9–56 The switch in Figure P9–55 has been open for a long time and is closed at t =0.

(a) Find the circuit differential equation in iLðtÞ and the initial conditions iLð0Þ and vCð0Þ .

(b) The circuit parameters are L=50H, C =0:25 μF, R1 =10 kΩ, R2 =10 Ω, and vS =10u t ð Þ V. Use Laplace transforms and MATLAB to solve for iLðtÞ for t ≥ 0.

(c) Simulate the circuit in Multisim to plot your resulting waveform.