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Perturbation Theory

  1. Feb 5, 2010 #1
    1. The problem statement, all variables and given/known data
    The length of a pendulum is slowly doubled (l=l_0(1+epsilon*t), 0<=t<=1/epsilon). How does the amplitude q_max of the oscillations vary?

    Any hints?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 6, 2010 #2
    Are you changing the total energy? By how much?
     
  4. Feb 6, 2010 #3
    I'm not sure...


    Ans. I = 1/2 * l^{3/2} * g^{1/2} *q_max^{2}.

    therefore

    q_max(t) = q_max(0)(l(0)/l(t))^3/4
     
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