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: \[\int_{-1}^{1} \frac{1}{\sqrt{1-x^{4}}}\,dx = 2.622\]
by
Jonathan Schirmer