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The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by

  1. $\dfrac{2}{s+1} \\$
  2. $\dfrac{4}{s+1} \\$
  3. $\dfrac{4}{s^2+1} \\$
  4. $\dfrac{2}{s^4+1}$
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