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GATE 2014 EE (EE2) – Question 19

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

An LTI system has $H(s)=1/[s(s+4)]$. Input is cos(3t) and steady-state output is A sin(3t + α). Find A.

  1. 1/30
  2. 1/15
  3. 3/4
  4. 4/3

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Correct answer: (B) 1/15

Explanation

For unit-amplitude input at ω=3,the sinusoidal amplitude multiplier is |H(j3)|. Its denominator magnitude is |j3| |4+j3|=3×5=15,so **A=1/15,B**. Writing the output as a sine rather than a cosine changes its phase parameter,not this amplitude.