Phase Space of an Intermittently Driven Oscillator

This Demonstration explores the position-velocity phase space of a damped oscillator, where a freely running drive is coupled to the oscillator only when the position is between and . The parameters: denotes the angular frequency of the oscillator, the damping coefficient, the amplitude of the drive, and the angular frequency of the drive. You can also vary the initial conditions of the position , velocity , and the initial phase of the drive .

The dynamical equation of the system can be written as

,

where

This can also be written as

,

,

.

The system behaves chaotically for smaller values of but reduces to an ordinary driven damped harmonic oscillator performing periodic oscillations as is increased.