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Mechanical Vibrations (4th Edition)

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Unformatted text preview: .(w)( x(t)= 770 ficaqsohq) m where A is :n mm ___.. (El) _ A 1(0) — Tm :05 IX : 01003 , A cos 4 = 3 _-._- (E2) 1(0) : —— €330 Sin d : 1 , A_ sin q -_- _20 _ ---(E-3) L A;{(Acos‘o()1+ (A Stlnct)z}/z: 20-2237 mm =fan-1 A 3'" _____f_r A cos 0" 26:) , 7.0- 2237 cos (sot — 1 4219) Inn (1)) C05 (A423): (105 A (.05 B - Sm A SIn B 53' (51) can be expressed as 35(15): A cos 5o{.cgso(—Asfr|501‘:-5fn' -1 = fan (—6-566'1)=-81-+592°:-1-4219rm = A1 cos {at + A2 s‘u‘n cat where as: so, A1=Acofq, Az=-Asinq -“—‘7‘(‘7) (3 C05 501‘: + 10 SM 50t2 mm :(t) = A1 cos (of + A2 sI‘n wt 2. Ti: #01:) = —A1” Sm cot + A263 C05 C43": , $:—A1wz’cuwf—Azmz sin 6.9%. 2. it: = __ Caz 7‘6) where ca: [5 a. consfant Hence 94%) is a. simple fiarmom‘c moi-(on (w) UsIng frigonovnetric relaficns: x1({:) : 5 (C05 3t cos 1 - sin at sin 1.) 110:) :10 (COS at ca: 2. — sin 3%: sm 2) 16:): 211(k) + :13) cos at (5' cos 1 + 10 Co: 2)— sin 3+: (”In 1 + 10 I'm 2) If ‘10:): A C°5(”t+°‘)= Acos wt cosq— Asia cat sinqt, (3:3, A6054: 5 coSi+to £052 :-1-4-539, Ash‘ICK = 5 Arn1+Io sI‘nz = 13.3003 A: #0“ c05001+ (A shelf 2 13-3802 oI _—. hm“ Lil .—_ {mI'i(-9- 1104): 96 264o°= 1-68 me! A C0564 Augle between 711(k) amt x(l:) is 36 26°40 - 57- 3° =3a-964° (1") Using vector addl'han: For ‘an arLI'i-raxy value of (at +1.) , Aux manic moi-ions 1‘13') am! 110:) Can be shown 0.5 In Hue figure. From vector addition, we final 20:): 13.38 cas(cat + 1-63) 22 ...
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