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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