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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?
by
David Mattingly