The GATE Grind

GATE 2020 EE – Question 20

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 1 mark · Multiple choice

Consider a linear time-invariant system whose input $r(t)$ and output $y(t)$ are related by the following differential equation:

$$\frac{d^2y(t)}{dt^2}+4y(t)=6r(t)$$

The poles of this system are at

  1. $+2j,-2j$
  2. $+2,-2$
  3. $+4,-4$
  4. $+4j,-4j$

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Show answer and explanation

Correct answer: (A) $+2j,-2j$

Explanation

The transfer function is $\frac{6}{s^2+4}$, so the poles satisfy $s^2=-4$, i.e. $s=\pm2j$.