# Duffing_Orbit Applet

## Position y(t) of a Duffing-oscillator

The time-dependent position y(t) of a Duffing-Oscillator is a solution of the following differential equation:

d^{2}y/dt^{2} + δ·dy/dt + α·y + β·y^{3} = γ·cos(ω·t)

α is the square of the angular resonance-frequency for β = 0. In a mechanical system, α is the spring-constant divided by the mass of the oscillator.

β is the nonlinear spring-constant divided by the mass. β>0 is a hardening spring.

γ is the amplitude of the harmonic forcing (force per mass).

δ is a coefficient of friction (friction proportional to velocity).

ω is the angular frequency of the forcing.

y(0) is the initial value of the position at time t=0.

The initial velocity is 0.

steps is the number of steps (per cycle of the forcing) for the numerical integration of the motion (4th order Runge-Kutta integrator).

And here is the source-code: Duffing_Orbit.java

Created with BlueJ 3.0.5 (Java version 1.6.0_26) running on Mac OS X 10.6.8

October 10th, 2011, Martin Lieberherr