Consider the block diagram of a feedback control system shown below, where the controller gain is such

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Consider the block diagram of a feedback control system shown below, where the controller gain is such that \(K \geq 0\).

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(a) Find the system root locus with respect to the controller gain K.

(b) For what range of \(K\) is the system stable?

(c) Find the value of the gain \(K\) that will allow the system to have a root at \(s=-1+3 j\).

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