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GATE 2020 BM – Question 11

Measurements and Control Systems · Control System Transfer Functions · 1 mark · Multiple choice

For roots m₁,m₂ of a second-order characteristic equation, match P real distinct,Q equal,R complex conjugate with K critically damped,L overdamped,M underdamped.

  1. P–L,Q–M,R–K
  2. P–M,Q–L,R–K
  3. P–L,Q–K,R–M
  4. P–M,Q–K,R–L

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Show answer and explanation

Correct answer: (C) P–L,Q–K,R–M

Explanation

For the usual stable second-order model, two distinct real negative poles give an overdamped response, equal negative poles critical damping, and a complex-conjugate pair with negative real parts underdamping. Thus P–L,Q–K,R–M, C. Pole stability is implicit in these standard damping labels.

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