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## Homework Statement

The potential energy function of a particle of mass m is V(x) = cx/(x

^{2}+a

^{2}), where c and a are positive constants.

Qualitatively sketch V as a function of x. Find two equilibrium points: identify which is a position of stable equilibrium, and find the period of small oscillations about it.

## Homework Equations

PE=0.5mv

^{2}=-0.5kx

^{2}

## The Attempt at a Solution

I think I'm supposed to differentiate and let it equal to zero which gave me:

(c(x

^{2}+a

^{2}) - 2cx

^{2}) / (x

^{2}+a

^{2})

^{2}= 0

cx

^{2}+ ca

^{2}- 2cx

^{2}= 0

x = a

Putting that into the function gave me: V(x) = cx

^{2}/2x

^{2}= c/2

I don't know if any of this is necessary but it doesn't answer the question. Also when it says sketch do I just sub value of x in? Any help would be greatly appreciated.