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I have to wait at time capital T so that ω·T is 2π.
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Because that's when the cosine returns to 1
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That means the time that you have to wait is 2π over ω
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Or you can say ω is 2π over T,
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or you can also write it a 2π times frequency,
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where frequency is what you and I would call frequency,
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how many oscillations it does per second.
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That's the inverse of the time period.
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So, if you pull a mass and you let it go,
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it oscillates with a frequency
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which is connected to the force constant and the mass.
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If the spring is very stiff and k is very large, frequency is very high.