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Plotting the position of a pendulum

  1. Dec 6, 2008 #1
    Does anyone know where I could find some information about solving a pendulum position. What I mean is a swinging pendulum and the position. The position would be the spot on the ground that a sun directly above would cast. I don't really know where to start other then the pythagorean theorum, Ke and Pe equations. Any help would be great. thanks
     
  2. jcsd
  3. Dec 6, 2008 #2

    HallsofIvy

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    The simple pendulum satisfies the differential equation [itex]d^2\theta/dt^2[/itex]= -(g/l) sin(\theta)[/itex] where g is the acceleration due to gravity, l is the length of the pendulum, t is the time, and [itex]\theta[/itex] is the angle the pendulum makes with the vertical. Assuming the sun is directly overhead the shadow of the pendulm bob will be the horizontal coordinate, [itex]l cos(\theta)[/itex].

    That is an extremely difficult equation to solve but for small angles, [itex]sin(\theta)[/itex] is approximately equal to [itex]\theta[/itex] so the equation can be approximated by [itex]d^2\theta/dt^2= -(g/l)\theta[/itex] which has general solution
    [tex]\theta(t)= C cos(\sqrt{g/l} t)+ D sin(\sqrt{g/l} t)[/tex].

    Determine C and D by the intitial value of [itex]\theta[/itex] and the angular velocity.
     
  4. Dec 6, 2008 #3
    thanks a lot!
     
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