The input-output differential equation of an electr·ical circuit whose input is a voltage vi(t) and the output is a voltage v 0 (t), is given by

(a) Find the crpressions for the damping ratio C and the undamped natural frequency :»n.
1 1

(b) Given the information: R1 = H1, R2 = 2n, C = 1F, L = 2H, vi(t) = 2t and assum·ing zero initial conditions, use Laplace transforms to solve the d~fferential equation, i.e., obtain the system response.

(c) Plot the system response.

(d) Illustrate that the initial and final values of the response are the same as those obtained by using the IVT and FVT.
Problem