A unity feedback system has a loop transfer function

L(s) = Ge(s)G(s) = 4(s + z) s(s + 1)(s + 3) (a) Draw the root locus as z varies from 0 to 100. (b) Using the root locus, estimate the percent overshoot and settling time (with a 2% criterion) of the system at z = 0.6, 2, and 4 for a step input. (c) Determine the actual overshoot and settling time at z = 0.6, 2, and 4.