GATE 2020 EE – Question 51
A stable real linear time-invariant system with single pole at $p$, has a transfer function $H(s)=\dfrac{s^2+100}{s-p}$ with a dc gain of 5. The smallest positive frequency, in rad/s, at unity gain is closest to:
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Correct answer: (A) 8.84
Explanation
The dc gain is $H(0)=\frac{100}{-p}=5$, so $p=-20$. Unity gain requires $\frac{|100-\omega^2|}{\sqrt{\omega^2+400}}=1$, i.e. $\omega^4-201\omega^2+9600=0$, so $\omega^2=78.1$ or $122.9$. The smallest positive frequency is $\omega=8.84$ rad/s.