Sine Waveform Cars
Manish Jain

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 509–512
Short Papers

Abstract

We construct a car with a pen holder which is such that the locus of the pen traces the waveform of the sine curve. Further, we show how adjustments to different aspects of the construction lead to changes in the frequency or the amplitude of the waveform. This is driven entirely by the mechanism that is fitted on the front wheels. By additional tweaks to the rear wheels and by shifting the location of where the pen attaches to the overall mechanism, we also design cars that can “draw” linear combinations of the sine and the cosine functions. By incorporating additional circles to the car, we can get Fourier series, and by adding any number of sinusoids we can approximate any function. A similar machine was made by Michelson almost 100 years ago, although the mechanism for addition of sinusoids and generating sinusoids was completely different.

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