d$2$ io$($t$)+6$d io$($t$)+8$io$($t$)=0$

dt dt

Find:

$($a$)$ Characteristic Equation

$($b$)$ Natural frequencies

$($c$)$ State whether the system is critically damped, over damped, or under$-$damped

$($d$)$ the expression for io$($t$)$