Question

Assertion (A): All the systems which exhibit overshoot in transient response will also exhibit resonance peak in frequency response.

Reason (R): Large resonance peak in frequency response corresponds to a large overshoot in transient response.

(a) Both A and R are true and R is the correct explanation of A

(b) Both A and R are true and R is not the correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

I got this question during an internship interview.

The origin of the question is Correlation between Time and Frequency Response in portion Frequency Response Analysis of Control Systems

Answer 1

Correct choice is (a) Both A and R are true and R is the correct explanation of A

The explanation: For G<1/√2 frequency parameters ex Mr resonant peak and time response parameters eg. Mp peak overshoot are well correlated. For G>1/√2 the resonant peak Mr does not exist and the correlation breaks down. This is not a serious problem as for this range of G, the step response oscillations are well-damped and Mp is hardly perceptible.