Answer
$\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$
Work Step by Step
We know that the force is given by $F=-\frac{dU}{dx}=-2ax$. Thus, we use Hooke's Law and the equation for frequency to find:
$-kx=-2ax \\ k=2a$
Thus, it follows:
$f= \frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$
