Use Nyquist stability criterion to investigate range of \(\mathrm{K}\) for closed loop stability for unity feedback systems with following loop transmittances.

(a) \(\mathrm{G}_{1}(s)=\frac{\mathrm{K}(s+1)}{\left(s+\frac{1}{2}ight)(s-2)} ; \mathrm{K}>0\)

(b) \(\mathrm{G}_{2}(s)=\frac{\mathrm{K}}{s(\tau s-1)} ; \quad \tau>0\)

(c) \(\mathrm{G}_{3}(s)=\frac{\mathrm{K}}{s(s+1)\left(s^{2}+2 s+2ight)}\)