[neltnerb]

Excellent point, lots and lots and lots and lots of physical objects are harmonic oscillators. That does have pretty fundamental grounding in physics.

I can think of lots of other places I'd use fourier analysis (at least qualitatively as with doing diffusion modeling in my head) but you're right that sinusoids are more physically "real" whereas being possible to represent in any basis set is more "valid" if that makes any sense.

Not quite sure what the right word is on this one, but I agree "real" kind of suggests real oscillators underlying the phenomena. Square waves are less physical because of discontinuities in both the signal and derivative; nature really doesn't care for discontinuities.