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Oscillation above the Surface of the Earth

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A pendulum consists of point mass Mo swinging on a massless string of length Lo, with period To = 7.23 s on the surface of the Earth (at RE, the radius of the Earth). Find T1, the period of the same pendulum if it swings on a horizontal platform of height H = 2.23RE (stationary, not orbiting) above the Earth's surface.


    2. Relevant equations
    T = 2∏√(L/g)
    g = G * Mass of Earth/R^2, where R = radius of Earth


    3. The attempt at a solution
    Squaring both sides of the Period, T, equation, we get,

    T on surface of Earth: T^2 = 7.23^2 = 4∏^2(L/g), = 4∏^2(L)*R^2 / (G)(Mearth), and,
    T at 2.23R above the Earth: T^2 = 4∏^2(L)*(2.23R)^2 / (G)(Mearth)

    Dividing both equations, and solving for T, T = √(7.23^2)(2.23)^2 = 16.1229

    Am I doing something wrong here? Many thanks in advance.
     
  2. jcsd
  3. Dec 4, 2012 #2

    haruspex

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    In the formula GMe/r2, what exactly is r?
     
  4. Dec 4, 2012 #3
    Hi Haruspex,

    This r should be (r PLUS 2.23R), or (R + 2.23R) = 3.23R ... Would I be correct here? Thank you for your assistance!
     
  5. Dec 4, 2012 #4
    Go figure, it is! Thanks!
     
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