Problems

Problem 8.1 (FRESHMAKER)

Solve the following initial value problem with forcing using the Laplace transform method.

$$\begin{equation*} \frac{d^2 y}{d t^2} + 1 \frac{d y}{d t} + 16 y = 1 u_s(t), \quad y(0) = 0, \quad \frac{d y}{d t}\Big|_{t=0} = 0 \end{equation*}$$

where \(u_s(t)\) is the unit step function.