[QUE/CM-01006] Periodic Motion, Relativistic Oscillator

Question: Show that the time period of a relativistic oscillator as  function of amplitude $a$ is given by $$ T\approx \frac{2\pi}{\omega}\left[ 1 + \frac{3\omega^2a^2}{16 c^2} + \cdots \right] $$ where the restoring force is $- kx$ and $k=m \omega2 $.