Natural Modes of Vibrations for Some Simple Systems

This Demonstration displays the animation of eigenmodes of some simple vibrating systems. The eigenfunctions and eigenvalues are evaluated by solving the eigenvalue
problem associated with the one- or two-dimensional wave equation. The systems considered are a fixed-fixed (left boundary condition-right boundary condition) string, fixed-fixed 1D rod, a 1D rod free at both ends, and a fixed square membrane. The rod in consideration is a 1D thin rod with no flexural bending. As the time slider moves, the evolution of the eigenmode in time is simulated using the general form of the solution to the wave equation. The sliders for mode 1 and mode 2 simulate the different eigenmodes—the first 10 modes for the system. Mode 2 is specifically for the simulation of the membrane, and is disabled for the one-dimensional systems.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+