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

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