Question

The response of a servomechanism is 1+0.2e^-60t-1.2e^-10t when subjected to a unit step input. What is the damping ratio?

(a) 1.21

(b) 1.43

(c) 1.59

(d) 1.74

Answer 1

The correct choice is (b) 1.43

The best I can explain: First we apply Laplace Transform to the system and as R(s) = 1/s we get closed loop transfer function as C(s)/R(s) = 600/s^2+70s+600. Then we compare it with the standard equation for second order transfer function we got damping ratio = 70/2wn = 1.43.