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Math Help - Mass spring differential equation

  1. #1
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    Mass spring differential equation

    I am good at Matlab programming but over here I am stuck in the maths of the problem, I am dealing with the differential equation of spring mass system
    mx+cx+kx=0
    where x=dx2/dt2 and x=dx/dt. I have the values of mass and I also have the array of time and x i.e x is given for a particular value of time so I can find x and x easily. I am stuck at what method to apply to find the value of c and k. I can program any method but have searched several books but didnt get how to find c and k. If I get to know the method I can program it easily.
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  2. #2
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    Re: Mass spring differential equation

    Let x", x' and x be column vectors of results calculated at each time step (each vector has n entries).

    Then create the matrices:

    A = [x" x'] this is a n row, 2 column matrix, and
    y = [m ; c] this is a 2 row, 1 column matrix, and
    x = [x] this is a n row, 1 column matrix.

    Now your DE can be written:

    Ay = -kx

    we can find the minimum squares solution of this as follows

    Ay = -kx

    so

    A'Ay = -kA'x

    so


    (A'A)^{-1} A'Ay = -k(A'A)^{-1} A'x

    so

    y = -k(A'A)^{-1} A'x
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  3. #3
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    Re: Mass spring differential equation

    Thanks alot
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