A fourth order system is expressed in terms of the characteristic equation as \$s^4 + 8s^3 + 24s^2 + 32s + k = 0\$
Using the Routh’s array criterion determines the value of the gain parameter k and the corresponding roots for the following two cases:
(i) System time-domain response is undamped oscillations.
(ii) System time-domain response comprises of damped oscillations.
I was able to find the stability range of parameter k as \$0<k<80\$, but I'm struggling to understand how to find the roots when system gives undamped and damped oscillations.