Harvard University,FAS
Fall 2003

Mathematics Math21b
Fall 2003

Linear Algebra and Differential Equations

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu

The double pendulum (An example of a chaotic dynamical system)

Computer Simulation

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Here is what it would look like:
Credit: Java program written by Peter Selinger


A real pendulum



Credit: The pendulum was built by Kyle Clark (a student of this linear algebra class), in January 2004.
We wondered, whether it is possible to track the motion of the pendulum by placing a buzzer on the pendulum, record the sound, analyze the frequency of the buzzer, which changes due to the Doppler effect. We recorded the motion with a standard digital camera, extracted the sound from it and fed it into Mathematica, with which we computed the Fourier spectrum on 2600 time intervals within the recorded 30 seconds (see movie) and plotted the data (see picture). The experiment shows that such measurements are in principle possible.




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