Vibrations of a Hanging String

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


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



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.


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

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.