Wolfram Demonstrations Project

This Demonstration plots the

vibrational mode of a freely hanging string, with horizontal amplitude given by

The label at the top of the plot gives the frequency

of the mode

selected by the second slider.

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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Vibrations of a Hanging String