Problem 1 The closed-loop transfer function of a certain linear system is KF(s) 1+ KF(s) H(s) = with + 88 + 52 s( + 6s + 288 + 40) (s+ 4)? + 36 s(s + 2)(s + 2)2 + 16| F(*) = Find the range (if any) of the forward gain K for which the closed-loop system is stable. Problem 2 Sketch the locus of poles of the system of Problem 1, showing important parameters, including segments (if any) on the real axis crossings (if any) of the imaginary axis asymptotes as K o. Problem 3 Sketch the Nyquist diagram for F(s) of the system of Problem 1, showing important properties, including behavior as w0 behavior as w0 crossings (if any) of the real axis crossings (if any) of the imaginary axis region of stability