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Homework Help: Pendulum and spring oscillation

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data
    A 5 kg sphere is connected to a thin
    massless, but rigid rod of length L = 1.3 m to
    form a simple pendulum. The rod is connected
    to a nearby vertical wall by a spring with spring
    constant k = 75 N/m, connected to it at a
    distance h = 1.1 m below its point of
    suspension. What is the angular frequency (in
    rad/s) of the system for small amplitude

    2. Relevant equations

    3. The attempt at a solution
    So I was listening to my teacher start to solve this problem. He starting talking about summing the torques between these two. I have the equation he wrote down from it, but I am not too sure what to do with it... ([tex]\tau[/tex])net = -Lmgsin[tex]\theta[/tex] - hk[tex]\Delta[/tex]xsin[tex]\beta[/tex] = m(l^2)[tex]\alpha[/tex]
    Note: alpha is not a power...
    I know that the small angle theorum makes sin go away. But how is beta and alpha related? And what about delta x? I don't know I've been working on it for a while and now I'm tired. Thanks for helping!
  2. jcsd
  3. Apr 28, 2010 #2


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    Science Advisor
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    Gold Member

    If you draw the drawing, you will see that you get two right triangles, one above the sphere and one below. They have a common right side that is Δx. Relate this side to L and θ using the top triangle and to h and β using the bottom triangle.
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