Question: The open loop transfer function of a closed loop system is [ mathrm{G}(s) mathrm{H}(s)=frac{mathrm{K}}{s(s+1)(2 s+1)} ] Determine phase cross over frequency (omega_{p c}) and gain

The open loop transfer function of a closed loop system is

\[
\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}}{s(s+1)(2 s+1)}
\]

Determine phase cross over frequency \(\omega_{p c}\) and gain margin in terms of \(\mathrm{K}\). Is the closed loop system stable for \(\mathrm{K}=2\) ? What is critical value of \(\mathrm{K}\) for stability ?

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