GATE 2022 EE – Question 37

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 2 marks · Multiple choice

An LTI system is shown in the figure where

$$G(s)=\frac{100}{s^2+0.1s+100}.$$

The steady state output of the system, to the input $r(t)$, is given as $y(t)=a+b\sin(10t+\theta)$. The values of '$a$' and '$b$' will be

$a=1,\ b=10$
$a=10,\ b=1$
$a=1,\ b=100$
$a=100,\ b=1$

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Correct answer: (A) $a=1,\ b=10$

Explanation

The input is $r(t)=1+0.1\sin(10t)$. The DC gain is $G(0)=1$, so $a=1$. At $\omega=10$, $G(j10)=\frac{100}{-100+j1+100}=\frac{100}{j}$, which has magnitude 100, so $b=0.1\times100=10$.