Vibrations of a Hanging String
This Demonstration plots the vibrational mode of a freely hanging string, with horizontal amplitude given by[more]
The label at the top of the plot gives the frequency of the mode selected by the second slider.[less]
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.
 P. Hagedorn and A. DasGupta, Vibrations and Waves in Continuous Mechanical Systems, Chichester, England: John Wiley & Sons, 2007.