- #1

Jean-C

- 5

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## Homework Statement

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 x

_{eq}. 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.

## Homework Equations

The electric force between two charges :

F=k

_{ec}qQ/r

^{2}

where r is the distance between the two charges.

Note : I used k

_{ec}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.

## The Attempt at a Solution

[/B]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=k

_{ec}(2*-1)/(x

_{eq}-0)

^{2}+ k

_{ec}(-1*-1)/(x

_{eq}-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/x

^{2}.

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!