E6.6 A negative feedback system has a loop transfer function (a) Find the value of the gain when the of the closed-loop roots is

E6.6 A negative feedback system has a loop transfer function

(a) Find the value of the gain when the ζ of the closed-loop roots is equal to 0.5.

(b) Find the value of the gain when the closed-loop system has two roots on the imaginary axis.

L(s) = G(s)G(s) = K(s+1) s(s-2)