# You're getting very sleepy

**Classical Mechanics**Level 4

A simple pendulum is pulled back to some angle \(\theta_{max}\) and released so it swings back and forth. The angle the pendulum makes with the vertical is given by \(\theta(t)\). The maximum value \(\theta_{max}\) of \(\theta(t)\) is small, so you may treat the pendulum as a simple harmonic oscillator. For what fraction of time is \(|\theta(t)|>\theta_{max}/3\) as the pendulum swings back and forth many times?