For a mass-spring-damper system under harmonic loading per unit mass \(F(t) / m=\cos \omega t \mathrm{ft} / \mathrm{s}^{2}\), solve for the response amplitude for the case where \(k=\) \(20 \mathrm{lb} / \mathrm{in}, W=40 \mathrm{lb}\), and then plot \(\beta\) for a broad range of driving frequencies \(\omega\). If \(0 \leq \omega \leq 3 \omega_{n}\), discuss design considerations for the system as the force is varied from the rest state \((\omega=0)\) to its highest frequency \(\left(\omega=3 \omega_{n}\right)\). Consider the damping cases: \(\zeta=0.01,0.1,0.5\). Discuss parameters of possible concern such as \(x_{\max }\) and whether material yielding could be of concern.