Exploring the non-linear oscillation of a rigid sphere on an elastic half-space

摘要

The nonlinear behavior characterises a wide range of physical phenomena. Finding solutions that describe the behavior of nonlinear systems with respect to time is usually a challenging procedure. In addition, it is important to express the solutions using elementary functions so they can be easily applied in practical applications. In this paper, an interesting nonlinear oscillation was explored; the oscillation of a rigid sphere on an elastic half-space. A simple methodology based on the conservation of energy was used to find the position of the sphere with respect to time. The data was then fitted to appropriate functions that can be used to describe the behavior of the system with different levels of accuracy. It was found that a Fourier series function is an accurate, yet simple solution to describe the sphere's behavior. In addition, approximate expressions that relate the period of the motion with respect to the range of displacements was also presented.