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with a massless rod and a bob at the end,
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the time it takes to finish an oscillation,
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in fact, will depend on the amplitude.
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But only for small oscillations,
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when sin(θ) can be approximated by θ,
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you will find whether you do that oscillation, or that oscillation,
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the time is the same.
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But if you go too far,
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the other terms in sin(θ) will kick in,
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and the result is no longer true.
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The period of a pendulum, in fact, is not just a function of l and g,
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but also a function of the amplitude.