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GATE 2021 BM – Question 46

Measurements and Control Systems · Control System Transfer Functions · 2 marks · Multiple choice

The closed-loop characteristic equation is s⁴+2s³+8s²+8s+16=0. Find its steady-state oscillation frequency in rad/s.

  1. 1
  2. 2
  3. 4
  4. 8

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Correct answer: (B) 2

Explanation

Factor the polynomial as (s²+4)(s²+2s+4). The latter factor has roots with negative real part and decays. The first gives poles s=±j2, producing sustained oscillation at angular frequency two rad/s. Thus B.

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