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But the force of a spring definitely varies with x in a noticeable way.
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The force of a spring is one concrete example;
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it's what you all seem to recognize; it's this one .
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So then, we have to ask
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what is the Work Energy Theorem when the forces itself vary?
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So, let's draw ourselves a force which is varying,
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here is x, here is my force; it does something.
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F = k · x or - k · x is a particular graph,
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I'm just taking any function of x that I want.
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Now, the acceleration is not constant
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because the force is not a constant.
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So, if you wait for one hour