Consider the open loop transfer function of a system
\(G\left( s \right)H\left( s \right) = \frac{{K\left( {s + 4} \right)}}{{s\left( {s + 3} \right)}}\)
The root locus of the system consists of a circle as shown in the figure below.
The equation of the circle is
1
(σ + 3)2 + ω2 = 4
2
(σ – 3)2 + ω2 = 16
3
(σ – 4)2 + ω2 = 3
4
(σ + 4)2 + ω2 = 4