Problem 3: (30 points)
For the circuit shown in the Figure:
Ni
L
R
+
CV
L = 0.625 H, R = 25 \Omega, C = 1,000 \mu F
Find:
(a) The circuit's natural frequency, $\omega_n$.
(b) The damping constant, $\zeta$
(c) The % overshoot in the circuit's unit step response.
(d) The circuit's settling time, $T_s$, for a unit step input.
(e) The peak time, $T_p$, of the circuit's unit step response.
(f) The poles of the system. Draw a diagram to show the location of the poles on the
complex plane.
(g) Suppose that we want to redesign the circuit, so that it exhibits the fastest unit step
response with no overshoot. Calculate the value of the resistance that we must use.