Examples
The animations below depict several different modes of oscillation given different initial conditions. The small graph above the pendulums are their phase portraits.
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Initial angle of 0°, a stable equilibrium.
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Initial angle of 45°
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Initial angle of 90°
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Initial angle of 135°
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Initial angle of 170°
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Pendulum with just barely enough energy for a full swing
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Pendulum with enough energy for a full swing
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Initial angle of 180°, unstable equilibrium.
Read more about this topic: Pendulum (mathematics)
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