Far Away for a Long Time

The dynamics of a particle's motion are described by the following Lagrangian:

$L = \frac{1}{2} m \dot{x}^2 - \frac{1}{2} k x^2$

If the particle oscillates between $x = -1$ and $x = +1$ , for what fraction of the oscillation time period is $|x| > \frac{1}{2}$ ?

Details and Assumptions:
1) $m = k = 1$
2) Assume standard $SI$ units