The switch in Figure P \(9=3 \underline{8}\) has been in position A for a long time and at \(t=0\) it is moved to position \(\mathrm{B}\). The circuit parameters are \(R=100 \Omega, L=200 \mathrm{mH}\), and \(i_{S}(t)=2 \cos\) \((2 \pi 60 t) u(t) \mathrm{mA}\).

(a) Find the differential equation for the inductor current \(i\) L \((t)\).

(b) Transform the equation into the \(s\)-domain and solve the equation for \(I_{\mathrm{L}}(s)\).

(c) Solve for \(i_{\mathrm{L}}(t)\) and \(v_{\mathrm{O}}(t)\).

(d) Validate your result using Multisim.