Consider the following block diagram where (K) has a fixed value (e.g., (K=1)) and the parameter of

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Consider the following block diagram where \(K\) has a fixed value (e.g., \(K=1)\) and the parameter of interest is \(c\).

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(a) Find the root locus of the system with respect to the parameter \(c\).

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

(c) Find the value of the gain \(c\) that will allow the system to have a root at \(s=-\frac{1}{2}\).

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