Nonlinear Resonance

This program demonstrates the properties of nonlinear resonance in the following equation. At the moment it is not very sophisticated nor interactive. See pages 87 to 93 of Landau and Lifshitz Mechanics for a detailed explanation. The differential equation is that of a damped, driven anharmonic oscillator with fourth order/higher terms dropped. One finds interesting facts about what resonant frequencies can be chosen. The simulation needs more work done before it can be interacted with in real time, though it should be straightforward to more accurately plot the steady state magnitude (Fig. 32 L & L) and plot the oscillator movement without so many dumb/time consuming calculations.

\[\ddot{x}+2\lambda \dot{x}+\omega_0^2 x=\frac{f}{m} \cos(\gamma t) - \alpha x^2 - \beta x^3 \]