Consider the RLC electTical cirw'it given below, where the input is cunmt ii ( t) and the outvut is voltage V0 ( t).

(a) The input-output differential equation for the circuit is given by C .. 1 . 1 ·.( ) V0 + RV0 + LV0 = Z t .
253 1 1 Oiven that R = 4o, L = 3H, C = 1F and assuming zero initial conditions, find the system transfer function H(s).
{b) Find the impulse {natural) response of the system.

(c) Find the unit step response of the system.
{d) What is the relationship between the natural and unit step responses?
Problem