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Homework Help: Determine pendulum's maximum angular displacement

  1. Apr 28, 2008 #1
    [SOLVED] Simple Pendulum

    1. The problem statement, all variables and given/known data
    A simple pendulum with a length of 1.23 m and a mass of 6.64 kg is given an initial speed of 1.96 m/s at its equilibrium position.
    (a) Assuming it undergoes simple harmonic motion, determine its period.
    (b) Determine its total energy.
    (c) Determine its maximum angular displacement. (For large v, and/or small l, the small angle approximation may not be good enough here.)

    3. The attempt at a solution
    I have solved up to part c), and I can't figure out how to set it up. I thought at first it was
    .5mv^2 = mgh and then solving for h, but once I get h I am not sure what to do. Can someone help me get this set up? Thanks.
  2. jcsd
  3. Apr 28, 2008 #2


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    Homework Helper

    That is what you want to do. So the pendulum bob is now at a height h (what is the value?) above the bottom of the pendulum's arc. Draw a picture of the pendulum tilted off the vertical so that the length of the pendulum is 1.23 m and the bob is at a height h from the lowest point of the swing. The pendulum shaft is now the hypotenuse of a right triangle. What must the altitude of that triangle be? From that, how do you find the apex angle of that triangle?
  4. Apr 28, 2008 #3
    Excellent, made sense. Thanks for the help
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