1) I utterly misread Paul's note. The dictionary and I agree with what he
was saying. Sorry.
2) My paraphrase of the dictionary unwisely omitted the requirement that
all the frequencies in a harmonic function must be in arithmetic
progression. Sorry again.
This requirement is important; otherwise you could construct an aperiodic
function (by using sine waves with incommensurable frequencies). We say
that a real-world piano string is slightly anharmonic because the higher
partials are not exact multiples of the fundamental.
At 03:06 PM 6/28/01 -0400, John S. Denker wrote:
>At 11:36 AM 6/28/01 -0700, Paul O. Johnson wrote:
>>I believe that Harmonic Motion is any motion that is repetitive and
>>follows the same closed path in one direction or the same open path in
>>two directions (forth and back). The rate of motion (velocity) can vary
>>with time in any way.
>>
>>Simple Harmonic Motion is Harmonic Motion in which the rate of motion
>>varies sinusoidally with time.
>
>I don't think that's the usual definition.
>
>According to the Century dictionary
> http://216.156.253.178/CENTURY/04/index04.djvu?djvuopts&page=53
>
> -- A harmonic function is a sum of sine waves.
> -- A simple harmonic function is a single sine wave.
> -- Simple harmonic motion is expressible as a simple harmonic function of
>time.
>
>... which sounds about right to me.