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

- $\dfrac{2}{s+1} \\$
- $\dfrac{4}{s+1} \\$
- $\dfrac{4}{s^2+1} \\$
- $\dfrac{2}{s^4+1}$