For Problem 14 where \(k=20 \mathrm{lb} /\) in and \(W=40 \mathrm{lb}\), solve for the steady-state responses in \(\mathrm{ft} / \mathrm{s}^{2}\) to the following excitation forces per unit mass:

(a) \(F(t) / m=100 \sin \left(0.9 \omega_{n} t\right)\)

(b) \(F(t) / m=100 \sin \left(\omega_{n} t\right)\)

(c) \(F(t) / m=100 \sin \left(1.1 \omega_{n} t\right)\)

(d) \(F(t) / m=100 \sin \left(0.5 \omega_{n} t\right)\)

(e) \(F(t) / m=100 \sin \left(2 \omega_{n} t\right)\).
Plot and discuss each case.