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Prove that (V max) of a mass is (2*pie*f*A) where f is frequence and A is amplitude

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Prove that (V max) of a mass is (2*pie*f*A) where f is frequence and A is amplitude

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  1. To do this, you have to make an assumption that the equation of motion is:

    x = A cos (2 pi t/f)

    then

    v = dx/dt = A 2 pi f sin (2 pi f t)

    This will have a max where (sin 2pi f t) =1, ergo

    Vmax = A 2 pi f

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