Obtain and plot free vibration response for the system shown in Figure P4.1 when \(m=1 \mathrm{~kg}, k=530 \mathrm{~N} / \mathrm{m}, k_{c}=130 \mathrm{~N} / \mathrm{m}\). Assume that \(x_{1}(0)=0.01 \mathrm{~m}, \dot{x}_{1}(0)=1 \mathrm{~m} / \mathrm{sec}, x_{2}(0)=0\), and \(\dot{x}_{2}(0)=0\).