The free vibrations of a system are governed by

\[ 2 \ddot{x}+1800 x= \begin{cases}3 & \dot{x}<0 \\ -3 & \dot{x}>0\end{cases} \]

with \(x(0)=0.02 \mathrm{~m}\) and \(\dot{x}(0)=0\). Calculate or specify the following.

(a) The period of motion

(b) The change in amplitude per cycle of motion

(c) The permanent displacement when motion ceases

(d) The number of cycles before motion ceases