Use the Laplace transform method to determine the response of a system at rest in equilibrium when subject to

\[ F(t)=F_{0} \cos \omega t\left[1-u\left(t-t_{0}\right)\right] \]

for

(a) \(\zeta=0\),

(b) \(0<\zeta<1\),

(c) \(\zeta=1\),

(d) \(\zeta>1\).