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GATE 2016 ME (ME2) – Question 13

Engineering Mathematics · Differential Equations: Initial and boundary value problems, Laplace transforms · 1 mark · Multiple choice

The Laplace transform of $\cos(\omega t)$ is ______.

  1. $s/(s^2+\omega^2)$
  2. $\omega/(s^2+\omega^2)$
  3. $s/(s^2-\omega^2)$
  4. $\omega/(s^2-\omega^2)$

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Correct answer: (A) $s/(s^2+\omega^2)$

Explanation

Integrating exp(−st)cosωt from0 to infinity, or taking the real part of1/(s−iω), gives s/(s²+ω²). Therefore **A**. The sine transform has numeratorω, distinguishing it from this cosine result.