Consider the RLC circuit in Problem 11.

a. Write the governing equation in terms of the electric charge q.

b. Assuming initial conditions are q(0) = 0, (0) = 1, plot q and i versus t (same figure) when the applied voltage v_a is a unit impulse.

PROBLEM 11 The governing equation for an RLC circuit driven by the applied voltage v_a(t) is derived as

where L = 4 H, R = 4 Ω, and C =  F.

a. Write the governing equation in terms of the electric charge q.

b. Assuming zero initial conditions, plot q and i versus t (same figure) when the applied voltage v_a is a unit impulse.