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Lissajous figures are commonly created on oscilloscopes, by using signal generators to plot two oscillating signals against each other. The figure presented is created when there is a frequency ratio of 1:1 (in the video, the frequecies are both 100 Hz).
The same Lissajous figure can be created mechanically, as shown. The two tuning forks drive the oscillation of the laser beam. The upright tuning fork provides the vertical oscillation, and the horizontal tuning fork provides the horizontal oscillation. Striking both tuning forks is the equivalent of plotting two oscillating signals on the x- and y-axes of an oscilloscope.
If you're looking to build this, I used 256 Hz tuning forks. Higher frequency tuning forks will have a smaller amplitude signal. I clamped the tuning forks down to get a crisp sound and to deter misalignment from striking the tuning forks. I would highly recommend a lab jack or another sturdy object to raise your rotated tuning fork. Flexible objects (such as thin cardboard boxes) can dampen the tuning fork's oscillation. Tuning forks are not made with reflective surfaces, so a mirror is needed. Mylar is reflective, but it is not sturdy enough to stay flat enough to reflect a clear image. Common back-surface mirrors may not have a clear image since the light must be refracted through the glass before reflection. A green laser was used because it is in the middle of our visibility spectrum (so we see it as the brightest color).
This video was created thanks to expertise of many professors at the Buffalo State College Physics Department, and was funded by the Interdisciplinary Science and Engineering Partnership grant. The video was also prompted by the Western New York Physics Teachers Alliance.
For more information, visit Wikipedia or email me at eternalpupilphysics@gmail.com.
For more cool videos, visit my channel.