In a control system with a negative unity feedback, the open-loop transfer function is as follows: Determine

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In a control system with a negative unity feedback, the open-loop transfer function is as follows:

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Determine the sensitivity of the maximum overshoot percentage of the closed-loop system's response to a unit step input with respect to the damping ratio \(\left(S_{\xi}^{O . S}ight)\) around the rated damping ratio \(\left(\xi=\frac{\sqrt{2}}{2}ight)\).


1) \(-2 \pi\)
2) \(-\pi\)
3) \(2 \pi\)
4) \(\pi\)

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