Frequency of oscillation near a potential minimum

Expand U(x) about its minimum at x=xm.

U(x) = U(xm) + (x-xm) dU/dx(xm) + 1/2 (x-xm)^2 d^2U/dx^2(xm) + ...

letting U(z) = U(x)-U(xm), and z = x-xm we find

U(z) = 1/2 d^2U/dz^2(0) z^2 + higher powers of z

A mass moving in this potential resembles a mass on a spring, where the PE is

U(x) = 1/2 k x^2.

You know the frequency of oscillation of a mass and spring is sqrt(k/m) so you
can determine by analogy the frequency of oscillation near the minimum of
U(x).