Consider a causal LTI system implemented as the RL circuit shown in Figure P3.19. A curr...

Consider a causal LTI system implemented as the RL circuit shown in Figure P3.19. A current source produces an input current x(t), and the system output is considered to be the current y(t) flowing through the inductor.

(a) Find the differential equation relating x(t) and y(t).

(b) Determine the frequency response of this system by considering the output of the system to inputs of the form

(c) Determine the output y(t) if x(t) = cos(t).