Sketch Nyquist plot for each of the following loop transmittances and investigate range of \(\mathrm{K}\) for closed loop stability:

(a) \(\mathrm{G}(s) \mathrm{H}(\mathrm{s})=\frac{\mathrm{K}(s+1)}{\mathrm{s}^{2}(s+2)(s+4)} ; \mathrm{K}>0\)

(b) \(\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(s-1)}{s(s+5)(s+6)(s+7)} ; \mathrm{K}>0\)

(c) \(\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}(s+3)}{s(s-1)} ; \mathrm{K}>0\)