Question: The open loop transfer function of a unity feedback system is [ mathrm{G}(s)=frac{k}{s(s+2)} ] It is specified that the response of the system to a

The open loop transfer function of a unity feedback system is
\[
\mathrm{G}(s)=\frac{k}{s(s+2)}
\]
It is specified that the response of the system to a unit step input should have maximum overshoot of $10 \%$ and the settling time should be less than one second.
(a) Is it possible to satisfy both the specification simultaneously by adjusting $k$ ?
(b) If not, determine values of $k$ that will satisfy the first specification. What will be the settling time and the time to reach the first peak for this case?

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