As a math person, I look at this and think "Fourier series".
I encountered the ideas in both Classical Mechanics 1 (third year physics course where I took it) and Differential Equations (third year math course where I took it).
It's very close to Fourier series, but since the "solutions" (the equilibria) are not integer multiples of a fundamental, but solutions to a 3-dimensional wave equation, it's more like "wave equation."
From a mathematician's point of view it is a Fourier series. You have the property that any starting state can be divided into the sum of orthogonal components. No matter how complex the components are, that's still a Fourier series.
A physicist would disagree, I am sure. But to a mathematician, an orthonormal wavelet basis is also a Fourier series.
