Study of Cubic Characteristic Equation by Root-Locus Method

It is shown in this paper that all possible roots of a cubic characteristic equation lie on a portion of a hyperbola and of its axis. This hyperbola may be sketched readily from the values of the coefficients of the cubic equation. Hence the change of the roots of the cubic equation due to any change in its coefficients may be visualized. The discussion of the transient response in relation to possible root configurations is included. A root-locus chart is provided for “universal” use. Results from an analog computer are shown to be agreeable with those in this paper.