7932	21	18	]	]	PUNCT
american_scientific_journal-7932	21	19	,	,	PUNCT
american_scientific_journal-7932	21	20	in	in	ADP
american_scientific_journal-7932	21	21	particular	particular	ADJ
american_scientific_journal-7932	21	22	,	,	PUNCT
american_scientific_journal-7932	21	23	the	the	DET
american_scientific_journal-7932	21	24	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	21	25	and	and	CCONJ
american_scientific_journal-7932	21	26	torsional	torsional	ADJ
american_scientific_journal-7932	21	27	oscillations	oscillation	NOUN
american_scientific_journal-7932	21	28	of	of	ADP
american_scientific_journal-7932	21	29	the	the	DET
american_scientific_journal-7932	21	30	cylinder	cylinder	NOUN
american_scientific_journal-7932	21	31	is	be	AUX
american_scientific_journal-7932	21	32	considered	consider	VERB
american_scientific_journal-7932	21	33	to	to	PART
american_scientific_journal-7932	21	34	have	have	VERB
american_scientific_journal-7932	21	35	different	different	ADJ
american_scientific_journal-7932	21	36	frequencies	frequency	NOUN
american_scientific_journal-7932	21	37	.	.	PUNCT
american_scientific_journal-7932	22	1	analytical	analytical	ADJ
american_scientific_journal-7932	22	2	expressions	expression	NOUN
american_scientific_journal-7932	22	3	for	for	ADP
american_scientific_journal-7932	22	4	the	the	DET
american_scientific_journal-7932	22	5	velocity	velocity	NOUN
american_scientific_journal-7932	22	6	field	field	NOUN
american_scientific_journal-7932	22	7	,	,	PUNCT
american_scientific_journal-7932	22	8	shear	shear	NOUN
american_scientific_journal-7932	22	9	stresses	stress	NOUN
american_scientific_journal-7932	22	10	,	,	PUNCT
american_scientific_journal-7932	22	11	drag	drag	VERB
american_scientific_journal-7932	22	12	on	on	ADP
american_scientific_journal-7932	22	13	the	the	DET
american_scientific_journal-7932	22	14	cylinder	cylinder	NOUN
american_scientific_journal-7932	22	15	,	,	PUNCT
american_scientific_journal-7932	22	16	work	work	NOUN
american_scientific_journal-7932	22	17	done	do	VERB
american_scientific_journal-7932	22	18	and	and	CCONJ
american_scientific_journal-7932	22	19	the	the	DET
american_scientific_journal-7932	22	20	drag	drag	NOUN
american_scientific_journal-7932	22	21	coefficient	coefficient	NOUN
american_scientific_journal-7932	22	22	are	be	AUX
american_scientific_journal-7932	22	23	obtained	obtain	VERB
american_scientific_journal-7932	22	24	.	.	PUNCT
american_scientific_journal-7932	23	1	the	the	DET
american_scientific_journal-7932	23	2	behaviour	behaviour	NOUN
american_scientific_journal-7932	23	3	of	of	ADP
american_scientific_journal-7932	23	4	the	the	DET
american_scientific_journal-7932	23	5	velocity	velocity	NOUN
american_scientific_journal-7932	23	6	components	component	NOUN
american_scientific_journal-7932	23	7	,	,	PUNCT
american_scientific_journal-7932	23	8	the	the	DET
american_scientific_journal-7932	23	9	drag	drag	NOUN
american_scientific_journal-7932	23	10	and	and	CCONJ
american_scientific_journal-7932	23	11	the	the	DET
american_scientific_journal-7932	23	12	work	work	NOUN
american_scientific_journal-7932	23	13	done	do	VERB
american_scientific_journal-7932	23	14	are	be	AUX
american_scientific_journal-7932	23	15	illustrated	illustrate	VERB
american_scientific_journal-7932	23	16	graphically	graphically	ADV
american_scientific_journal-7932	23	17	and	and	CCONJ
american_scientific_journal-7932	23	18	conclusions	conclusion	NOUN
american_scientific_journal-7932	23	19	made	make	VERB
american_scientific_journal-7932	23	20	.	.	PUNCT
american_scientific_journal-7932	24	1	2	2	X
american_scientific_journal-7932	24	2	.	.	X
american_scientific_journal-7932	24	3	statement	statement	NOUN
american_scientific_journal-7932	24	4	of	of	ADP
american_scientific_journal-7932	24	5	the	the	DET
american_scientific_journal-7932	24	6	problem	problem	NOUN
american_scientific_journal-7932	24	7	.	.	PUNCT
american_scientific_journal-7932	25	1	the	the	DET
american_scientific_journal-7932	25	2	unsteady	unsteady	ADJ
american_scientific_journal-7932	25	3	flow	flow	NOUN
american_scientific_journal-7932	25	4	of	of	ADP
american_scientific_journal-7932	25	5	an	an	DET
american_scientific_journal-7932	25	6	incompressible	incompressible	ADJ
american_scientific_journal-7932	25	7	viscous	viscous	ADJ
american_scientific_journal-7932	25	8	fluid	fluid	NOUN
american_scientific_journal-7932	25	9	contained	contain	VERB
american_scientific_journal-7932	25	10	in	in	ADP
american_scientific_journal-7932	25	11	a	a	DET
american_scientific_journal-7932	25	12	cylinder	cylinder	NOUN
american_scientific_journal-7932	25	13	which	which	PRON
american_scientific_journal-7932	25	14	is	be	AUX
american_scientific_journal-7932	25	15	infinite	infinite	ADJ
american_scientific_journal-7932	25	16	in	in	ADP
american_scientific_journal-7932	25	17	length	length	NOUN
american_scientific_journal-7932	25	18	and	and	CCONJ
american_scientific_journal-7932	25	19	radius	radius	NOUN
american_scientific_journal-7932	25	20	‘	'	PUNCT
american_scientific_journal-7932	25	21	a	a	PRON
american_scientific_journal-7932	25	22	’	'	PUNCT
american_scientific_journal-7932	25	23	,	,	PUNCT
american_scientific_journal-7932	25	24	is	be	AUX
american_scientific_journal-7932	25	25	undergoing	undergo	VERB
american_scientific_journal-7932	25	26	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	25	27	and	and	CCONJ
american_scientific_journal-7932	25	28	torsional	torsional	ADJ
american_scientific_journal-7932	25	29	oscillations	oscillation	NOUN
american_scientific_journal-7932	25	30	with	with	ADP
american_scientific_journal-7932	25	31	different	different	ADJ
american_scientific_journal-7932	25	32	frequencies	frequency	NOUN
american_scientific_journal-7932	25	33	.	.	PUNCT
american_scientific_journal-7932	26	1	due	due	ADP
american_scientific_journal-7932	26	2	to	to	ADP
american_scientific_journal-7932	26	3	the	the	DET
american_scientific_journal-7932	26	4	nature	nature	NOUN
american_scientific_journal-7932	26	5	of	of	ADP
american_scientific_journal-7932	26	6	the	the	DET
american_scientific_journal-7932	26	7	flow	flow	NOUN
american_scientific_journal-7932	26	8	,	,	PUNCT
american_scientific_journal-7932	26	9	cylindrical	cylindrical	ADJ
american_scientific_journal-7932	26	10	polar	polar	ADJ
american_scientific_journal-7932	26	11	coordinates	coordinate	NOUN
american_scientific_journal-7932	26	12	,	,	PUNCT
american_scientific_journal-7932	26	13	(	(	PUNCT
american_scientific_journal-7932	26	14	𝑅	𝑅	PROPN
american_scientific_journal-7932	26	15	,	,	PUNCT
american_scientific_journal-7932	26	16	𝜃	𝜃	NOUN
american_scientific_journal-7932	26	17	,	,	PUNCT
american_scientific_journal-7932	26	18	𝑧	𝑧	PART
american_scientific_journal-7932	26	19	)	)	PUNCT
american_scientific_journal-7932	26	20	,	,	PUNCT
american_scientific_journal-7932	26	21	will	will	AUX
american_scientific_journal-7932	26	22	be	be	AUX
american_scientific_journal-7932	26	23	used	use	VERB
american_scientific_journal-7932	26	24	,	,	PUNCT
american_scientific_journal-7932	26	25	with	with	ADP
american_scientific_journal-7932	26	26	the	the	DET
american_scientific_journal-7932	26	27	axis	axis	NOUN
american_scientific_journal-7932	26	28	of	of	ADP
american_scientific_journal-7932	26	29	the	the	DET
american_scientific_journal-7932	26	30	cylinder	cylinder	NOUN
american_scientific_journal-7932	26	31	coinciding	coincide	VERB
american_scientific_journal-7932	26	32	with	with	ADP
american_scientific_journal-7932	26	33	the	the	DET
american_scientific_journal-7932	26	34	z	z	NOUN
american_scientific_journal-7932	26	35	axis	axis	NOUN
american_scientific_journal-7932	26	36	.	.	PUNCT
american_scientific_journal-7932	27	1	similar	similar	ADJ
american_scientific_journal-7932	27	2	to	to	ADP
american_scientific_journal-7932	27	3	that	that	PRON
american_scientific_journal-7932	27	4	done	do	VERB
american_scientific_journal-7932	27	5	in	in	ADP
american_scientific_journal-7932	27	6	[	[	X
american_scientific_journal-7932	27	7	2	2	NUM
american_scientific_journal-7932	27	8	]	]	PUNCT
american_scientific_journal-7932	27	9	and	and	CCONJ
american_scientific_journal-7932	27	10	[	[	X
american_scientific_journal-7932	27	11	3	3	NUM
american_scientific_journal-7932	27	12	]	]	PUNCT
american_scientific_journal-7932	27	13	,	,	PUNCT
american_scientific_journal-7932	27	14	the	the	DET
american_scientific_journal-7932	27	15	velocity	velocity	NOUN
american_scientific_journal-7932	27	16	of	of	ADP
american_scientific_journal-7932	27	17	the	the	DET
american_scientific_journal-7932	27	18	cylinder	cylinder	NOUN
american_scientific_journal-7932	27	19	,	,	PUNCT
american_scientific_journal-7932	27	20	𝑞𝑏	𝑞𝑏	NOUN
american_scientific_journal-7932	27	21	,	,	PUNCT
american_scientific_journal-7932	27	22	at	at	ADP
american_scientific_journal-7932	27	23	𝑅	𝑅	PROPN
american_scientific_journal-7932	27	24	=	=	PROPN
american_scientific_journal-7932	27	25	𝑎	𝑎	NOUN
american_scientific_journal-7932	27	26	takes	take	VERB
american_scientific_journal-7932	27	27	the	the	DET
american_scientific_journal-7932	27	28	form	form	NOUN
american_scientific_journal-7932	27	29	,	,	PUNCT
american_scientific_journal-7932	27	30	𝑞𝑏	𝑞𝑏	NOUN
american_scientific_journal-7932	27	31	=	=	NOUN
american_scientific_journal-7932	27	32	𝑞0	𝑞0	VERB
american_scientific_journal-7932	27	33	cos	cos	ADP
american_scientific_journal-7932	27	34	𝛽	𝛽	NOUN
american_scientific_journal-7932	27	35	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	27	36	)	)	PUNCT
american_scientific_journal-7932	27	37	�	�	PROPN
american_scientific_journal-7932	27	38	̂	̂	NUM
american_scientific_journal-7932	27	39	�	�	PROPN
american_scientific_journal-7932	27	40	+	+	NUM
american_scientific_journal-7932	27	41	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	27	42	sin	sin	NOUN
american_scientific_journal-7932	27	43	𝛽	𝛽	PROPN
american_scientific_journal-7932	27	44	cos(ω2𝑡)	cos(ω2𝑡)	PROPN
american_scientific_journal-7932	27	45	�	�	PROPN
american_scientific_journal-7932	27	46	̂	̂	PROPN
american_scientific_journal-7932	27	47	�	�	PROPN
american_scientific_journal-7932	27	48	(	(	PUNCT
american_scientific_journal-7932	27	49	2.1	2.1	NUM
american_scientific_journal-7932	27	50	)	)	PUNCT
american_scientific_journal-7932	27	51	where	where	SCONJ
american_scientific_journal-7932	27	52	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	27	53	,	,	PUNCT
american_scientific_journal-7932	27	54	𝛽	𝛽	NOUN
american_scientific_journal-7932	27	55	,	,	PUNCT
american_scientific_journal-7932	27	56	ω1	ω1	PROPN
american_scientific_journal-7932	27	57	and	and	CCONJ
american_scientific_journal-7932	27	58	ω2	ω2	NOUN
american_scientific_journal-7932	27	59	are	be	AUX
american_scientific_journal-7932	27	60	real	real	ADJ
american_scientific_journal-7932	27	61	constants	constant	NOUN
american_scientific_journal-7932	27	62	.	.	PUNCT
american_scientific_journal-7932	28	1	it	it	PRON
american_scientific_journal-7932	28	2	is	be	AUX
american_scientific_journal-7932	28	3	noted	note	VERB
american_scientific_journal-7932	28	4	that	that	SCONJ
american_scientific_journal-7932	28	5	when	when	SCONJ
american_scientific_journal-7932	28	6	𝛽	𝛽	PROPN
american_scientific_journal-7932	28	7	=	=	SYM
american_scientific_journal-7932	28	8	0	0	NUM
american_scientific_journal-7932	28	9	or	or	CCONJ
american_scientific_journal-7932	28	10	𝜋	𝜋	PRON
american_scientific_journal-7932	28	11	the	the	DET
american_scientific_journal-7932	28	12	oscillations	oscillation	NOUN
american_scientific_journal-7932	28	13	are	be	AUX
american_scientific_journal-7932	28	14	purely	purely	ADV
american_scientific_journal-7932	28	15	torsional	torsional	ADJ
american_scientific_journal-7932	28	16	and	and	CCONJ
american_scientific_journal-7932	28	17	when	when	SCONJ
american_scientific_journal-7932	28	18	𝛽	𝛽	NOUN
american_scientific_journal-7932	28	19	=	=	SYM
american_scientific_journal-7932	28	20	𝜋	𝜋	NOUN
american_scientific_journal-7932	28	21	2	2	NUM
american_scientific_journal-7932	28	22	or	or	CCONJ
american_scientific_journal-7932	28	23	3𝜋	3𝜋	NUM
american_scientific_journal-7932	28	24	2	2	NUM
american_scientific_journal-7932	28	25	they	they	PRON
american_scientific_journal-7932	28	26	are	be	AUX
american_scientific_journal-7932	28	27	purely	purely	ADV
american_scientific_journal-7932	28	28	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	28	29	.	.	PUNCT
american_scientific_journal-7932	29	1	due	due	ADP
american_scientific_journal-7932	29	2	to	to	ADP
american_scientific_journal-7932	29	3	the	the	DET
american_scientific_journal-7932	29	4	motion	motion	NOUN
american_scientific_journal-7932	29	5	of	of	ADP
american_scientific_journal-7932	29	6	the	the	DET
american_scientific_journal-7932	29	7	cylinder	cylinder	NOUN
american_scientific_journal-7932	29	8	,	,	PUNCT
american_scientific_journal-7932	29	9	it	it	PRON
american_scientific_journal-7932	29	10	is	be	AUX
american_scientific_journal-7932	29	11	fair	fair	ADJ
american_scientific_journal-7932	29	12	to	to	PART
american_scientific_journal-7932	29	13	assume	assume	VERB
american_scientific_journal-7932	29	14	that	that	SCONJ
american_scientific_journal-7932	29	15	the	the	DET
american_scientific_journal-7932	29	16	radial	radial	ADJ
american_scientific_journal-7932	29	17	component	component	NOUN
american_scientific_journal-7932	29	18	of	of	ADP
american_scientific_journal-7932	29	19	the	the	DET
american_scientific_journal-7932	29	20	fluid	fluid	NOUN
american_scientific_journal-7932	29	21	’s	’s	PART
american_scientific_journal-7932	29	22	velocity	velocity	NOUN
american_scientific_journal-7932	29	23	is	be	AUX
american_scientific_journal-7932	29	24	zero	zero	NUM
american_scientific_journal-7932	29	25	.	.	PUNCT
american_scientific_journal-7932	30	1	further	far	ADV
american_scientific_journal-7932	30	2	,	,	PUNCT
american_scientific_journal-7932	30	3	it	it	PRON
american_scientific_journal-7932	30	4	will	will	AUX
american_scientific_journal-7932	30	5	be	be	AUX
american_scientific_journal-7932	30	6	assumed	assume	VERB
american_scientific_journal-7932	30	7	that	that	SCONJ
american_scientific_journal-7932	30	8	the	the	DET
american_scientific_journal-7932	30	9	flow	flow	NOUN
american_scientific_journal-7932	30	10	is	be	AUX
american_scientific_journal-7932	30	11	axisymmetric	axisymmetric	ADJ
american_scientific_journal-7932	30	12	about	about	ADP
american_scientific_journal-7932	30	13	the	the	DET
american_scientific_journal-7932	30	14	z	z	NOUN
american_scientific_journal-7932	30	15	-	-	PUNCT
american_scientific_journal-7932	30	16	axis	axis	NOUN
american_scientific_journal-7932	30	17	.	.	PUNCT
american_scientific_journal-7932	31	1	hence	hence	ADV
american_scientific_journal-7932	31	2	,	,	PUNCT
american_scientific_journal-7932	31	3	the	the	DET
american_scientific_journal-7932	31	4	velocity	velocity	NOUN
american_scientific_journal-7932	31	5	of	of	ADP
american_scientific_journal-7932	31	6	the	the	DET
american_scientific_journal-7932	31	7	fluid	fluid	NOUN
american_scientific_journal-7932	31	8	takes	take	VERB
american_scientific_journal-7932	31	9	the	the	DET
american_scientific_journal-7932	31	10	form	form	NOUN
american_scientific_journal-7932	31	11	,	,	PUNCT
american_scientific_journal-7932	31	12	𝑞	𝑞	X
american_scientific_journal-7932	31	13	=	=	X
american_scientific_journal-7932	31	14	v(𝑅	v(𝑅	PROPN
american_scientific_journal-7932	31	15	,	,	PUNCT
american_scientific_journal-7932	31	16	𝑡)	𝑡)	PROPN
american_scientific_journal-7932	31	17	�	�	PROPN
american_scientific_journal-7932	31	18	̂	̂	NUM
american_scientific_journal-7932	31	19	�	�	NOUN
american_scientific_journal-7932	31	20	+	+	CCONJ
american_scientific_journal-7932	31	21	𝑤(𝑅	𝑤(𝑅	PROPN
american_scientific_journal-7932	31	22	,	,	PUNCT
american_scientific_journal-7932	31	23	𝑡	𝑡	NOUN
american_scientific_journal-7932	31	24	)	)	PUNCT
american_scientific_journal-7932	31	25	�	�	PROPN
american_scientific_journal-7932	31	26	̂	̂	SYM
american_scientific_journal-7932	31	27	�	�	PROPN
american_scientific_journal-7932	31	28	(	(	PUNCT
american_scientific_journal-7932	31	29	2.2	2.2	NUM
american_scientific_journal-7932	31	30	)	)	PUNCT
american_scientific_journal-7932	31	31	since	since	SCONJ
american_scientific_journal-7932	31	32	the	the	DET
american_scientific_journal-7932	31	33	fluid	fluid	NOUN
american_scientific_journal-7932	31	34	is	be	AUX
american_scientific_journal-7932	31	35	incompressible	incompressible	ADJ
american_scientific_journal-7932	31	36	,	,	PUNCT
american_scientific_journal-7932	31	37	the	the	DET
american_scientific_journal-7932	31	38	continuity	continuity	NOUN
american_scientific_journal-7932	31	39	equation	equation	NOUN
american_scientific_journal-7932	31	40	[	[	X
american_scientific_journal-7932	31	41	9	9	NUM
american_scientific_journal-7932	31	42	]	]	X
american_scientific_journal-7932	31	43	is	be	AUX
american_scientific_journal-7932	31	44	,	,	PUNCT
american_scientific_journal-7932	31	45	∇	∇	X
american_scientific_journal-7932	31	46	⋅	⋅	X
american_scientific_journal-7932	31	47	𝑞	𝑞	X
american_scientific_journal-7932	31	48	=	=	SYM
american_scientific_journal-7932	31	49	0	0	PROPN
american_scientific_journal-7932	31	50	(	(	PUNCT
american_scientific_journal-7932	31	51	2.3	2.3	NUM
american_scientific_journal-7932	31	52	)	)	PUNCT
american_scientific_journal-7932	31	53	which	which	PRON
american_scientific_journal-7932	31	54	is	be	AUX
american_scientific_journal-7932	31	55	satisfied	satisfied	ADJ
american_scientific_journal-7932	31	56	by	by	ADP
american_scientific_journal-7932	31	57	(	(	PUNCT
american_scientific_journal-7932	31	58	2.2	2.2	NUM
american_scientific_journal-7932	31	59	)	)	PUNCT
american_scientific_journal-7932	31	60	.	.	PUNCT
american_scientific_journal-7932	32	1	in	in	ADP
american_scientific_journal-7932	32	2	the	the	DET
american_scientific_journal-7932	32	3	absence	absence	NOUN
american_scientific_journal-7932	32	4	of	of	ADP
american_scientific_journal-7932	32	5	external	external	ADJ
american_scientific_journal-7932	32	6	forces	force	NOUN
american_scientific_journal-7932	32	7	,	,	PUNCT
american_scientific_journal-7932	32	8	the	the	DET
american_scientific_journal-7932	32	9	navier	navier	NOUN
american_scientific_journal-7932	32	10	-	-	PUNCT
american_scientific_journal-7932	32	11	stokes	stoke	NOUN
american_scientific_journal-7932	32	12	equation	equation	NOUN
american_scientific_journal-7932	32	13	[	[	X
american_scientific_journal-7932	32	14	9	9	X
american_scientific_journal-7932	32	15	]	]	PUNCT
american_scientific_journal-7932	32	16	to	to	PART
american_scientific_journal-7932	32	17	be	be	AUX
american_scientific_journal-7932	32	18	solved	solve	VERB
american_scientific_journal-7932	32	19	is	be	AUX
american_scientific_journal-7932	32	20	,	,	PUNCT
american_scientific_journal-7932	32	21	−	−	PROPN
american_scientific_journal-7932	32	22	1	1	NUM
american_scientific_journal-7932	32	23	𝜌	𝜌	X
american_scientific_journal-7932	32	24	∇𝑝	∇𝑝	ADJ
american_scientific_journal-7932	32	25	+	+	CCONJ
american_scientific_journal-7932	32	26	𝜈∇2𝑞	𝜈∇2𝑞	NOUN
american_scientific_journal-7932	32	27	=	=	SYM
american_scientific_journal-7932	32	28	𝜕𝑞	𝜕𝑞	PROPN
american_scientific_journal-7932	32	29	𝜕𝑡	𝜕𝑡	PROPN
american_scientific_journal-7932	32	30	+	+	CCONJ
american_scientific_journal-7932	32	31	(	(	PUNCT
american_scientific_journal-7932	32	32	𝑞	𝑞	X
american_scientific_journal-7932	32	33	⋅	⋅	PROPN
american_scientific_journal-7932	32	34	∇	∇	X
american_scientific_journal-7932	32	35	)	)	PUNCT
american_scientific_journal-7932	32	36	𝑞	𝑞	X
american_scientific_journal-7932	32	37	(	(	PUNCT
american_scientific_journal-7932	32	38	2.4	2.4	NUM
american_scientific_journal-7932	32	39	)	)	PUNCT
american_scientific_journal-7932	32	40	where	where	SCONJ
american_scientific_journal-7932	32	41	𝜌	𝜌	PRON
american_scientific_journal-7932	32	42	is	be	AUX
american_scientific_journal-7932	32	43	the	the	DET
american_scientific_journal-7932	32	44	density	density	NOUN
american_scientific_journal-7932	32	45	,	,	PUNCT
american_scientific_journal-7932	32	46	𝑝	𝑝	PROPN
american_scientific_journal-7932	32	47	is	be	AUX
american_scientific_journal-7932	32	48	the	the	DET
american_scientific_journal-7932	32	49	pressure	pressure	NOUN
american_scientific_journal-7932	32	50	and	and	CCONJ
american_scientific_journal-7932	32	51	𝜈	𝜈	X
american_scientific_journal-7932	32	52	is	be	AUX
american_scientific_journal-7932	32	53	the	the	DET
american_scientific_journal-7932	32	54	kinematic	kinematic	ADJ
american_scientific_journal-7932	32	55	viscosity	viscosity	NOUN
american_scientific_journal-7932	32	56	.	.	PUNCT
american_scientific_journal-7932	33	1	american	american	ADJ
american_scientific_journal-7932	33	2	academic	academic	ADJ
american_scientific_journal-7932	33	3	scientific	scientific	ADJ
american_scientific_journal-7932	33	4	research	research	NOUN
american_scientific_journal-7932	33	5	journal	journal	NOUN
american_scientific_journal-7932	33	6	for	for	ADP
american_scientific_journal-7932	33	7	engineering	engineering	NOUN
american_scientific_journal-7932	33	8	,	,	PUNCT
american_scientific_journal-7932	33	9	technology	technology	NOUN
american_scientific_journal-7932	33	10	,	,	PUNCT
american_scientific_journal-7932	33	11	and	and	CCONJ
american_scientific_journal-7932	33	12	sciences	science	NOUN
american_scientific_journal-7932	33	13	(	(	PUNCT
american_scientific_journal-7932	33	14	asrjets	asrjet	NOUN
american_scientific_journal-7932	33	15	)	)	PUNCT
american_scientific_journal-7932	33	16	(	(	PUNCT
american_scientific_journal-7932	33	17	2022	2022	NUM
american_scientific_journal-7932	33	18	)	)	PUNCT
american_scientific_journal-7932	33	19	volume	volume	NOUN
american_scientific_journal-7932	33	20	89	89	NUM
american_scientific_journal-7932	33	21	,	,	PUNCT
american_scientific_journal-7932	33	22	no	no	DET
american_scientific_journal-7932	33	23	1	1	NUM
american_scientific_journal-7932	33	24	,	,	PUNCT
american_scientific_journal-7932	33	25	pp229	pp229	NOUN
american_scientific_journal-7932	33	26	-	-	PUNCT
american_scientific_journal-7932	33	27	240	240	NUM
american_scientific_journal-7932	33	28	231	231	NUM
american_scientific_journal-7932	33	29	3	3	NUM
american_scientific_journal-7932	33	30	.	.	PUNCT
american_scientific_journal-7932	33	31	velocity	velocity	NOUN
american_scientific_journal-7932	33	32	components	component	NOUN
american_scientific_journal-7932	33	33	,	,	PUNCT
american_scientific_journal-7932	33	34	stresses	stress	NOUN
american_scientific_journal-7932	33	35	and	and	CCONJ
american_scientific_journal-7932	33	36	drag	drag	VERB
american_scientific_journal-7932	33	37	on	on	ADP
american_scientific_journal-7932	33	38	substituting	substitute	VERB
american_scientific_journal-7932	33	39	(	(	PUNCT
american_scientific_journal-7932	33	40	2.2	2.2	NUM
american_scientific_journal-7932	33	41	)	)	PUNCT
american_scientific_journal-7932	33	42	into	into	ADP
american_scientific_journal-7932	33	43	(	(	PUNCT
american_scientific_journal-7932	33	44	2.4	2.4	NUM
american_scientific_journal-7932	33	45	)	)	PUNCT
american_scientific_journal-7932	33	46	gives	give	VERB
american_scientific_journal-7932	33	47	the	the	DET
american_scientific_journal-7932	33	48	following	follow	VERB
american_scientific_journal-7932	33	49	linear	linear	ADJ
american_scientific_journal-7932	33	50	system	system	NOUN
american_scientific_journal-7932	33	51	of	of	ADP
american_scientific_journal-7932	33	52	equations	equation	NOUN
american_scientific_journal-7932	33	53	,	,	PUNCT
american_scientific_journal-7932	33	54	−	−	PROPN
american_scientific_journal-7932	33	55	1	1	NUM
american_scientific_journal-7932	33	56	𝜌	𝜌	X
american_scientific_journal-7932	33	57	𝜕𝑝	𝜕𝑝	NOUN
american_scientific_journal-7932	33	58	𝜕𝑅	𝜕𝑅	PROPN
american_scientific_journal-7932	33	59	=	=	PUNCT
american_scientific_journal-7932	34	1	−	−	PROPN
american_scientific_journal-7932	34	2	v2	v2	PROPN
american_scientific_journal-7932	34	3	𝑅	𝑅	PROPN
american_scientific_journal-7932	34	4	(	(	PUNCT
american_scientific_journal-7932	34	5	3.1	3.1	NUM
american_scientific_journal-7932	34	6	)	)	PUNCT
american_scientific_journal-7932	34	7	𝜈	𝜈	X
american_scientific_journal-7932	34	8	(	(	PUNCT
american_scientific_journal-7932	34	9	1	1	NUM
american_scientific_journal-7932	34	10	𝑅	𝑅	PROPN
american_scientific_journal-7932	34	11	𝜕v	𝜕v	PROPN
american_scientific_journal-7932	34	12	𝜕𝑅	𝜕𝑅	PROPN
american_scientific_journal-7932	34	13	+	+	NUM
american_scientific_journal-7932	34	14	𝜕2v	𝜕2v	ADP
american_scientific_journal-7932	34	15	𝜕𝑅2	𝜕𝑅2	NOUN
american_scientific_journal-7932	34	16	−	−	NOUN
american_scientific_journal-7932	34	17	v	v	NOUN
american_scientific_journal-7932	34	18	𝑅2	𝑅2	NOUN
american_scientific_journal-7932	34	19	)	)	PUNCT
american_scientific_journal-7932	35	1	=	=	PUNCT
american_scientific_journal-7932	36	1	𝜕v	𝜕v	PROPN
american_scientific_journal-7932	36	2	𝜕𝑡	𝜕𝑡	PROPN
american_scientific_journal-7932	36	3	(	(	PUNCT
american_scientific_journal-7932	36	4	3.2	3.2	NUM
american_scientific_journal-7932	36	5	)	)	PUNCT
american_scientific_journal-7932	36	6	𝜈	𝜈	PROPN
american_scientific_journal-7932	36	7	(	(	PUNCT
american_scientific_journal-7932	36	8	1	1	NUM
american_scientific_journal-7932	36	9	𝑅	𝑅	PROPN
american_scientific_journal-7932	36	10	𝜕𝑤	𝜕𝑤	ADJ
american_scientific_journal-7932	36	11	𝜕𝑅	𝜕𝑅	VERB
american_scientific_journal-7932	36	12	+	+	X
american_scientific_journal-7932	36	13	𝜕2𝑤	𝜕2𝑤	PRON
american_scientific_journal-7932	36	14	𝜕𝑅2	𝜕𝑅2	ADJ
american_scientific_journal-7932	36	15	)	)	PUNCT
american_scientific_journal-7932	37	1	=	=	PRON
american_scientific_journal-7932	37	2	𝜕𝑤	𝜕𝑤	VERB
american_scientific_journal-7932	37	3	𝜕𝑡	𝜕𝑡	NOUN
american_scientific_journal-7932	37	4	(	(	PUNCT
american_scientific_journal-7932	37	5	3.3	3.3	NUM
american_scientific_journal-7932	37	6	)	)	PUNCT
american_scientific_journal-7932	37	7	assuming	assume	VERB
american_scientific_journal-7932	37	8	that	that	SCONJ
american_scientific_journal-7932	37	9	the	the	DET
american_scientific_journal-7932	37	10	�	�	PROPN
american_scientific_journal-7932	37	11	̂	̂	SYM
american_scientific_journal-7932	37	12	�	�	PROPN
american_scientific_journal-7932	37	13	component	component	NOUN
american_scientific_journal-7932	37	14	of	of	ADP
american_scientific_journal-7932	37	15	the	the	DET
american_scientific_journal-7932	37	16	velocity	velocity	NOUN
american_scientific_journal-7932	37	17	field	field	NOUN
american_scientific_journal-7932	37	18	takes	take	VERB
american_scientific_journal-7932	37	19	the	the	DET
american_scientific_journal-7932	37	20	form	form	NOUN
american_scientific_journal-7932	37	21	,	,	PUNCT
american_scientific_journal-7932	37	22	v(𝑅	v(𝑅	PROPN
american_scientific_journal-7932	37	23	,	,	PUNCT
american_scientific_journal-7932	37	24	𝑡	𝑡	NOUN
american_scientific_journal-7932	37	25	)	)	PUNCT
american_scientific_journal-7932	37	26	=	=	SYM
american_scientific_journal-7932	37	27	re[𝑓(𝑅)𝑒𝑖ω1𝑡	re[𝑓(𝑅)𝑒𝑖ω1𝑡	NOUN
american_scientific_journal-7932	37	28	]	]	PUNCT
american_scientific_journal-7932	37	29	(	(	PUNCT
american_scientific_journal-7932	37	30	3.4	3.4	NUM
american_scientific_journal-7932	37	31	)	)	PUNCT
american_scientific_journal-7932	37	32	where	where	SCONJ
american_scientific_journal-7932	37	33	re	re	NOUN
american_scientific_journal-7932	37	34	refers	refer	VERB
american_scientific_journal-7932	37	35	to	to	ADP
american_scientific_journal-7932	37	36	the	the	DET
american_scientific_journal-7932	37	37	real	real	ADJ
american_scientific_journal-7932	37	38	part	part	NOUN
american_scientific_journal-7932	37	39	,	,	PUNCT
american_scientific_journal-7932	37	40	along	along	ADP
american_scientific_journal-7932	37	41	with	with	ADP
american_scientific_journal-7932	37	42	the	the	DET
american_scientific_journal-7932	37	43	fact	fact	NOUN
american_scientific_journal-7932	37	44	that	that	SCONJ
american_scientific_journal-7932	37	45	the	the	DET
american_scientific_journal-7932	37	46	velocity	velocity	NOUN
american_scientific_journal-7932	37	47	must	must	AUX
american_scientific_journal-7932	37	48	remain	remain	VERB
american_scientific_journal-7932	37	49	finite	finite	ADJ
american_scientific_journal-7932	37	50	as	as	ADP
american_scientific_journal-7932	37	51	𝑅	𝑅	PROPN
american_scientific_journal-7932	37	52	→	→	SYM
american_scientific_journal-7932	37	53	0	0	PROPN
american_scientific_journal-7932	37	54	,	,	PUNCT
american_scientific_journal-7932	37	55	one	one	PRON
american_scientific_journal-7932	37	56	gets	get	VERB
american_scientific_journal-7932	37	57	,	,	PUNCT
american_scientific_journal-7932	37	58	on	on	ADP
american_scientific_journal-7932	37	59	solving	solve	VERB
american_scientific_journal-7932	37	60	(	(	PUNCT
american_scientific_journal-7932	37	61	3.2	3.2	NUM
american_scientific_journal-7932	37	62	)	)	PUNCT
american_scientific_journal-7932	37	63	and	and	CCONJ
american_scientific_journal-7932	37	64	using	use	VERB
american_scientific_journal-7932	37	65	the	the	DET
american_scientific_journal-7932	37	66	no	no	DET
american_scientific_journal-7932	37	67	-	-	PUNCT
american_scientific_journal-7932	37	68	slip	slip	NOUN
american_scientific_journal-7932	37	69	condition	condition	NOUN
american_scientific_journal-7932	37	70	with	with	ADP
american_scientific_journal-7932	37	71	(	(	PUNCT
american_scientific_journal-7932	37	72	2.1	2.1	NUM
american_scientific_journal-7932	37	73	)	)	PUNCT
american_scientific_journal-7932	37	74	,	,	PUNCT
american_scientific_journal-7932	37	75	v(𝑅	v(𝑅	PROPN
american_scientific_journal-7932	37	76	,	,	PUNCT
american_scientific_journal-7932	37	77	𝑡	𝑡	X
american_scientific_journal-7932	37	78	)	)	PUNCT
american_scientific_journal-7932	37	79	=	=	SYM
american_scientific_journal-7932	37	80	re	re	ADP
american_scientific_journal-7932	38	1	[	[	X
american_scientific_journal-7932	38	2	𝑞0	𝑞0	NOUN
american_scientific_journal-7932	38	3	cos	cos	ADP
american_scientific_journal-7932	38	4	𝛽	𝛽	NOUN
american_scientific_journal-7932	38	5	𝐼1(√𝑖𝜎1𝑅	𝐼1(√𝑖𝜎1𝑅	NOUN
american_scientific_journal-7932	38	6	)	)	PUNCT
american_scientific_journal-7932	38	7	𝐼1(√𝑖𝜎1𝑎	𝐼1(√𝑖𝜎1𝑎	NOUN
american_scientific_journal-7932	38	8	)	)	PUNCT
american_scientific_journal-7932	38	9	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	NOUN
american_scientific_journal-7932	38	10	]	]	PUNCT
american_scientific_journal-7932	38	11	(	(	PUNCT
american_scientific_journal-7932	38	12	3.5	3.5	NUM
american_scientific_journal-7932	38	13	)	)	PUNCT
american_scientific_journal-7932	38	14	where	where	SCONJ
american_scientific_journal-7932	38	15	𝜎1	𝜎1	ADJ
american_scientific_journal-7932	38	16	=	=	SYM
american_scientific_journal-7932	38	17	√	√	PROPN
american_scientific_journal-7932	38	18	ω1	ω1	PROPN
american_scientific_journal-7932	38	19	𝜈	𝜈	X
american_scientific_journal-7932	38	20	in	in	ADP
american_scientific_journal-7932	38	21	a	a	DET
american_scientific_journal-7932	38	22	similar	similar	ADJ
american_scientific_journal-7932	38	23	manner	manner	NOUN
american_scientific_journal-7932	38	24	,	,	PUNCT
american_scientific_journal-7932	38	25	the	the	DET
american_scientific_journal-7932	38	26	�	�	PROPN
american_scientific_journal-7932	38	27	̂	̂	SYM
american_scientific_journal-7932	38	28	�	�	PROPN
american_scientific_journal-7932	38	29	component	component	NOUN
american_scientific_journal-7932	38	30	of	of	ADP
american_scientific_journal-7932	38	31	the	the	DET
american_scientific_journal-7932	38	32	velocity	velocity	NOUN
american_scientific_journal-7932	38	33	is	be	AUX
american_scientific_journal-7932	38	34	,	,	PUNCT
american_scientific_journal-7932	38	35	𝑤(𝑅	𝑤(𝑅	PROPN
american_scientific_journal-7932	38	36	,	,	PUNCT
american_scientific_journal-7932	38	37	𝑡	𝑡	X
american_scientific_journal-7932	38	38	)	)	PUNCT
american_scientific_journal-7932	38	39	=	=	SYM
american_scientific_journal-7932	38	40	re	re	ADP
american_scientific_journal-7932	39	1	[	[	X
american_scientific_journal-7932	39	2	𝑞0	𝑞0	VERB
american_scientific_journal-7932	39	3	sin	sin	NOUN
american_scientific_journal-7932	39	4	𝛽	𝛽	NOUN
american_scientific_journal-7932	39	5	𝐼0(√𝑖𝜎2𝑅	𝐼0(√𝑖𝜎2𝑅	NOUN
american_scientific_journal-7932	39	6	)	)	PUNCT
american_scientific_journal-7932	39	7	𝐼0(√𝑖𝜎2𝑎	𝐼0(√𝑖𝜎2𝑎	NOUN
american_scientific_journal-7932	39	8	)	)	PUNCT
american_scientific_journal-7932	40	1	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	PROPN
american_scientific_journal-7932	40	2	]	]	X
american_scientific_journal-7932	40	3	(	(	PUNCT
american_scientific_journal-7932	40	4	3.6	3.6	NUM
american_scientific_journal-7932	40	5	)	)	PUNCT
american_scientific_journal-7932	40	6	where	where	SCONJ
american_scientific_journal-7932	40	7	𝜎2	𝜎2	NOUN
american_scientific_journal-7932	40	8	=	=	PUNCT
american_scientific_journal-7932	40	9	√	√	PROPN
american_scientific_journal-7932	40	10	ω2	ω2	CCONJ
american_scientific_journal-7932	40	11	𝜈	𝜈	X
american_scientific_journal-7932	40	12	the	the	DET
american_scientific_journal-7932	40	13	tangential	tangential	ADJ
american_scientific_journal-7932	40	14	stresses	stress	NOUN
american_scientific_journal-7932	40	15	on	on	ADP
american_scientific_journal-7932	40	16	the	the	DET
american_scientific_journal-7932	40	17	wall	wall	NOUN
american_scientific_journal-7932	40	18	of	of	ADP
american_scientific_journal-7932	40	19	the	the	DET
american_scientific_journal-7932	40	20	cylinder	cylinder	NOUN
american_scientific_journal-7932	40	21	are	be	AUX
american_scientific_journal-7932	40	22	given	give	VERB
american_scientific_journal-7932	40	23	by	by	ADP
american_scientific_journal-7932	40	24	[	[	PUNCT
american_scientific_journal-7932	40	25	10	10	NUM
american_scientific_journal-7932	40	26	]	]	PUNCT
american_scientific_journal-7932	40	27	,	,	PUNCT
american_scientific_journal-7932	40	28	𝜏𝑅𝜃|𝑅=𝑎	𝜏𝑅𝜃|𝑅=𝑎	PROPN
american_scientific_journal-7932	40	29	=	=	SYM
american_scientific_journal-7932	40	30	𝜇	𝜇	X
american_scientific_journal-7932	40	31	[	[	PUNCT
american_scientific_journal-7932	40	32	𝜕v	𝜕v	PROPN
american_scientific_journal-7932	40	33	𝜕𝑅	𝜕𝑅	PROPN
american_scientific_journal-7932	40	34	−	−	PROPN
american_scientific_journal-7932	40	35	v	v	PROPN
american_scientific_journal-7932	40	36	𝑅	𝑅	PROPN
american_scientific_journal-7932	40	37	]	]	PUNCT
american_scientific_journal-7932	40	38	𝑅=𝑎	𝑅=𝑎	NOUN
american_scientific_journal-7932	40	39	(	(	PUNCT
american_scientific_journal-7932	40	40	3.7	3.7	NUM
american_scientific_journal-7932	40	41	)	)	PUNCT
american_scientific_journal-7932	40	42	𝜏𝑅𝑧|𝑅=𝑎	𝜏𝑅𝑧|𝑅=𝑎	PROPN
american_scientific_journal-7932	40	43	=	=	SYM
american_scientific_journal-7932	40	44	𝜇	𝜇	X
american_scientific_journal-7932	40	45	[	[	PUNCT
american_scientific_journal-7932	40	46	𝜕𝑤	𝜕𝑤	ADJ
american_scientific_journal-7932	40	47	𝜕𝑅	𝜕𝑅	NOUN
american_scientific_journal-7932	40	48	]	]	PUNCT
american_scientific_journal-7932	40	49	𝑅=𝑎	𝑅=𝑎	X
american_scientific_journal-7932	40	50	(	(	PUNCT
american_scientific_journal-7932	40	51	3.8	3.8	NUM
american_scientific_journal-7932	40	52	)	)	PUNCT
american_scientific_journal-7932	40	53	substituting	substitute	VERB
american_scientific_journal-7932	40	54	(	(	PUNCT
american_scientific_journal-7932	40	55	3.5	3.5	NUM
american_scientific_journal-7932	40	56	)	)	PUNCT
american_scientific_journal-7932	40	57	into	into	ADP
american_scientific_journal-7932	40	58	(	(	PUNCT
american_scientific_journal-7932	40	59	3.7	3.7	NUM
american_scientific_journal-7932	40	60	)	)	PUNCT
american_scientific_journal-7932	40	61	gives	give	VERB
american_scientific_journal-7932	40	62	for	for	ADP
american_scientific_journal-7932	40	63	the	the	DET
american_scientific_journal-7932	40	64	torsional	torsional	ADJ
american_scientific_journal-7932	40	65	stress	stress	NOUN
american_scientific_journal-7932	40	66	on	on	ADP
american_scientific_journal-7932	40	67	the	the	DET
american_scientific_journal-7932	40	68	cylinder	cylinder	NOUN
american_scientific_journal-7932	40	69	’s	’s	PART
american_scientific_journal-7932	40	70	wall	wall	NOUN
american_scientific_journal-7932	40	71	,	,	PUNCT
american_scientific_journal-7932	40	72	𝜏𝑅𝜃	𝜏𝑅𝜃	NOUN
american_scientific_journal-7932	40	73	=	=	SYM
american_scientific_journal-7932	40	74	re	re	ADP
american_scientific_journal-7932	40	75	[	[	X
american_scientific_journal-7932	40	76	𝜇	𝜇	ADP
american_scientific_journal-7932	40	77	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	40	78	cos	cos	ADP
american_scientific_journal-7932	40	79	𝛽	𝛽	PROPN
american_scientific_journal-7932	40	80	√𝑖𝜎1	√𝑖𝜎1	PROPN
american_scientific_journal-7932	40	81	𝐼0(√𝑖𝛼1)−	𝐼0(√𝑖𝛼1)−	NOUN
american_scientific_journal-7932	40	82	2	2	NUM
american_scientific_journal-7932	40	83	𝑎	𝑎	NOUN
american_scientific_journal-7932	40	84	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	40	85	)	)	PUNCT
american_scientific_journal-7932	40	86	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	40	87	)	)	PUNCT
american_scientific_journal-7932	40	88	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	NOUN
american_scientific_journal-7932	40	89	]	]	PUNCT
american_scientific_journal-7932	40	90	(	(	PUNCT
american_scientific_journal-7932	40	91	3.9	3.9	NUM
american_scientific_journal-7932	40	92	)	)	PUNCT
american_scientific_journal-7932	40	93	american	american	ADJ
american_scientific_journal-7932	40	94	academic	academic	ADJ
american_scientific_journal-7932	40	95	scientific	scientific	ADJ
american_scientific_journal-7932	40	96	research	research	NOUN
american_scientific_journal-7932	40	97	journal	journal	NOUN
american_scientific_journal-7932	40	98	for	for	ADP
american_scientific_journal-7932	40	99	engineering	engineering	NOUN
american_scientific_journal-7932	40	100	,	,	PUNCT
american_scientific_journal-7932	40	101	technology	technology	NOUN
american_scientific_journal-7932	40	102	,	,	PUNCT
american_scientific_journal-7932	40	103	and	and	CCONJ
american_scientific_journal-7932	40	104	sciences	science	NOUN
american_scientific_journal-7932	40	105	(	(	PUNCT
american_scientific_journal-7932	40	106	asrjets	asrjet	NOUN
american_scientific_journal-7932	40	107	)	)	PUNCT
american_scientific_journal-7932	40	108	(	(	PUNCT
american_scientific_journal-7932	40	109	2022	2022	NUM
american_scientific_journal-7932	40	110	)	)	PUNCT
american_scientific_journal-7932	40	111	volume	volume	NOUN
american_scientific_journal-7932	40	112	89	89	NUM
american_scientific_journal-7932	40	113	,	,	PUNCT
american_scientific_journal-7932	40	114	no	no	DET
american_scientific_journal-7932	40	115	1	1	NUM
american_scientific_journal-7932	40	116	,	,	PUNCT
american_scientific_journal-7932	40	117	pp229	pp229	NOUN
american_scientific_journal-7932	40	118	-	-	PUNCT
american_scientific_journal-7932	40	119	240	240	NUM
american_scientific_journal-7932	40	120	232	232	NUM
american_scientific_journal-7932	40	121	where	where	SCONJ
american_scientific_journal-7932	40	122	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	40	123	=	=	SYM
american_scientific_journal-7932	40	124	𝜎1𝑎.	𝜎1𝑎.	PROPN
american_scientific_journal-7932	40	125	also	also	ADV
american_scientific_journal-7932	40	126	,	,	PUNCT
american_scientific_journal-7932	40	127	substituting	substitute	VERB
american_scientific_journal-7932	40	128	(	(	PUNCT
american_scientific_journal-7932	40	129	3.6	3.6	NUM
american_scientific_journal-7932	40	130	)	)	PUNCT
american_scientific_journal-7932	40	131	into	into	ADP
american_scientific_journal-7932	40	132	(	(	PUNCT
american_scientific_journal-7932	40	133	3.8	3.8	NUM
american_scientific_journal-7932	40	134	)	)	PUNCT
american_scientific_journal-7932	40	135	gives	give	VERB
american_scientific_journal-7932	40	136	for	for	ADP
american_scientific_journal-7932	40	137	the	the	DET
american_scientific_journal-7932	40	138	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	40	139	stress	stress	NOUN
american_scientific_journal-7932	40	140	on	on	ADP
american_scientific_journal-7932	40	141	the	the	DET
american_scientific_journal-7932	40	142	cylinder	cylinder	NOUN
american_scientific_journal-7932	40	143	’s	’s	PART
american_scientific_journal-7932	40	144	wall	wall	NOUN
american_scientific_journal-7932	40	145	,	,	PUNCT
american_scientific_journal-7932	40	146	𝜏𝑅𝑧	𝜏𝑅𝑧	PROPN
american_scientific_journal-7932	40	147	=	=	SYM
american_scientific_journal-7932	40	148	re	re	NOUN
american_scientific_journal-7932	40	149	[	[	X
american_scientific_journal-7932	40	150	𝜇	𝜇	ADP
american_scientific_journal-7932	40	151	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	40	152	sin	sin	VERB
american_scientific_journal-7932	40	153	𝛽	𝛽	NOUN
american_scientific_journal-7932	40	154	√𝑖𝜎2	√𝑖𝜎2	NOUN
american_scientific_journal-7932	40	155	𝐼1(√𝑖𝛼2	𝐼1(√𝑖𝛼2	PROPN
american_scientific_journal-7932	40	156	)	)	PUNCT
american_scientific_journal-7932	40	157	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	NOUN
american_scientific_journal-7932	40	158	)	)	PUNCT
american_scientific_journal-7932	40	159	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	PROPN
american_scientific_journal-7932	40	160	]	]	X
american_scientific_journal-7932	40	161	(	(	PUNCT
american_scientific_journal-7932	40	162	3.10	3.10	NUM
american_scientific_journal-7932	40	163	)	)	PUNCT
american_scientific_journal-7932	40	164	where	where	SCONJ
american_scientific_journal-7932	40	165	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	40	166	=	=	SYM
american_scientific_journal-7932	40	167	𝜎2𝑎.	𝜎2𝑎.	NOUN
american_scientific_journal-7932	40	168	the	the	DET
american_scientific_journal-7932	40	169	tangential	tangential	ADJ
american_scientific_journal-7932	40	170	drag	drag	NOUN
american_scientific_journal-7932	40	171	per	per	ADP
american_scientific_journal-7932	40	172	unit	unit	NOUN
american_scientific_journal-7932	40	173	length	length	NOUN
american_scientific_journal-7932	40	174	acting	act	VERB
american_scientific_journal-7932	40	175	on	on	ADP
american_scientific_journal-7932	40	176	the	the	DET
american_scientific_journal-7932	40	177	cylinder	cylinder	NOUN
american_scientific_journal-7932	40	178	is	be	AUX
american_scientific_journal-7932	40	179	given	give	VERB
american_scientific_journal-7932	40	180	by	by	ADP
american_scientific_journal-7932	40	181	[	[	X
american_scientific_journal-7932	40	182	3	3	NUM
american_scientific_journal-7932	40	183	]	]	PUNCT
american_scientific_journal-7932	40	184	,	,	PUNCT
american_scientific_journal-7932	40	185	𝐷	𝐷	PROPN
american_scientific_journal-7932	40	186	=	=	SYM
american_scientific_journal-7932	40	187	−2𝜋𝑎(𝜏𝑅𝜃	−2𝜋𝑎(𝜏𝑅𝜃	PROPN
american_scientific_journal-7932	40	188	�	�	PROPN
american_scientific_journal-7932	40	189	̂	̂	NUM
american_scientific_journal-7932	40	190	�	�	PROPN
american_scientific_journal-7932	40	191	+	+	CCONJ
american_scientific_journal-7932	40	192	𝜏𝑅𝑧	𝜏𝑅𝑧	PROPN
american_scientific_journal-7932	40	193	�	�	PROPN
american_scientific_journal-7932	40	194	̂	̂	NOUN
american_scientific_journal-7932	40	195	�	�	NOUN
american_scientific_journal-7932	40	196	)|𝑅=𝑎	)|𝑅=𝑎	PUNCT
american_scientific_journal-7932	40	197	(	(	PUNCT
american_scientific_journal-7932	40	198	3.11	3.11	NUM
american_scientific_journal-7932	40	199	)	)	PUNCT
american_scientific_journal-7932	40	200	which	which	PRON
american_scientific_journal-7932	40	201	on	on	ADP
american_scientific_journal-7932	40	202	using	use	VERB
american_scientific_journal-7932	40	203	(	(	PUNCT
american_scientific_journal-7932	40	204	3.9	3.9	NUM
american_scientific_journal-7932	40	205	)	)	PUNCT
american_scientific_journal-7932	40	206	and	and	CCONJ
american_scientific_journal-7932	40	207	(	(	PUNCT
american_scientific_journal-7932	40	208	3.10	3.10	NUM
american_scientific_journal-7932	40	209	)	)	PUNCT
american_scientific_journal-7932	40	210	gives	give	VERB
american_scientific_journal-7932	40	211	,	,	PUNCT
american_scientific_journal-7932	40	212	𝐷	𝐷	NOUN
american_scientific_journal-7932	40	213	=	=	NOUN
american_scientific_journal-7932	40	214	−2𝜋𝑎𝜇𝑞0re	−2𝜋𝑎𝜇𝑞0re	PUNCT
american_scientific_journal-7932	40	215	[	[	X
american_scientific_journal-7932	40	216	cos	cos	ADP
american_scientific_journal-7932	40	217	𝛽	𝛽	PROPN
american_scientific_journal-7932	40	218	√𝑖𝜎1	√𝑖𝜎1	PROPN
american_scientific_journal-7932	40	219	𝐼0(√𝑖𝛼1)−	𝐼0(√𝑖𝛼1)−	NOUN
american_scientific_journal-7932	40	220	2	2	NUM
american_scientific_journal-7932	40	221	𝑎	𝑎	NOUN
american_scientific_journal-7932	40	222	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	40	223	)	)	PUNCT
american_scientific_journal-7932	40	224	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	40	225	)	)	PUNCT
american_scientific_journal-7932	40	226	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	PROPN
american_scientific_journal-7932	40	227	�	�	PROPN
american_scientific_journal-7932	40	228	̂	̂	VERB
american_scientific_journal-7932	40	229	�	�	NOUN
american_scientific_journal-7932	40	230	+	+	CCONJ
american_scientific_journal-7932	40	231	sin	sin	NOUN
american_scientific_journal-7932	40	232	𝛽	𝛽	NOUN
american_scientific_journal-7932	40	233	√𝑖𝜎2	√𝑖𝜎2	NOUN
american_scientific_journal-7932	40	234	𝐼1(√𝑖𝛼2	𝐼1(√𝑖𝛼2	PROPN
american_scientific_journal-7932	40	235	)	)	PUNCT
american_scientific_journal-7932	40	236	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	PROPN
american_scientific_journal-7932	40	237	)	)	PUNCT
american_scientific_journal-7932	40	238	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	NOUN
american_scientific_journal-7932	40	239	�	�	PROPN
american_scientific_journal-7932	40	240	̂	̂	NOUN
american_scientific_journal-7932	40	241	�	�	NOUN
american_scientific_journal-7932	40	242	]	]	X
american_scientific_journal-7932	40	243	(	(	PUNCT
american_scientific_journal-7932	40	244	3.12	3.12	NUM
american_scientific_journal-7932	40	245	)	)	PUNCT
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american_scientific_journal-7932	40	248	noted	note	VERB
american_scientific_journal-7932	40	249	that	that	SCONJ
american_scientific_journal-7932	40	250	in	in	ADP
american_scientific_journal-7932	40	251	the	the	DET
american_scientific_journal-7932	40	252	case	case	NOUN
american_scientific_journal-7932	40	253	of	of	ADP
american_scientific_journal-7932	40	254	the	the	DET
american_scientific_journal-7932	40	255	same	same	ADJ
american_scientific_journal-7932	40	256	frequencies	frequency	NOUN
american_scientific_journal-7932	40	257	of	of	ADP
american_scientific_journal-7932	40	258	oscillations	oscillation	NOUN
american_scientific_journal-7932	40	259	,	,	PUNCT
american_scientific_journal-7932	40	260	(	(	PUNCT
american_scientific_journal-7932	40	261	3.5	3.5	NUM
american_scientific_journal-7932	40	262	)	)	PUNCT
american_scientific_journal-7932	40	263	,	,	PUNCT
american_scientific_journal-7932	40	264	(	(	PUNCT
american_scientific_journal-7932	40	265	3.6	3.6	NUM
american_scientific_journal-7932	40	266	)	)	PUNCT
american_scientific_journal-7932	40	267	,	,	PUNCT
american_scientific_journal-7932	40	268	(	(	PUNCT
american_scientific_journal-7932	40	269	3.9	3.9	NUM
american_scientific_journal-7932	40	270	)	)	PUNCT
american_scientific_journal-7932	40	271	,	,	PUNCT
american_scientific_journal-7932	40	272	(	(	PUNCT
american_scientific_journal-7932	40	273	3.10	3.10	NUM
american_scientific_journal-7932	40	274	)	)	PUNCT
american_scientific_journal-7932	40	275	and	and	CCONJ
american_scientific_journal-7932	40	276	(	(	PUNCT
american_scientific_journal-7932	40	277	3.12	3.12	NUM
american_scientific_journal-7932	40	278	)	)	PUNCT
american_scientific_journal-7932	40	279	reduce	reduce	VERB
american_scientific_journal-7932	40	280	to	to	ADP
american_scientific_journal-7932	40	281	that	that	PRON
american_scientific_journal-7932	40	282	obtained	obtain	VERB
american_scientific_journal-7932	40	283	in	in	ADP
american_scientific_journal-7932	40	284	[	[	X
american_scientific_journal-7932	40	285	3	3	NUM
american_scientific_journal-7932	40	286	]	]	PUNCT
american_scientific_journal-7932	40	287	.	.	PUNCT
american_scientific_journal-7932	41	1	4	4	X
american_scientific_journal-7932	41	2	.	.	NOUN
american_scientific_journal-7932	41	3	alternative	alternative	ADJ
american_scientific_journal-7932	41	4	expressions	expression	NOUN
american_scientific_journal-7932	41	5	for	for	ADP
american_scientific_journal-7932	41	6	the	the	DET
american_scientific_journal-7932	41	7	velocity	velocity	NOUN
american_scientific_journal-7932	41	8	and	and	CCONJ
american_scientific_journal-7932	41	9	stress	stress	NOUN
american_scientific_journal-7932	41	10	components	component	NOUN
american_scientific_journal-7932	41	11	using	use	VERB
american_scientific_journal-7932	41	12	that	that	PRON
american_scientific_journal-7932	41	13	given	give	VERB
american_scientific_journal-7932	41	14	in	in	ADP
american_scientific_journal-7932	41	15	[	[	PUNCT
american_scientific_journal-7932	41	16	11	11	NUM
american_scientific_journal-7932	41	17	]	]	PUNCT
american_scientific_journal-7932	41	18	,	,	PUNCT
american_scientific_journal-7932	41	19	one	one	PRON
american_scientific_journal-7932	41	20	gets	get	VERB
american_scientific_journal-7932	41	21	in	in	ADP
american_scientific_journal-7932	41	22	terms	term	NOUN
american_scientific_journal-7932	41	23	of	of	ADP
american_scientific_journal-7932	41	24	the	the	DET
american_scientific_journal-7932	41	25	real	real	ADV
american_scientific_journal-7932	41	26	-	-	PUNCT
american_scientific_journal-7932	41	27	valued	value	VERB
american_scientific_journal-7932	41	28	kelvin	kelvin	PROPN
american_scientific_journal-7932	41	29	functions	function	NOUN
american_scientific_journal-7932	41	30	𝑏𝑒𝑟𝜔𝑥	𝑏𝑒𝑟𝜔𝑥	ADJ
american_scientific_journal-7932	41	31	and	and	CCONJ
american_scientific_journal-7932	41	32	𝑏𝑒𝑖𝜔𝑥	𝑏𝑒𝑖𝜔𝑥	ADJ
american_scientific_journal-7932	41	33	,	,	PUNCT
american_scientific_journal-7932	41	34	𝑒𝑖	𝑒𝑖	ADP
american_scientific_journal-7932	41	35	3𝜔𝜋	3𝜔𝜋	NOUN
american_scientific_journal-7932	41	36	2	2	NUM
american_scientific_journal-7932	41	37	𝐼𝜔(√𝑖𝜎𝑅	𝐼𝜔(√𝑖𝜎𝑅	PROPN
american_scientific_journal-7932	41	38	)	)	PUNCT
american_scientific_journal-7932	41	39	=	=	SYM
american_scientific_journal-7932	41	40	𝑏𝑒𝑟𝜔(−𝜎𝑅	𝑏𝑒𝑟𝜔(−𝜎𝑅	NOUN
american_scientific_journal-7932	41	41	)	)	PUNCT
american_scientific_journal-7932	42	1	+	+	CCONJ
american_scientific_journal-7932	42	2	𝑖	𝑖	SYM
american_scientific_journal-7932	42	3	𝑏𝑒𝑖𝜔(−𝜎𝑅	𝑏𝑒𝑖𝜔(−𝜎𝑅	NOUN
american_scientific_journal-7932	42	4	)	)	PUNCT
american_scientific_journal-7932	42	5	(	(	PUNCT
american_scientific_journal-7932	42	6	4.1	4.1	NUM
american_scientific_journal-7932	42	7	)	)	PUNCT
american_scientific_journal-7932	42	8	from	from	ADP
american_scientific_journal-7932	42	9	[	[	X
american_scientific_journal-7932	42	10	11	11	NUM
american_scientific_journal-7932	42	11	]	]	PUNCT
american_scientific_journal-7932	42	12	,	,	PUNCT
american_scientific_journal-7932	42	13	𝑏𝑒𝑟𝑛(−𝑥	𝑏𝑒𝑟𝑛(−𝑥	PROPN
american_scientific_journal-7932	42	14	)	)	PUNCT
american_scientific_journal-7932	42	15	=	=	PUNCT
american_scientific_journal-7932	43	1	(	(	PUNCT
american_scientific_journal-7932	43	2	−)𝑛𝑏𝑒𝑟𝑛𝑥	−)𝑛𝑏𝑒𝑟𝑛𝑥	PROPN
american_scientific_journal-7932	43	3	,	,	PUNCT
american_scientific_journal-7932	43	4	𝑏𝑒𝑖𝑛(−𝑥	𝑏𝑒𝑖𝑛(−𝑥	PROPN
american_scientific_journal-7932	43	5	)	)	PUNCT
american_scientific_journal-7932	43	6	=	=	SYM
american_scientific_journal-7932	43	7	(	(	PUNCT
american_scientific_journal-7932	43	8	−)𝑛𝑏𝑒𝑖𝑛𝑥	−)𝑛𝑏𝑒𝑖𝑛𝑥	X
american_scientific_journal-7932	43	9	(	(	PUNCT
american_scientific_journal-7932	43	10	4.2	4.2	NUM
american_scientific_journal-7932	43	11	)	)	PUNCT
american_scientific_journal-7932	43	12	which	which	PRON
american_scientific_journal-7932	43	13	on	on	ADP
american_scientific_journal-7932	43	14	using	use	VERB
american_scientific_journal-7932	43	15	in	in	ADP
american_scientific_journal-7932	43	16	(	(	PUNCT
american_scientific_journal-7932	43	17	4.1	4.1	NUM
american_scientific_journal-7932	43	18	)	)	PUNCT
american_scientific_journal-7932	43	19	,	,	PUNCT
american_scientific_journal-7932	43	20	gives	give	VERB
american_scientific_journal-7932	43	21	,	,	PUNCT
american_scientific_journal-7932	43	22	𝐼0(√𝑖𝜎𝑅	𝐼0(√𝑖𝜎𝑅	NOUN
american_scientific_journal-7932	43	23	)	)	PUNCT
american_scientific_journal-7932	43	24	=	=	SYM
american_scientific_journal-7932	43	25	𝑏𝑒𝑟0(𝜎𝑅	𝑏𝑒𝑟0(𝜎𝑅	X
american_scientific_journal-7932	43	26	)	)	PUNCT
american_scientific_journal-7932	44	1	+	+	CCONJ
american_scientific_journal-7932	44	2	𝑖	𝑖	SYM
american_scientific_journal-7932	44	3	𝑏𝑒𝑖0	𝑏𝑒𝑖0	NOUN
american_scientific_journal-7932	44	4	(	(	PUNCT
american_scientific_journal-7932	44	5	𝜎𝑅	𝜎𝑅	PROPN
american_scientific_journal-7932	44	6	)	)	PUNCT
american_scientific_journal-7932	44	7	(	(	PUNCT
american_scientific_journal-7932	44	8	4.3	4.3	NUM
american_scientific_journal-7932	44	9	)	)	PUNCT
american_scientific_journal-7932	44	10	and	and	CCONJ
american_scientific_journal-7932	44	11	𝑖	𝑖	ADP
american_scientific_journal-7932	44	12	𝐼1(√𝑖𝜎𝑅	𝐼1(√𝑖𝜎𝑅	NOUN
american_scientific_journal-7932	44	13	)	)	PUNCT
american_scientific_journal-7932	44	14	=	=	SYM
american_scientific_journal-7932	44	15	𝑏𝑒𝑟1(𝜎𝑅	𝑏𝑒𝑟1(𝜎𝑅	X
american_scientific_journal-7932	44	16	)	)	PUNCT
american_scientific_journal-7932	44	17	+	+	CCONJ
american_scientific_journal-7932	44	18	𝑖	𝑖	SYM
american_scientific_journal-7932	44	19	𝑏𝑒𝑖1(𝜎𝑅	𝑏𝑒𝑖1(𝜎𝑅	X
american_scientific_journal-7932	44	20	)	)	PUNCT
american_scientific_journal-7932	44	21	(	(	PUNCT
american_scientific_journal-7932	44	22	4.4	4.4	NUM
american_scientific_journal-7932	44	23	)	)	PUNCT
american_scientific_journal-7932	44	24	if	if	SCONJ
american_scientific_journal-7932	44	25	𝑀𝜔(𝑥	𝑀𝜔(𝑥	NOUN
american_scientific_journal-7932	44	26	)	)	PUNCT
american_scientific_journal-7932	44	27	and	and	CCONJ
american_scientific_journal-7932	44	28	𝜃𝜔(𝑥	𝜃𝜔(𝑥	NOUN
american_scientific_journal-7932	44	29	)	)	PUNCT
american_scientific_journal-7932	44	30	are	be	AUX
american_scientific_journal-7932	44	31	the	the	DET
american_scientific_journal-7932	44	32	modulus	modulus	NOUN
american_scientific_journal-7932	44	33	and	and	CCONJ
american_scientific_journal-7932	44	34	argument	argument	NOUN
american_scientific_journal-7932	44	35	respectively	respectively	ADV
american_scientific_journal-7932	44	36	of	of	ADP
american_scientific_journal-7932	44	37	𝐼𝜔(𝑥	𝐼𝜔(𝑥	NOUN
american_scientific_journal-7932	44	38	)	)	PUNCT
american_scientific_journal-7932	44	39	then	then	ADV
american_scientific_journal-7932	44	40	[	[	X
american_scientific_journal-7932	44	41	11	11	NUM
american_scientific_journal-7932	44	42	]	]	PUNCT
american_scientific_journal-7932	44	43	,	,	PUNCT
american_scientific_journal-7932	44	44	𝑀𝜔(𝑥	𝑀𝜔(𝑥	NOUN
american_scientific_journal-7932	44	45	)	)	PUNCT
american_scientific_journal-7932	44	46	=	=	SYM
american_scientific_journal-7932	44	47	√𝑏𝑒𝑟𝜔	√𝑏𝑒𝑟𝜔	NOUN
american_scientific_journal-7932	44	48	2(𝑥	2(𝑥	NUM
american_scientific_journal-7932	44	49	)	)	PUNCT
american_scientific_journal-7932	45	1	+	+	CCONJ
american_scientific_journal-7932	45	2	𝑏𝑒𝑖𝜔	𝑏𝑒𝑖𝜔	NOUN
american_scientific_journal-7932	45	3	2	2	NUM
american_scientific_journal-7932	45	4	(	(	PUNCT
american_scientific_journal-7932	45	5	𝑥	𝑥	NOUN
american_scientific_journal-7932	45	6	)	)	PUNCT
american_scientific_journal-7932	45	7	(	(	PUNCT
american_scientific_journal-7932	45	8	4.5	4.5	NUM
american_scientific_journal-7932	45	9	)	)	PUNCT
american_scientific_journal-7932	45	10	american	american	ADJ
american_scientific_journal-7932	45	11	academic	academic	ADJ
american_scientific_journal-7932	45	12	scientific	scientific	ADJ
american_scientific_journal-7932	45	13	research	research	NOUN
american_scientific_journal-7932	45	14	journal	journal	NOUN
american_scientific_journal-7932	45	15	for	for	ADP
american_scientific_journal-7932	45	16	engineering	engineering	NOUN
american_scientific_journal-7932	45	17	,	,	PUNCT
american_scientific_journal-7932	45	18	technology	technology	NOUN
american_scientific_journal-7932	45	19	,	,	PUNCT
american_scientific_journal-7932	45	20	and	and	CCONJ
american_scientific_journal-7932	45	21	sciences	science	NOUN
american_scientific_journal-7932	45	22	(	(	PUNCT
american_scientific_journal-7932	45	23	asrjets	asrjet	NOUN
american_scientific_journal-7932	45	24	)	)	PUNCT
american_scientific_journal-7932	45	25	(	(	PUNCT
american_scientific_journal-7932	45	26	2022	2022	NUM
american_scientific_journal-7932	45	27	)	)	PUNCT
american_scientific_journal-7932	45	28	volume	volume	NOUN
american_scientific_journal-7932	45	29	89	89	NUM
american_scientific_journal-7932	45	30	,	,	PUNCT
american_scientific_journal-7932	45	31	no	no	DET
american_scientific_journal-7932	45	32	1	1	NUM
american_scientific_journal-7932	45	33	,	,	PUNCT
american_scientific_journal-7932	45	34	pp229	pp229	NOUN
american_scientific_journal-7932	45	35	-	-	PUNCT
american_scientific_journal-7932	45	36	240	240	NUM
american_scientific_journal-7932	45	37	233	233	NUM
american_scientific_journal-7932	45	38	𝜃𝜔(𝑥	𝜃𝜔(𝑥	NOUN
american_scientific_journal-7932	45	39	)	)	PUNCT
american_scientific_journal-7932	45	40	=	=	SYM
american_scientific_journal-7932	45	41	tan−1	tan−1	PROPN
american_scientific_journal-7932	45	42	(	(	PUNCT
american_scientific_journal-7932	45	43	𝑏𝑒𝑖𝜔𝑥	𝑏𝑒𝑖𝜔𝑥	ADJ
american_scientific_journal-7932	45	44	𝑏𝑒𝑟𝜔𝑥	𝑏𝑒𝑟𝜔𝑥	NOUN
american_scientific_journal-7932	45	45	)	)	PUNCT
american_scientific_journal-7932	45	46	(	(	PUNCT
american_scientific_journal-7932	45	47	4.6	4.6	NUM
american_scientific_journal-7932	45	48	)	)	PUNCT
american_scientific_journal-7932	45	49	which	which	PRON
american_scientific_journal-7932	45	50	gives	give	VERB
american_scientific_journal-7932	45	51	,	,	PUNCT
american_scientific_journal-7932	45	52	𝐼0(√𝑖𝜎𝑅	𝐼0(√𝑖𝜎𝑅	NOUN
american_scientific_journal-7932	45	53	)	)	PUNCT
american_scientific_journal-7932	45	54	=	=	SYM
american_scientific_journal-7932	45	55	𝑀0(𝜎𝑅)𝑒𝑖𝜃0(𝜎𝑅	𝑀0(𝜎𝑅)𝑒𝑖𝜃0(𝜎𝑅	X
american_scientific_journal-7932	45	56	)	)	PUNCT
american_scientific_journal-7932	45	57	(	(	PUNCT
american_scientific_journal-7932	45	58	4.7	4.7	NUM
american_scientific_journal-7932	45	59	)	)	PUNCT
american_scientific_journal-7932	45	60	and	and	CCONJ
american_scientific_journal-7932	45	61	𝐼1(√𝑖𝜎𝑅	𝐼1(√𝑖𝜎𝑅	NOUN
american_scientific_journal-7932	45	62	)	)	PUNCT
american_scientific_journal-7932	45	63	=	=	SYM
american_scientific_journal-7932	45	64	−𝑖	−𝑖	ADJ
american_scientific_journal-7932	45	65	𝑀1(𝜎𝑅)𝑒𝑖𝜃1(𝜎𝑅	𝑀1(𝜎𝑅)𝑒𝑖𝜃1(𝜎𝑅	NOUN
american_scientific_journal-7932	45	66	)	)	PUNCT
american_scientific_journal-7932	45	67	(	(	PUNCT
american_scientific_journal-7932	45	68	4.8	4.8	NUM
american_scientific_journal-7932	45	69	)	)	PUNCT
american_scientific_journal-7932	45	70	resulting	result	VERB
american_scientific_journal-7932	45	71	in	in	ADP
american_scientific_journal-7932	45	72	,	,	PUNCT
american_scientific_journal-7932	45	73	v(𝑅	v(𝑅	PROPN
american_scientific_journal-7932	45	74	,	,	PUNCT
american_scientific_journal-7932	45	75	𝑡	𝑡	X
american_scientific_journal-7932	45	76	)	)	PUNCT
american_scientific_journal-7932	45	77	=	=	SYM
american_scientific_journal-7932	45	78	re	re	X
american_scientific_journal-7932	45	79	[	[	PUNCT
american_scientific_journal-7932	45	80	𝑀1(𝜎1𝑅	𝑀1(𝜎1𝑅	PROPN
american_scientific_journal-7932	45	81	)	)	PUNCT
american_scientific_journal-7932	45	82	𝑀1(𝛼1	𝑀1(𝛼1	NOUN
american_scientific_journal-7932	45	83	)	)	PUNCT
american_scientific_journal-7932	45	84	𝑒𝑖[𝜃1(𝜎1𝑅)−𝜃1(𝛼1)]𝑞0	𝑒𝑖[𝜃1(𝜎1𝑅)−𝜃1(𝛼1)]𝑞0	PUNCT
american_scientific_journal-7932	46	1	cos	cos	ADP
american_scientific_journal-7932	46	2	𝛽	𝛽	NOUN
american_scientific_journal-7932	46	3	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	PROPN
american_scientific_journal-7932	46	4	]	]	PUNCT
american_scientific_journal-7932	46	5	(	(	PUNCT
american_scientific_journal-7932	46	6	4.9	4.9	NUM
american_scientific_journal-7932	46	7	)	)	PUNCT
american_scientific_journal-7932	46	8	and	and	CCONJ
american_scientific_journal-7932	46	9	𝑤(𝑅	𝑤(𝑅	PROPN
american_scientific_journal-7932	46	10	,	,	PUNCT
american_scientific_journal-7932	46	11	𝑡	𝑡	X
american_scientific_journal-7932	46	12	)	)	PUNCT
american_scientific_journal-7932	46	13	=	=	SYM
american_scientific_journal-7932	46	14	re	re	X
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american_scientific_journal-7932	46	16	𝑀0(𝜎2𝑅	𝑀0(𝜎2𝑅	NOUN
american_scientific_journal-7932	46	17	)	)	PUNCT
american_scientific_journal-7932	46	18	𝑀0(𝛼2	𝑀0(𝛼2	VERB
american_scientific_journal-7932	46	19	)	)	PUNCT
american_scientific_journal-7932	46	20	𝑒𝑖[𝜃0(𝜎2𝑅)−𝜃0(𝛼2)]𝑞0	𝑒𝑖[𝜃0(𝜎2𝑅)−𝜃0(𝛼2)]𝑞0	NOUN
american_scientific_journal-7932	46	21	sin	sin	NOUN
american_scientific_journal-7932	46	22	𝛽	𝛽	PROPN
american_scientific_journal-7932	46	23	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	PROPN
american_scientific_journal-7932	46	24	]	]	X
american_scientific_journal-7932	46	25	(	(	PUNCT
american_scientific_journal-7932	46	26	4.10	4.10	NUM
american_scientific_journal-7932	46	27	)	)	PUNCT
american_scientific_journal-7932	46	28	it	it	PRON
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american_scientific_journal-7932	46	30	observed	observe	VERB
american_scientific_journal-7932	46	31	again	again	ADV
american_scientific_journal-7932	46	32	that	that	SCONJ
american_scientific_journal-7932	46	33	for	for	ADP
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american_scientific_journal-7932	46	35	same	same	ADJ
american_scientific_journal-7932	46	36	frequencies	frequency	NOUN
american_scientific_journal-7932	46	37	of	of	ADP
american_scientific_journal-7932	46	38	oscillations	oscillation	NOUN
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american_scientific_journal-7932	46	41	4.9	4.9	NUM
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american_scientific_journal-7932	46	43	and	and	CCONJ
american_scientific_journal-7932	46	44	(	(	PUNCT
american_scientific_journal-7932	46	45	4.10	4.10	NUM
american_scientific_journal-7932	46	46	)	)	PUNCT
american_scientific_journal-7932	46	47	reduce	reduce	VERB
american_scientific_journal-7932	46	48	to	to	ADP
american_scientific_journal-7932	46	49	that	that	PRON
american_scientific_journal-7932	46	50	obtained	obtain	VERB
american_scientific_journal-7932	46	51	in	in	ADP
american_scientific_journal-7932	46	52	[	[	X
american_scientific_journal-7932	46	53	3	3	NUM
american_scientific_journal-7932	46	54	]	]	PUNCT
american_scientific_journal-7932	46	55	.	.	PUNCT
american_scientific_journal-7932	47	1	similarly	similarly	ADV
american_scientific_journal-7932	47	2	,	,	PUNCT
american_scientific_journal-7932	47	3	from	from	ADP
american_scientific_journal-7932	47	4	(	(	PUNCT
american_scientific_journal-7932	47	5	3.9	3.9	NUM
american_scientific_journal-7932	47	6	)	)	PUNCT
american_scientific_journal-7932	47	7	,	,	PUNCT
american_scientific_journal-7932	47	8	𝜏𝑅𝜃|𝑅=𝑎	𝜏𝑅𝜃|𝑅=𝑎	PROPN
american_scientific_journal-7932	47	9	=	=	PUNCT
american_scientific_journal-7932	47	10	𝜇𝛼1	𝜇𝛼1	PROPN
american_scientific_journal-7932	47	11	𝑎	𝑎	DET
american_scientific_journal-7932	47	12	𝑞0	𝑞0	NOUN
american_scientific_journal-7932	47	13	cos	cos	ADP
american_scientific_journal-7932	47	14	𝛽	𝛽	NOUN
american_scientific_journal-7932	47	15	𝑀0(𝛼1	𝑀0(𝛼1	PROPN
american_scientific_journal-7932	47	16	)	)	PUNCT
american_scientific_journal-7932	47	17	𝑀1(𝛼1	𝑀1(𝛼1	NOUN
american_scientific_journal-7932	47	18	)	)	PUNCT
american_scientific_journal-7932	47	19	𝐿	𝐿	PROPN
american_scientific_journal-7932	47	20	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	47	21	+	+	CCONJ
american_scientific_journal-7932	47	22	𝛿	𝛿	X
american_scientific_journal-7932	47	23	)	)	PUNCT
american_scientific_journal-7932	47	24	(	(	PUNCT
american_scientific_journal-7932	47	25	4.11	4.11	NUM
american_scientific_journal-7932	47	26	)	)	PUNCT
american_scientific_journal-7932	47	27	where	where	SCONJ
american_scientific_journal-7932	47	28	𝐿2	𝐿2	NOUN
american_scientific_journal-7932	47	29	=	=	SYM
american_scientific_journal-7932	47	30	(	(	PUNCT
american_scientific_journal-7932	47	31	cos	cos	ADP
american_scientific_journal-7932	47	32	𝜂	𝜂	NOUN
american_scientific_journal-7932	47	33	−	−	PROPN
american_scientific_journal-7932	47	34	2	2	NUM
american_scientific_journal-7932	47	35	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	47	36	𝑀1(𝛼1	𝑀1(𝛼1	NOUN
american_scientific_journal-7932	47	37	)	)	PUNCT
american_scientific_journal-7932	47	38	𝑀0(𝛼1	𝑀0(𝛼1	PROPN
american_scientific_journal-7932	47	39	)	)	PUNCT
american_scientific_journal-7932	47	40	)	)	PUNCT
american_scientific_journal-7932	47	41	2	2	NUM
american_scientific_journal-7932	48	1	+	+	NUM
american_scientific_journal-7932	48	2	sin2	sin2	NOUN
american_scientific_journal-7932	48	3	𝜂	𝜂	PROPN
american_scientific_journal-7932	48	4	(	(	PUNCT
american_scientific_journal-7932	48	5	4.12	4.12	NUM
american_scientific_journal-7932	48	6	)	)	PUNCT
american_scientific_journal-7932	48	7	tan	tan	PROPN
american_scientific_journal-7932	48	8	𝛿	𝛿	ADJ
american_scientific_journal-7932	48	9	=	=	PUNCT
american_scientific_journal-7932	48	10	sin	sin	NOUN
american_scientific_journal-7932	48	11	𝜂	𝜂	NOUN
american_scientific_journal-7932	48	12	cos𝜂−	cos𝜂−	ADJ
american_scientific_journal-7932	48	13	2	2	NUM
american_scientific_journal-7932	48	14	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	48	15	𝑀1(𝛼1	𝑀1(𝛼1	NOUN
american_scientific_journal-7932	48	16	)	)	PUNCT
american_scientific_journal-7932	48	17	𝑀0(𝛼1	𝑀0(𝛼1	PROPN
american_scientific_journal-7932	48	18	)	)	PUNCT
american_scientific_journal-7932	48	19	(	(	PUNCT
american_scientific_journal-7932	48	20	4.13	4.13	NUM
american_scientific_journal-7932	48	21	)	)	PUNCT
american_scientific_journal-7932	48	22	𝜂	𝜂	NOUN
american_scientific_journal-7932	48	23	=	=	SYM
american_scientific_journal-7932	48	24	𝜃0(𝛼1	𝜃0(𝛼1	NUM
american_scientific_journal-7932	48	25	)	)	PUNCT
american_scientific_journal-7932	48	26	−	−	NOUN
american_scientific_journal-7932	48	27	𝜃1(𝛼1	𝜃1(𝛼1	NOUN
american_scientific_journal-7932	48	28	)	)	PUNCT
american_scientific_journal-7932	49	1	+	+	CCONJ
american_scientific_journal-7932	49	2	3𝜋	3𝜋	NUM
american_scientific_journal-7932	49	3	4	4	NUM
american_scientific_journal-7932	49	4	(	(	PUNCT
american_scientific_journal-7932	49	5	4.14	4.14	NUM
american_scientific_journal-7932	49	6	)	)	PUNCT
american_scientific_journal-7932	49	7	also	also	ADV
american_scientific_journal-7932	49	8	,	,	PUNCT
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american_scientific_journal-7932	49	10	(	(	PUNCT
american_scientific_journal-7932	49	11	3.10	3.10	NUM
american_scientific_journal-7932	49	12	)	)	PUNCT
american_scientific_journal-7932	49	13	,	,	PUNCT
american_scientific_journal-7932	49	14	𝜏𝑅𝑧|𝑅=𝑎	𝜏𝑅𝑧|𝑅=𝑎	PROPN
american_scientific_journal-7932	49	15	=	=	PUNCT
american_scientific_journal-7932	49	16	𝜇𝛼2	𝜇𝛼2	NOUN
american_scientific_journal-7932	49	17	𝑎	𝑎	NOUN
american_scientific_journal-7932	49	18	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	49	19	sin	sin	NOUN
american_scientific_journal-7932	49	20	𝛽	𝛽	NOUN
american_scientific_journal-7932	49	21	𝑀1(𝛼2	𝑀1(𝛼2	PROPN
american_scientific_journal-7932	49	22	)	)	PUNCT
american_scientific_journal-7932	49	23	𝑀0(𝛼2	𝑀0(𝛼2	PROPN
american_scientific_journal-7932	49	24	)	)	PUNCT
american_scientific_journal-7932	49	25	cos(ω2𝑡	cos(ω2𝑡	PROPN
american_scientific_journal-7932	50	1	+	+	NUM
american_scientific_journal-7932	50	2	𝜉	𝜉	X
american_scientific_journal-7932	50	3	)	)	PUNCT
american_scientific_journal-7932	50	4	(	(	PUNCT
american_scientific_journal-7932	50	5	4.15	4.15	NUM
american_scientific_journal-7932	50	6	)	)	PUNCT
american_scientific_journal-7932	50	7	where	where	SCONJ
american_scientific_journal-7932	50	8	𝜉	𝜉	NOUN
american_scientific_journal-7932	50	9	=	=	SYM
american_scientific_journal-7932	50	10	𝜃1(𝛼2	𝜃1(𝛼2	NOUN
american_scientific_journal-7932	50	11	)	)	PUNCT
american_scientific_journal-7932	50	12	−	−	ADP
american_scientific_journal-7932	50	13	𝜃0(𝛼2	𝜃0(𝛼2	NOUN
american_scientific_journal-7932	50	14	)	)	PUNCT
american_scientific_journal-7932	50	15	−	−	NOUN
american_scientific_journal-7932	50	16	𝜋	𝜋	NOUN
american_scientific_journal-7932	50	17	4	4	NUM
american_scientific_journal-7932	50	18	(	(	PUNCT
american_scientific_journal-7932	50	19	4.16	4.16	NUM
american_scientific_journal-7932	50	20	)	)	PUNCT
american_scientific_journal-7932	50	21	american	american	ADJ
american_scientific_journal-7932	50	22	academic	academic	ADJ
american_scientific_journal-7932	50	23	scientific	scientific	ADJ
american_scientific_journal-7932	50	24	research	research	NOUN
american_scientific_journal-7932	50	25	journal	journal	NOUN
american_scientific_journal-7932	50	26	for	for	ADP
american_scientific_journal-7932	50	27	engineering	engineering	NOUN
american_scientific_journal-7932	50	28	,	,	PUNCT
american_scientific_journal-7932	50	29	technology	technology	NOUN
american_scientific_journal-7932	50	30	,	,	PUNCT
american_scientific_journal-7932	50	31	and	and	CCONJ
american_scientific_journal-7932	50	32	sciences	science	NOUN
american_scientific_journal-7932	50	33	(	(	PUNCT
american_scientific_journal-7932	50	34	asrjets	asrjet	NOUN
american_scientific_journal-7932	50	35	)	)	PUNCT
american_scientific_journal-7932	50	36	(	(	PUNCT
american_scientific_journal-7932	50	37	2022	2022	NUM
american_scientific_journal-7932	50	38	)	)	PUNCT
american_scientific_journal-7932	50	39	volume	volume	NOUN
american_scientific_journal-7932	50	40	89	89	NUM
american_scientific_journal-7932	50	41	,	,	PUNCT
american_scientific_journal-7932	50	42	no	no	DET
american_scientific_journal-7932	50	43	1	1	NUM
american_scientific_journal-7932	50	44	,	,	PUNCT
american_scientific_journal-7932	50	45	pp229	pp229	NOUN
american_scientific_journal-7932	50	46	-	-	PUNCT
american_scientific_journal-7932	50	47	240	240	NUM
american_scientific_journal-7932	50	48	234	234	NUM
american_scientific_journal-7932	50	49	5	5	NUM
american_scientific_journal-7932	50	50	.	.	PUNCT
american_scientific_journal-7932	51	1	work	work	NOUN
american_scientific_journal-7932	51	2	done	do	VERB
american_scientific_journal-7932	51	3	and	and	CCONJ
american_scientific_journal-7932	51	4	the	the	DET
american_scientific_journal-7932	51	5	drag	drag	NOUN
american_scientific_journal-7932	51	6	coefficient	coefficient	NOUN
american_scientific_journal-7932	51	7	(	(	PUNCT
american_scientific_journal-7932	51	8	3.11	3.11	NUM
american_scientific_journal-7932	51	9	)	)	PUNCT
american_scientific_journal-7932	51	10	can	can	AUX
american_scientific_journal-7932	51	11	be	be	AUX
american_scientific_journal-7932	51	12	written	write	VERB
american_scientific_journal-7932	51	13	as	as	ADP
american_scientific_journal-7932	51	14	,	,	PUNCT
american_scientific_journal-7932	51	15	𝐷	𝐷	PROPN
american_scientific_journal-7932	51	16	=	=	SYM
american_scientific_journal-7932	51	17	−2𝜋𝑎(𝑇	−2𝜋𝑎(𝑇	PROPN
american_scientific_journal-7932	52	1	cos	cos	ADP
american_scientific_journal-7932	52	2	𝜙	𝜙	PRON
american_scientific_journal-7932	52	3	�	�	PROPN
american_scientific_journal-7932	52	4	̂	̂	NUM
american_scientific_journal-7932	52	5	�	�	PROPN
american_scientific_journal-7932	52	6	+	+	CCONJ
american_scientific_journal-7932	52	7	𝑇	𝑇	PROPN
american_scientific_journal-7932	52	8	sin𝜙	sin𝜙	NOUN
american_scientific_journal-7932	52	9	�	�	PROPN
american_scientific_journal-7932	52	10	̂	̂	NOUN
american_scientific_journal-7932	52	11	�	�	PROPN
american_scientific_journal-7932	52	12	)	)	PUNCT
american_scientific_journal-7932	52	13	(	(	PUNCT
american_scientific_journal-7932	52	14	5.1	5.1	NUM
american_scientific_journal-7932	52	15	)	)	PUNCT
american_scientific_journal-7932	52	16	where	where	SCONJ
american_scientific_journal-7932	52	17	𝜏𝑅𝜃|𝑅=𝑎	𝜏𝑅𝜃|𝑅=𝑎	PROPN
american_scientific_journal-7932	52	18	=	=	SYM
american_scientific_journal-7932	52	19	𝑇	𝑇	PROPN
american_scientific_journal-7932	52	20	cos𝜙	cos𝜙	NOUN
american_scientific_journal-7932	52	21	(	(	PUNCT
american_scientific_journal-7932	52	22	5.2	5.2	NUM
american_scientific_journal-7932	52	23	)	)	PUNCT
american_scientific_journal-7932	52	24	and	and	CCONJ
american_scientific_journal-7932	52	25	𝜏𝑅𝑧|𝑅=𝑎	𝜏𝑅𝑧|𝑅=𝑎	NUM
american_scientific_journal-7932	52	26	=	=	SYM
american_scientific_journal-7932	52	27	𝑇	𝑇	PROPN
american_scientific_journal-7932	52	28	sin	sin	NOUN
american_scientific_journal-7932	52	29	𝜙	𝜙	X
american_scientific_journal-7932	52	30	(	(	PUNCT
american_scientific_journal-7932	52	31	5.3	5.3	NUM
american_scientific_journal-7932	52	32	)	)	PUNCT
american_scientific_journal-7932	52	33	using	use	VERB
american_scientific_journal-7932	52	34	(	(	PUNCT
american_scientific_journal-7932	52	35	3.9	3.9	NUM
american_scientific_journal-7932	52	36	)	)	PUNCT
american_scientific_journal-7932	52	37	and	and	CCONJ
american_scientific_journal-7932	52	38	(	(	PUNCT
american_scientific_journal-7932	52	39	3.10	3.10	NUM
american_scientific_journal-7932	52	40	)	)	PUNCT
american_scientific_journal-7932	52	41	,	,	PUNCT
american_scientific_journal-7932	52	42	it	it	PRON
american_scientific_journal-7932	52	43	follows	follow	VERB
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american_scientific_journal-7932	52	45	,	,	PUNCT
american_scientific_journal-7932	52	46	𝑇2	𝑇2	PROPN
american_scientific_journal-7932	52	47	=	=	SYM
american_scientific_journal-7932	52	48	(	(	PUNCT
american_scientific_journal-7932	52	49	re	re	X
american_scientific_journal-7932	52	50	[	[	PUNCT
american_scientific_journal-7932	52	51	√𝑖𝜎1	√𝑖𝜎1	ADV
american_scientific_journal-7932	52	52	𝐼0(√𝑖𝛼1)−	𝐼0(√𝑖𝛼1)−	NOUN
american_scientific_journal-7932	52	53	2	2	NUM
american_scientific_journal-7932	52	54	𝑎	𝑎	NOUN
american_scientific_journal-7932	52	55	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	52	56	)	)	PUNCT
american_scientific_journal-7932	52	57	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	52	58	)	)	PUNCT
american_scientific_journal-7932	52	59	𝜇𝑞0	𝜇𝑞0	NOUN
american_scientific_journal-7932	52	60	cos	cos	ADP
american_scientific_journal-7932	52	61	𝛽	𝛽	PROPN
american_scientific_journal-7932	52	62	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	PROPN
american_scientific_journal-7932	52	63	]	]	PUNCT
american_scientific_journal-7932	52	64	)	)	PUNCT
american_scientific_journal-7932	52	65	2	2	NUM
american_scientific_journal-7932	52	66	+	+	CCONJ
american_scientific_journal-7932	52	67	(	(	PUNCT
american_scientific_journal-7932	52	68	re	re	X
american_scientific_journal-7932	52	69	[	[	PUNCT
american_scientific_journal-7932	52	70	√𝑖𝜎2𝐼1	√𝑖𝜎2𝐼1	X
american_scientific_journal-7932	52	71	(	(	PUNCT
american_scientific_journal-7932	52	72	√𝑖𝛼2	√𝑖𝛼2	NOUN
american_scientific_journal-7932	52	73	)	)	PUNCT
american_scientific_journal-7932	52	74	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	NOUN
american_scientific_journal-7932	52	75	)	)	PUNCT
american_scientific_journal-7932	52	76	𝜇𝑞0	𝜇𝑞0	NOUN
american_scientific_journal-7932	52	77	sin	sin	VERB
american_scientific_journal-7932	52	78	𝛽	𝛽	NOUN
american_scientific_journal-7932	52	79	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	NOUN
american_scientific_journal-7932	52	80	]	]	PUNCT
american_scientific_journal-7932	52	81	)	)	PUNCT
american_scientific_journal-7932	52	82	2	2	NUM
american_scientific_journal-7932	52	83	(	(	PUNCT
american_scientific_journal-7932	52	84	5.4	5.4	NUM
american_scientific_journal-7932	52	85	)	)	PUNCT
american_scientific_journal-7932	52	86	and	and	CCONJ
american_scientific_journal-7932	52	87	,	,	PUNCT
american_scientific_journal-7932	52	88	with	with	ADP
american_scientific_journal-7932	52	89	the	the	DET
american_scientific_journal-7932	52	90	use	use	NOUN
american_scientific_journal-7932	52	91	of	of	ADP
american_scientific_journal-7932	52	92	(	(	PUNCT
american_scientific_journal-7932	52	93	5.2	5.2	NUM
american_scientific_journal-7932	52	94	)	)	PUNCT
american_scientific_journal-7932	52	95	and	and	CCONJ
american_scientific_journal-7932	52	96	(	(	PUNCT
american_scientific_journal-7932	52	97	5.3	5.3	NUM
american_scientific_journal-7932	52	98	)	)	PUNCT
american_scientific_journal-7932	52	99	,	,	PUNCT
american_scientific_journal-7932	52	100	tan𝜙	tan𝜙	PROPN
american_scientific_journal-7932	52	101	=	=	SYM
american_scientific_journal-7932	52	102	re	re	X
american_scientific_journal-7932	52	103	[	[	PUNCT
american_scientific_journal-7932	52	104	√𝑖𝜎2𝐼1(√𝑖𝛼2	√𝑖𝜎2𝐼1(√𝑖𝛼2	ADJ
american_scientific_journal-7932	52	105	)	)	PUNCT
american_scientific_journal-7932	52	106	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	NOUN
american_scientific_journal-7932	52	107	)	)	PUNCT
american_scientific_journal-7932	52	108	𝜇𝑞0	𝜇𝑞0	NOUN
american_scientific_journal-7932	52	109	sin	sin	VERB
american_scientific_journal-7932	52	110	𝛽	𝛽	PROPN
american_scientific_journal-7932	52	111	𝑒𝑖ω2𝑡	𝑒𝑖ω2𝑡	NOUN
american_scientific_journal-7932	52	112	]	]	X
american_scientific_journal-7932	52	113	re	re	ADP
american_scientific_journal-7932	52	114	[	[	PUNCT
american_scientific_journal-7932	52	115	√𝑖𝜎1	√𝑖𝜎1	ADV
american_scientific_journal-7932	52	116	𝐼0(√𝑖𝛼1)−	𝐼0(√𝑖𝛼1)−	NOUN
american_scientific_journal-7932	52	117	2	2	NUM
american_scientific_journal-7932	52	118	𝑎	𝑎	NOUN
american_scientific_journal-7932	52	119	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	52	120	)	)	PUNCT
american_scientific_journal-7932	52	121	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	52	122	)	)	PUNCT
american_scientific_journal-7932	52	123	𝜇𝑞0	𝜇𝑞0	NOUN
american_scientific_journal-7932	53	1	cos	cos	SCONJ
american_scientific_journal-7932	53	2	𝛽	𝛽	PROPN
american_scientific_journal-7932	53	3	𝑒𝑖ω1𝑡	𝑒𝑖ω1𝑡	PROPN
american_scientific_journal-7932	53	4	]	]	X
american_scientific_journal-7932	53	5	⁄	⁄	PROPN
american_scientific_journal-7932	53	6	(	(	PUNCT
american_scientific_journal-7932	53	7	5.5	5.5	NUM
american_scientific_journal-7932	53	8	)	)	PUNCT
american_scientific_journal-7932	53	9	the	the	DET
american_scientific_journal-7932	53	10	work	work	NOUN
american_scientific_journal-7932	53	11	done	do	VERB
american_scientific_journal-7932	53	12	on	on	ADP
american_scientific_journal-7932	53	13	the	the	DET
american_scientific_journal-7932	53	14	fluid	fluid	NOUN
american_scientific_journal-7932	53	15	per	per	ADP
american_scientific_journal-7932	53	16	half	half	ADJ
american_scientific_journal-7932	53	17	-	-	PUNCT
american_scientific_journal-7932	53	18	cycle	cycle	NOUN
american_scientific_journal-7932	53	19	of	of	ADP
american_scientific_journal-7932	53	20	motion	motion	NOUN
american_scientific_journal-7932	53	21	is	be	AUX
american_scientific_journal-7932	53	22	[	[	X
american_scientific_journal-7932	53	23	3	3	NUM
american_scientific_journal-7932	53	24	]	]	PUNCT
american_scientific_journal-7932	53	25	,	,	PUNCT
american_scientific_journal-7932	53	26	𝑊𝑗	𝑊𝑗	PROPN
american_scientific_journal-7932	53	27	=	=	PUNCT
american_scientific_journal-7932	54	1	−	−	PROPN
american_scientific_journal-7932	54	2	∫	∫	PROPN
american_scientific_journal-7932	54	3	𝐷	𝐷	PROPN
american_scientific_journal-7932	54	4	⋅	⋅	PROPN
american_scientific_journal-7932	54	5	𝑞(𝑎	𝑞(𝑎	PROPN
american_scientific_journal-7932	54	6	,	,	PUNCT
american_scientific_journal-7932	54	7	𝑡)d𝑡	𝑡)d𝑡	PROPN
american_scientific_journal-7932	54	8	𝜋	𝜋	PRON
american_scientific_journal-7932	54	9	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	54	10	0	0	NUM
american_scientific_journal-7932	54	11	(	(	PUNCT
american_scientific_journal-7932	54	12	5.6	5.6	NUM
american_scientific_journal-7932	54	13	)	)	PUNCT
american_scientific_journal-7932	54	14	where	where	SCONJ
american_scientific_journal-7932	54	15	𝑗	𝑗	NOUN
american_scientific_journal-7932	54	16	=	=	SYM
american_scientific_journal-7932	54	17	1	1	NUM
american_scientific_journal-7932	54	18	,	,	PUNCT
american_scientific_journal-7932	54	19	2	2	NUM
american_scientific_journal-7932	54	20	refers	refer	VERB
american_scientific_journal-7932	54	21	to	to	ADP
american_scientific_journal-7932	54	22	the	the	DET
american_scientific_journal-7932	54	23	torsional	torsional	ADJ
american_scientific_journal-7932	54	24	and	and	CCONJ
american_scientific_journal-7932	54	25	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	54	26	motions	motion	NOUN
american_scientific_journal-7932	54	27	respectively	respectively	ADV
american_scientific_journal-7932	54	28	.	.	PUNCT
american_scientific_journal-7932	55	1	with	with	ADP
american_scientific_journal-7932	55	2	the	the	DET
american_scientific_journal-7932	55	3	use	use	NOUN
american_scientific_journal-7932	55	4	of	of	ADP
american_scientific_journal-7932	55	5	(	(	PUNCT
american_scientific_journal-7932	55	6	2.1	2.1	NUM
american_scientific_journal-7932	55	7	)	)	PUNCT
american_scientific_journal-7932	55	8	and	and	CCONJ
american_scientific_journal-7932	55	9	(	(	PUNCT
american_scientific_journal-7932	55	10	3.12	3.12	NUM
american_scientific_journal-7932	55	11	)	)	PUNCT
american_scientific_journal-7932	55	12	,	,	PUNCT
american_scientific_journal-7932	55	13	(	(	PUNCT
american_scientific_journal-7932	55	14	5.6	5.6	NUM
american_scientific_journal-7932	55	15	)	)	PUNCT
american_scientific_journal-7932	55	16	gives	give	VERB
american_scientific_journal-7932	55	17	the	the	DET
american_scientific_journal-7932	55	18	work	work	NOUN
american_scientific_journal-7932	55	19	done	do	VERB
american_scientific_journal-7932	55	20	,	,	PUNCT
american_scientific_journal-7932	55	21	wj	wj	X
american_scientific_journal-7932	55	22	,	,	PUNCT
american_scientific_journal-7932	55	23	by	by	ADP
american_scientific_journal-7932	55	24	the	the	DET
american_scientific_journal-7932	55	25	drag	drag	NOUN
american_scientific_journal-7932	55	26	force	force	NOUN
american_scientific_journal-7932	55	27	,	,	PUNCT
american_scientific_journal-7932	55	28	𝐷	𝐷	PROPN
american_scientific_journal-7932	55	29	,	,	PUNCT
american_scientific_journal-7932	55	30	per	per	ADP
american_scientific_journal-7932	55	31	half	half	ADJ
american_scientific_journal-7932	55	32	cycle	cycle	NOUN
american_scientific_journal-7932	55	33	of	of	ADP
american_scientific_journal-7932	55	34	torsional	torsional	ADJ
american_scientific_journal-7932	55	35	and	and	CCONJ
american_scientific_journal-7932	55	36	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	55	37	motion	motion	NOUN
american_scientific_journal-7932	55	38	as	as	ADP
american_scientific_journal-7932	55	39	,	,	PUNCT
american_scientific_journal-7932	55	40	𝑊𝑗	𝑊𝑗	PROPN
american_scientific_journal-7932	55	41	=	=	PUNCT
american_scientific_journal-7932	55	42	−𝜋𝑎𝜇𝑞0	−𝜋𝑎𝜇𝑞0	X
american_scientific_journal-7932	55	43	2	2	NUM
american_scientific_journal-7932	55	44	[	[	X
american_scientific_journal-7932	55	45	𝑅𝑒	𝑅𝑒	PROPN
american_scientific_journal-7932	55	46	{	{	PUNCT
american_scientific_journal-7932	55	47	√𝑖𝜎1	√𝑖𝜎1	ADV
american_scientific_journal-7932	55	48	𝐼0(√𝑖𝛼1)−	𝐼0(√𝑖𝛼1)−	NOUN
american_scientific_journal-7932	55	49	2	2	NUM
american_scientific_journal-7932	55	50	𝑎	𝑎	NOUN
american_scientific_journal-7932	55	51	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	55	52	)	)	PUNCT
american_scientific_journal-7932	55	53	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	55	54	)	)	PUNCT
american_scientific_journal-7932	55	55	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	55	56	)	)	PUNCT
american_scientific_journal-7932	55	57	cos2	cos2	PROPN
american_scientific_journal-7932	55	58	𝛽	𝛽	NOUN
american_scientific_journal-7932	55	59	𝐼(ω𝑗	𝐼(ω𝑗	NOUN
american_scientific_journal-7932	55	60	,	,	PUNCT
american_scientific_journal-7932	55	61	ω1	ω1	PROPN
american_scientific_journal-7932	55	62	)	)	PUNCT
american_scientific_journal-7932	55	63	}	}	PUNCT
american_scientific_journal-7932	56	1	+	+	CCONJ
american_scientific_journal-7932	56	2	𝑅𝑒	𝑅𝑒	ADJ
american_scientific_journal-7932	56	3	{	{	PUNCT
american_scientific_journal-7932	56	4	√𝑖𝜎2𝐼1(√𝑖𝛼2	√𝑖𝜎2𝐼1(√𝑖𝛼2	ADJ
american_scientific_journal-7932	56	5	)	)	PUNCT
american_scientific_journal-7932	56	6	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	NOUN
american_scientific_journal-7932	56	7	)	)	PUNCT
american_scientific_journal-7932	56	8	cos(ω2𝑡	cos(ω2𝑡	NOUN
american_scientific_journal-7932	56	9	)	)	PUNCT
american_scientific_journal-7932	56	10	sin2	sin2	NOUN
american_scientific_journal-7932	56	11	𝛽	𝛽	PROPN
american_scientific_journal-7932	56	12	𝐼(ω𝑗	𝐼(ω𝑗	NOUN
american_scientific_journal-7932	56	13	,	,	PUNCT
american_scientific_journal-7932	56	14	ω2	ω2	ADJ
american_scientific_journal-7932	56	15	)	)	PUNCT
american_scientific_journal-7932	56	16	}	}	PUNCT
american_scientific_journal-7932	56	17	]	]	PUNCT
american_scientific_journal-7932	56	18	(	(	PUNCT
american_scientific_journal-7932	56	19	5.7	5.7	NUM
american_scientific_journal-7932	56	20	)	)	PUNCT
american_scientific_journal-7932	56	21	where	where	SCONJ
american_scientific_journal-7932	56	22	american	american	ADJ
american_scientific_journal-7932	56	23	academic	academic	ADJ
american_scientific_journal-7932	56	24	scientific	scientific	ADJ
american_scientific_journal-7932	56	25	research	research	NOUN
american_scientific_journal-7932	56	26	journal	journal	NOUN
american_scientific_journal-7932	56	27	for	for	ADP
american_scientific_journal-7932	56	28	engineering	engineering	NOUN
american_scientific_journal-7932	56	29	,	,	PUNCT
american_scientific_journal-7932	56	30	technology	technology	NOUN
american_scientific_journal-7932	56	31	,	,	PUNCT
american_scientific_journal-7932	56	32	and	and	CCONJ
american_scientific_journal-7932	56	33	sciences	science	NOUN
american_scientific_journal-7932	56	34	(	(	PUNCT
american_scientific_journal-7932	56	35	asrjets	asrjet	NOUN
american_scientific_journal-7932	56	36	)	)	PUNCT
american_scientific_journal-7932	56	37	(	(	PUNCT
american_scientific_journal-7932	56	38	2022	2022	NUM
american_scientific_journal-7932	56	39	)	)	PUNCT
american_scientific_journal-7932	56	40	volume	volume	NOUN
american_scientific_journal-7932	56	41	89	89	NUM
american_scientific_journal-7932	56	42	,	,	PUNCT
american_scientific_journal-7932	56	43	no	no	DET
american_scientific_journal-7932	56	44	1	1	NUM
american_scientific_journal-7932	56	45	,	,	PUNCT
american_scientific_journal-7932	56	46	pp229	pp229	NOUN
american_scientific_journal-7932	56	47	-	-	PUNCT
american_scientific_journal-7932	56	48	240	240	NUM
american_scientific_journal-7932	56	49	235	235	NUM
american_scientific_journal-7932	56	50	𝐼(ω𝑗	𝐼(ω𝑗	NOUN
american_scientific_journal-7932	56	51	,	,	PUNCT
american_scientific_journal-7932	56	52	ω	ω	NOUN
american_scientific_journal-7932	56	53	)	)	PUNCT
american_scientific_journal-7932	56	54	=	=	SYM
american_scientific_journal-7932	56	55	2∫	2∫	NUM
american_scientific_journal-7932	56	56	𝑒𝑖ω𝑡	𝑒𝑖ω𝑡	NOUN
american_scientific_journal-7932	56	57	cos(ω𝑡	cos(ω𝑡	NOUN
american_scientific_journal-7932	56	58	)	)	PUNCT
american_scientific_journal-7932	56	59	𝜋	𝜋	NOUN
american_scientific_journal-7932	56	60	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	56	61	0	0	NUM
american_scientific_journal-7932	56	62	𝑑𝑡	𝑑𝑡	ADP
american_scientific_journal-7932	56	63	=	=	PUNCT
american_scientific_journal-7932	56	64	ω𝑗	ω𝑗	PROPN
american_scientific_journal-7932	56	65	cos	cos	NOUN
american_scientific_journal-7932	56	66	(	(	PUNCT
american_scientific_journal-7932	56	67	πω	πω	INTJ
american_scientific_journal-7932	56	68	ω𝑗	ω𝑗	ADJ
american_scientific_journal-7932	56	69	)	)	PUNCT
american_scientific_journal-7932	56	70	sin	sin	NOUN
american_scientific_journal-7932	56	71	(	(	PUNCT
american_scientific_journal-7932	56	72	πω	πω	NOUN
american_scientific_journal-7932	56	73	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	56	74	)	)	PUNCT
american_scientific_journal-7932	57	1	+	+	CCONJ
american_scientific_journal-7932	57	2	πω	πω	ADP
american_scientific_journal-7932	57	3	−	−	PROPN
american_scientific_journal-7932	57	4	iω𝑗	iω𝑗	NOUN
american_scientific_journal-7932	57	5	cos2	cos2	NOUN
american_scientific_journal-7932	57	6	(	(	PUNCT
american_scientific_journal-7932	57	7	πω	πω	NOUN
american_scientific_journal-7932	57	8	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	57	9	)	)	PUNCT
american_scientific_journal-7932	58	1	+	+	CCONJ
american_scientific_journal-7932	58	2	𝑖ω𝑗	𝑖ω𝑗	ADJ
american_scientific_journal-7932	58	3	ωω𝑗	ωω𝑗	NOUN
american_scientific_journal-7932	58	4	(	(	PUNCT
american_scientific_journal-7932	58	5	5.8	5.8	NUM
american_scientific_journal-7932	58	6	)	)	PUNCT
american_scientific_journal-7932	58	7	substituting	substitute	VERB
american_scientific_journal-7932	58	8	(	(	PUNCT
american_scientific_journal-7932	58	9	2.1	2.1	NUM
american_scientific_journal-7932	58	10	)	)	PUNCT
american_scientific_journal-7932	58	11	and	and	CCONJ
american_scientific_journal-7932	58	12	(	(	PUNCT
american_scientific_journal-7932	58	13	5.1	5.1	NUM
american_scientific_journal-7932	58	14	)	)	PUNCT
american_scientific_journal-7932	58	15	into	into	ADP
american_scientific_journal-7932	58	16	(	(	PUNCT
american_scientific_journal-7932	58	17	5.6	5.6	NUM
american_scientific_journal-7932	58	18	)	)	PUNCT
american_scientific_journal-7932	58	19	gives	give	VERB
american_scientific_journal-7932	58	20	an	an	DET
american_scientific_journal-7932	58	21	alternative	alternative	ADJ
american_scientific_journal-7932	58	22	expression	expression	NOUN
american_scientific_journal-7932	58	23	for	for	ADP
american_scientific_journal-7932	58	24	the	the	DET
american_scientific_journal-7932	58	25	work	work	NOUN
american_scientific_journal-7932	58	26	done	do	VERB
american_scientific_journal-7932	58	27	,	,	PUNCT
american_scientific_journal-7932	58	28	𝑊𝑗	𝑊𝑗	PROPN
american_scientific_journal-7932	58	29	=	=	PROPN
american_scientific_journal-7932	58	30	2𝜋𝑎𝑞0	2𝜋𝑎𝑞0	NUM
american_scientific_journal-7932	58	31	∫	∫	PROPN
american_scientific_journal-7932	58	32	𝑇[cos𝜙	𝑇[cos𝜙	X
american_scientific_journal-7932	58	33	cos	cos	PROPN
american_scientific_journal-7932	58	34	𝛽	𝛽	PROPN
american_scientific_journal-7932	58	35	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	58	36	)	)	PUNCT
american_scientific_journal-7932	58	37	+	+	NUM
american_scientific_journal-7932	58	38	sin𝜙	sin𝜙	NOUN
american_scientific_journal-7932	58	39	sin	sin	NOUN
american_scientific_journal-7932	58	40	𝛽	𝛽	PROPN
american_scientific_journal-7932	58	41	cos(ω2𝑡	cos(ω2𝑡	PROPN
american_scientific_journal-7932	58	42	)	)	PUNCT
american_scientific_journal-7932	58	43	]	]	PUNCT
american_scientific_journal-7932	59	1	𝜋	𝜋	NOUN
american_scientific_journal-7932	59	2	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	59	3	0	0	NUM
american_scientific_journal-7932	59	4	𝑑𝑡	𝑑𝑡	ADP
american_scientific_journal-7932	59	5	(	(	PUNCT
american_scientific_journal-7932	59	6	5.9	5.9	NUM
american_scientific_journal-7932	59	7	)	)	PUNCT
american_scientific_journal-7932	59	8	it	it	PRON
american_scientific_journal-7932	59	9	is	be	AUX
american_scientific_journal-7932	59	10	noted	note	VERB
american_scientific_journal-7932	59	11	that	that	SCONJ
american_scientific_journal-7932	59	12	for	for	ADP
american_scientific_journal-7932	59	13	the	the	DET
american_scientific_journal-7932	59	14	same	same	ADJ
american_scientific_journal-7932	59	15	frequencies	frequency	NOUN
american_scientific_journal-7932	59	16	of	of	ADP
american_scientific_journal-7932	59	17	oscillations	oscillation	NOUN
american_scientific_journal-7932	59	18	,	,	PUNCT
american_scientific_journal-7932	59	19	this	this	PRON
american_scientific_journal-7932	59	20	reduces	reduce	VERB
american_scientific_journal-7932	59	21	to	to	ADP
american_scientific_journal-7932	59	22	that	that	PRON
american_scientific_journal-7932	59	23	obtained	obtain	VERB
american_scientific_journal-7932	59	24	in	in	ADP
american_scientific_journal-7932	59	25	[	[	X
american_scientific_journal-7932	59	26	3	3	NUM
american_scientific_journal-7932	59	27	]	]	PUNCT
american_scientific_journal-7932	59	28	.	.	PUNCT
american_scientific_journal-7932	60	1	the	the	DET
american_scientific_journal-7932	60	2	drag	drag	NOUN
american_scientific_journal-7932	60	3	coefficient	coefficient	NOUN
american_scientific_journal-7932	60	4	,	,	PUNCT
american_scientific_journal-7932	60	5	c	c	AUX
american_scientific_journal-7932	60	6	,	,	PUNCT
american_scientific_journal-7932	60	7	can	can	AUX
american_scientific_journal-7932	60	8	be	be	AUX
american_scientific_journal-7932	60	9	obtained	obtain	VERB
american_scientific_journal-7932	60	10	by	by	ADP
american_scientific_journal-7932	60	11	equating	equate	VERB
american_scientific_journal-7932	60	12	the	the	DET
american_scientific_journal-7932	60	13	work	work	NOUN
american_scientific_journal-7932	60	14	done	do	VERB
american_scientific_journal-7932	60	15	on	on	ADP
american_scientific_journal-7932	60	16	the	the	DET
american_scientific_journal-7932	60	17	fluid	fluid	NOUN
american_scientific_journal-7932	60	18	by	by	ADP
american_scientific_journal-7932	60	19	a	a	DET
american_scientific_journal-7932	60	20	hypothesized	hypothesized	ADJ
american_scientific_journal-7932	60	21	drag	drag	NOUN
american_scientific_journal-7932	60	22	force	force	NOUN
american_scientific_journal-7932	60	23	,	,	PUNCT
american_scientific_journal-7932	60	24	which	which	PRON
american_scientific_journal-7932	60	25	is	be	AUX
american_scientific_journal-7932	60	26	given	give	VERB
american_scientific_journal-7932	60	27	by	by	ADP
american_scientific_journal-7932	60	28	[	[	X
american_scientific_journal-7932	60	29	3	3	NUM
american_scientific_journal-7932	60	30	]	]	PUNCT
american_scientific_journal-7932	60	31	,	,	PUNCT
american_scientific_journal-7932	60	32	𝐷	𝐷	PROPN
american_scientific_journal-7932	60	33	𝐻	𝐻	PROPN
american_scientific_journal-7932	60	34	=	=	PUNCT
american_scientific_journal-7932	60	35	−𝐶𝑞𝑏	−𝐶𝑞𝑏	PROPN
american_scientific_journal-7932	60	36	𝑛(cos	𝑛(cos	PROPN
american_scientific_journal-7932	60	37	𝛽	𝛽	PROPN
american_scientific_journal-7932	60	38	�	�	PROPN
american_scientific_journal-7932	60	39	̂	̂	VERB
american_scientific_journal-7932	60	40	�	�	NOUN
american_scientific_journal-7932	60	41	+	+	CCONJ
american_scientific_journal-7932	60	42	sin	sin	NOUN
american_scientific_journal-7932	60	43	𝛽	𝛽	PROPN
american_scientific_journal-7932	60	44	�	�	PROPN
american_scientific_journal-7932	60	45	̂	̂	VERB
american_scientific_journal-7932	60	46	�	�	NOUN
american_scientific_journal-7932	60	47	)	)	PUNCT
american_scientific_journal-7932	60	48	using	use	VERB
american_scientific_journal-7932	60	49	this	this	PRON
american_scientific_journal-7932	60	50	in	in	ADP
american_scientific_journal-7932	60	51	(	(	PUNCT
american_scientific_journal-7932	60	52	5.6	5.6	NUM
american_scientific_journal-7932	60	53	)	)	PUNCT
american_scientific_journal-7932	60	54	and	and	CCONJ
american_scientific_journal-7932	60	55	equating	equate	VERB
american_scientific_journal-7932	60	56	it	it	PRON
american_scientific_journal-7932	60	57	to	to	ADP
american_scientific_journal-7932	60	58	(	(	PUNCT
american_scientific_journal-7932	60	59	5.7	5.7	NUM
american_scientific_journal-7932	60	60	)	)	PUNCT
american_scientific_journal-7932	60	61	gives	give	VERB
american_scientific_journal-7932	60	62	on	on	ADP
american_scientific_journal-7932	60	63	solving	solve	VERB
american_scientific_journal-7932	60	64	,	,	PUNCT
american_scientific_journal-7932	60	65	𝐶	𝐶	PROPN
american_scientific_journal-7932	60	66	=	=	PRON
american_scientific_journal-7932	60	67	−𝜋𝑎𝜇𝑞0	−𝜋𝑎𝜇𝑞0	X
american_scientific_journal-7932	60	68	2	2	NUM
american_scientific_journal-7932	60	69	[	[	X
american_scientific_journal-7932	60	70	𝑅𝑒	𝑅𝑒	PROPN
american_scientific_journal-7932	60	71	{	{	PUNCT
american_scientific_journal-7932	60	72	√𝑖𝜎1	√𝑖𝜎1	ADV
american_scientific_journal-7932	60	73	𝐼0(√𝑖𝛼1	𝐼0(√𝑖𝛼1	NOUN
american_scientific_journal-7932	60	74	)	)	PUNCT
american_scientific_journal-7932	60	75	−	−	NOUN
american_scientific_journal-7932	60	76	2	2	NUM
american_scientific_journal-7932	60	77	𝑎	𝑎	NOUN
american_scientific_journal-7932	60	78	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	60	79	)	)	PUNCT
american_scientific_journal-7932	60	80	𝐼1(√𝑖𝛼1	𝐼1(√𝑖𝛼1	NOUN
american_scientific_journal-7932	60	81	)	)	PUNCT
american_scientific_journal-7932	60	82	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	60	83	)	)	PUNCT
american_scientific_journal-7932	60	84	cos2	cos2	PROPN
american_scientific_journal-7932	60	85	𝛽	𝛽	NOUN
american_scientific_journal-7932	60	86	𝐼(ω𝑗	𝐼(ω𝑗	NOUN
american_scientific_journal-7932	60	87	,	,	PUNCT
american_scientific_journal-7932	60	88	ω1	ω1	PROPN
american_scientific_journal-7932	60	89	)	)	PUNCT
american_scientific_journal-7932	60	90	}	}	PUNCT
american_scientific_journal-7932	61	1	+	+	CCONJ
american_scientific_journal-7932	61	2	𝑅𝑒	𝑅𝑒	ADJ
american_scientific_journal-7932	61	3	{	{	PUNCT
american_scientific_journal-7932	61	4	√𝑖𝜎2𝐼1(√𝑖𝛼2	√𝑖𝜎2𝐼1(√𝑖𝛼2	ADJ
american_scientific_journal-7932	61	5	)	)	PUNCT
american_scientific_journal-7932	61	6	𝐼0(√𝑖𝛼2	𝐼0(√𝑖𝛼2	NOUN
american_scientific_journal-7932	61	7	)	)	PUNCT
american_scientific_journal-7932	61	8	cos(ω2𝑡	cos(ω2𝑡	NOUN
american_scientific_journal-7932	61	9	)	)	PUNCT
american_scientific_journal-7932	61	10	sin2	sin2	NOUN
american_scientific_journal-7932	61	11	𝛽	𝛽	PROPN
american_scientific_journal-7932	61	12	𝐼(ω𝑗	𝐼(ω𝑗	NOUN
american_scientific_journal-7932	61	13	,	,	PUNCT
american_scientific_journal-7932	61	14	ω2	ω2	ADJ
american_scientific_journal-7932	61	15	)	)	PUNCT
american_scientific_journal-7932	61	16	}	}	PUNCT
american_scientific_journal-7932	61	17	]	]	PUNCT
american_scientific_journal-7932	62	1	⁄	⁄	PROPN
american_scientific_journal-7932	62	2	[	[	PUNCT
american_scientific_journal-7932	62	3	∫	∫	PROPN
american_scientific_journal-7932	62	4	[	[	X
american_scientific_journal-7932	62	5	𝑞0	𝑞0	NOUN
american_scientific_journal-7932	62	6	𝑛+1	𝑛+1	ADP
american_scientific_journal-7932	62	7	cos𝑛+2	cos𝑛+2	PROPN
american_scientific_journal-7932	62	8	𝛽	𝛽	PROPN
american_scientific_journal-7932	62	9	cos𝑛+1(ω1𝑡	cos𝑛+1(ω1𝑡	NOUN
american_scientific_journal-7932	62	10	)	)	PUNCT
american_scientific_journal-7932	62	11	+	+	NUM
american_scientific_journal-7932	62	12	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	62	13	cos2	cos2	PROPN
american_scientific_journal-7932	62	14	𝛽	𝛽	PROPN
american_scientific_journal-7932	62	15	cos𝑛(ω2𝑡	cos𝑛(ω2𝑡	PROPN
american_scientific_journal-7932	62	16	)	)	PUNCT
american_scientific_journal-7932	62	17	sin𝑛	sin𝑛	PROPN
american_scientific_journal-7932	62	18	𝛽	𝛽	PROPN
american_scientific_journal-7932	62	19	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	62	20	)	)	PUNCT
american_scientific_journal-7932	62	21	𝜋	𝜋	NOUN
american_scientific_journal-7932	62	22	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	62	23	0	0	NUM
american_scientific_journal-7932	63	1	+	+	NUM
american_scientific_journal-7932	63	2	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	63	3	sin	sin	NOUN
american_scientific_journal-7932	63	4	𝑛+2	𝑛+2	PROPN
american_scientific_journal-7932	63	5	𝛽	𝛽	NOUN
american_scientific_journal-7932	63	6	cos𝑛+1(ω2𝑡)+𝑞0	cos𝑛+1(ω2𝑡)+𝑞0	NOUN
american_scientific_journal-7932	63	7	𝑛+1	𝑛+1	PART
american_scientific_journal-7932	63	8	cos𝑛	cos𝑛	VERB
american_scientific_journal-7932	63	9	𝛽	𝛽	PROPN
american_scientific_journal-7932	63	10	cos𝑛(ω1𝑡	cos𝑛(ω1𝑡	PROPN
american_scientific_journal-7932	63	11	)	)	PUNCT
american_scientific_journal-7932	63	12	sin2	sin2	NOUN
american_scientific_journal-7932	63	13	𝛽	𝛽	PROPN
american_scientific_journal-7932	63	14	cos(ω2𝑡	cos(ω2𝑡	PROPN
american_scientific_journal-7932	63	15	)	)	PUNCT
american_scientific_journal-7932	63	16	]	]	PUNCT
american_scientific_journal-7932	63	17	𝑑𝑡	𝑑𝑡	ADP
american_scientific_journal-7932	63	18	]	]	PUNCT
american_scientific_journal-7932	63	19	(	(	PUNCT
american_scientific_journal-7932	63	20	5.10	5.10	NUM
american_scientific_journal-7932	63	21	)	)	PUNCT
american_scientific_journal-7932	63	22	an	an	DET
american_scientific_journal-7932	63	23	alternate	alternate	ADJ
american_scientific_journal-7932	63	24	expression	expression	NOUN
american_scientific_journal-7932	63	25	for	for	ADP
american_scientific_journal-7932	63	26	the	the	DET
american_scientific_journal-7932	63	27	drag	drag	NOUN
american_scientific_journal-7932	63	28	coefficient	coefficient	NOUN
american_scientific_journal-7932	63	29	is	be	AUX
american_scientific_journal-7932	63	30	obtained	obtain	VERB
american_scientific_journal-7932	63	31	by	by	ADP
american_scientific_journal-7932	63	32	substituting	substitute	VERB
american_scientific_journal-7932	63	33	(	(	PUNCT
american_scientific_journal-7932	63	34	5.9	5.9	NUM
american_scientific_journal-7932	63	35	)	)	PUNCT
american_scientific_journal-7932	63	36	into	into	ADP
american_scientific_journal-7932	63	37	(	(	PUNCT
american_scientific_journal-7932	63	38	5.6	5.6	NUM
american_scientific_journal-7932	63	39	)	)	PUNCT
american_scientific_journal-7932	63	40	which	which	PRON
american_scientific_journal-7932	63	41	gives	give	VERB
american_scientific_journal-7932	63	42	,	,	PUNCT
american_scientific_journal-7932	63	43	american	american	ADJ
american_scientific_journal-7932	63	44	academic	academic	ADJ
american_scientific_journal-7932	63	45	scientific	scientific	ADJ
american_scientific_journal-7932	63	46	research	research	NOUN
american_scientific_journal-7932	63	47	journal	journal	NOUN
american_scientific_journal-7932	63	48	for	for	ADP
american_scientific_journal-7932	63	49	engineering	engineering	NOUN
american_scientific_journal-7932	63	50	,	,	PUNCT
american_scientific_journal-7932	63	51	technology	technology	NOUN
american_scientific_journal-7932	63	52	,	,	PUNCT
american_scientific_journal-7932	63	53	and	and	CCONJ
american_scientific_journal-7932	63	54	sciences	science	NOUN
american_scientific_journal-7932	63	55	(	(	PUNCT
american_scientific_journal-7932	63	56	asrjets	asrjet	NOUN
american_scientific_journal-7932	63	57	)	)	PUNCT
american_scientific_journal-7932	63	58	(	(	PUNCT
american_scientific_journal-7932	63	59	2022	2022	NUM
american_scientific_journal-7932	63	60	)	)	PUNCT
american_scientific_journal-7932	63	61	volume	volume	NOUN
american_scientific_journal-7932	63	62	89	89	NUM
american_scientific_journal-7932	63	63	,	,	PUNCT
american_scientific_journal-7932	63	64	no	no	DET
american_scientific_journal-7932	63	65	1	1	NUM
american_scientific_journal-7932	63	66	,	,	PUNCT
american_scientific_journal-7932	63	67	pp229	pp229	NOUN
american_scientific_journal-7932	63	68	-	-	PUNCT
american_scientific_journal-7932	63	69	240	240	NUM
american_scientific_journal-7932	63	70	236	236	NUM
american_scientific_journal-7932	63	71	𝐶	𝐶	PROPN
american_scientific_journal-7932	63	72	=	=	SYM
american_scientific_journal-7932	63	73	2𝜋𝑎𝑞0	2𝜋𝑎𝑞0	NUM
american_scientific_journal-7932	63	74	∫	∫	PROPN
american_scientific_journal-7932	63	75	𝑇[cos𝜙	𝑇[cos𝜙	X
american_scientific_journal-7932	63	76	cos	cos	PROPN
american_scientific_journal-7932	63	77	𝛽	𝛽	PROPN
american_scientific_journal-7932	63	78	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	63	79	)	)	PUNCT
american_scientific_journal-7932	64	1	+	+	CCONJ
american_scientific_journal-7932	64	2	sin	sin	NOUN
american_scientific_journal-7932	64	3	𝜙	𝜙	PROPN
american_scientific_journal-7932	64	4	sin	sin	NOUN
american_scientific_journal-7932	64	5	𝛽	𝛽	PROPN
american_scientific_journal-7932	64	6	cos(ω2𝑡	cos(ω2𝑡	PROPN
american_scientific_journal-7932	64	7	)	)	PUNCT
american_scientific_journal-7932	64	8	]	]	PUNCT
american_scientific_journal-7932	65	1	𝜋	𝜋	NOUN
american_scientific_journal-7932	65	2	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	65	3	0	0	NUM
american_scientific_journal-7932	65	4	𝑑𝑡	𝑑𝑡	ADP
american_scientific_journal-7932	65	5	⁄	⁄	PROPN
american_scientific_journal-7932	65	6	[	[	PUNCT
american_scientific_journal-7932	65	7	∫	∫	PROPN
american_scientific_journal-7932	66	1	[	[	X
american_scientific_journal-7932	66	2	𝑞0	𝑞0	NOUN
american_scientific_journal-7932	66	3	𝑛+1	𝑛+1	ADP
american_scientific_journal-7932	66	4	cos𝑛+2	cos𝑛+2	PROPN
american_scientific_journal-7932	66	5	𝛽	𝛽	PROPN
american_scientific_journal-7932	66	6	cos𝑛+1(ω1𝑡	cos𝑛+1(ω1𝑡	NOUN
american_scientific_journal-7932	66	7	)	)	PUNCT
american_scientific_journal-7932	66	8	+	+	NUM
american_scientific_journal-7932	66	9	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	66	10	cos2	cos2	PROPN
american_scientific_journal-7932	66	11	𝛽	𝛽	PROPN
american_scientific_journal-7932	66	12	cos𝑛(ω2𝑡	cos𝑛(ω2𝑡	PROPN
american_scientific_journal-7932	66	13	)	)	PUNCT
american_scientific_journal-7932	66	14	sin𝑛	sin𝑛	PROPN
american_scientific_journal-7932	66	15	𝛽	𝛽	PROPN
american_scientific_journal-7932	66	16	cos(ω1𝑡	cos(ω1𝑡	PROPN
american_scientific_journal-7932	66	17	)	)	PUNCT
american_scientific_journal-7932	66	18	𝜋	𝜋	NOUN
american_scientific_journal-7932	66	19	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	66	20	0	0	NUM
american_scientific_journal-7932	67	1	+	+	NUM
american_scientific_journal-7932	67	2	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	67	3	sin	sin	NOUN
american_scientific_journal-7932	67	4	𝑛+2	𝑛+2	PROPN
american_scientific_journal-7932	67	5	𝛽	𝛽	NOUN
american_scientific_journal-7932	67	6	cos𝑛+1(ω2𝑡)+𝑞0	cos𝑛+1(ω2𝑡)+𝑞0	NOUN
american_scientific_journal-7932	67	7	𝑛+1	𝑛+1	PART
american_scientific_journal-7932	67	8	cos𝑛	cos𝑛	VERB
american_scientific_journal-7932	67	9	𝛽	𝛽	PROPN
american_scientific_journal-7932	67	10	cos𝑛(ω1𝑡	cos𝑛(ω1𝑡	PROPN
american_scientific_journal-7932	67	11	)	)	PUNCT
american_scientific_journal-7932	67	12	sin2	sin2	NOUN
american_scientific_journal-7932	67	13	𝛽	𝛽	PROPN
american_scientific_journal-7932	67	14	cos(ω2𝑡	cos(ω2𝑡	PROPN
american_scientific_journal-7932	67	15	)	)	PUNCT
american_scientific_journal-7932	67	16	]	]	PUNCT
american_scientific_journal-7932	67	17	𝑑𝑡	𝑑𝑡	ADP
american_scientific_journal-7932	67	18	]	]	PUNCT
american_scientific_journal-7932	67	19	(	(	PUNCT
american_scientific_journal-7932	67	20	5.11	5.11	NUM
american_scientific_journal-7932	67	21	)	)	PUNCT
american_scientific_journal-7932	67	22	in	in	ADP
american_scientific_journal-7932	67	23	the	the	DET
american_scientific_journal-7932	67	24	case	case	NOUN
american_scientific_journal-7932	67	25	when	when	SCONJ
american_scientific_journal-7932	67	26	that	that	SCONJ
american_scientific_journal-7932	67	27	frequencies	frequency	NOUN
american_scientific_journal-7932	67	28	of	of	ADP
american_scientific_journal-7932	67	29	oscillations	oscillation	NOUN
american_scientific_journal-7932	67	30	are	be	AUX
american_scientific_journal-7932	67	31	the	the	DET
american_scientific_journal-7932	67	32	same	same	ADJ
american_scientific_journal-7932	67	33	,	,	PUNCT
american_scientific_journal-7932	67	34	one	one	PRON
american_scientific_journal-7932	67	35	gets	get	VERB
american_scientific_journal-7932	67	36	that	that	PRON
american_scientific_journal-7932	67	37	obtained	obtain	VERB
american_scientific_journal-7932	67	38	in	in	ADP
american_scientific_journal-7932	67	39	[	[	X
american_scientific_journal-7932	67	40	3	3	NUM
american_scientific_journal-7932	67	41	]	]	PUNCT
american_scientific_journal-7932	67	42	.	.	PUNCT
american_scientific_journal-7932	68	1	6	6	X
american_scientific_journal-7932	68	2	.	.	X
american_scientific_journal-7932	68	3	graphical	graphical	ADJ
american_scientific_journal-7932	68	4	results	result	NOUN
american_scientific_journal-7932	68	5	for	for	ADP
american_scientific_journal-7932	68	6	the	the	DET
american_scientific_journal-7932	68	7	following	follow	VERB
american_scientific_journal-7932	68	8	graphs	graph	NOUN
american_scientific_journal-7932	68	9	,	,	PUNCT
american_scientific_journal-7932	68	10	the	the	DET
american_scientific_journal-7932	68	11	effects	effect	NOUN
american_scientific_journal-7932	68	12	of	of	ADP
american_scientific_journal-7932	68	13	having	have	VERB
american_scientific_journal-7932	68	14	independent	independent	ADJ
american_scientific_journal-7932	68	15	oscillating	oscillate	VERB
american_scientific_journal-7932	68	16	frequencies	frequency	NOUN
american_scientific_journal-7932	68	17	is	be	AUX
american_scientific_journal-7932	68	18	examined	examine	VERB
american_scientific_journal-7932	68	19	.	.	PUNCT
american_scientific_journal-7932	69	1	due	due	ADP
american_scientific_journal-7932	69	2	to	to	ADP
american_scientific_journal-7932	69	3	some	some	DET
american_scientific_journal-7932	69	4	practical	practical	ADJ
american_scientific_journal-7932	69	5	oceanographic	oceanographic	ADJ
american_scientific_journal-7932	69	6	problems	problem	NOUN
american_scientific_journal-7932	69	7	,	,	PUNCT
american_scientific_journal-7932	69	8	[	[	X
american_scientific_journal-7932	69	9	2	2	NUM
american_scientific_journal-7932	69	10	]	]	PUNCT
american_scientific_journal-7932	69	11	gives	give	VERB
american_scientific_journal-7932	69	12	,	,	PUNCT
american_scientific_journal-7932	69	13	1	1	NUM
american_scientific_journal-7932	69	14	≤	≤	NUM
american_scientific_journal-7932	69	15	ω𝑗	ω𝑗	ADP
american_scientific_journal-7932	69	16	2𝜋	2𝜋	NOUN
american_scientific_journal-7932	69	17	≤	≤	NUM
american_scientific_journal-7932	69	18	10	10	NUM
american_scientific_journal-7932	69	19	hz	hz	VERB
american_scientific_journal-7932	69	20	and	and	CCONJ
american_scientific_journal-7932	69	21	9.30	9.30	NUM
american_scientific_journal-7932	69	22	×	×	NOUN
american_scientific_journal-7932	69	23	10−7	10−7	NUM
american_scientific_journal-7932	69	24	≤	≤	NOUN
american_scientific_journal-7932	69	25	𝜈	𝜈	X
american_scientific_journal-7932	69	26	≤	≤	NUM
american_scientific_journal-7932	69	27	1.86	1.86	NUM
american_scientific_journal-7932	69	28	×	×	NOUN
american_scientific_journal-7932	69	29	10−7	10−7	NUM
american_scientific_journal-7932	69	30	m2s−1	m2s−1	NOUN
american_scientific_journal-7932	69	31	hence	hence	ADV
american_scientific_journal-7932	69	32	,	,	PUNCT
american_scientific_journal-7932	69	33	based	base	VERB
american_scientific_journal-7932	69	34	on	on	ADP
american_scientific_journal-7932	69	35	this	this	PRON
american_scientific_journal-7932	69	36	,	,	PUNCT
american_scientific_journal-7932	69	37	the	the	DET
american_scientific_journal-7932	69	38	values	value	NOUN
american_scientific_journal-7932	69	39	ω𝑗	ω𝑗	X
american_scientific_journal-7932	69	40	and	and	CCONJ
american_scientific_journal-7932	69	41	𝜈	𝜈	X
american_scientific_journal-7932	69	42	have	have	AUX
american_scientific_journal-7932	69	43	been	be	AUX
american_scientific_journal-7932	69	44	chosen	choose	VERB
american_scientific_journal-7932	69	45	.	.	PUNCT
american_scientific_journal-7932	70	1	it	it	PRON
american_scientific_journal-7932	70	2	should	should	AUX
american_scientific_journal-7932	70	3	be	be	AUX
american_scientific_journal-7932	70	4	noted	note	VERB
american_scientific_journal-7932	70	5	that	that	SCONJ
american_scientific_journal-7932	70	6	various	various	ADJ
american_scientific_journal-7932	70	7	values	value	NOUN
american_scientific_journal-7932	70	8	of	of	ADP
american_scientific_journal-7932	70	9	𝛼𝑖	𝛼𝑖	PRON
american_scientific_journal-7932	70	10	correspond	correspond	VERB
american_scientific_journal-7932	70	11	to	to	ADP
american_scientific_journal-7932	70	12	different	different	ADJ
american_scientific_journal-7932	70	13	frequencies	frequency	NOUN
american_scientific_journal-7932	70	14	.	.	PUNCT
american_scientific_journal-7932	71	1	figures	figure	NOUN
american_scientific_journal-7932	71	2	1	1	NUM
american_scientific_journal-7932	71	3	and	and	CCONJ
american_scientific_journal-7932	71	4	2	2	NUM
american_scientific_journal-7932	71	5	illustrate	illustrate	VERB
american_scientific_journal-7932	71	6	the	the	DET
american_scientific_journal-7932	71	7	effects	effect	NOUN
american_scientific_journal-7932	71	8	of	of	ADP
american_scientific_journal-7932	71	9	different	different	ADJ
american_scientific_journal-7932	71	10	frequencies	frequency	NOUN
american_scientific_journal-7932	71	11	of	of	ADP
american_scientific_journal-7932	71	12	oscillations	oscillation	NOUN
american_scientific_journal-7932	71	13	in	in	ADP
american_scientific_journal-7932	71	14	the	the	DET
american_scientific_journal-7932	71	15	torsional	torsional	ADJ
american_scientific_journal-7932	71	16	and	and	CCONJ
american_scientific_journal-7932	71	17	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	71	18	directions	direction	NOUN
american_scientific_journal-7932	71	19	of	of	ADP
american_scientific_journal-7932	71	20	the	the	DET
american_scientific_journal-7932	71	21	velocity	velocity	NOUN
american_scientific_journal-7932	71	22	components	component	NOUN
american_scientific_journal-7932	71	23	respectively	respectively	ADV
american_scientific_journal-7932	71	24	.	.	PUNCT
american_scientific_journal-7932	72	1	the	the	DET
american_scientific_journal-7932	72	2	torsional	torsional	ADJ
american_scientific_journal-7932	72	3	frequency	frequency	NOUN
american_scientific_journal-7932	72	4	is	be	AUX
american_scientific_journal-7932	72	5	taken	take	VERB
american_scientific_journal-7932	72	6	to	to	PART
american_scientific_journal-7932	72	7	be	be	AUX
american_scientific_journal-7932	72	8	the	the	DET
american_scientific_journal-7932	72	9	same	same	ADJ
american_scientific_journal-7932	72	10	as	as	ADP
american_scientific_journal-7932	72	11	that	that	PRON
american_scientific_journal-7932	72	12	in	in	ADP
american_scientific_journal-7932	72	13	[	[	X
american_scientific_journal-7932	72	14	3	3	NUM
american_scientific_journal-7932	72	15	]	]	PUNCT
american_scientific_journal-7932	72	16	,	,	PUNCT
american_scientific_journal-7932	72	17	which	which	PRON
american_scientific_journal-7932	72	18	is	be	AUX
american_scientific_journal-7932	72	19	different	different	ADJ
american_scientific_journal-7932	72	20	to	to	ADP
american_scientific_journal-7932	72	21	the	the	DET
american_scientific_journal-7932	72	22	higher	high	ADJ
american_scientific_journal-7932	72	23	frequency	frequency	NOUN
american_scientific_journal-7932	72	24	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	72	25	oscillation	oscillation	NOUN
american_scientific_journal-7932	72	26	in	in	ADP
american_scientific_journal-7932	72	27	figure	figure	NOUN
american_scientific_journal-7932	72	28	2	2	NUM
american_scientific_journal-7932	72	29	.	.	PUNCT
american_scientific_journal-7932	73	1	it	it	PRON
american_scientific_journal-7932	73	2	is	be	AUX
american_scientific_journal-7932	73	3	observed	observe	VERB
american_scientific_journal-7932	73	4	,	,	PUNCT
american_scientific_journal-7932	73	5	when	when	SCONJ
american_scientific_journal-7932	73	6	also	also	ADV
american_scientific_journal-7932	73	7	comparing	compare	VERB
american_scientific_journal-7932	73	8	with	with	ADP
american_scientific_journal-7932	73	9	figure	figure	NOUN
american_scientific_journal-7932	73	10	4	4	NUM
american_scientific_journal-7932	73	11	which	which	PRON
american_scientific_journal-7932	73	12	has	have	VERB
american_scientific_journal-7932	73	13	the	the	DET
american_scientific_journal-7932	73	14	same	same	ADJ
american_scientific_journal-7932	73	15	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	73	16	frequency	frequency	NOUN
american_scientific_journal-7932	73	17	as	as	ADP
american_scientific_journal-7932	73	18	in	in	ADP
american_scientific_journal-7932	73	19	[	[	X
american_scientific_journal-7932	73	20	3	3	NUM
american_scientific_journal-7932	73	21	]	]	PUNCT
american_scientific_journal-7932	73	22	,	,	PUNCT
american_scientific_journal-7932	73	23	that	that	SCONJ
american_scientific_journal-7932	73	24	the	the	DET
american_scientific_journal-7932	73	25	magnitude	magnitude	NOUN
american_scientific_journal-7932	73	26	of	of	ADP
american_scientific_journal-7932	73	27	the	the	DET
american_scientific_journal-7932	73	28	higher	high	ADJ
american_scientific_journal-7932	73	29	frequency	frequency	NOUN
american_scientific_journal-7932	73	30	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	73	31	component	component	NOUN
american_scientific_journal-7932	73	32	of	of	ADP
american_scientific_journal-7932	73	33	the	the	DET
american_scientific_journal-7932	73	34	velocity	velocity	NOUN
american_scientific_journal-7932	73	35	field	field	NOUN
american_scientific_journal-7932	73	36	is	be	AUX
american_scientific_journal-7932	73	37	smaller	smaller	ADV
american_scientific_journal-7932	73	38	closer	close	ADJ
american_scientific_journal-7932	73	39	to	to	ADP
american_scientific_journal-7932	73	40	the	the	DET
american_scientific_journal-7932	73	41	centre	centre	NOUN
american_scientific_journal-7932	73	42	of	of	ADP
american_scientific_journal-7932	73	43	the	the	DET
american_scientific_journal-7932	73	44	cylinder	cylinder	NOUN
american_scientific_journal-7932	73	45	.	.	PUNCT
american_scientific_journal-7932	74	1	as	as	ADP
american_scientific_journal-7932	74	2	a	a	DET
american_scientific_journal-7932	74	3	result	result	NOUN
american_scientific_journal-7932	74	4	,	,	PUNCT
american_scientific_journal-7932	74	5	the	the	DET
american_scientific_journal-7932	74	6	overall	overall	ADJ
american_scientific_journal-7932	74	7	velocity	velocity	NOUN
american_scientific_journal-7932	74	8	field	field	NOUN
american_scientific_journal-7932	74	9	in	in	ADP
american_scientific_journal-7932	74	10	this	this	DET
american_scientific_journal-7932	74	11	case	case	NOUN
american_scientific_journal-7932	74	12	would	would	AUX
american_scientific_journal-7932	74	13	have	have	VERB
american_scientific_journal-7932	74	14	a	a	DET
american_scientific_journal-7932	74	15	greater	great	ADJ
american_scientific_journal-7932	74	16	contribution	contribution	NOUN
american_scientific_journal-7932	74	17	from	from	ADP
american_scientific_journal-7932	74	18	the	the	DET
american_scientific_journal-7932	74	19	torsional	torsional	ADJ
american_scientific_journal-7932	74	20	component	component	NOUN
american_scientific_journal-7932	74	21	.	.	PUNCT
american_scientific_journal-7932	75	1	the	the	DET
american_scientific_journal-7932	75	2	general	general	ADJ
american_scientific_journal-7932	75	3	characteristic	characteristic	ADJ
american_scientific_journal-7932	75	4	shapes	shape	NOUN
american_scientific_journal-7932	75	5	of	of	ADP
american_scientific_journal-7932	75	6	the	the	DET
american_scientific_journal-7932	75	7	curves	curve	NOUN
american_scientific_journal-7932	75	8	are	be	AUX
american_scientific_journal-7932	75	9	however	however	ADV
american_scientific_journal-7932	75	10	similar	similar	ADJ
american_scientific_journal-7932	75	11	.	.	PUNCT
american_scientific_journal-7932	76	1	figures	figure	NOUN
american_scientific_journal-7932	76	2	3	3	NUM
american_scientific_journal-7932	76	3	and	and	CCONJ
american_scientific_journal-7932	76	4	4	4	NUM
american_scientific_journal-7932	76	5	also	also	ADV
american_scientific_journal-7932	76	6	show	show	VERB
american_scientific_journal-7932	76	7	the	the	DET
american_scientific_journal-7932	76	8	effects	effect	NOUN
american_scientific_journal-7932	76	9	of	of	ADP
american_scientific_journal-7932	76	10	different	different	ADJ
american_scientific_journal-7932	76	11	frequencies	frequency	NOUN
american_scientific_journal-7932	76	12	of	of	ADP
american_scientific_journal-7932	76	13	oscillations	oscillation	NOUN
american_scientific_journal-7932	76	14	in	in	ADP
american_scientific_journal-7932	76	15	the	the	DET
american_scientific_journal-7932	76	16	torsional	torsional	ADJ
american_scientific_journal-7932	76	17	and	and	CCONJ
american_scientific_journal-7932	76	18	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	76	19	directions	direction	NOUN
american_scientific_journal-7932	76	20	of	of	ADP
american_scientific_journal-7932	76	21	the	the	DET
american_scientific_journal-7932	76	22	velocity	velocity	NOUN
american_scientific_journal-7932	76	23	components	component	NOUN
american_scientific_journal-7932	76	24	respectively	respectively	ADV
american_scientific_journal-7932	76	25	.	.	PUNCT
american_scientific_journal-7932	77	1	american	american	ADJ
american_scientific_journal-7932	77	2	academic	academic	ADJ
american_scientific_journal-7932	77	3	scientific	scientific	ADJ
american_scientific_journal-7932	77	4	research	research	NOUN
american_scientific_journal-7932	77	5	journal	journal	NOUN
american_scientific_journal-7932	77	6	for	for	ADP
american_scientific_journal-7932	77	7	engineering	engineering	NOUN
american_scientific_journal-7932	77	8	,	,	PUNCT
american_scientific_journal-7932	77	9	technology	technology	NOUN
american_scientific_journal-7932	77	10	,	,	PUNCT
american_scientific_journal-7932	77	11	and	and	CCONJ
american_scientific_journal-7932	77	12	sciences	science	NOUN
american_scientific_journal-7932	77	13	(	(	PUNCT
american_scientific_journal-7932	77	14	asrjets	asrjet	NOUN
american_scientific_journal-7932	77	15	)	)	PUNCT
american_scientific_journal-7932	77	16	(	(	PUNCT
american_scientific_journal-7932	77	17	2022	2022	NUM
american_scientific_journal-7932	77	18	)	)	PUNCT
american_scientific_journal-7932	77	19	volume	volume	NOUN
american_scientific_journal-7932	77	20	89	89	NUM
american_scientific_journal-7932	77	21	,	,	PUNCT
american_scientific_journal-7932	77	22	no	no	DET
american_scientific_journal-7932	77	23	1	1	NUM
american_scientific_journal-7932	77	24	,	,	PUNCT
american_scientific_journal-7932	77	25	pp229	pp229	NOUN
american_scientific_journal-7932	77	26	-	-	PUNCT
american_scientific_journal-7932	77	27	240	240	NUM
american_scientific_journal-7932	77	28	237	237	NUM
american_scientific_journal-7932	77	29	the	the	DET
american_scientific_journal-7932	77	30	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	77	31	frequency	frequency	NOUN
american_scientific_journal-7932	77	32	is	be	AUX
american_scientific_journal-7932	77	33	now	now	ADV
american_scientific_journal-7932	77	34	taken	take	VERB
american_scientific_journal-7932	77	35	to	to	PART
american_scientific_journal-7932	77	36	be	be	AUX
american_scientific_journal-7932	77	37	the	the	DET
american_scientific_journal-7932	77	38	same	same	ADJ
american_scientific_journal-7932	77	39	as	as	ADP
american_scientific_journal-7932	77	40	that	that	PRON
american_scientific_journal-7932	77	41	in	in	ADP
american_scientific_journal-7932	77	42	[	[	X
american_scientific_journal-7932	77	43	3	3	NUM
american_scientific_journal-7932	77	44	]	]	PUNCT
american_scientific_journal-7932	77	45	,	,	PUNCT
american_scientific_journal-7932	77	46	which	which	PRON
american_scientific_journal-7932	77	47	is	be	AUX
american_scientific_journal-7932	77	48	different	different	ADJ
american_scientific_journal-7932	77	49	to	to	ADP
american_scientific_journal-7932	77	50	the	the	DET
american_scientific_journal-7932	77	51	torsionafrequency	torsionafrequency	NOUN
american_scientific_journal-7932	77	52	figure	figure	NOUN
american_scientific_journal-7932	77	53	1	1	NUM
american_scientific_journal-7932	77	54	:	:	PUNCT
american_scientific_journal-7932	77	55	𝑅	𝑅	PROPN
american_scientific_journal-7932	77	56	𝑎	𝑎	PROPN
american_scientific_journal-7932	77	57	versus	versus	ADP
american_scientific_journal-7932	77	58	𝑣(𝑅,𝑡	𝑣(𝑅,𝑡	NOUN
american_scientific_journal-7932	77	59	)	)	PUNCT
american_scientific_journal-7932	77	60	𝑞0	𝑞0	NOUN
american_scientific_journal-7932	77	61	cos𝛽	cos𝛽	NOUN
american_scientific_journal-7932	77	62	,	,	PUNCT
american_scientific_journal-7932	77	63	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	77	64	=	=	SYM
american_scientific_journal-7932	77	65	6	6	NUM
american_scientific_journal-7932	77	66	figure	figure	NOUN
american_scientific_journal-7932	77	67	2	2	NUM
american_scientific_journal-7932	77	68	:	:	PUNCT
american_scientific_journal-7932	77	69	𝑅	𝑅	PROPN
american_scientific_journal-7932	77	70	𝑎	𝑎	NOUN
american_scientific_journal-7932	77	71	versus	versus	X
american_scientific_journal-7932	77	72	𝑤(𝑅,𝑡	𝑤(𝑅,𝑡	NOUN
american_scientific_journal-7932	77	73	)	)	PUNCT
american_scientific_journal-7932	77	74	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	77	75	sin	sin	NOUN
american_scientific_journal-7932	77	76	𝛽	𝛽	PROPN
american_scientific_journal-7932	77	77	,	,	PUNCT
american_scientific_journal-7932	77	78	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	77	79	=	=	SYM
american_scientific_journal-7932	77	80	10	10	NUM
american_scientific_journal-7932	77	81	figure	figure	NOUN
american_scientific_journal-7932	77	82	3	3	NUM
american_scientific_journal-7932	77	83	:	:	PUNCT
american_scientific_journal-7932	77	84	𝑅	𝑅	PROPN
american_scientific_journal-7932	77	85	𝑎	𝑎	PROPN
american_scientific_journal-7932	77	86	versus	versus	ADP
american_scientific_journal-7932	77	87	𝑣(𝑅,𝑡	𝑣(𝑅,𝑡	NOUN
american_scientific_journal-7932	77	88	)	)	PUNCT
american_scientific_journal-7932	77	89	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	77	90	cos	cos	ADP
american_scientific_journal-7932	77	91	𝛽	𝛽	PROPN
american_scientific_journal-7932	77	92	,	,	PUNCT
american_scientific_journal-7932	77	93	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	77	94	=	=	SYM
american_scientific_journal-7932	77	95	10	10	NUM
american_scientific_journal-7932	77	96	figure	figure	NOUN
american_scientific_journal-7932	77	97	4	4	NUM
american_scientific_journal-7932	77	98	:	:	PUNCT
american_scientific_journal-7932	77	99	𝑅	𝑅	PROPN
american_scientific_journal-7932	77	100	𝑎	𝑎	NOUN
american_scientific_journal-7932	77	101	versus	versus	X
american_scientific_journal-7932	77	102	𝑤(𝑅,𝑡	𝑤(𝑅,𝑡	NOUN
american_scientific_journal-7932	77	103	)	)	PUNCT
american_scientific_journal-7932	77	104	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	77	105	sin	sin	NOUN
american_scientific_journal-7932	77	106	𝛽	𝛽	PROPN
american_scientific_journal-7932	77	107	,	,	PUNCT
american_scientific_journal-7932	77	108	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	77	109	=	=	SYM
american_scientific_journal-7932	77	110	6	6	NUM
american_scientific_journal-7932	77	111	american	american	ADJ
american_scientific_journal-7932	77	112	academic	academic	ADJ
american_scientific_journal-7932	77	113	scientific	scientific	ADJ
american_scientific_journal-7932	77	114	research	research	NOUN
american_scientific_journal-7932	77	115	journal	journal	NOUN
american_scientific_journal-7932	77	116	for	for	ADP
american_scientific_journal-7932	77	117	engineering	engineering	NOUN
american_scientific_journal-7932	77	118	,	,	PUNCT
american_scientific_journal-7932	77	119	technology	technology	NOUN
american_scientific_journal-7932	77	120	,	,	PUNCT
american_scientific_journal-7932	77	121	and	and	CCONJ
american_scientific_journal-7932	77	122	sciences	science	NOUN
american_scientific_journal-7932	77	123	(	(	PUNCT
american_scientific_journal-7932	77	124	asrjets	asrjet	NOUN
american_scientific_journal-7932	77	125	)	)	PUNCT
american_scientific_journal-7932	77	126	(	(	PUNCT
american_scientific_journal-7932	77	127	2022	2022	NUM
american_scientific_journal-7932	77	128	)	)	PUNCT
american_scientific_journal-7932	77	129	volume	volume	NOUN
american_scientific_journal-7932	77	130	89	89	NUM
american_scientific_journal-7932	77	131	,	,	PUNCT
american_scientific_journal-7932	77	132	no	no	DET
american_scientific_journal-7932	77	133	1	1	NUM
american_scientific_journal-7932	77	134	,	,	PUNCT
american_scientific_journal-7932	77	135	pp229	pp229	NOUN
american_scientific_journal-7932	77	136	-	-	PUNCT
american_scientific_journal-7932	77	137	240	240	NUM
american_scientific_journal-7932	77	138	238	238	NUM
american_scientific_journal-7932	77	139	in	in	ADP
american_scientific_journal-7932	77	140	figure	figure	NOUN
american_scientific_journal-7932	77	141	3	3	X
american_scientific_journal-7932	77	142	.	.	PUNCT
american_scientific_journal-7932	78	1	it	it	PRON
american_scientific_journal-7932	78	2	is	be	AUX
american_scientific_journal-7932	78	3	observed	observe	VERB
american_scientific_journal-7932	78	4	,	,	PUNCT
american_scientific_journal-7932	78	5	when	when	SCONJ
american_scientific_journal-7932	78	6	also	also	ADV
american_scientific_journal-7932	78	7	comparing	compare	VERB
american_scientific_journal-7932	78	8	with	with	ADP
american_scientific_journal-7932	78	9	figure	figure	NOUN
american_scientific_journal-7932	78	10	1	1	NUM
american_scientific_journal-7932	78	11	,	,	PUNCT
american_scientific_journal-7932	78	12	which	which	PRON
american_scientific_journal-7932	78	13	has	have	VERB
american_scientific_journal-7932	78	14	the	the	DET
american_scientific_journal-7932	78	15	same	same	ADJ
american_scientific_journal-7932	78	16	torsional	torsional	ADJ
american_scientific_journal-7932	78	17	frequency	frequency	NOUN
american_scientific_journal-7932	78	18	as	as	ADP
american_scientific_journal-7932	78	19	in	in	ADP
american_scientific_journal-7932	78	20	[	[	X
american_scientific_journal-7932	78	21	3	3	NUM
american_scientific_journal-7932	78	22	]	]	PUNCT
american_scientific_journal-7932	78	23	,	,	PUNCT
american_scientific_journal-7932	78	24	that	that	SCONJ
american_scientific_journal-7932	78	25	the	the	DET
american_scientific_journal-7932	78	26	magnitude	magnitude	NOUN
american_scientific_journal-7932	78	27	of	of	ADP
american_scientific_journal-7932	78	28	the	the	DET
american_scientific_journal-7932	78	29	higher	high	ADJ
american_scientific_journal-7932	78	30	frequency	frequency	NOUN
american_scientific_journal-7932	78	31	torsional	torsional	ADJ
american_scientific_journal-7932	78	32	component	component	NOUN
american_scientific_journal-7932	78	33	of	of	ADP
american_scientific_journal-7932	78	34	the	the	DET
american_scientific_journal-7932	78	35	velocity	velocity	NOUN
american_scientific_journal-7932	78	36	field	field	NOUN
american_scientific_journal-7932	78	37	is	be	AUX
american_scientific_journal-7932	78	38	smaller	smaller	ADV
american_scientific_journal-7932	78	39	closer	close	ADJ
american_scientific_journal-7932	78	40	to	to	ADP
american_scientific_journal-7932	78	41	the	the	DET
american_scientific_journal-7932	78	42	centre	centre	NOUN
american_scientific_journal-7932	78	43	of	of	ADP
american_scientific_journal-7932	78	44	the	the	DET
american_scientific_journal-7932	78	45	cylinder	cylinder	NOUN
american_scientific_journal-7932	78	46	.	.	PUNCT
american_scientific_journal-7932	79	1	as	as	ADP
american_scientific_journal-7932	79	2	a	a	DET
american_scientific_journal-7932	79	3	result	result	NOUN
american_scientific_journal-7932	79	4	,	,	PUNCT
american_scientific_journal-7932	79	5	the	the	DET
american_scientific_journal-7932	79	6	overall	overall	ADJ
american_scientific_journal-7932	79	7	velocity	velocity	NOUN
american_scientific_journal-7932	79	8	field	field	NOUN
american_scientific_journal-7932	79	9	in	in	ADP
american_scientific_journal-7932	79	10	this	this	DET
american_scientific_journal-7932	79	11	case	case	NOUN
american_scientific_journal-7932	79	12	would	would	AUX
american_scientific_journal-7932	79	13	have	have	VERB
american_scientific_journal-7932	79	14	a	a	DET
american_scientific_journal-7932	79	15	greater	great	ADJ
american_scientific_journal-7932	79	16	contribution	contribution	NOUN
american_scientific_journal-7932	79	17	from	from	ADP
american_scientific_journal-7932	79	18	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	79	19	component	component	NOUN
american_scientific_journal-7932	79	20	.	.	PUNCT
american_scientific_journal-7932	80	1	the	the	DET
american_scientific_journal-7932	80	2	general	general	ADJ
american_scientific_journal-7932	80	3	characteristic	characteristic	ADJ
american_scientific_journal-7932	80	4	shapes	shape	NOUN
american_scientific_journal-7932	80	5	of	of	ADP
american_scientific_journal-7932	80	6	the	the	DET
american_scientific_journal-7932	80	7	curves	curve	NOUN
american_scientific_journal-7932	80	8	are	be	AUX
american_scientific_journal-7932	80	9	again	again	ADV
american_scientific_journal-7932	80	10	similar	similar	ADJ
american_scientific_journal-7932	80	11	.	.	PUNCT
american_scientific_journal-7932	81	1	as	as	ADP
american_scientific_journal-7932	81	2	a	a	DET
american_scientific_journal-7932	81	3	result	result	NOUN
american_scientific_journal-7932	81	4	,	,	PUNCT
american_scientific_journal-7932	81	5	it	it	PRON
american_scientific_journal-7932	81	6	seems	seem	VERB
american_scientific_journal-7932	81	7	that	that	SCONJ
american_scientific_journal-7932	81	8	in	in	ADP
american_scientific_journal-7932	81	9	each	each	DET
american_scientific_journal-7932	81	10	case	case	NOUN
american_scientific_journal-7932	81	11	of	of	ADP
american_scientific_journal-7932	81	12	different	different	ADJ
american_scientific_journal-7932	81	13	frequencies	frequency	NOUN
american_scientific_journal-7932	81	14	,	,	PUNCT
american_scientific_journal-7932	81	15	that	that	SCONJ
american_scientific_journal-7932	81	16	with	with	ADP
american_scientific_journal-7932	81	17	the	the	DET
american_scientific_journal-7932	81	18	higher	high	ADJ
american_scientific_journal-7932	81	19	one	one	NOUN
american_scientific_journal-7932	81	20	seems	seem	VERB
american_scientific_journal-7932	81	21	to	to	PART
american_scientific_journal-7932	81	22	suppress	suppress	VERB
american_scientific_journal-7932	81	23	the	the	DET
american_scientific_journal-7932	81	24	magnitude	magnitude	NOUN
american_scientific_journal-7932	81	25	of	of	ADP
american_scientific_journal-7932	81	26	that	that	DET
american_scientific_journal-7932	81	27	component	component	NOUN
american_scientific_journal-7932	81	28	of	of	ADP
american_scientific_journal-7932	81	29	the	the	DET
american_scientific_journal-7932	81	30	velocity	velocity	NOUN
american_scientific_journal-7932	81	31	field	field	NOUN
american_scientific_journal-7932	81	32	closer	close	ADV
american_scientific_journal-7932	81	33	to	to	ADP
american_scientific_journal-7932	81	34	the	the	DET
american_scientific_journal-7932	81	35	centre	centre	NOUN
american_scientific_journal-7932	81	36	of	of	ADP
american_scientific_journal-7932	81	37	the	the	DET
american_scientific_journal-7932	81	38	oscillating	oscillate	VERB
american_scientific_journal-7932	81	39	cylinder	cylinder	NOUN
american_scientific_journal-7932	81	40	.	.	PUNCT
american_scientific_journal-7932	82	1	in	in	ADP
american_scientific_journal-7932	82	2	figures	figure	NOUN
american_scientific_journal-7932	82	3	5	5	NUM
american_scientific_journal-7932	82	4	and	and	CCONJ
american_scientific_journal-7932	82	5	6	6	NUM
american_scientific_journal-7932	82	6	,	,	PUNCT
american_scientific_journal-7932	82	7	the	the	DET
american_scientific_journal-7932	82	8	�	�	PROPN
american_scientific_journal-7932	82	9	̂	̂	SYM
american_scientific_journal-7932	82	10	�	�	PROPN
american_scientific_journal-7932	82	11	component	component	NOUN
american_scientific_journal-7932	82	12	of	of	ADP
american_scientific_journal-7932	82	13	the	the	DET
american_scientific_journal-7932	82	14	drag	drag	NOUN
american_scientific_journal-7932	82	15	is	be	AUX
american_scientific_journal-7932	82	16	depicted	depict	VERB
american_scientific_journal-7932	82	17	graphically	graphically	ADV
american_scientific_journal-7932	82	18	for	for	ADP
american_scientific_journal-7932	82	19	different	different	ADJ
american_scientific_journal-7932	82	20	values	value	NOUN
american_scientific_journal-7932	82	21	of	of	ADP
american_scientific_journal-7932	82	22	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	82	23	.	.	PUNCT
american_scientific_journal-7932	83	1	similarly	similarly	ADV
american_scientific_journal-7932	83	2	,	,	PUNCT
american_scientific_journal-7932	83	3	figures	figure	VERB
american_scientific_journal-7932	83	4	7	7	NUM
american_scientific_journal-7932	83	5	and	and	CCONJ
american_scientific_journal-7932	83	6	8	8	NUM
american_scientific_journal-7932	83	7	display	display	VERB
american_scientific_journal-7932	83	8	the	the	DET
american_scientific_journal-7932	83	9	�	�	PROPN
american_scientific_journal-7932	83	10	̂	̂	SYM
american_scientific_journal-7932	83	11	�	�	PROPN
american_scientific_journal-7932	83	12	component	component	NOUN
american_scientific_journal-7932	83	13	of	of	ADP
american_scientific_journal-7932	83	14	the	the	DET
american_scientific_journal-7932	83	15	drag	drag	NOUN
american_scientific_journal-7932	83	16	for	for	ADP
american_scientific_journal-7932	83	17	different	different	ADJ
american_scientific_journal-7932	83	18	values	value	NOUN
american_scientific_journal-7932	83	19	of	of	ADP
american_scientific_journal-7932	83	20	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	83	21	.	.	PUNCT
american_scientific_journal-7932	84	1	the	the	DET
american_scientific_journal-7932	84	2	magnitude	magnitude	NOUN
american_scientific_journal-7932	84	3	of	of	ADP
american_scientific_journal-7932	84	4	the	the	DET
american_scientific_journal-7932	84	5	drag	drag	NOUN
american_scientific_journal-7932	84	6	in	in	ADP
american_scientific_journal-7932	84	7	the	the	DET
american_scientific_journal-7932	84	8	�	�	PROPN
american_scientific_journal-7932	84	9	̂	̂	SYM
american_scientific_journal-7932	84	10	�	�	PROPN
american_scientific_journal-7932	84	11	direction	direction	NOUN
american_scientific_journal-7932	84	12	oscillates	oscillate	NOUN
american_scientific_journal-7932	84	13	between	between	ADP
american_scientific_journal-7932	84	14	negative	negative	ADJ
american_scientific_journal-7932	84	15	values	value	NOUN
american_scientific_journal-7932	84	16	,	,	PUNCT
american_scientific_journal-7932	84	17	while	while	SCONJ
american_scientific_journal-7932	84	18	the	the	DET
american_scientific_journal-7932	84	19	magnitude	magnitude	NOUN
american_scientific_journal-7932	84	20	in	in	ADP
american_scientific_journal-7932	84	21	the	the	DET
american_scientific_journal-7932	84	22	�	�	PROPN
american_scientific_journal-7932	84	23	̂	̂	SYM
american_scientific_journal-7932	84	24	�	�	PROPN
american_scientific_journal-7932	84	25	direction	direction	NOUN
american_scientific_journal-7932	84	26	oscillates	oscillate	NOUN
american_scientific_journal-7932	84	27	between	between	ADP
american_scientific_journal-7932	84	28	positive	positive	ADJ
american_scientific_journal-7932	84	29	and	and	CCONJ
american_scientific_journal-7932	84	30	negative	negative	ADJ
american_scientific_journal-7932	84	31	values	value	NOUN
american_scientific_journal-7932	84	32	.	.	PUNCT
american_scientific_journal-7932	85	1	it	it	PRON
american_scientific_journal-7932	85	2	is	be	AUX
american_scientific_journal-7932	85	3	noted	note	VERB
american_scientific_journal-7932	85	4	that	that	SCONJ
american_scientific_journal-7932	85	5	for	for	ADP
american_scientific_journal-7932	85	6	each	each	DET
american_scientific_journal-7932	85	7	component	component	NOUN
american_scientific_journal-7932	85	8	,	,	PUNCT
american_scientific_journal-7932	85	9	when	when	SCONJ
american_scientific_journal-7932	85	10	the	the	DET
american_scientific_journal-7932	85	11	oscillating	oscillate	VERB
american_scientific_journal-7932	85	12	frequencies	frequency	NOUN
american_scientific_journal-7932	85	13	increase	increase	VERB
american_scientific_journal-7932	85	14	,	,	PUNCT
american_scientific_journal-7932	85	15	such	such	ADJ
american_scientific_journal-7932	85	16	results	result	NOUN
american_scientific_journal-7932	85	17	in	in	ADP
american_scientific_journal-7932	85	18	an	an	DET
american_scientific_journal-7932	85	19	increase	increase	NOUN
american_scientific_journal-7932	85	20	in	in	ADP
american_scientific_journal-7932	85	21	the	the	DET
american_scientific_journal-7932	85	22	respective	respective	ADJ
american_scientific_journal-7932	85	23	magnitudes	magnitude	NOUN
american_scientific_journal-7932	85	24	.	.	PUNCT
american_scientific_journal-7932	86	1	figure	figure	NOUN
american_scientific_journal-7932	86	2	5	5	NUM
american_scientific_journal-7932	86	3	:	:	PUNCT
american_scientific_journal-7932	86	4	𝐷𝜃	𝐷𝜃	PART
american_scientific_journal-7932	86	5	𝑞0	𝑞0	VERB
american_scientific_journal-7932	86	6	μ	μ	PROPN
american_scientific_journal-7932	86	7	cos	cos	PROPN
american_scientific_journal-7932	86	8	𝛽	𝛽	PROPN
american_scientific_journal-7932	86	9	versus	versus	ADP
american_scientific_journal-7932	86	10	ω1𝑡	ω1𝑡	NUM
american_scientific_journal-7932	86	11	,	,	PUNCT
american_scientific_journal-7932	86	12	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	86	13	=	=	SYM
american_scientific_journal-7932	86	14	6	6	NUM
american_scientific_journal-7932	86	15	figure	figure	NOUN
american_scientific_journal-7932	86	16	6	6	NUM
american_scientific_journal-7932	86	17	:	:	PUNCT
american_scientific_journal-7932	86	18	𝐷𝜃	𝐷𝜃	PART
american_scientific_journal-7932	86	19	𝑞0	𝑞0	VERB
american_scientific_journal-7932	86	20	μ	μ	PROPN
american_scientific_journal-7932	86	21	cos	cos	PROPN
american_scientific_journal-7932	86	22	𝛽	𝛽	PROPN
american_scientific_journal-7932	86	23	versus	versus	ADP
american_scientific_journal-7932	86	24	ω1𝑡	ω1𝑡	NUM
american_scientific_journal-7932	86	25	,	,	PUNCT
american_scientific_journal-7932	86	26	𝛼1	𝛼1	NOUN
american_scientific_journal-7932	86	27	=	=	SYM
american_scientific_journal-7932	86	28	10	10	NUM
american_scientific_journal-7932	86	29	figure	figure	NOUN
american_scientific_journal-7932	86	30	7	7	NUM
american_scientific_journal-7932	86	31	:	:	PUNCT
american_scientific_journal-7932	86	32	𝐷𝑧	𝐷𝑧	PROPN
american_scientific_journal-7932	86	33	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	86	34	μ	μ	PROPN
american_scientific_journal-7932	86	35	sin	sin	PROPN
american_scientific_journal-7932	86	36	𝛽	𝛽	PROPN
american_scientific_journal-7932	86	37	versus	versus	ADP
american_scientific_journal-7932	86	38	ω2𝑡	ω2𝑡	NOUN
american_scientific_journal-7932	86	39	,	,	PUNCT
american_scientific_journal-7932	86	40	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	86	41	=	=	SYM
american_scientific_journal-7932	86	42	6	6	NUM
american_scientific_journal-7932	86	43	figure	figure	NOUN
american_scientific_journal-7932	86	44	8	8	NUM
american_scientific_journal-7932	86	45	:	:	PUNCT
american_scientific_journal-7932	86	46	𝐷𝑧	𝐷𝑧	PROPN
american_scientific_journal-7932	86	47	𝑞0	𝑞0	PROPN
american_scientific_journal-7932	86	48	μ	μ	PROPN
american_scientific_journal-7932	86	49	sin	sin	PROPN
american_scientific_journal-7932	86	50	𝛽	𝛽	PROPN
american_scientific_journal-7932	86	51	versus	versus	ADP
american_scientific_journal-7932	86	52	ω2𝑡	ω2𝑡	NOUN
american_scientific_journal-7932	86	53	,	,	PUNCT
american_scientific_journal-7932	86	54	𝛼2	𝛼2	PROPN
american_scientific_journal-7932	86	55	=	=	SYM
american_scientific_journal-7932	86	56	10	10	NUM
american_scientific_journal-7932	86	57	american	american	ADJ
american_scientific_journal-7932	86	58	academic	academic	ADJ
american_scientific_journal-7932	86	59	scientific	scientific	ADJ
american_scientific_journal-7932	86	60	research	research	NOUN
american_scientific_journal-7932	86	61	journal	journal	NOUN
american_scientific_journal-7932	86	62	for	for	ADP
american_scientific_journal-7932	86	63	engineering	engineering	NOUN
american_scientific_journal-7932	86	64	,	,	PUNCT
american_scientific_journal-7932	86	65	technology	technology	NOUN
american_scientific_journal-7932	86	66	,	,	PUNCT
american_scientific_journal-7932	86	67	and	and	CCONJ
american_scientific_journal-7932	86	68	sciences	science	NOUN
american_scientific_journal-7932	86	69	(	(	PUNCT
american_scientific_journal-7932	86	70	asrjets	asrjet	NOUN
american_scientific_journal-7932	86	71	)	)	PUNCT
american_scientific_journal-7932	86	72	(	(	PUNCT
american_scientific_journal-7932	86	73	2022	2022	NUM
american_scientific_journal-7932	86	74	)	)	PUNCT
american_scientific_journal-7932	86	75	volume	volume	NOUN
american_scientific_journal-7932	86	76	89	89	NUM
american_scientific_journal-7932	86	77	,	,	PUNCT
american_scientific_journal-7932	86	78	no	no	DET
american_scientific_journal-7932	86	79	1	1	NUM
american_scientific_journal-7932	86	80	,	,	PUNCT
american_scientific_journal-7932	86	81	pp229	pp229	NOUN
american_scientific_journal-7932	86	82	-	-	PUNCT
american_scientific_journal-7932	86	83	240	240	NUM
american_scientific_journal-7932	86	84	239	239	NUM
american_scientific_journal-7932	86	85	in	in	ADP
american_scientific_journal-7932	86	86	figure	figure	NOUN
american_scientific_journal-7932	86	87	9	9	NUM
american_scientific_journal-7932	86	88	,	,	PUNCT
american_scientific_journal-7932	86	89	the	the	DET
american_scientific_journal-7932	86	90	work	work	NOUN
american_scientific_journal-7932	86	91	done	do	VERB
american_scientific_journal-7932	86	92	in	in	ADP
american_scientific_journal-7932	86	93	the	the	DET
american_scientific_journal-7932	86	94	�	�	PROPN
american_scientific_journal-7932	86	95	̂	̂	SYM
american_scientific_journal-7932	86	96	�	�	PROPN
american_scientific_journal-7932	86	97	direction	direction	NOUN
american_scientific_journal-7932	86	98	is	be	AUX
american_scientific_journal-7932	86	99	depicted	depict	VERB
american_scientific_journal-7932	86	100	graphically	graphically	ADV
american_scientific_journal-7932	86	101	,	,	PUNCT
american_scientific_journal-7932	86	102	where	where	SCONJ
american_scientific_journal-7932	86	103	two	two	NUM
american_scientific_journal-7932	86	104	scenarios	scenario	NOUN
american_scientific_journal-7932	86	105	are	be	AUX
american_scientific_journal-7932	86	106	considered	consider	VERB
american_scientific_journal-7932	86	107	;	;	PUNCT
american_scientific_journal-7932	86	108	a	a	DET
american_scientific_journal-7932	86	109	plot	plot	NOUN
american_scientific_journal-7932	86	110	when	when	SCONJ
american_scientific_journal-7932	86	111	ω1	ω1	PROPN
american_scientific_journal-7932	86	112	=	=	PROPN
american_scientific_journal-7932	86	113	30	30	NUM
american_scientific_journal-7932	86	114	and	and	CCONJ
american_scientific_journal-7932	86	115	ω2	ω2	NOUN
american_scientific_journal-7932	86	116	=	=	SYM
american_scientific_journal-7932	86	117	60	60	NUM
american_scientific_journal-7932	86	118	,	,	PUNCT
american_scientific_journal-7932	86	119	and	and	CCONJ
american_scientific_journal-7932	86	120	another	another	PRON
american_scientific_journal-7932	86	121	when	when	SCONJ
american_scientific_journal-7932	86	122	ω1	ω1	PROPN
american_scientific_journal-7932	86	123	=	=	PROPN
american_scientific_journal-7932	86	124	60	60	NUM
american_scientific_journal-7932	86	125	and	and	CCONJ
american_scientific_journal-7932	86	126	ω2	ω2	ADJ
american_scientific_journal-7932	86	127	=	=	SYM
american_scientific_journal-7932	86	128	30	30	NUM
american_scientific_journal-7932	86	129	.	.	PUNCT
american_scientific_journal-7932	87	1	both	both	DET
american_scientific_journal-7932	87	2	graphs	graph	NOUN
american_scientific_journal-7932	87	3	are	be	AUX
american_scientific_journal-7932	87	4	periodic	periodic	ADJ
american_scientific_journal-7932	87	5	and	and	CCONJ
american_scientific_journal-7932	87	6	it	it	PRON
american_scientific_journal-7932	87	7	is	be	AUX
american_scientific_journal-7932	87	8	observed	observe	VERB
american_scientific_journal-7932	87	9	that	that	SCONJ
american_scientific_journal-7932	87	10	the	the	DET
american_scientific_journal-7932	87	11	magnitudes	magnitude	NOUN
american_scientific_journal-7932	87	12	are	be	AUX
american_scientific_journal-7932	87	13	negative	negative	ADJ
american_scientific_journal-7932	87	14	,	,	PUNCT
american_scientific_journal-7932	87	15	with	with	ADP
american_scientific_journal-7932	87	16	the	the	DET
american_scientific_journal-7932	87	17	amplitude	amplitude	NOUN
american_scientific_journal-7932	87	18	for	for	ADP
american_scientific_journal-7932	87	19	ω1	ω1	PROPN
american_scientific_journal-7932	87	20	=	=	SYM
american_scientific_journal-7932	87	21	30	30	NUM
american_scientific_journal-7932	87	22	and	and	CCONJ
american_scientific_journal-7932	87	23	ω2	ω2	NOUN
american_scientific_journal-7932	87	24	=	=	SYM
american_scientific_journal-7932	87	25	60	60	NUM
american_scientific_journal-7932	87	26	being	be	AUX
american_scientific_journal-7932	87	27	greater	great	ADJ
american_scientific_journal-7932	87	28	than	than	ADP
american_scientific_journal-7932	87	29	that	that	PRON
american_scientific_journal-7932	87	30	for	for	ADP
american_scientific_journal-7932	87	31	ω1	ω1	PROPN
american_scientific_journal-7932	87	32	=	=	SYM
american_scientific_journal-7932	87	33	60	60	NUM
american_scientific_journal-7932	87	34	and	and	CCONJ
american_scientific_journal-7932	87	35	ω2	ω2	ADJ
american_scientific_journal-7932	87	36	=	=	SYM
american_scientific_journal-7932	87	37	30	30	NUM
american_scientific_journal-7932	87	38	,	,	PUNCT
american_scientific_journal-7932	87	39	which	which	PRON
american_scientific_journal-7932	87	40	indicates	indicate	VERB
american_scientific_journal-7932	87	41	more	more	ADJ
american_scientific_journal-7932	87	42	work	work	NOUN
american_scientific_journal-7932	87	43	is	be	AUX
american_scientific_journal-7932	87	44	being	be	AUX
american_scientific_journal-7932	87	45	done	do	VERB
american_scientific_journal-7932	87	46	.	.	PUNCT
american_scientific_journal-7932	88	1	in	in	ADP
american_scientific_journal-7932	88	2	figure	figure	NOUN
american_scientific_journal-7932	88	3	10	10	NUM
american_scientific_journal-7932	88	4	,	,	PUNCT
american_scientific_journal-7932	88	5	the	the	DET
american_scientific_journal-7932	88	6	work	work	NOUN
american_scientific_journal-7932	88	7	done	do	VERB
american_scientific_journal-7932	88	8	in	in	ADP
american_scientific_journal-7932	88	9	the	the	DET
american_scientific_journal-7932	88	10	�	�	PROPN
american_scientific_journal-7932	88	11	̂	̂	SYM
american_scientific_journal-7932	88	12	�	�	PROPN
american_scientific_journal-7932	88	13	direction	direction	NOUN
american_scientific_journal-7932	88	14	is	be	AUX
american_scientific_journal-7932	88	15	examined	examine	VERB
american_scientific_journal-7932	88	16	for	for	ADP
american_scientific_journal-7932	88	17	two	two	NUM
american_scientific_journal-7932	88	18	cases	case	NOUN
american_scientific_journal-7932	88	19	,	,	PUNCT
american_scientific_journal-7932	88	20	in	in	ADP
american_scientific_journal-7932	88	21	particular	particular	ADJ
american_scientific_journal-7932	88	22	,	,	PUNCT
american_scientific_journal-7932	88	23	when	when	SCONJ
american_scientific_journal-7932	88	24	ω1	ω1	PROPN
american_scientific_journal-7932	88	25	=	=	PROPN
american_scientific_journal-7932	88	26	30	30	NUM
american_scientific_journal-7932	88	27	and	and	CCONJ
american_scientific_journal-7932	88	28	ω2	ω2	NOUN
american_scientific_journal-7932	88	29	=	=	SYM
american_scientific_journal-7932	88	30	60	60	NUM
american_scientific_journal-7932	88	31	,	,	PUNCT
american_scientific_journal-7932	88	32	and	and	CCONJ
american_scientific_journal-7932	88	33	when	when	SCONJ
american_scientific_journal-7932	88	34	ω1	ω1	PROPN
american_scientific_journal-7932	88	35	=	=	PROPN
american_scientific_journal-7932	88	36	60	60	NUM
american_scientific_journal-7932	88	37	and	and	CCONJ
american_scientific_journal-7932	88	38	ω2	ω2	ADJ
american_scientific_journal-7932	88	39	=	=	SYM
american_scientific_journal-7932	88	40	30	30	NUM
american_scientific_journal-7932	88	41	.	.	PUNCT
american_scientific_journal-7932	89	1	these	these	DET
american_scientific_journal-7932	89	2	plots	plot	NOUN
american_scientific_journal-7932	89	3	appear	appear	VERB
american_scientific_journal-7932	89	4	to	to	PART
american_scientific_journal-7932	89	5	be	be	AUX
american_scientific_journal-7932	89	6	periodic	periodic	ADJ
american_scientific_journal-7932	89	7	,	,	PUNCT
american_scientific_journal-7932	89	8	each	each	PRON
american_scientific_journal-7932	89	9	with	with	ADP
american_scientific_journal-7932	89	10	a	a	DET
american_scientific_journal-7932	89	11	negative	negative	ADJ
american_scientific_journal-7932	89	12	magnitude	magnitude	NOUN
american_scientific_journal-7932	89	13	.	.	PUNCT
american_scientific_journal-7932	90	1	the	the	DET
american_scientific_journal-7932	90	2	amplitude	amplitude	NOUN
american_scientific_journal-7932	90	3	of	of	ADP
american_scientific_journal-7932	90	4	the	the	DET
american_scientific_journal-7932	90	5	work	work	NOUN
american_scientific_journal-7932	90	6	done	do	VERB
american_scientific_journal-7932	90	7	in	in	ADP
american_scientific_journal-7932	90	8	this	this	DET
american_scientific_journal-7932	90	9	�	�	PROPN
american_scientific_journal-7932	90	10	̂	̂	SYM
american_scientific_journal-7932	90	11	�	�	PROPN
american_scientific_journal-7932	90	12	direction	direction	NOUN
american_scientific_journal-7932	90	13	when	when	SCONJ
american_scientific_journal-7932	90	14	ω1	ω1	PROPN
american_scientific_journal-7932	90	15	=	=	PROPN
american_scientific_journal-7932	90	16	60	60	NUM
american_scientific_journal-7932	90	17	and	and	CCONJ
american_scientific_journal-7932	90	18	ω2	ω2	ADJ
american_scientific_journal-7932	90	19	=	=	SYM
american_scientific_journal-7932	90	20	30	30	NUM
american_scientific_journal-7932	90	21	is	be	AUX
american_scientific_journal-7932	90	22	observed	observe	VERB
american_scientific_journal-7932	90	23	to	to	PART
american_scientific_journal-7932	90	24	be	be	AUX
american_scientific_journal-7932	90	25	larger	large	ADJ
american_scientific_journal-7932	90	26	than	than	ADP
american_scientific_journal-7932	90	27	when	when	SCONJ
american_scientific_journal-7932	90	28	ω1	ω1	PROPN
american_scientific_journal-7932	90	29	=	=	PROPN
american_scientific_journal-7932	90	30	30	30	NUM
american_scientific_journal-7932	90	31	and	and	CCONJ
american_scientific_journal-7932	90	32	ω2	ω2	NOUN
american_scientific_journal-7932	90	33	=	=	SYM
american_scientific_journal-7932	90	34	60	60	NUM
american_scientific_journal-7932	90	35	,	,	PUNCT
american_scientific_journal-7932	90	36	which	which	PRON
american_scientific_journal-7932	90	37	shows	show	VERB
american_scientific_journal-7932	90	38	that	that	SCONJ
american_scientific_journal-7932	90	39	more	more	ADJ
american_scientific_journal-7932	90	40	work	work	NOUN
american_scientific_journal-7932	90	41	is	be	AUX
american_scientific_journal-7932	90	42	being	be	AUX
american_scientific_journal-7932	90	43	done	do	VERB
american_scientific_journal-7932	90	44	.	.	PUNCT
american_scientific_journal-7932	91	1	6	6	X
american_scientific_journal-7932	91	2	.	.	X
american_scientific_journal-7932	91	3	conclusion	conclusion	VERB
american_scientific_journal-7932	91	4	the	the	DET
american_scientific_journal-7932	91	5	velocity	velocity	NOUN
american_scientific_journal-7932	91	6	of	of	ADP
american_scientific_journal-7932	91	7	the	the	DET
american_scientific_journal-7932	91	8	fluid	fluid	NOUN
american_scientific_journal-7932	91	9	is	be	AUX
american_scientific_journal-7932	91	10	affected	affect	VERB
american_scientific_journal-7932	91	11	if	if	SCONJ
american_scientific_journal-7932	91	12	the	the	DET
american_scientific_journal-7932	91	13	frequencies	frequency	NOUN
american_scientific_journal-7932	91	14	of	of	ADP
american_scientific_journal-7932	91	15	the	the	DET
american_scientific_journal-7932	91	16	cylinder	cylinder	NOUN
american_scientific_journal-7932	91	17	’s	’s	PART
american_scientific_journal-7932	91	18	oscillations	oscillation	NOUN
american_scientific_journal-7932	91	19	are	be	AUX
american_scientific_journal-7932	91	20	different	different	ADJ
american_scientific_journal-7932	91	21	,	,	PUNCT
american_scientific_journal-7932	91	22	as	as	SCONJ
american_scientific_journal-7932	91	23	was	be	AUX
american_scientific_journal-7932	91	24	observed	observe	VERB
american_scientific_journal-7932	91	25	when	when	SCONJ
american_scientific_journal-7932	91	26	compared	compare	VERB
american_scientific_journal-7932	91	27	to	to	ADP
american_scientific_journal-7932	91	28	when	when	SCONJ
american_scientific_journal-7932	91	29	the	the	DET
american_scientific_journal-7932	91	30	frequencies	frequency	NOUN
american_scientific_journal-7932	91	31	were	be	AUX
american_scientific_journal-7932	91	32	the	the	DET
american_scientific_journal-7932	91	33	same	same	ADJ
american_scientific_journal-7932	91	34	.	.	PUNCT
american_scientific_journal-7932	92	1	in	in	ADP
american_scientific_journal-7932	92	2	particular	particular	ADJ
american_scientific_journal-7932	92	3	,	,	PUNCT
american_scientific_journal-7932	92	4	it	it	PRON
american_scientific_journal-7932	92	5	was	be	AUX
american_scientific_journal-7932	92	6	noted	note	VERB
american_scientific_journal-7932	92	7	that	that	SCONJ
american_scientific_journal-7932	92	8	the	the	DET
american_scientific_journal-7932	92	9	higher	high	ADJ
american_scientific_journal-7932	92	10	oscillating	oscillate	VERB
american_scientific_journal-7932	92	11	frequency	frequency	NOUN
american_scientific_journal-7932	92	12	tended	tend	VERB
american_scientific_journal-7932	92	13	to	to	PART
american_scientific_journal-7932	92	14	suppress	suppress	VERB
american_scientific_journal-7932	92	15	the	the	DET
american_scientific_journal-7932	92	16	magnitude	magnitude	NOUN
american_scientific_journal-7932	92	17	of	of	ADP
american_scientific_journal-7932	92	18	the	the	DET
american_scientific_journal-7932	92	19	corresponding	corresponding	ADJ
american_scientific_journal-7932	92	20	component	component	NOUN
american_scientific_journal-7932	92	21	of	of	ADP
american_scientific_journal-7932	92	22	the	the	DET
american_scientific_journal-7932	92	23	velocity	velocity	NOUN
american_scientific_journal-7932	92	24	field	field	NOUN
american_scientific_journal-7932	92	25	closer	close	ADV
american_scientific_journal-7932	92	26	to	to	ADP
american_scientific_journal-7932	92	27	the	the	DET
american_scientific_journal-7932	92	28	centre	centre	NOUN
american_scientific_journal-7932	92	29	of	of	ADP
american_scientific_journal-7932	92	30	the	the	DET
american_scientific_journal-7932	92	31	cylinder	cylinder	NOUN
american_scientific_journal-7932	92	32	.	.	PUNCT
american_scientific_journal-7932	93	1	the	the	DET
american_scientific_journal-7932	93	2	magnitude	magnitude	NOUN
american_scientific_journal-7932	93	3	of	of	ADP
american_scientific_journal-7932	93	4	the	the	DET
american_scientific_journal-7932	93	5	drag	drag	NOUN
american_scientific_journal-7932	93	6	increased	increase	VERB
american_scientific_journal-7932	93	7	with	with	ADP
american_scientific_journal-7932	93	8	an	an	DET
american_scientific_journal-7932	93	9	increase	increase	NOUN
american_scientific_journal-7932	93	10	in	in	ADP
american_scientific_journal-7932	93	11	the	the	DET
american_scientific_journal-7932	93	12	oscillating	oscillate	VERB
american_scientific_journal-7932	93	13	frequency	frequency	NOUN
american_scientific_journal-7932	93	14	.	.	PUNCT
american_scientific_journal-7932	94	1	the	the	DET
american_scientific_journal-7932	94	2	work	work	NOUN
american_scientific_journal-7932	94	3	done	do	VERB
american_scientific_journal-7932	94	4	in	in	ADP
american_scientific_journal-7932	94	5	the	the	DET
american_scientific_journal-7932	94	6	�	�	PROPN
american_scientific_journal-7932	94	7	̂	̂	SYM
american_scientific_journal-7932	94	8	�	�	PROPN
american_scientific_journal-7932	94	9	direction	direction	NOUN
american_scientific_journal-7932	94	10	is	be	AUX
american_scientific_journal-7932	94	11	more	more	ADJ
american_scientific_journal-7932	94	12	when	when	SCONJ
american_scientific_journal-7932	94	13	the	the	DET
american_scientific_journal-7932	94	14	torsional	torsional	ADJ
american_scientific_journal-7932	94	15	frequency	frequency	NOUN
american_scientific_journal-7932	94	16	is	be	AUX
american_scientific_journal-7932	94	17	less	less	ADJ
american_scientific_journal-7932	94	18	than	than	ADP
american_scientific_journal-7932	94	19	that	that	PRON
american_scientific_journal-7932	94	20	of	of	ADP
american_scientific_journal-7932	94	21	the	the	DET
american_scientific_journal-7932	94	22	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	94	23	one	one	NUM
american_scientific_journal-7932	94	24	.	.	PUNCT
american_scientific_journal-7932	95	1	in	in	ADP
american_scientific_journal-7932	95	2	the	the	DET
american_scientific_journal-7932	95	3	�	�	PROPN
american_scientific_journal-7932	95	4	̂	̂	PROPN
american_scientific_journal-7932	95	5	�	�	PROPN
american_scientific_journal-7932	95	6	direction	direction	NOUN
american_scientific_journal-7932	95	7	,	,	PUNCT
american_scientific_journal-7932	95	8	the	the	DET
american_scientific_journal-7932	95	9	work	work	NOUN
american_scientific_journal-7932	95	10	done	do	VERB
american_scientific_journal-7932	95	11	is	be	AUX
american_scientific_journal-7932	95	12	less	less	ADJ
american_scientific_journal-7932	95	13	when	when	SCONJ
american_scientific_journal-7932	95	14	the	the	DET
american_scientific_journal-7932	95	15	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	95	16	frequency	frequency	NOUN
american_scientific_journal-7932	95	17	is	be	AUX
american_scientific_journal-7932	95	18	more	more	ADJ
american_scientific_journal-7932	95	19	than	than	ADP
american_scientific_journal-7932	95	20	that	that	PRON
american_scientific_journal-7932	95	21	of	of	ADP
american_scientific_journal-7932	95	22	the	the	DET
american_scientific_journal-7932	95	23	torsional	torsional	ADJ
american_scientific_journal-7932	95	24	oscillation	oscillation	NOUN
american_scientific_journal-7932	95	25	.	.	PUNCT
american_scientific_journal-7932	96	1	references	reference	NOUN
american_scientific_journal-7932	96	2	[	[	X
american_scientific_journal-7932	96	3	1	1	NUM
american_scientific_journal-7932	96	4	]	]	PUNCT
american_scientific_journal-7932	96	5	.	.	PUNCT
american_scientific_journal-7932	97	1	g.	g.	PROPN
american_scientific_journal-7932	97	2	g.	g.	PROPN
american_scientific_journal-7932	97	3	stokes	stokes	PROPN
american_scientific_journal-7932	97	4	.	.	PUNCT
american_scientific_journal-7932	98	1	“	"	PUNCT
american_scientific_journal-7932	98	2	on	on	ADP
american_scientific_journal-7932	98	3	the	the	DET
american_scientific_journal-7932	98	4	effect	effect	NOUN
american_scientific_journal-7932	98	5	of	of	ADP
american_scientific_journal-7932	98	6	rotation	rotation	NOUN
american_scientific_journal-7932	98	7	of	of	ADP
american_scientific_journal-7932	98	8	cylinders	cylinder	NOUN
american_scientific_journal-7932	98	9	and	and	CCONJ
american_scientific_journal-7932	98	10	spheres	sphere	NOUN
american_scientific_journal-7932	98	11	about	about	ADP
american_scientific_journal-7932	98	12	their	their	PRON
american_scientific_journal-7932	98	13	own	own	ADJ
american_scientific_journal-7932	98	14	axes	axis	NOUN
american_scientific_journal-7932	98	15	in	in	ADP
american_scientific_journal-7932	98	16	increasing	increase	VERB
american_scientific_journal-7932	98	17	the	the	DET
american_scientific_journal-7932	98	18	logarithmic	logarithmic	ADJ
american_scientific_journal-7932	98	19	decrement	decrement	NOUN
american_scientific_journal-7932	98	20	of	of	ADP
american_scientific_journal-7932	98	21	the	the	DET
american_scientific_journal-7932	98	22	arc	arc	NOUN
american_scientific_journal-7932	98	23	of	of	ADP
american_scientific_journal-7932	98	24	vibration	vibration	NOUN
american_scientific_journal-7932	98	25	”	"	PUNCT
american_scientific_journal-7932	98	26	.	.	PUNCT
american_scientific_journal-7932	99	1	mathematical	mathematical	ADJ
american_scientific_journal-7932	99	2	and	and	CCONJ
american_scientific_journal-7932	99	3	philosophical	philosophical	ADJ
american_scientific_journal-7932	99	4	papers	paper	NOUN
american_scientific_journal-7932	99	5	5	5	NUM
american_scientific_journal-7932	99	6	cambridge	cambridge	PROPN
american_scientific_journal-7932	99	7	:	:	PUNCT
american_scientific_journal-7932	99	8	cambridge	cambridge	PROPN
american_scientific_journal-7932	99	9	university	university	PROPN
american_scientific_journal-7932	99	10	press	press	PROPN
american_scientific_journal-7932	99	11	,	,	PUNCT
american_scientific_journal-7932	99	12	england	england	PROPN
american_scientific_journal-7932	99	13	,	,	PUNCT
american_scientific_journal-7932	99	14	pp	pp	PROPN
american_scientific_journal-7932	99	15	.	.	PUNCT
american_scientific_journal-7932	100	1	207	207	NUM
american_scientific_journal-7932	100	2	-	-	SYM
american_scientific_journal-7932	100	3	214	214	NUM
american_scientific_journal-7932	100	4	,	,	PUNCT
american_scientific_journal-7932	100	5	1886	1886	NUM
american_scientific_journal-7932	100	6	.	.	PUNCT
american_scientific_journal-7932	101	1	[	[	X
american_scientific_journal-7932	101	2	2	2	NUM
american_scientific_journal-7932	101	3	]	]	PUNCT
american_scientific_journal-7932	101	4	.	.	PUNCT
american_scientific_journal-7932	102	1	m.j	m.j	PROPN
american_scientific_journal-7932	102	2	.	.	PROPN
american_scientific_journal-7932	102	3	casarella	casarella	PROPN
american_scientific_journal-7932	102	4	,	,	PUNCT
american_scientific_journal-7932	102	5	p.a	p.a	PROPN
american_scientific_journal-7932	102	6	.	.	PROPN
american_scientific_journal-7932	102	7	laura	laura	PROPN
american_scientific_journal-7932	102	8	.	.	PUNCT
american_scientific_journal-7932	103	1	“	"	PUNCT
american_scientific_journal-7932	103	2	drag	drag	VERB
american_scientific_journal-7932	103	3	on	on	ADP
american_scientific_journal-7932	103	4	an	an	DET
american_scientific_journal-7932	103	5	oscillating	oscillate	VERB
american_scientific_journal-7932	103	6	rod	rod	NOUN
american_scientific_journal-7932	103	7	with	with	ADP
american_scientific_journal-7932	103	8	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	103	9	and	and	CCONJ
american_scientific_journal-7932	103	10	torsional	torsional	ADJ
american_scientific_journal-7932	103	11	motion	motion	NOUN
american_scientific_journal-7932	103	12	”	"	PUNCT
american_scientific_journal-7932	103	13	.	.	PUNCT
american_scientific_journal-7932	104	1	journal	journal	PROPN
american_scientific_journal-7932	104	2	of	of	ADP
american_scientific_journal-7932	104	3	hydronautics	hydronautic	NOUN
american_scientific_journal-7932	104	4	,	,	PUNCT
american_scientific_journal-7932	104	5	v.	v.	ADP
american_scientific_journal-7932	104	6	3	3	NUM
american_scientific_journal-7932	104	7	,	,	PUNCT
american_scientific_journal-7932	104	8	n.	n.	NOUN
american_scientific_journal-7932	104	9	4	4	NUM
american_scientific_journal-7932	104	10	,	,	PUNCT
american_scientific_journal-7932	104	11	pp	pp	ADJ
american_scientific_journal-7932	104	12	.	.	PUNCT
american_scientific_journal-7932	105	1	180	180	NUM
american_scientific_journal-7932	105	2	-	-	SYM
american_scientific_journal-7932	105	3	183	183	NUM
american_scientific_journal-7932	105	4	,	,	PUNCT
american_scientific_journal-7932	105	5	1969	1969	NUM
american_scientific_journal-7932	105	6	.	.	PUNCT
american_scientific_journal-7932	106	1	[	[	X
american_scientific_journal-7932	106	2	3	3	NUM
american_scientific_journal-7932	106	3	]	]	PUNCT
american_scientific_journal-7932	106	4	.	.	PUNCT
american_scientific_journal-7932	107	1	h.	h.	PROPN
american_scientific_journal-7932	107	2	ramkissoon	ramkissoon	PROPN
american_scientific_journal-7932	107	3	,	,	PUNCT
american_scientific_journal-7932	107	4	s.r	s.r	PROPN
american_scientific_journal-7932	107	5	.	.	PROPN
american_scientific_journal-7932	107	6	majumdar	majumdar	PROPN
american_scientific_journal-7932	107	7	.	.	PUNCT
american_scientific_journal-7932	108	1	“	"	PUNCT
american_scientific_journal-7932	108	2	flow	flow	VERB
american_scientific_journal-7932	108	3	due	due	ADP
american_scientific_journal-7932	108	4	to	to	ADP
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american_scientific_journal-7932	108	7	and	and	CCONJ
american_scientific_journal-7932	108	8	torsional	torsional	ADJ
american_scientific_journal-7932	108	9	oscillation	oscillation	NOUN
american_scientific_journal-7932	108	10	of	of	ADP
american_scientific_journal-7932	108	11	a	a	DET
american_scientific_journal-7932	108	12	figure	figure	NOUN
american_scientific_journal-7932	108	13	9	9	NUM
american_scientific_journal-7932	108	14	:	:	PUNCT
american_scientific_journal-7932	108	15	𝑊1	𝑊1	PROPN
american_scientific_journal-7932	108	16	𝑞0	𝑞0	VERB
american_scientific_journal-7932	108	17	2μ	2μ	NOUN
american_scientific_journal-7932	108	18	versus	versus	ADP
american_scientific_journal-7932	108	19	𝑡	𝑡	PROPN
american_scientific_journal-7932	108	20	figure	figure	NOUN
american_scientific_journal-7932	108	21	10	10	NUM
american_scientific_journal-7932	108	22	:	:	PUNCT
american_scientific_journal-7932	108	23	𝑊2	𝑊2	PROPN
american_scientific_journal-7932	108	24	𝑞0	𝑞0	VERB
american_scientific_journal-7932	108	25	2μ	2μ	NOUN
american_scientific_journal-7932	108	26	versus	versus	ADP
american_scientific_journal-7932	108	27	𝑡	𝑡	PROPN
american_scientific_journal-7932	108	28	american	american	ADJ
american_scientific_journal-7932	108	29	academic	academic	ADJ
american_scientific_journal-7932	108	30	scientific	scientific	ADJ
american_scientific_journal-7932	108	31	research	research	NOUN
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american_scientific_journal-7932	108	33	for	for	ADP
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american_scientific_journal-7932	108	35	,	,	PUNCT
american_scientific_journal-7932	108	36	technology	technology	NOUN
american_scientific_journal-7932	108	37	,	,	PUNCT
american_scientific_journal-7932	108	38	and	and	CCONJ
american_scientific_journal-7932	108	39	sciences	science	NOUN
american_scientific_journal-7932	108	40	(	(	PUNCT
american_scientific_journal-7932	108	41	asrjets	asrjet	NOUN
american_scientific_journal-7932	108	42	)	)	PUNCT
american_scientific_journal-7932	108	43	(	(	PUNCT
american_scientific_journal-7932	108	44	2022	2022	NUM
american_scientific_journal-7932	108	45	)	)	PUNCT
american_scientific_journal-7932	108	46	volume	volume	NOUN
american_scientific_journal-7932	108	47	89	89	NUM
american_scientific_journal-7932	108	48	,	,	PUNCT
american_scientific_journal-7932	108	49	no	no	DET
american_scientific_journal-7932	108	50	1	1	NUM
american_scientific_journal-7932	108	51	,	,	PUNCT
american_scientific_journal-7932	108	52	pp229	pp229	NOUN
american_scientific_journal-7932	108	53	-	-	PUNCT
american_scientific_journal-7932	108	54	240	240	NUM
american_scientific_journal-7932	108	55	240	240	NUM
american_scientific_journal-7932	108	56	cylinder	cylinder	NOUN
american_scientific_journal-7932	108	57	”	"	PUNCT
american_scientific_journal-7932	108	58	.	.	PUNCT
american_scientific_journal-7932	109	1	journal	journal	PROPN
american_scientific_journal-7932	109	2	of	of	ADP
american_scientific_journal-7932	109	3	applied	apply	VERB
american_scientific_journal-7932	109	4	mathematics	mathematic	NOUN
american_scientific_journal-7932	109	5	and	and	CCONJ
american_scientific_journal-7932	109	6	physics	physics	NOUN
american_scientific_journal-7932	109	7	,	,	PUNCT
american_scientific_journal-7932	109	8	v.	v.	ADP
american_scientific_journal-7932	109	9	41	41	NUM
american_scientific_journal-7932	109	10	,	,	PUNCT
american_scientific_journal-7932	109	11	pp	pp	ADJ
american_scientific_journal-7932	109	12	.	.	PUNCT
american_scientific_journal-7932	110	1	598	598	NUM
american_scientific_journal-7932	110	2	-	-	SYM
american_scientific_journal-7932	110	3	603	603	NUM
american_scientific_journal-7932	110	4	,	,	PUNCT
american_scientific_journal-7932	110	5	1990	1990	NUM
american_scientific_journal-7932	110	6	.	.	PUNCT
american_scientific_journal-7932	111	1	[	[	X
american_scientific_journal-7932	111	2	4	4	NUM
american_scientific_journal-7932	111	3	]	]	PUNCT
american_scientific_journal-7932	111	4	.	.	PUNCT
american_scientific_journal-7932	112	1	w.	w.	PROPN
american_scientific_journal-7932	112	2	phillips	phillips	PROPN
american_scientific_journal-7932	112	3	,	,	PUNCT
american_scientific_journal-7932	112	4	k.	k.	PROPN
american_scientific_journal-7932	112	5	rahaman	rahaman	PROPN
american_scientific_journal-7932	112	6	.	.	PUNCT
american_scientific_journal-7932	113	1	“	"	PUNCT
american_scientific_journal-7932	113	2	motion	motion	NOUN
american_scientific_journal-7932	113	3	of	of	ADP
american_scientific_journal-7932	113	4	a	a	DET
american_scientific_journal-7932	113	5	viscous	viscous	ADJ
american_scientific_journal-7932	113	6	fluid	fluid	NOUN
american_scientific_journal-7932	113	7	contained	contain	VERB
american_scientific_journal-7932	113	8	in	in	ADP
american_scientific_journal-7932	113	9	a	a	DET
american_scientific_journal-7932	113	10	cylinder	cylinder	NOUN
american_scientific_journal-7932	113	11	of	of	ADP
american_scientific_journal-7932	113	12	infinite	infinite	ADJ
american_scientific_journal-7932	113	13	length	length	NOUN
american_scientific_journal-7932	113	14	subjected	subject	VERB
american_scientific_journal-7932	113	15	to	to	ADP
american_scientific_journal-7932	113	16	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	113	17	and	and	CCONJ
american_scientific_journal-7932	113	18	torsional	torsional	ADJ
american_scientific_journal-7932	113	19	oscillations	oscillation	NOUN
american_scientific_journal-7932	113	20	of	of	ADP
american_scientific_journal-7932	113	21	independent	independent	ADJ
american_scientific_journal-7932	113	22	amplitudes	amplitude	NOUN
american_scientific_journal-7932	113	23	”	"	PUNCT
american_scientific_journal-7932	113	24	.	.	PUNCT
american_scientific_journal-7932	114	1	american	american	PROPN
american_scientific_journal-7932	114	2	international	international	PROPN
american_scientific_journal-7932	114	3	journal	journal	PROPN
american_scientific_journal-7932	114	4	of	of	ADP
american_scientific_journal-7932	114	5	contemporary	contemporary	PROPN
american_scientific_journal-7932	114	6	research	research	NOUN
american_scientific_journal-7932	114	7	,	,	PUNCT
american_scientific_journal-7932	114	8	v.	v.	ADP
american_scientific_journal-7932	114	9	2	2	NUM
american_scientific_journal-7932	114	10	,	,	PUNCT
american_scientific_journal-7932	114	11	n.	n.	NOUN
american_scientific_journal-7932	114	12	12	12	NUM
american_scientific_journal-7932	114	13	,	,	PUNCT
american_scientific_journal-7932	114	14	pp	pp	ADJ
american_scientific_journal-7932	114	15	.	.	PUNCT
american_scientific_journal-7932	115	1	58	58	NUM
american_scientific_journal-7932	115	2	-	-	SYM
american_scientific_journal-7932	115	3	71	71	NUM
american_scientific_journal-7932	115	4	,	,	PUNCT
american_scientific_journal-7932	115	5	2012	2012	NUM
american_scientific_journal-7932	115	6	.	.	PUNCT
american_scientific_journal-7932	116	1	[	[	X
american_scientific_journal-7932	116	2	5	5	NUM
american_scientific_journal-7932	116	3	]	]	PUNCT
american_scientific_journal-7932	116	4	.	.	PUNCT
american_scientific_journal-7932	117	1	c.	c.	PROPN
american_scientific_journal-7932	117	2	calmelet	calmelet	PROPN
american_scientific_journal-7932	117	3	-	-	PUNCT
american_scientific_journal-7932	117	4	eluhu	eluhu	NOUN
american_scientific_journal-7932	117	5	,	,	PUNCT
american_scientific_journal-7932	117	6	d.	d.	PROPN
american_scientific_journal-7932	117	7	majumdar	majumdar	PROPN
american_scientific_journal-7932	117	8	.	.	PUNCT
american_scientific_journal-7932	118	1	“	"	PUNCT
american_scientific_journal-7932	118	2	flow	flow	NOUN
american_scientific_journal-7932	118	3	of	of	ADP
american_scientific_journal-7932	118	4	a	a	DET
american_scientific_journal-7932	118	5	micropolar	micropolar	ADJ
american_scientific_journal-7932	118	6	fluid	fluid	NOUN
american_scientific_journal-7932	118	7	through	through	ADP
american_scientific_journal-7932	118	8	a	a	DET
american_scientific_journal-7932	118	9	circular	circular	ADJ
american_scientific_journal-7932	118	10	cylinder	cylinder	NOUN
american_scientific_journal-7932	118	11	subject	subject	NOUN
american_scientific_journal-7932	118	12	to	to	ADP
american_scientific_journal-7932	118	13	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	118	14	and	and	CCONJ
american_scientific_journal-7932	118	15	torsional	torsional	ADJ
american_scientific_journal-7932	118	16	oscillations	oscillation	NOUN
american_scientific_journal-7932	118	17	”	"	PUNCT
american_scientific_journal-7932	118	18	.	.	PUNCT
american_scientific_journal-7932	119	1	mathematical	mathematical	ADJ
american_scientific_journal-7932	119	2	and	and	CCONJ
american_scientific_journal-7932	119	3	computer	computer	NOUN
american_scientific_journal-7932	119	4	modelling	modelling	NOUN
american_scientific_journal-7932	119	5	,	,	PUNCT
american_scientific_journal-7932	119	6	v.	v.	ADP
american_scientific_journal-7932	119	7	27	27	NUM
american_scientific_journal-7932	119	8	,	,	PUNCT
american_scientific_journal-7932	119	9	n.	n.	NOUN
american_scientific_journal-7932	119	10	8	8	NUM
american_scientific_journal-7932	119	11	,	,	PUNCT
american_scientific_journal-7932	119	12	pp	pp	ADJ
american_scientific_journal-7932	119	13	.	.	PUNCT
american_scientific_journal-7932	120	1	69	69	NUM
american_scientific_journal-7932	120	2	-	-	SYM
american_scientific_journal-7932	120	3	78	78	NUM
american_scientific_journal-7932	120	4	,	,	PUNCT
american_scientific_journal-7932	120	5	1998	1998	NUM
american_scientific_journal-7932	120	6	.	.	PUNCT
american_scientific_journal-7932	121	1	[	[	X
american_scientific_journal-7932	121	2	6	6	NUM
american_scientific_journal-7932	121	3	]	]	PUNCT
american_scientific_journal-7932	121	4	.	.	PUNCT
american_scientific_journal-7932	122	1	k.	k.	PROPN
american_scientific_journal-7932	122	2	rahaman	rahaman	PROPN
american_scientific_journal-7932	122	3	.	.	PUNCT
american_scientific_journal-7932	123	1	“	"	PUNCT
american_scientific_journal-7932	123	2	internal	internal	ADJ
american_scientific_journal-7932	123	3	flow	flow	NOUN
american_scientific_journal-7932	123	4	due	due	ADP
american_scientific_journal-7932	123	5	to	to	ADP
american_scientific_journal-7932	123	6	the	the	DET
american_scientific_journal-7932	123	7	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	123	8	and	and	CCONJ
american_scientific_journal-7932	123	9	torsional	torsional	ADJ
american_scientific_journal-7932	123	10	oscillation	oscillation	NOUN
american_scientific_journal-7932	123	11	of	of	ADP
american_scientific_journal-7932	123	12	a	a	DET
american_scientific_journal-7932	123	13	cylinder	cylinder	NOUN
american_scientific_journal-7932	123	14	”	"	PUNCT
american_scientific_journal-7932	123	15	.	.	PUNCT
american_scientific_journal-7932	124	1	asia	asia	PROPN
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american_scientific_journal-7932	124	3	of	of	ADP
american_scientific_journal-7932	124	4	information	information	NOUN
american_scientific_journal-7932	124	5	technology	technology	NOUN
american_scientific_journal-7932	124	6	,	,	PUNCT
american_scientific_journal-7932	124	7	v.	v.	ADP
american_scientific_journal-7932	124	8	3	3	NUM
american_scientific_journal-7932	124	9	,	,	PUNCT
american_scientific_journal-7932	124	10	n.	n.	NOUN
american_scientific_journal-7932	124	11	10	10	NUM
american_scientific_journal-7932	124	12	,	,	PUNCT
american_scientific_journal-7932	124	13	pp	pp	ADJ
american_scientific_journal-7932	124	14	.	.	PUNCT
american_scientific_journal-7932	125	1	985	985	NUM
american_scientific_journal-7932	125	2	-	-	SYM
american_scientific_journal-7932	125	3	991	991	NUM
american_scientific_journal-7932	125	4	,	,	PUNCT
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american_scientific_journal-7932	125	6	.	.	PUNCT
american_scientific_journal-7932	126	1	[	[	X
american_scientific_journal-7932	126	2	7	7	NUM
american_scientific_journal-7932	126	3	]	]	PUNCT
american_scientific_journal-7932	126	4	.	.	PUNCT
american_scientific_journal-7932	127	1	d.	d.	PROPN
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american_scientific_journal-7932	127	3	,	,	PUNCT
american_scientific_journal-7932	127	4	k.	k.	PROPN
american_scientific_journal-7932	127	5	rahaman	rahaman	PROPN
american_scientific_journal-7932	127	6	.	.	PUNCT
american_scientific_journal-7932	128	1	“	"	PUNCT
american_scientific_journal-7932	128	2	on	on	ADP
american_scientific_journal-7932	128	3	the	the	DET
american_scientific_journal-7932	128	4	flow	flow	NOUN
american_scientific_journal-7932	128	5	of	of	ADP
american_scientific_journal-7932	128	6	an	an	DET
american_scientific_journal-7932	128	7	oldroyd	oldroyd	VERB
american_scientific_journal-7932	128	8	-	-	PUNCT
american_scientific_journal-7932	128	9	b	b	NOUN
american_scientific_journal-7932	128	10	liquid	liquid	NOUN
american_scientific_journal-7932	128	11	through	through	ADP
american_scientific_journal-7932	128	12	a	a	DET
american_scientific_journal-7932	128	13	straight	straight	ADJ
american_scientific_journal-7932	128	14	tube	tube	NOUN
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american_scientific_journal-7932	128	16	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	128	17	and	and	CCONJ
american_scientific_journal-7932	128	18	torsional	torsional	ADJ
american_scientific_journal-7932	128	19	oscillations	oscillation	NOUN
american_scientific_journal-7932	128	20	of	of	ADP
american_scientific_journal-7932	128	21	different	different	ADJ
american_scientific_journal-7932	128	22	frequencies	frequency	NOUN
american_scientific_journal-7932	128	23	”	"	PUNCT
american_scientific_journal-7932	128	24	.	.	PUNCT
american_scientific_journal-7932	129	1	math	math	NOUN
american_scientific_journal-7932	129	2	:	:	PUNCT
american_scientific_journal-7932	129	3	ensenanza	ensenanza	PROPN
american_scientific_journal-7932	129	4	univ	univ	PROPN
american_scientific_journal-7932	129	5	.	.	PROPN
american_scientific_journal-7932	129	6	,	,	PUNCT
american_scientific_journal-7932	129	7	v.	v.	ADP
american_scientific_journal-7932	129	8	14	14	NUM
american_scientific_journal-7932	129	9	,	,	PUNCT
american_scientific_journal-7932	129	10	pp	pp	ADJ
american_scientific_journal-7932	129	11	.	.	PUNCT
american_scientific_journal-7932	129	12	3443	3443	NUM
american_scientific_journal-7932	129	13	,	,	PUNCT
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american_scientific_journal-7932	129	15	.	.	PUNCT
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american_scientific_journal-7932	130	2	8	8	NUM
american_scientific_journal-7932	130	3	]	]	PUNCT
american_scientific_journal-7932	130	4	.	.	PUNCT
american_scientific_journal-7932	131	1	j.	j.	PROPN
american_scientific_journal-7932	131	2	v.	v.	PROPN
american_scientific_journal-7932	131	3	r.	r.	PROPN
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american_scientific_journal-7932	131	5	,	,	PUNCT
american_scientific_journal-7932	131	6	n.	n.	PROPN
american_scientific_journal-7932	131	7	k.	k.	PROPN
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american_scientific_journal-7932	131	9	.	.	PUNCT
american_scientific_journal-7932	132	1	“	"	PUNCT
american_scientific_journal-7932	132	2	micropolar	micropolar	ADJ
american_scientific_journal-7932	132	3	fluid	fluid	ADJ
american_scientific_journal-7932	132	4	flow	flow	NOUN
american_scientific_journal-7932	132	5	in	in	ADP
american_scientific_journal-7932	132	6	a	a	DET
american_scientific_journal-7932	132	7	straight	straight	ADJ
american_scientific_journal-7932	132	8	circular	circular	ADJ
american_scientific_journal-7932	132	9	cylinder	cylinder	NOUN
american_scientific_journal-7932	132	10	performing	perform	VERB
american_scientific_journal-7932	132	11	longitudinal	longitudinal	ADJ
american_scientific_journal-7932	132	12	and	and	CCONJ
american_scientific_journal-7932	132	13	torsional	torsional	ADJ
american_scientific_journal-7932	132	14	oscillations	oscillation	NOUN
american_scientific_journal-7932	132	15	”	"	PUNCT
american_scientific_journal-7932	132	16	.	.	PUNCT
american_scientific_journal-7932	133	1	computational	computational	ADJ
american_scientific_journal-7932	133	2	thermal	thermal	ADJ
american_scientific_journal-7932	133	3	sciences	science	NOUN
american_scientific_journal-7932	133	4	:	:	PUNCT
american_scientific_journal-7932	133	5	an	an	DET
american_scientific_journal-7932	133	6	international	international	ADJ
american_scientific_journal-7932	133	7	journal	journal	NOUN
american_scientific_journal-7932	133	8	,	,	PUNCT
american_scientific_journal-7932	133	9	v.	v.	ADP
american_scientific_journal-7932	133	10	3	3	NUM
american_scientific_journal-7932	133	11	,	,	PUNCT
american_scientific_journal-7932	133	12	n.	n.	NOUN
american_scientific_journal-7932	133	13	2	2	NUM
american_scientific_journal-7932	133	14	,	,	PUNCT
american_scientific_journal-7932	133	15	pp	pp	ADJ
american_scientific_journal-7932	133	16	.	.	PUNCT
american_scientific_journal-7932	134	1	123	123	NUM
american_scientific_journal-7932	134	2	-	-	SYM
american_scientific_journal-7932	134	3	131	131	NUM
american_scientific_journal-7932	134	4	,	,	PUNCT
american_scientific_journal-7932	134	5	2011	2011	NUM
american_scientific_journal-7932	134	6	.	.	PUNCT
american_scientific_journal-7932	135	1	[	[	X
american_scientific_journal-7932	135	2	9	9	NUM
american_scientific_journal-7932	135	3	]	]	PUNCT
american_scientific_journal-7932	135	4	.	.	PUNCT
american_scientific_journal-7932	136	1	g.k	g.k	PROPN
american_scientific_journal-7932	136	2	.	.	PROPN
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american_scientific_journal-7932	136	4	.	.	PUNCT
american_scientific_journal-7932	137	1	an	an	DET
american_scientific_journal-7932	137	2	introduction	introduction	NOUN
american_scientific_journal-7932	137	3	to	to	ADP
american_scientific_journal-7932	137	4	fluid	fluid	ADJ
american_scientific_journal-7932	137	5	dynamics	dynamic	NOUN
american_scientific_journal-7932	137	6	.	.	PUNCT
american_scientific_journal-7932	138	1	cambridge	cambridge	PROPN
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american_scientific_journal-7932	138	3	press	press	NOUN
american_scientific_journal-7932	138	4	,	,	PUNCT
american_scientific_journal-7932	138	5	pp	pp	X
american_scientific_journal-7932	138	6	.	.	PUNCT
american_scientific_journal-7932	139	1	75	75	NUM
american_scientific_journal-7932	139	2	,	,	PUNCT
american_scientific_journal-7932	139	3	1967	1967	NUM
american_scientific_journal-7932	139	4	.	.	PUNCT
american_scientific_journal-7932	140	1	[	[	X
american_scientific_journal-7932	140	2	10	10	NUM
american_scientific_journal-7932	140	3	]	]	PUNCT
american_scientific_journal-7932	140	4	.	.	PUNCT
american_scientific_journal-7932	141	1	w.	w.	PROPN
american_scientific_journal-7932	141	2	hughes	hughes	PROPN
american_scientific_journal-7932	141	3	.	.	PUNCT
american_scientific_journal-7932	142	1	an	an	DET
american_scientific_journal-7932	142	2	introduction	introduction	NOUN
american_scientific_journal-7932	142	3	to	to	ADP
american_scientific_journal-7932	142	4	viscous	viscous	ADJ
american_scientific_journal-7932	142	5	flows	flow	NOUN
american_scientific_journal-7932	142	6	.	.	PUNCT
american_scientific_journal-7932	143	1	new	new	PROPN
american_scientific_journal-7932	143	2	york	york	PROPN
american_scientific_journal-7932	143	3	.	.	PUNCT
american_scientific_journal-7932	144	1	hemisphere	hemisphere	PROPN
american_scientific_journal-7932	144	2	publishing	publishing	PROPN
american_scientific_journal-7932	144	3	corporation	corporation	NOUN
american_scientific_journal-7932	144	4	,	,	PUNCT
american_scientific_journal-7932	144	5	1979	1979	NUM
american_scientific_journal-7932	144	6	.	.	PUNCT
american_scientific_journal-7932	145	1	[	[	X
american_scientific_journal-7932	145	2	11	11	NUM
american_scientific_journal-7932	145	3	]	]	PUNCT
american_scientific_journal-7932	145	4	.	.	PUNCT
american_scientific_journal-7932	146	1	m.	m.	PROPN
american_scientific_journal-7932	146	2	abramowitz	abramowitz	PROPN
american_scientific_journal-7932	146	3	,	,	PUNCT
american_scientific_journal-7932	146	4	i.a	i.a	PROPN
american_scientific_journal-7932	146	5	.	.	PROPN
american_scientific_journal-7932	146	6	stegun	stegun	PROPN
american_scientific_journal-7932	146	7	.	.	PUNCT
american_scientific_journal-7932	147	1	handbook	handbook	NOUN
american_scientific_journal-7932	147	2	of	of	ADP
american_scientific_journal-7932	147	3	mathematical	mathematical	ADJ
american_scientific_journal-7932	147	4	functions	function	NOUN
american_scientific_journal-7932	147	5	with	with	ADP
american_scientific_journal-7932	147	6	formulas	formula	NOUN
american_scientific_journal-7932	147	7	,	,	PUNCT
american_scientific_journal-7932	147	8	graphs	graph	NOUN
american_scientific_journal-7932	147	9	and	and	CCONJ
american_scientific_journal-7932	147	10	mathematical	mathematical	ADJ
american_scientific_journal-7932	147	11	tables	table	NOUN
american_scientific_journal-7932	147	12	.	.	PUNCT
american_scientific_journal-7932	148	1	u.s	u.s	PROPN
american_scientific_journal-7932	148	2	.	.	PROPN
american_scientific_journal-7932	148	3	government	government	NOUN
american_scientific_journal-7932	148	4	printing	printing	NOUN
american_scientific_journal-7932	148	5	office	office	NOUN
american_scientific_journal-7932	148	6	,	,	PUNCT
american_scientific_journal-7932	148	7	pp	pp	ADP
american_scientific_journal-7932	148	8	.	.	PUNCT
american_scientific_journal-7932	149	1	379	379	NUM
american_scientific_journal-7932	149	2	-	-	SYM
american_scientific_journal-7932	149	3	382	382	NUM
american_scientific_journal-7932	149	4	,	,	PUNCT
american_scientific_journal-7932	149	5	1972	1972	NUM
american_scientific_journal-7932	149	6	.	.	PUNCT