Analytical Mech Homework Solutions 27

Analytical Mech Homework Solutions 27 - 3.16 (b) Q = 2 2 d...

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3.16 (b) 22 d Q ω γ γγ D == 2 1 LC = D , 2 R L = 2 2 2 1 4 1 4 2 2 R LC L L R RC L    Q (c) 2 L R C Q R R === DD 3.17 sin Im it ext FF t F e   and () x t is the imaginary part of the solution to: mx cx kx F e ++= D ±± ± i.e. xt Im sin A e A t ωφ φ where, as derived in the text, 1 2 2 2 F A km c ωω = −+  D and 2 tan γω = D 3.18 Using the hint, , where Re t ext FF β = D e i α = , and x(t) is the real part of the solution to: mx t cx kx F e D ± . Assuming a solution of the form: ti xA e = 2 i F mck x x e A ββ ++ = D 2c F mi mmc i c k i A o s s i n αω −−
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