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GATE 2024 BM – Question 24

Signals and Systems · LTI Systems and Convolution · 1 mark · Multiple choice

An LTI system obeys y(t)+y′(t)+0.5y″(t)=x(t)+0.1x′(t). Find the Laplace transform of its impulse response under zero initial conditions.

  1. $(0.5s^2+s+1)/(0.1s+1)$
  2. $(0.1s+1)/(0.5s^2+s+1)$
  3. $(0.1s+s^2)/(s^2+s+0.5)$
  4. $(s^2+s+0.5)/(0.1s^2+s)$

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Show answer and explanation

Correct answer: (B) $(0.1s+1)/(0.5s^2+s+1)$

Explanation

Taking Laplace transforms gives (1+s+0.5s²)Y=(1+0.1s)X. The impulse-response transform is the transfer function Y/X, giving (0.1s+1)/(0.5s²+s+1), B. Initial-condition terms vanish for the stated impulse-response definition.

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