1. a) For the open loop transfer function given G(s)H(s): = K s(s+4s+5) draw the root loci and obtain the following i) Limiting value of K for stability ii) Find K and closed loop poles corresponds to a damping ratio of 0.5. iii) Analyze the stability of the system. iv) for K =2, what are the closed loop poles, is it a part of the root locus? Clearly mention all steps used to plot root locus and K. b) Verify the answers by obtaining root locus and step response using simulation tools.