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Vibrations of a Hanging String

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This Demonstration plots the vibrational mode of a freely hanging string, with horizontal amplitude given by

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The label at the top of the plot gives the frequency of the mode selected by the second slider.

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Contributed by: Enrique Zeleny (September 2012)
Open content licensed under CC BY-NC-SA

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Details

The general solution for the vibrational problem is

,

with for , where is the length of the string, is the gravitational acceleration, and is the zero-order Bessel function of the first kind; the are the eigenfunctions. Only one term of the expansion, for a single value of , is plotted. The constants and are chosen here to be 1 and 0, respectively.

Reference

[1] P. Hagedorn and A. DasGupta, Vibrations and Waves in Continuous Mechanical Systems, Chichester, England: John Wiley & Sons, 2007.

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