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Homework Help: Mechanical Vibrations Differential Equation

  1. Oct 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the general solution for the differential equation

    2. Relevant equations

    y'' + 16y = tan(4t)

    3. The attempt at a solution

    I get C1cos(4t) + C2sin(4t) = 0 for my homogeneous equation.

    I did the usual method of undetermined coefficients (I think I took all of the derivatives correctly). However I'm getting something strange for yp. I can't really make sense of the solution. Does this have something to do with the fact that the tangent function has discontinuities? Would this be some kind of resonance?
    Last edited: Oct 22, 2011
  2. jcsd
  3. Oct 22, 2011 #2


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    Homework Helper

    There is no sort of 'fixed' form for the PI of tan(4t), you might need to try variation of parameters to solve it.
  4. Oct 22, 2011 #3
    Oh yeah! Thanks for the help!
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