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Weakly Coupled Oscillators

  1. Oct 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Two simple pendulums os equal lenght L=1m are connected with spring with a spring constant K=0,05 Mg/L. The pendulums are started by realeasing one of them from a displaced position. The subsequent motion is characterized by an oscillatory energy exchange between the pendulums. What is te period of this transfer?

    2. Relevant equations


    3. The attempt at a solution
    In this situation, as a pendulum is displaced and the another is static, I suppose that when the amplitude of pendulum 1 is a maximum, the amplitude of pendulum 2 is minimum, because the result is displaying "beat" frequency. That's correct?
     
  2. jcsd
  3. Oct 25, 2016 #2

    BvU

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    Yes. Why ask ?
     
  4. Oct 25, 2016 #3

    Orodruin

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    Yes. When the amplitude of one of the pendula is zero, the amplitude of the other is maximal. This follows directly from energy conservation.
     
  5. Oct 25, 2016 #4
    Well, just to get rid of the doubt.

    Them, starting from the equation of position, and I found that the maximum values of the amplitude for the pendulum 1 occurs when:

    επ(t/T) = nπ ---> t/T = n/ε

    The time between maxima is T/ε, inversely proportional to the coupling spring constant.

    And for the pendulum 2 when:

    επ(t/T) = (2n +1)* π/2 ---> t/T = (2n+1)/2ε

    Them, I stuck in here. Can I relate that with period of transfer in the oscillatory energy exchange in some way?
     
  6. Oct 25, 2016 #5

    BvU

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    Good. So what's this exercise ? In a chapter on differential equations, on Larangian mechanics, a lab instruction preparation perhaps ?

    The motion described is asymmetric and one can expect the pendulum that's initially immobile to start swingning too.
    There are simple modes possible where there is no transfer; can you guess which ? Wht are their frequencies ?
     
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