For an underdamped second-order system (0 < zeta < 1), the unit step response exhibits:

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Mechanical Engineering QUESTION #2389

Question 1

For an underdamped second-order system (\(0 < \zeta < 1\)), the unit step response exhibits:

\(\text{Overdamped, no oscillation — slow return to steady state}
Oscillatory response with exponentially decaying amplitude — undershoots and overshoots✔️
Critically damped — fastest return to steady state without oscillation
Unstable growing oscillations

Correct Answer Explanation

For \(0<\zeta<1\) (underdamped): poles are complex conjugate with negative real parts, producing an exponentially decaying sinusoidal response with overshoot. The response oscillates about the final value before settling.

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