Look at Figure 2, which presents the trigonometry of a simple pendulum.
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Figure 5. Potential energy and phase portrait of a simple pendulum.
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Consider Figure 1, showing the forces acting on a simple pendulum.
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The key device, believe it or not, is a simple pendulum.
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In the small-angle approximation, the motion of a simple pendulum is approximated by simple harmonic motion.
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In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration.
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Owing to the expansion of metal, the length of a simple pendulum will vary with temperature, slowing the clock as the temperature rises.
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Galileo claimed that a simple pendulum is isochronous, i.e. that its swings always take the same amount of time, independently of the amplitude.
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The length L of the ideal simple pendulum above, used for calculating the period, is the distance from the pivot point to the center of mass of the bob.