A robot force control system with unity feedback has a loop transfer function [6]

L(s) = KG(s) = K(s + 2.5) (s2 +25+2)(s2 + 4s +5)* (a) Find the gain K that results in dominant roots with a damping ratio of 0.707. Sketch the root locus. (b) Find the actual percent overshoot and peak time for the gain K of part (a).