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GATE 2016 EE – Question 13

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

The Laplace Transform of $f(t) = e^{2t} \sin(5t) u(t)$ is

  1. $\frac{5}{s^2 - 4s + 29}$
  2. $\frac{5}{s^2 + 5}$
  3. $\frac{s - 2}{s^2 - 4s + 29}$
  4. $\frac{5}{s + 5}$

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Correct answer: (A) $\frac{5}{s^2 - 4s + 29}$

Explanation

The transform of $\sin(5t) u(t)$ is $\frac{5}{s^2 + 25}$. Multiplying by $e^{2t}$ shifts $s$ to $s - 2$, giving $\frac{5}{(s - 2)^2 + 25} = \frac{5}{s^2 - 4s + 29}$.