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Potential Energy Formulae

The potential...

Question

The potential energy of an oscillating system is given by
$U = a - \frac{b}{x} + \frac{c}{x^{2}}$ where $a, b, c$ are constants and $x$ is the displacement. What is the force constant of the system for small oscillations?

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Solution

$F = \frac{d U}{d x}$
$= \frac{d}{d x} a - b x^{- 1} + c x^{- 2}$
$F = \frac{b}{x^{2}} - \frac{2 c}{x^{3}}$

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