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:
d2y/dt2 + δ·dy/dt + α·y + β·y3 = 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