### Oscillations

Equilibrium: $dU/dx=0 \rightarrow -13a/x^{14}+7b/x^8=0 \rightarrow x_0=(13a/7b)^{1/6}$. Taylor expansion: $d^2U/dx^2=182a/x_0^{15}-56 b/x_0^9$. Now $\omega^2=(182a/x_0^{15}-56 b/x_0^9)/m$.