# You're getting very sleepy

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?

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