This problem concerns four second$-$order systems System $1$: x$[$n$]=$ y$[$n$]0\mathrm{.}8$y$[$n $1]+0\mathrm{.}64$y$[$n $2]$ System $2$: x$[$n$]=$ y$[$n$]1\mathrm{.}7$y$[$n $1]+0\mathrm{.}72$y$[$n $2]$ System $3$: x$[$n$]=$ y$[$n$]+0\mathrm{.}9025$y$[$n $2]($a$)$ For each of the three systems, specify if it is over$-$damped, under$-$damped or critically$-$damped. $($b$)$ Which system$$s impulse response will die out most slowly? Why? $($c$)$ Among the underdamped systems, which system$$s impulse response oscillates with the shortest period? Why?