## Essential University Physics: Volume 1 (3rd Edition)

$\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$
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: $f= \frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{2\pi}\sqrt{\frac{2a}{m}}$