Not-So-Simple Harmonic Motion

Classical Mechanics Level 5

A certain spring produces a force that goes as $F=-kx^{3}$ .

A mass of $m = 1kg$ is attached to the spring. If $k= 1000 N m^{-3}$ and the mass is initially displaced by $10 cm$ , what is the period of the mass's motion in seconds?

You may find the following useful: $\int_{-1}^{1} \frac{1}{\sqrt{1-x^{4}}}\,dx = 2.622$