1.

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

A. \(\frac{2}{{s + 1}}\)
B. \(\frac{4}{{s + 1}}\)
C. \(\frac{4}{{{s^2} + 1}}\)
D. \(\frac{2}{{{s^4} + 1}}\)
Answer» D. \(\frac{2}{{{s^4} + 1}}\)


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