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

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.