Credit: The pendulum was built by
Kyle Clark
(a student of this linear algebra class), in January 2004.
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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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