Large amplitude free vibrations of a mass grounded by linear and nonlinear springs in series

This communication is concerned with the large amplitude free vibration of a mass grounded by linear and nonlinear springs in series. Based on a single equation of motion in terms of relative displacement variable, a qualitative analysis is completed and some new and interesting dynamic behaviors are discovered. These behaviors include oscillations in asymmetric single potential wells and existence of asymptotes in phase plane for the case of softening springs. The ranges of oscillations are determined and expressions of exact periods for symmetric and asymmetric oscillations are established. Furthermore, the construction of analytical approximations to period and periodic solution is briefly described.