Consider the system shown below, where gain K is any real number and P(s): r K...

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Consider the system shown below, where gain K is any real number and P(s): r K P(s) y 35 2 1 = S+4 (a) First find A(s) and then use it to compute the characteristic polynomial. [2 marks] (b) Suppose we require one closed-loop pole to be located at s = -3. Determine the required value of K (- < K < ) and the resulting location of the second pole. [3 marks] (c) Suppose we require the closed-loop system to be critically damped. Determine the required value of K (-o < K < o) and the locations of the closed-loop poles. [3 marks] Consider the system shown below, where gain K is any real number and P(s): r K P(s) y 35 2 1 = S+4 (a) First find A(s) and then use it to compute the characteristic polynomial. [2 marks] (b) Suppose we require one closed-loop pole to be located at s = -3. Determine the required value of K (- < K < ) and the resulting location of the second pole. [3 marks] (c) Suppose we require the closed-loop system to be critically damped. Determine the required value of K (-o < K < o) and the locations of the closed-loop poles. [3 marks]