PRO/VS-02003

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 $.