The Yo-yo Oscillator (Analysis of a Nonlinear System using Spice)

Abstract

Unlike the simplest (Hooke's law spring) oscillator, where the restoring force is in magnitude proportional to the displacement; the yo-yo oscillator has a constant force-magnitude. In other words, its potential energy function is linear, as contrasted to the quadratic (harmonic) potential of the simple harmonic oscillator. The linear potential is responsible for a nonlinear equation of motion which yields many surprising solutions. Rich in complexity, these solutions are in some cases chaotic. Numerical solutions to the equation of motion are presently obtained using the 'simulation program for integrated circuit engineering' (Spice). The circuit employed involves operational amplifiers and solid state switches.