The switch in Figure P9-41 has been open for a long time and is closed at \(t=0\). The circuit parameters are \(R=\) \(50 \Omega, L=50 \mathrm{mH}, C=5 \mu \mathrm{F}\), and \(V_{\mathrm{A}}=1000 \mathrm{~V}\).

(a) Find the circuit differential equation in \(i_{L}(t)\) and the initial conditions \(i_{\mathrm{L}}(\mathrm{O})\) and \(v_{\mathrm{C}}(\mathrm{o})\).

(b) Use Laplace transforms to solve for \(i_{\mathrm{L}}(t)\) for \(t \geq 0\).

(c) Build the circuit for \(t>0\) in Multisim. Plot \(i_{\mathrm{L}}(t), i_{\mathrm{R}}(t\) ), \(i_{\mathrm{C}}(t)\), and \(v_{\mathrm{C}}(t)\). Use the left axis for the voltage and the right axis for the three currents. Comment on the plots.