Analytical Mech Homework Solutions 30

Analytical Mech Homework Solutions 30 - 3.22 In steady...

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3.22 In steady state, () ( ) n in t n n Ae xt ω φ = 1 2 2 22 2 2 2 2 4 n n F m A nn ωω γ =  −+   D Now 4 n F n F π = , . . . and D 1,3,5, n = 3 = D 100 2 Q =≈ D so 2 2 9 40,000 1 1 2 2 41 9 94 40000 F A m =⋅ D 1 2 2 F A m πω D 3 1 2 2 2 2 3 9 99 4 200 F A m    D 3 2 400 27 F A m D 5 1 2 2 2 2 5 3 92 5 4 5 200 F A m D 5 2 20 F A m D i.e., A : A : 1 : 29.6 : 0.1 1 3 5 A = 3.23 (a) Thus 2 0 xx += D ±± yx = ± 2 =− D ± x y = ± divide these two equations: 2 yd y x x dx y == D ± ± (b) Solving 2 0 ydy xdx + = D and Integrating 2 C D Let 2 2 CA = 2 1 AA D an ellipse 9
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