Laplace II: Steps, Impulses & Convolution · Superchallenge problem

An undamped oscillator at rest is struck with a unit impulse every second: $y''+y=\displaystyle\sum_{k=0}^{\infty}\delta(t-k)$, $y(0^-)=y'(0^-)=0$. Find the least upper bound of $y(t)$ over $t\ge0$.