Now, how are damping factors used? Well, one way they are used is in the only thing as cool as math: MUSIC! 
rednote.gif (1817 bytes) Music is an intricate combination of sine waves. This is what 5 seconds of  Autumn Fell looks like:

af1.gif (6549 bytes)

If we zoom in to look at just .07 seconds (7/100 of a second) of this song, we find something that looks just like a messy trig function!

af2.gif (7641 bytes)

It looks similar to something I can graph on my calculator...

csine2.gif (773 bytes)

sinecmb1.gif (4468 bytes)
(Graphing window: x on [-15.58, 15.58], y on [-4, 4])

So, where do damping functions come in? They're used at the end of the song, where the sound "fades out!"

When the song's final mix is done, the producer decides if and how the song should be faded out. The process is all done by computer! The software used,SAW Plus in this case, gives the engineer three main choices:

1) Linear Fade
2) Logarithmic Fade
3) Inverse Logarithmic Fade
    (Remember that inverse logs are just exponentials!)

This is how the end of Autumn Fell looks and sounds before it is faded:

af1.gif (6549 bytes) speaker1.gif (364 bytes) press to listen