Kinematics of a 2D Asymmetric Nonlinear Oscillator

Abstract

Motion of a point-like massive particle under the influence of two nonidentical linear springs conducive to an irregular planar oscillation is analyzed. For a two dimensional oscillations the equation of motion is a coupled highly nonlinear differential equation. The set of equations cannot be solved analytically. Utilizing a Computer Algebra System (CAS) such as Mathematica [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390031003500360035003100380030000000 we solve the equations numerically. Kinematics of the particle is presented. For a comprehensive visual understanding the oscillations are simulated. We also include an extended atlas of useful two-dimensional time-folded diagrams.