The loop transmittance of unity feedback system is

\[
\mathrm{G}(s)=\frac{\mathrm{K}}{s(1+s)(1+0.1 s)(1+0.01 s)}
\]

(a) Sketch asymptotic \(\mathrm{dB}\) plot and phase plot for \(\mathrm{K}=1\) to find gain cross over frequency, phase cross over frequency, GM, PM and whether closed loop system is stable?

(b) Determine valve of \(\mathrm{K}\) so that \(\mathrm{GM}=+10 \mathrm{~dB}\)

(c) Determine value of \(\mathrm{K}\) so that \(\mathrm{PM}=+25^{\circ}\)

(d) Determine value of \(\mathrm{K}\) so that gain cross over frequency is \(0.3 \mathrm{rad} / \mathrm{sec}\). Is the system closed loop stable for this value of \(\mathrm{K}\) ?