Answer
$f=\frac{1}{2\pi}\sqrt{\frac{2k}{m}}$.
Work Step by Step
This is a mass on a spring, with an effective spring constant of 2k. We can then calculate the frequency of vibration.
$$f=\frac{1}{2\pi}\sqrt{\frac{k_{effective}}{m}}=\frac{1}{2\pi}\sqrt{\frac{2k}{m}}$$