2. (a) Plot a pole-zero map for the system G(s) = S - 10 (s-1)(s + 4) (s + 2s + 10) (i) Comment on the stability of this system. (ii) Which, if any, of the poles of this system give rise to oscillations? (b) Consider the second order differential equation dx dt +4r(t) = r(t) given that r(0) = '(0) = 0. Find the transfer function for the input-output system governed by this differential equation. [4 marks] Find the total response to the input r(t) = sin(3t), indicating the tran- sient response and the steady state response. [A complete solution is required here.] (c) Sketch a graph of the function defined by h(t) = and find its Laplace Transform. [6 marks] 2, 0