Conclusion

When there is no forcing on the system, one of the magnets attracts the beam until it comes to rest. The initial velocity, forcing term and parameters play a role in deciding where the beam oscillates. By increasing the amplitude of the forcing term, solutions went from oscillating around one steady state, to being chaotic, to oscillating around both steady states.

One way to improve the model would be to include a constant that measured the strength of the magnets.