Question

force function help

Answer 1

\[h(t) = u_{\pi}(t)-u_{4\pi}(t)\]
how to solve y'y=h(t), y(0)=y'(0=0

i do not understand the force function?

Answer 2

\[y"+y=h(t),y(0)=y'(0)=0\]

Answer 3

This problem will involve the Laplace transform, so you're probably familiar with that.

\(u_c(t)\) is the Heaviside step function, defined as follows:
\[u_c(t)=\begin{cases}1&\text{for }t\ge c\\ 0&\text{for }t<c\end{cases}\]
Here's a sketch: