Modes of Vibration - Animation

A guitar string, plucked at the centre, will be stretched into a triangular shape before you let it go. Once you let it go it will vibrate in a "triangular sort of way". The thing about its motion is that it can be thought of as a superposition of simple harmonic motions, with harmonically related frequencies, as shown here. The "more or less triangular" vibration in the lowest panel arises as a weighted sum of the three modes of vibration shown above it. 

This animation complements Figure 1-3 of "Auditory Neuroscience"

Modes of vibration of a 2-D plate - youtube video

In this youtube video, a black, square plate is made to vibrate sinusoidally at a given, gradually increasing frequency. A white powder, sprinkled onto the plate, will come to rest only at the nodes of the predominant mode of vibration of the plate, which renders the nodes visible as white lines. As the frequency increases, it excites modes of vibration of ever higher order, making intricate patterns consisting of increasingly larger numbers of lines.  Note that here the plate is excited with a sinusoidal vibration, so it will exhibit only one mode of vibration at a time, the one that corresponds to the overtone closest to the input frequency. If the plate was instead struck, it would vibrate at all these modes at once, making a rich, metallic "clink" sound with lots of overtones.