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GATE2020-ME-1: 3

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The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is

  1. $f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t \right ) \\$
  2. $f\left ( t \right )=\dfrac{1}{\omega}\cos\:\omega t \\$
  3. $f\left ( t \right )=\dfrac{1}{\omega}\sin\:\omega t \\$
  4. $f\left ( t \right )=\dfrac{1}{\omega^{2}}\left ( 1-\sin\:\omega t \right )$
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