You seem to have some excellent s/w at your fingertips: have you tried fourier analysis?
Please see attachments.
Is it possible to derive the equation for the "wiggle" (green wave) given the wiggle's amplitude and period as shown?
Or are there any suggestions as to how I might reach my ultimate goal, which is to derive the equation for the red wave?
(I know, I know, this should go in the Physics Help Forum Waves page--But I had problems uploading my thumbnails there, whereas here everything works smoothly.)
I confess that the details of Fourier analysis are somewhat out of my immediate reach as well nowadays (I used to know, I'm rusty now).
What it does is separate out a more-or-less complicated (but periodic) function into a sum of sine waves of various frequencies. In this case I wouldn't dream of doing it analytically, but there do exist tools which do it automatically. I used to use one many many years ago written in Fortran for analysing the pitch, roll and yaw of ships in heavy seas. I'd be very surprised if there isn't some free program out there somewhere that would do the job for you - but I've not been able to find one with a bit of cursory googling.
It's obviously a practical problem (you have some unwanted harmonics on a signal that ought to be a pure sine wave). Here's a link that may help, apologies if it's over your head, it's heavy going.