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Math Help - harmonic motion differential eq

  1. #1
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    harmonic motion differential eq

    A body of mass 'm' is hung on the end of a vertical spring of spring constant 'k'; the body is pulled down and released. in the resulting harmonic motion, the displacement 'y' of a body is given by the dif eq

    m(d^2y)/(dt^2) + ky=0


    show that the function:


    y= cos(sqrt(k/m))* t


    is a solution to the dif eq satisfying the boundary conditions:

    y=1 when t=0 and y'=0 when t=0



    i see how the differential equation comes from that info, but i'm getting lost in the algebra of trying to simplify its derivatives...
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  2. #2
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    Re: harmonic motion differential eq

    If all you're doing is showing that a function satisfies the DE, differentiate it to get the derivatives and substitute into the DE. See if it works...
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  3. #3
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    Re: harmonic motion differential eq

    ok i see what i've been doing. i've been treating what's inside the square root as variables. whoops- my bad. sorry for wasting space on the forum...
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