The function f(t) satisfies the differential equation \(\frac{{{d^2}f}}{{d{t^2}}} + f = 0\) and the auxiliary conditions, \(f\left( 0 \right) = 0,\ \frac{{df}}{{dt}} \left( 0 \right) = 4\). The Laplace transform of f(t) is given by
1
\(\frac{2}{{s + 1}}\)
2
\(\frac{4}{{s + 1}}\)
3
\(\frac{4}{{{s^2} + 1}}\)
4
\(\frac{2}{{{s^4} + 1}}\)