You are given the following transfer function, H(s) = 20 (s + 5s + 25) (s + 0.2) (s + 5s + 2500) (a) Plot the bode diagram clearly showing the slopes of the asymptotes and the height of any peaks. Compute the exact phase and magnitude at the frequencies o = 5 rad/s, co= 50 rad/s. Specifically plot the points at co = 5 rad/s, o = 50 rad/s and clearly mark these points on your Bode plot. Explain why your results make sense with regards of heights of peaks and asymptotes. Your explanation is important. (Do not use Matlab! A Matlab graph will not be accepted) (b) The input to the system is x(t) = 10 sin(100t), what is the output, y(t) in steady state? Roughly sketch both the input and the output on the same graph. Explain your sketch based on the Bode diagram.