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## Homework Statement

A charge

*+q*of mass

*m*is free to move along the

*x*axis. It is in equilibrium at the origin, midway between a pair of identical point charges,

*+Q*, located on the

*x*axis at

*x = +b*and

*x = -b*. The charge at the origin is displaced a small distance

*x << a*and released. Show that it can undergo simple harmonic motion with an angular frequency

omega=(4kqQ/(mb^3))^(1/2)

## Homework Equations

E=k

_{e}(q/r

^{2})

(1+c)

^{n}is approximately equal to 1+nc

a=x(omega)^2

## The Attempt at a Solution

Well, I'm not really asking for a solution per se. I get the question, got the

*correct*answer, how it was done; what I want to know is why my method is wrong.

I got it by first using Coulomb's law to set up a force comparison, between the point-charge in the origin, and one of the point charges next to it. So...

F=kqQ/b

^{2}=ma

Where I substituted a for x(omega)^2.

Solving for omega got me close to the correct answer, but my TA could not explain why my method was wrong...so I'm curious why.

My answer was omega=(kqQ/(mb^3))^(1/2)

Any takers?