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Waves - Pendulums

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data
    The figure below shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The pendulum bob has mass 0.260 kg. What is the length of the pendulum?
    W0353-N.jpg

    2. Relevant equations
    K=(1/2)mv2
    U=mgh
    x(t)=xm*cos(w*t+phi)

    *where w is the angular frequency, and the wt + phi being the phase

    3. The attempt at a solution

    Basically I have gone through a series of approaches to this problem, but I have come to settle with this one:

    I started by getting phi from the graph, .100 radians. Then, I attempted to relate gravitational potential energy to the max kinetic energy that was given from the graph (.015 J). This way, I could get h, and relate h to the maximum angle and the pendulum length. To do that, I would use x(t)=xm*cos(w*t+phi). I'm not sure if I should use the simple pendulum equations, but I don't think I need to know the inertia.
     
  2. jcsd
  3. Apr 5, 2009 #2

    rl.bhat

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    Homework Helper

    x(t)=xm*cos(w*t+phi)
    From the above equation find the maximum velocity x(t)=xm*cos(w*t+phi)m.
    KE is given. Mass is given. Find the value of Vm.
    Since angular displacement is only 0.1 rad, it is SHM.
    In SHM f = -kx, ...(1)
    In simple pendulum, restoring force = -mg(theta) = -mgx/L......(2)
    From eq. 1 and 2. find the value of k = mg/L ......(3)
    From 3 find the value of omega. And proceed.
     
  4. Apr 6, 2009 #3
    Thanks for the help. : ) I computed the answer to be 1.177 m. This checked out. I understand the methodology behind it too, thanks again.
     
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