A closed loop system has a transfer function given by 8 s + (1 + 0.5a)s +8 where a is the smaller of the last nonzero digits of the 2 student IDs. (i) Calculate the damping ratio, . (ii) Calculate the resonant peak, Mr. (iii) M(s) = Assume that the theoretical transfer function of the system is unknown and you want to estimate the shape of the frequency response. Using a sampling interval of 0.1s and a random noise signal of length 1000 as input, obtain the frequency response magnitude plot using Scilab. (iv) Read the value of the resonant peak from your plot in (iii).