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Theory of small oscilations

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    (see pic)

    [itex]\frac{l_{2}}{l_{1}} = \frac{1}{4} [/itex]
    [itex]\frac{g}{l_{1}} = 1 [/itex]

    I need to find the normal modes of oscillation. (for small oscillations)


    3. The attempt at a solution

    I solved the problem using the matricial way and got the following matrix: (I simplified it using the above ratios)


    [itex] V - wT = m \begin{pmatrix}
    1 - w^2 & -1/4 \\
    -1/4 & 1/8 - w^2/48
    \end{pmatrix}

    [/itex]


    Solving the determinant of the matrix I got two positive solutions. Now the thing is for each solution I got two different configurations of amplitudes. I thought that each normal frequency would give me only one configuration of amplitudes. Can you make this clear for me? Thanks.
     

    Attached Files:

  2. jcsd
  3. Apr 23, 2014 #2

    BruceW

    User Avatar
    Homework Helper

    Hi, sorry but what was the problem statement? where is the mass located? It is hard to follow along without knowing that...
     
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