1. The problem statement, all variables and given/known data I got an alpha particle (charge 2+) fixed at x=0 and an electron fixed at x=2. I then add a fluor ion (charge 1-) to the right of the electron and we note his position xeq. The question is to find the constant spring (k) relative to the harmonic oscillation made by the fluor atom for small movements around its equilibrium. 2. Relevant equations The electric force between two charges : F=kecqQ/r2 where r is the distance between the two charges. Note : I used kec so It is clear it is different from the spring constant k. The force in an harmonic oscillator : F=-kx where k is the constant I'm looking for. 3. The attempt at a solution It is easy to see that the motion is that of an harmonic oscillator but I can't demonstrate it mathematically. I start off by finding the equilibrium position by finding where the resulting force is 0 : F=kec(2*-1)/(xeq-0)2 + kec(-1*-1)/(xeq-2)2 With that I found out the the equilibrium position was at 2(2+sqrt(2)). But then I have no idea how to find the relative constant k since the equation isn't linear in x like F=-kx but rather like F=k/x2. My first idea is to transform the equation to a linear one and then isolate k, but I can't seem to find how. If anyone can give me a cue as to how to do that or to find k I'd be very grateful! Thanks!