Consider a mass-damper-spring system (G(s)=Y(s) / U(s)=1 /left(m s^{2}+b s+k ight)), where (m=1 mathrm{~kg}, b=8 mathrm{~N} cdot

Consider a mass-damper-spring system \(G(s)=Y(s) / U(s)=1 /\left(m s^{2}+b s+k\right)\), where \(m=1 \mathrm{~kg}, b=8 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\), and \(k=40 \mathrm{~N} / \mathrm{m}\).

a. Assume that the system is controlled in an open-loop control system with a controller \(K=40\). Determine the steady-state value of the response to a unit-step input. If the spring stiffness is actually \(50 \mathrm{~N} / \mathrm{m}\), recalculate the steady-state value of the response and determine the fractional change in the steady-state value.

b. Repeat Part

(a) assuming that the system is controlled in a feedback control system with a controller \(K=2000\).