Find the circuit differential equation in ilt and the

Question

The switch in Figure has been open for a long time and is closed at t = 0.

(a) Find the circuit differential equation in i_L(t) and the initial conditions i_L(0) and v_C(0).

(b) The circuit parameters are L = 50 H, C = 0.25 μF, R₁ = 10 kΩ, R₂ = 10 Ω, and v_S = 10u (t) V. Use Laplace transforms and MATLAB to solve for i_L(t) for t ≥ 0.

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