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The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied from $0$ to $\infty.$

Select the transfer function $G(s)$ that results in the root-locus plot of the closed-loop system as shown in the figure.

  1. $G(s) = \frac{1}{(s+1)^{5}}$
  2. $G(s) = \frac{1}{s^{5}+1}$
  3. $G(s) = \frac{s – 1}{(s+1)^{6}}$
  4. $G(s) = \frac{s + 1}{s^{6}+1}$
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