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Math Help - Amplitude calculation

  1. #1
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    Amplitude calculation

    How can I solve for Amplitude and Period if I have the following data?
    a=-4^2.x (ie. SHM)

    x = 2m, speed = sqrt(10 )m/s

    given I cannot use k=4 from a=-4^2.x

    I was thinking to use v^2=k^2(A^2-x^2)

    so 10=k^2(A^2-4) but then I have 2 unknowns?
    Last edited by Neverquit; July 25th 2012 at 07:08 AM.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Amplitude calculation

    For simple harmonic motion

    x = A \sin(\omega t),

    v = \frac {dx}{dt} = A \omega \cos(\omega t) =  \omega \sqrt{A^2-x^2},

    a = \frac {d^2x}{dt^2} = -A \omega  \sin(\omega t) = -\omega^2 x

    From the acceleration equation if you are given that a = -4^2 x then  \omega = 4 s^{-1}.

    If  v = \sqrt{10} at x = 2m, then from the velocity equation:

     \sqrt{10} = 4 \sqrt{A^2 - 2^2
     A = \frac {\sqrt {74}} {4} m
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