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How can you guess solutions of parametric resonance equation?

  1. Aug 9, 2013 #1
    Hi, first time asking questions in this forum.
    I am self-learning classic mechanics this summer using Laudau's book and so far I feel everything is pretty interesting and makes sense for me. But still, I have some questions that needed to be answered. One of them is about the parametric resonance.
    The equation of motion is x'' +ω2(1+h*cosγt)*x = 0, and I am told that the resonance reaches its maximum when γ is close to 2ω,i.e. γ = 2ω+ε. To find out the solution for x, the author assumes the solution to be in the form of x = a(t)cos(ω+1/2ε)+b(t)sin(ω+1/2ε), I don't quite understand how the author comes up with this assumption. Really appreciated if someone can help me.
     
  2. jcsd
  3. Aug 9, 2013 #2

    Vanadium 50

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    Have you taken Differential Equations yet?
     
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