Problem $4.(20$pt$)$ Performance indicators of $2$nd order system.

$($a$)(10$pt$)$ Consider the following spring$-$mass$-$damper system with zero initial

conditions.

Let $m=1kg,k=36\frac{N}{m},b=8N*\frac{s}{m},$ and $F(t)=36f(t).$

For step response, find rise time, settling time, overshoot, peak time, and

peak value.

$($b$)(10$pt$)$ Find the steady state error of the ramp response $($ess $=$ f$($t$)$x$($t$)=$ t $$ x$($t$)).($hint: Use final value theorem.$)$

Bonus Problem. $(20$pt$)$ In Problem $4,$ find the steady state error of the time response where

f$($t$)=$ sin $6$t$.($hint: The steady state error would not converge.$)$