For a single degree of freedom spring-mass system, complete the following.

(a) If the free vibration is described as \(x(t)=A \cos \left(\omega_{n} t+\Phi_{c}\right)\), determine expressions for \(A\) and \(\Phi_{c}\) if the initial displacement is \(x_{0}\) and the initial velocity is \(\dot{x}_{0}\).

(b) If the free vibration is described as \(x(t)=A \cos \left(\omega_{n} t\right)+B \sin \left(\omega_{n} t\right)\), determine expressions for \(A\) and \(B\) if the initial displacement is \(x_{0}\) and the initial velocity is \(\dot{x}_{0}\).