Chapter 7.9, Problem 32E

A linear system is said to be asymptotically stable if its impulse response function satisfies $h\left(t\right)\to 0$ as $t\to +\infty$. If the linear system is governed by

$a{y}^{″}+b{y}^{\prime }+cy=g\left(t\right)$,

show that the system is asymptotically stable if and only if the real parts of the roots to

$a{r}^2+br+c=0$

are strictly less than zero.