K G(s) (s + 1)(s + 2)(s + 5) a) Determine the differential equation that describes the system in the time domain with x(t) as the input and y(t) as the output. (1 mark) b) What is the order of the open loop system G(s)? What is its type? (1 mark) c) Determine the steady state error of the open loop system if the input is a unit step function. (0.5 marks) d) Determine the steady state error of the closed loop system if the input is (i) an impulse of magnitude 5, and (ii) a unit step function. Assume H(s)=1. (2 marks) e) f) g) Sketch the root locus of the closed loop system for 0