In this experiment, we explore the notion of non-linear and chaotic dynamics using the magnetic pendulum, acquire time orbits and phase-space diagrams through simulation, and finally understand the phase portraits.
The magnetic pendulum is a pendulum whose magnetic tip is influenced by a magnetic field produced by a disc magnet. We vary the distance between the tip of the pendulum and the magnet, as well as the driving frequency of the pendulum’s support. This results in a highly nonlinear dynamical evolution of the pendulum.
Using Physlogger, our homegrown data acquisition box, we can control the entire system and measure the angular displacements as well as the angular frequencies. This generated data can be displayed in a variety of ways (time series, phase portraits etc.) each revealing a particular aspect of the nonlinear system. We can also see period doublings, bifurcations and chaos through the phase portraits. There is also some computational effort that is required to understand this experiment.