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GATE 2016 EE – Question 17

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

The phase cross-over frequency of the transfer function $G(s) = \frac{100}{(s + 1)^3}$ in rad/s is

  1. $\sqrt{3}$
  2. $\frac{1}{\sqrt{3}}$
  3. 3
  4. $3\sqrt{3}$

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Correct answer: (A) $\sqrt{3}$

Explanation

The phase of $G(j\omega)$ is $-3\tan^{-1}(\omega)$. The phase crossover frequency is where this equals $-180°$, so $\tan^{-1}(\omega) = 60°$ and $\omega = \tan 60° = \sqrt{3}$ rad/s.