(Solved): (a) Prove that from the Nyquist Plots (Figure 1 below), an open loop transfer function of GH(s)=s(1 ...

(a) Prove that from the Nyquist Plots (Figure 1 below), an open loop transfer function of $GH(s)=\frac{K}{s\left(1+s{T}_1\right)\left(1+s{T}_2\right)}$ where $K,T_1$ and $T_2$ are all positive will resulted in i) $K<\frac{\left(T_1+T_2\right)}{T_1{T}_2}$, the system is stable ii) $K=\frac{\left(T_1+T_2\right)}{T_1{T}_2}$, the system is oscillatory iii) $K>\frac{\left(T_1+T_2\right)}{T_1{T}_2}$, the system is unstable b) Determine whether the closed loop system represented by the following open loop sinusoidal transfer function is stable $GH(j?)=\frac{100}{j?(1+j0.8?)(1+j0.25?)}$ (a) Rajah 1 / Figure 1