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2. Question (25 marks) A typical 2nd order dynamic system, frequently encountered in autocars, is expressed by block diagram connections in Figure Q2. R(s) E(s) Y(s) s(s+260.) Figure Q2 a) Determine the closed loop transfer functions Y9 and ), and briefly interpret the roles R(s) R(S) of the transfer functions. [5 marks] b) The damping ratio 5 is a very important factor to influence the system response. With the five group of the damping ratios given below, indicate the corresponding pole's positions on the plane and sketch the system responses to a unit impulse stimulation. b.1) 0<5<1 [3 marks] b.2) (>1 [3 marks] b.3) 6 = 0 [3 marks] b.4) -1 < 5 <0 [3 marks] b.5) 5-1 [3 marks) c) With reference to Figure Q2, 5=0.5 and 6. = 2, determine the closed loop system steady state error to a unit reference input. [5 marks] =