Draw a Nyquist diagram for each of the following systems and compare the result with that obtained using the MATLAB command Nyquist.

(a) \(K G(s)=\frac{K(s+2)}{s+10}\)

(b) \(\quad K G(s)=\frac{K}{(s+10)(s+2)^{2}}\)

(c) \(\quad K G(s)=\frac{K(s+10)(s+1)}{(s+100)(s+2)^{3}}\)

Using the plots, estimate the range of \(K\) for which each system is stable, and qualitatively verify the result using root locus plot (generated by hand or using MATLAB).