5s HS) (s + 1)(8 + 4) a) Sketch the pole-zero plot on the s-plane. (5 pt.) b) Find the differential equation for the system with the transfer function, arranged in a standard form (descending orders of differentials with the coefficient of the highest order differential equal to 1). (10 pt.) c) Find the unit step response yu(t) and identify the transient and steady state components, yu(t)_tr, yu(t)_ss. (25 pt.) d) Find the steady state response Yss (t) to input u(t) = 1 + tsin(itt + Tt). (20 pt.) 5s HS) (s + 1)(8 + 4) a) Sketch the pole-zero plot on the s-plane. (5 pt.) b) Find the differential equation for the system with the transfer function, arranged in a standard form (descending orders of differentials with the coefficient of the highest order differential equal to 1). (10 pt.) c) Find the unit step response yu(t) and identify the transient and steady state components, yu(t)_tr, yu(t)_ss. (25 pt.) d) Find the steady state response Yss (t) to input u(t) = 1 + tsin(itt + Tt). (20 pt.)