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Homework Help: 2 D.O.F System - Natural Frequencies

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    The question is a 2 D.O.F system, m1 = 600kg, m2 = 50kg, k1 = k3 = 0.5MN/m, k2 = 0.2 MN/m. Calculate the natural frequencies.

    2. Relevant equations

    1167-w^2 -333.3 X1 0
    -4000 14000-w^2 X2 0

    3. The attempt at a solution

    I am at the point where I have put these values into Matrix form. The values (1167-w^2)(14000-w^2) - (-333.3 x -4000) = 0

    I have worked it out so I get values of:

    15 x 10^6 - 15167w^2 + w^4 = 0

    The answers are:

    w1^2 = 1.06 x 10^3
    w1 = 32.6 rad/s

    w2^2 = 14 x 10^3
    w2 = 118 rad/s

    However when I work out this I get answers of:

    w1^2 = 106
    w1 = 10 rad/s

    w2^2 = 137.9
    w2 = 11.7 rad/s

    Whats missing, what am I missing out? This is my first attempt at posting a HW question, so sorry if its not clear, just let me know if you need any extra info.

    I just can't see where the x10^3 comes from, I'm assuming something to do with the w^4, but I can't think what.
    Any input would be highly appreciated.

  2. jcsd
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