Differential Equations

Using the frequency-shifting property of Laplace transforms: $\mathcal{L}\{\cos(4t)\} = \frac{s}{s^2 + 4^2} = \frac{s}{s^2 + 16}$ $\mathcal{L}\{e^{-3t} \cos(4t)\} = \frac{s + 3}{(s + 3)^2 + 16}$ Evaluating at $s = 1$: $F(1) = \frac{1 + 3}{(1 + 3)^2 + 16} = \frac{4}{16 + 16} = \frac{4}{32} = 0.125$