An RL circuit includes a voltage source vs, a resistor R = 1.8 n, and an inductor L = 0.4 H, as shown in the figure. The differential equation that describes the response of the circuit is
L/R diL/dt + iL = Vs/R
where iL is the current in the inductor. Initially iL = 0, and then at t = 0 the voltage source is changed. Determine the response of the circuit for the following three cases:
(a) vs = 10sin(30πt) V for t > 0.
(b) vs = 10e-t/0·06sin(30πt) V for t > 0.