Solve for the response of the base-excited system governed by \(\ddot{x}+2 \zeta \omega_{n} \dot{x}+\omega_{n}^{2} x=2 \zeta \omega_{n} \dot{y}+\omega_{n}^{2} y\), where \(y(t)=A \exp \left(i \omega_{b} t\right)\) for the response \(x(t)=\) \(X(i \omega) \exp (i \omega t)\). Plot the response for parameter values: \(A=1, \zeta=0.1, \omega_{b}=1 \mathrm{rad} / \mathrm{s}\), and \(\omega_{n}=0.5\) \(\mathrm{rad} / \mathrm{s}\).