PhysMag: Nonlinear Dynamics with a Magnetic Pendulum

The Experiment
 

• Exploring the notion of nonlinear and chaotic dynamics using a "magnetic pendulum"
• Experimental observation of the onset of period-doubling bifurcations
• Acquiring time orbits and phase-space diagrams, through simulation and experiment
• Understanding phase portraits

 
How does it work?
 

        The apparatus, which Qosain Scientific calls Physmag, comprises a pendulum with adjustable height and detachable permanent disk magnets, one set on the tip of the pendulum and the second set on the top of the magnet holder, underneath the pendulum. The shaft of the pendulum is attached to a crank mechanism that gives rise to controlled horizontal oscillation. Our flagship data logger, Physlogger controls the stepper motor that drives the rank mechanism, and also logs angular displacement of the pendulum from the optical angle sensor attached with the hinge of the pendulum. Hence we can measure three quantities in real time:
 

1. Rotation rate of the crankshaft powered by a motor with user-variable RPM
2. Angular displacement of the pendulum measured by our specialized analog angle sensor
3. Derivative of the angular displacement is computed in our software

  
Explore further
 

• Phase portraits
• Poincare maps
• Bifurcations and Lyapunov exponents
• Hysteresis of nonlinear systems

 
Major parts included
 

• Magnetic pendulum machine
• Sets of disk magnets
• Specialized Physlogger with inbuilt motor control
• Qosain Scientific’s analog angle sensor

Not included
 

• PC