I'll assume you are like the rest of Americans, and can't read. So I'm transferring my private energy to the rubber band. That lubricates the surface, sending Tonya to go into her spins. And this tells you what those little vibrators are up to. This is a very rich topic, so if you really like algebra, you should go into plasma physics.
Physicists define interesting problems as the ones they can do.
So, a complicated dynamics problem is, by definition, uninteresting. This, of course, is only useful for scattering AM radio waves off a charged elephant. Theorists, of course, know how to take a Fourier Transform. You don't actually prove this, but there are ways to motivate it. Maybe I'll invite you not to think about it too much.