P$3.$ The position control system is described by the differential equation:

d$2$y$($t$)$dt$2+4$dy$($t$)$dt$+16$y$($t$)=8$Kr$($t$)\backslash$frac$\{$d$^2$y$($t$)\}\{$dt$^2\}+4\backslash$frac$\{$dy$($t$)\}\{$dt$\}+16$y$($t$)=8$K r$($t$)$dt$2$d$2$y$($t$)+4$dtdy$($t$)+16$y$($t$)=8$Kr$($t$)$

$($a$)$ Find the unity feedback gain KKK for a $12\%$ overshoot.

$($b$)$ Find the settling time for a $3\%$ error.

$($c$)$ Find the step response and the steady$-$state error.$\text{'}$