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Mechanical Vibrations (4th Edition)

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Unformatted text preview: (C) Using Complex numLers: ‘ _ 751(k): Re {A1 ei(os’c+x)} = Re 5 ef_(n§{'+ 1)} mar): Re {A2 ei(fi9t+7—)} = Re {10 eta“: +70} 2:— xm = Re{A 30"“ 4)}, A co$(3t+°() : A1 :05 (3t+1) + A: COS (3-in-2) ['9‘ A (cos at COS n( — sin at sir‘u 0!) x $030: it cos 1 — sin Tl:— fin 4.) +|0 (cos 3?: cos 2 «- sin at- sin 1) [-e- Ac05425co$1+10c032, Asinq=5sin1+lo$inz A: I3-3802, 4: 1-68 ma - 1-53 740:): Re {13-3802 e"(3t+ )} @ Mt): IO Sin (wf+60°) = xitt) + x2“) where 11(t) = 5 m. (wt-+36) mm! xz(t) = A sin (wt+a(°) 10(an wt cos 60° + cos (at sin 60.) = 5' (Aim cat-Cos ao°+ cos cat-sin ao') a a + A (Sin astcos ar°+ Cos cat-fin q") to (.05 60 r: 5 C05 30 + A C05 «0 ; A cos 6639 °(° = 0' IO sin 60' = 5 sin ao°+ A sin cc” ; A srn ac" = 54603 A = Jo-eassz-e- 5.15031 : 5.1%; q: f¢n_1( 6“503/o.6639) = aa-v‘ns' HG): 6-1966 sin (wt 4. 83-7‘7380) @ $00: "2 casgt+ sin fit 1(f) = i (05 3th (1+4. sr‘h %t) From He nature of H18 9"!” of Me). if can be [Seen {'wa x(1‘:) J-S PEH'OAI‘C “111:5 au 0 i t rh'me ref-30c! 00C 2': 4. @ If I“) is harmonic, 713M): _w2 7;“) Here 1(t) = 2 Cos at + cos it i(*)= --8 COS 2“: -9 £05 at :75 —- (onsfanf {'Eme! tar) Z‘H‘) is not harmonic 23 ...
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