Building and Analyzing the Bistable Duffing Oscillator

The Duffing oscillator is governed by the Duffing equation, which can produce linear, nonlinear, or chaotic motion. Chaos is a property of some types of differential equations which have sensitive dependence on initial conditions; any slight change in initial position will cause an exponential deviation from the expected trajectory. The Duffing oscillator can produce fractal behavior by transforming the phase portrait into cycles of the forcing term. The bistable case of the oscillator has been understudied analytically compared to the other cases of the Duffing oscillator. We designed a new magnetic Duffing oscillator with increased flexibility and degrees of freedom that other designs do not possess. Video tracking was used to measure the change in position, which is easier to implement than previous methods of position tracking. The unforced, damped and undamped bistable oscillator is analyzed, and steps are made towards deriving an analytical solution for these forms of the oscillator.