Prob. 4 (25 pts). A system is described by the diagram shown below: R(s) Ge(s) G(s) C(s) G(s) = 10 K s² + 3s + 2 (a) For the given G(s), find the time constant for the uncompensated system. (b) Write down the characteristic equation for the uncompensated system, and use it to find the value of K at the root locus break-away point. (c) With K = 0.5, find the static error constant and steady-state error for the uncompensated system. (d) Design a lag compensator to give the system a steady-state error of 0.1, and write down the transfer function designed for Gc(s).