Consider a unity feedback system with open loop transfer function G(s) = k(s+7)/(s+5)(s2+2s+5) (a) sketch the root locus of the system as k changes from zero to infinity. (b) if a series compensator with a transfer function (s+2) is inserted in the above loop, sketch the new root locus. (c) Comment on your result as related to the properties of PD compensators with regard to damping and transient response characteristics.