PERIODICALLY FORCED PENDULUM:  ILLUSTRATE PERIODIC, MULTIPLY PERIODIC AND CHAOTIC ORBITS.

 

The above sketch shows the hookup.  The torque motor is driven by an audio oscillator attached to an audio amplifier (DC - so very low frequency of forcing is possible).  Use the audio oscillator in the SINE WAVE MODE ONLY.

Clamp the pendulum firmly to a desk.  Driver and amplifier look like:

 

The motor connects to the right rear output as shown below:

 

Adjust amplitude and frequency of forcing to get various states:

  1. Weak amplitude "stable" oscillation about the down position.
  2. Periodic over the top modes
  3. Multiply periodic over the top modes (requires careful adjustment of amplitude and frequency - try it out ahead of time).
  4. Chaotic over the top modes.

 QT Movie of Periodic Orbits       (Big Screen Version)

QT Movie of Chaotic Orbits         (Big Screen Version)


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2000.  John Hart, University of Colorado