A $1$st order system is given with k$=250$ N$/$m$,$ c$=400$ N$/($m$/$sec$).(25$ pts$)$

Giving the system$$s transfer function G$($s$).$ Please indicate the value of time constant $\backslash$tau $.$

Write down the definitions for generic PI xss and ess.

Calculate its generic PI$,$ xss and ess, for step, impulse, ramp excitation, respectively.

Calculate its special PI$,$ tr for $95\%$ rise, td$,$ ts for $5\%$ error, for step excitation.