The GATE Grind

GATE 2023 EE – Question 17

Signals and Systems · Linear time invariant and causal systems · 1 mark · Multiple choice

A continuous-time system that is initially at rest is described by

$$\frac{dy(t)}{dt}+3y(t)=2x(t),$$

where $x(t)$ is the input voltage and $y(t)$ is the output voltage. The impulse response of the system is

  1. $3e^{-2t}$
  2. $\dfrac13e^{-2t}u(t)$
  3. $2e^{-3t}u(t)$
  4. $2e^{-3t}$

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Correct answer: (C) $2e^{-3t}u(t)$

Explanation

$H(s)=\dfrac{2}{s+3}$, and for a system initially at rest (causal) $h(t)=2e^{-3t}u(t)$.