Nonlinear effects in a simple mechanical system

Abstract

We describe a nonlinear mechanical system that is easy to construct and demonstrates most of the nonlinear effects associated with mechanical systems. The equation of motion for the system is easily derived through a geometrical argument and is found to be Duffing’s equation. The relative strengths of the linear and nonlinear terms can be easily varied and it is possible, in principle, to make the linear term vanish completely. The system is also considered in a driven form. Periodic motions of the system are analyzed theoretically and the results are compared with experiment. Nonperiodic motions are also considered.