\[G(s) = \frac{10}{s(s+1)(Ts+1)} \Rightarrow G(j\omega) = -10\frac{(T+1)\omega^2 + j(\omega - T\omega^3)}{(T+1)^2\omega^4 + (\omega - T\omega^3)^2}\]

\[T = \frac{1}{\omega^2} = 3,\ G\left(j\frac{\sqrt{3}}{3}\right) = -\frac{\pi}{4M} \Rightarrow M = 0.1\]

\[G(z) = 5(1-z^{-1})Z\left[\frac{1}{s-2} - \frac{1}{s}\right] = \frac{1.1}{z-1.22}\]

\[\Rightarrow \Phi(z) = \frac{G(z)}{1+G(z)} = \frac{1.1}{z-0.12}\]

\[\Rightarrow C(z) = R(z)\Phi(z) = \frac{1.1z}{(z-0.12)(z-1)}\]

\[|G(j\omega_c)| = 1 \Rightarrow \omega_c = 7.86\]