= Harmonic approximation
{title2=$V(x)\simeq V(x_0)+\tfrac12V''(x_0)(x-x_0)^2$}
Near a <stable equilibrium> $x_0$ with $V'(x_0)=0$ and $V''(x_0)>0$, the harmonic approximation truncates the <Taylor series> of the <potential energy> at quadratic order. With constant <mass> $m$, <Newton's second law> then gives a <harmonic oscillator> with <angular frequency> $\omega=\sqrt{V''(x_0)/m}$. The approximation requires displacements small enough that the omitted terms are negligible; it does not describe a flat minimum where $V''(x_0)=0$.
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