# Not-So-Simple Harmonic Motion

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: $\int_{-1}^{1} \frac{1}{\sqrt{1-x^{4}}}\,dx = 2.622$

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