Derive \(B_{1}\) and \(B_{2}\) in Equations 3.48 and 3.49:

\[ \begin{aligned} & -\omega_{b}^{2} B_{1}+2 \zeta \omega_{n} \omega_{b} B_{2}+\omega_{n}^{2} B_{1}=A_{1} \\ & -\omega_{b}^{2} B_{2}-2 \zeta \omega_{n} \omega_{b} B_{1}+\omega_{n}^{2} B_{2}=A_{2} \end{aligned} \]

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Table 3.2: Cases for Damped Harmonic Oscillators in Problem 21. wn (rad/s) (0) (cm) (0) (cm/s) (a) 0.5 0.1 1 1 (b) 1 0.1 1 1 (c) 10 0.1 1 1 (d) 0.5 0.1 0 1 (e) 0.5 0.1 10 1 (f) 0.5 0.1 1 0 (g) 0.5 0.1 1 10 (h) 0.5 0.01 1 1 (i) 0.5 0.95 1 1