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In fact, let's do it not just to be at the mid point here,
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but at any point x measured from equilibrium.
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Because we will say initially
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This is the truth;
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this is a constant that does not change with time.
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Now, to get some mileage out of this,
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you've got to know what the constant value is.
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Well, we know what it is in the beginning
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because when you pull this guy,
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at the instant we knew it had no velocity,
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and we knew it was sitting at the point A,
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so we know (1/2) · k · A^2 is the