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Amplitude of small oscilliations

  1. Aug 5, 2011 #1
    1. The problem statement, all variables and given/known data
    http://img717.imageshack.us/img717/418/unlednsf.th.png [Broken]
    The amplitude of small oscilliations for the bob is x0, and the amplitude of small oscilliations for the cart is y0. The length of the pivot is l . What is the maximum velocity of the bob relative to the Earth ?


    2. Relevant equations
    x=x0sin(wt)
    y=y0sin(wt)

    3. The attempt at a solution
    I tried taking derrivatives of the functions stated above, thus finding velocity as a function of time, and then adding those two velocity vectors using the law of cosines. (The length of the pivot is needed for finding the angle between the vectors)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 5, 2011 #2
    Re: Oscilliation

    also remember that for angles under 15 i think degrees the way to calculate period of the pendulum is 2piesqrtL/g which means that x can=x0sin(w2piesqrtL/g)

    since the same can go for the cart y=y0cos(w2piesqrtL/g)

    if you derive the two, you get the equation to find the velocity of each individually

    therefor dy/dt= -y0 times 2pie sqrt L/gsin(w2piesqrtL/g)
    and dx/dt= x0times 2piesqrt L/g cos(w2piesqrtL/g)

    find the resultant vector, plug in for L, g and w and you should get the right answer.
     
  4. Aug 5, 2011 #3
    Re: Oscilliation

    oh and another thing you probably have to do is find the second derivative to tell you when the velocity is a maximum. I forgot about that. once you know that time plug into resultant velocity equation to get max velocity.
     
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