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Meanwhile, this would have oscillated
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some number of times.
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But if you wait long enough
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this exponential will start coming into play
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and the way to think about it is,
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it's an oscillation whose amplitude itself falls with time.
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And if you draw a picture of that,
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I think you will not be surprised
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that if you draw the picture it will look like this.
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It's called a damped oscillation.
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So, that's the method by which you describe
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the three cases.