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GATE 2019 EE – Question 11

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

The inverse Laplace transform of $H(s)=\dfrac{s+3}{s^2+2s+1}$ for $t\ge0$ is

  1. $3te^{-t}+e^{-t}$
  2. $3e^{-t}$
  3. $2te^{-t}+e^{-t}$
  4. $4te^{-t}+e^{-t}$

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Correct answer: (C) $2te^{-t}+e^{-t}$

Explanation

$\frac{s+3}{(s+1)^2}=\frac{(s+1)+2}{(s+1)^2}=\frac{1}{s+1}+\frac{2}{(s+1)^2}$, so $h(t)=e^{-t}+2te^{-t}$.