Example 44.3
Consider the mass-spring oscillator without friction: $y'' + y = 0$. Suppose
we add a force which corresponds to a push (to the left) of the mass as it
oscillates. We will suppose the push is described by the function
$f(t) = −h(t − 2π) + u(t − (2n + a))$
for some $a > 2π$ which we are allowed to vary. (A small $a$ will correspond
to a short duration push and a large $a$ to a long duration push.) We are
interested in solving the initial value problem
$y'' + y = f(t), y(0) = 1, y'(0) = 0$.