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GATE 2021 IN – Question 19

Control Systems · Time response and steady-state error · 1 mark · Multiple select

A circuit’s step response oscillates, with oscillations dying down after some time. Which inferences about its input–output transfer function are correct?

  1. It is at least second order
  2. It has at least one underdamped pole pair
  3. It does not have a real pole
  4. It is a first-order system

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Show answer and explanation

Correct answer: (A) It is at least second order; (B) It has at least one underdamped pole pair

Explanation

A decaying oscillatory mode requires a complex-conjugate pole pair with negative real part. Consequently the transfer function is at least second order and has an underdamped pair: **A and B**. Additional real poles can coexist, so C need not hold; a real first-order system cannot produce the observed oscillation.