Acoustics and Vibration Animations
Daniel A. Russell, Ph.D.
Graduate Program in Acoustics
The Pennsylvania State University
All text and images on this page are ©2004-2011 by Daniel A. Russell
and may not used in other web pages or reports without permission.

Mode Shapes for a Hanging Chain

Take about 30 paper clips, and connect them end-to-end in a long chain. Hold one end of the chain in your fingers and let the other end dangle. Gently swing (or twirl) the chain and you should find that the chain will "lock" in on a very specific mode shape which occurs at a particular natural (resonance) frequency.

The shapes of vibration which the chain will "lock" onto are defined by Bessel Functions [More mathematical details to follow soon]

The figures below show the first three mode shapes for a hanging chain.

Mode 1	Mode 2	Mode 3

MPEG movie for mode 1	MPEG movie for mode 2	MPEG movie for mode 3

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