Q1. In simple cases the root locus diagram (the paths taken by the closed-loop poles then a parameter, e.g., the gain, is changed) can be found exactly by algebra. In this way (i.e., not using the 'rules') draw the root locus, for \( K \) increasing from zero, for the following open-loop transfer functions:
(a) \( G(s)=\frac{K}{s+1} \)
(c) \( G(s)=\frac{K}{s^{2}} \)
(b) \( G(s)=\frac{K}{s(s+1)} \)
(d) \( G(s)=\frac{K}{(s+1)^{4}} \)
