This came up when a student asked me. A simple question one might think. Except… how to define one without tautology? That is, without using the word "sine" (or cosine for that matter). Wikipedia does not help, although the moving disc might be of relevence.
In short, I suspect his teacher has given him a severely hard problem, though I may be wrong.
This came up as part of an electronics course. So presumably any answers can be derived from the characteristics of various components/circuits.
Best Answer
Start with this:
simulate this circuit – Schematic created using CircuitLab
Say:
Ask yourself (or the student(s)):
Clever students will say: yeah, well, it's a fast change of voltage across L1, so it will take some time until things look more "DC-y", and current starts flowing through L1 and discharge C1, so that the overall potential will be 0V.
Oh yeah, that now stores the energy from the capacitor
No, the magnetic field energy has to go somewhere. So the Capacitor charges again.
Now comes the hard part, and I'm afraid you'll be able to do nothing about it: You need to say: hey, this is a sine, it fulfills that condition.