Laplace II: Steps, Impulses & Convolution · Hard problem

An underdamped system is driven by a constant force switched on at $t=1$: $y''+2y'+5y=10u(t-1)$, $y(0)=y'(0)=0$. Find the time at which $y(t)$ reaches its FIRST peak (overshoot maximum) for $t>1$.