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Homework Help: Velocity in a Cycloidal Pendulum

  1. Sep 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Cycloidal Pendulum, with x= RΘ+RsinΘ and y = -RcosΘ
    I need to find the Lagragian.

    2. Relevant equations

    L = T - V

    3. The attempt at a solution

    I just want to know how do I find the velocity so I can find T, which is 1/2 mv². I thought it would be dx/dΘ but it didn't work. Can anyone explain to me how can I find the velocity?
  2. jcsd
  3. Sep 16, 2014 #2


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    Gold Member

    Remember that velocity is the derivative of position with respect to time and is a vector. What are its x and y components? Could you use these components to find ##v^2##?
  4. Sep 17, 2014 #3
    Ok, I realized that I must consider x and y and derivative in relation with time.

    v = dx/dt + dy/dt

    then v² would be (dx/dt + dy/dt)².

    I did the derivatives:

    x'= RΘ' + Rcos(Θ)Θ' and y' = Rsin(Θ)Θ',

    so x+y = RΘ' + RΘ' (cosΘ + sinΘ)

    Also, v² = ( RΘ' + RΘ' (cosΘ + sinΘ))² = (4R²Θ'² + R²Θ'²cos²Θsin²Θ)
    But in my answer it is


    What am I doing wrong?
    Last edited: Sep 17, 2014
  5. Sep 17, 2014 #4


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    ##v=\frac{dx}{dt}+\frac{dy}{dt}## is wrong. Remember that ##\vec{v}## is a vector! What is the x-component of ##\vec{v}##? What is the y-component of ##\vec{v}##? After you have the components, you can find ##v^2## by squaring the components and adding them, right?
  6. Sep 17, 2014 #5
    Ohhh, you are right! It worked now, thank you very much!
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