1) Construct the Bode log-magnitude and phase plots and then obtain the gain margin and phase margin for the following open loop transfer functions:- a) G(s) = b) G(s) = = 10,000 (s+5)(s+20)(s +50) 1 s(s+2)(s+4) 8 +5 c) G(s) = (s+2)(s+4) (8+3)(s+5) d) G(s)= s(s+2)(s+4) S e) G(s) = K(s+6) e) G(s): = f) G(s= (s+7)(s26s+13) s(s² +48 +25) 100(s+2) s(8 + 1)(s+4) = for K 4, 40, 400 2) Given the following system characteristic equations (assuming no open loop zeros, an open loop pole with value 0, and negative unity feedback), construct the Bode log-magnitude and phase plots and then obtain the gain margin and phase margin:- a) 83+5582 +2508 + 500 = 0 b) + 2682 +258 +50 0 c) 3+30s2+234 +420 = 0