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GATE 2018 EE – Question 19

Control Systems · Transient and Steady-state analysis of linear time invariant systems · 1 mark · Multiple choice

Match the transfer functions of the second-order systems with the nature of the systems given below.

P: $\dfrac{15}{s^2+5s+15}$, Q: $\dfrac{25}{s^2+10s+25}$, R: $\dfrac{35}{s^2+18s+35}$

I: Overdamped, II: Critically damped, III: Underdamped

  1. P-I, Q-II, R-III
  2. P-II, Q-I, R-III
  3. P-III, Q-II, R-I
  4. P-III, Q-I, R-II

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Correct answer: (C) P-III, Q-II, R-I

Explanation

The discriminant $b^2-4c$ decides: P has $25-60<0$ (underdamped), Q has $100-100=0$ (critically damped) and R has $324-140>0$ (overdamped). So P-III, Q-II, R-I.