E7.2 A tape recorder with a unity feedback speed control system has the loop transfer function

L(s) = Ge(s)G(s) = K s(s+1)(s2 +10s+24) a. Sketch a root locus for K, and show that the domi- nant roots are s = -0.41j0.384, when K = 8. b. For the dominant roots of part (a), calculate the settling time and overshoot for a step input.