Simulations. Consider the following parameter values exp

Simulations. Consider the following parameter values expressed in SI units: m = 12, L = 1 2 , g = 9.8, ? = 0.01, J = 400, ? = 20, ?0 = ??6, with ?0 determined by the relation (3). (a) Using the above parameter values, construct a root locus plot of the poles of HK(s) as K varies over an interval containing Kc. Verify that a pair of poles cross from the left half plane to the right half plane as K increases through Kc. (b) Conduct computer simulations of the system (i), (ii) in Problem 6 using the above parameter values. Do this for various values of K less than Kc and greater than Kc while experimenting with different values of y(0) ? 0 to represent departures from the equilibrium operating point. For simplicity, you may always assume that ?(0) = ?? (0) = 0. Plot graphs of the functions ?(t) and y(t) generated from the simulations. Note that if ?(t) wanders outside the interval [??0, ? ? ?0], the results are nonphysical. (Why?) Are the results of your simulations consistent with your theoretical predictions? Discuss the results of your computer experiments addressing such issues as whether the feedback control strategy actually works, good choices for K, stability and instability, and the