The GATE Grind

GATE 2022 IN – Question 11

Signals and Systems · Laplace and z-transforms · 1 mark · Multiple choice

The input $x(t)$ and output $y(t)$ satisfy $dy(t)/dt+y(t)=3x(t-3)u(t-3)$, where $u(t)$ is the unit-step function. The transfer function is ______.

  1. $e^{-3s}/(s+3)$
  2. $3e^{-3s}/(s+1)$
  3. $3e^{-s/3}/(s+1)$
  4. $e^{-s/3}/(s+3)$

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Correct answer: (B) $3e^{-3s}/(s+1)$

Explanation

With zero initial conditions and a causal input, differentiation transforms to sY and the delayed input to e⁻³ˢX.

Thus (s+1)Y=3e⁻³ˢX, giving **H=3e⁻³ˢ/(s+1), B**.