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Bead on a Wire and Harmonic Motion

  1. Aug 10, 2006 #1
    A wire could be shaped like a sinusoidal function and then we could say the bead moves harmonically.

    The shape of the wire, so that bead occilates around X = 0.

    Y = -50*cos(10X)

    If we ignore friction and give it a small dispalcement then it is possible to find angular frequency.

    However, when I applied my method to a varation of this problem in a text book I got a wrong answer.

    Part I:
    Here was my attempt where Z is the angle from the center of the circle that the bottom of the sinudosoidal function fits on:

    S = (r)*(Z) = (50)*(Zmax sin wt)

    V= 50*Zmax*w*coswt

    V(max) = 50*Zmax*w

    Part II:
    Energy at the lowest place
    E = .5 m (Vmax)^2 - 50mg

    Energy at the highest place
    E = -50mg*cos(Zmax)

    Setting the energies equal:
    .5 m (Vmax)^2 - 50g =-50mg*cos(Zmax)

    Solving for the velocity:

    (Vmax)^2 = 100g*[1-cos(Zmax)]

    Part III: combing part I & II
    (Vmax)^2 = 100g*cos(Zmax)
    (50*Zmax*w)^2 = 100g*[1-cos(Zmax)]

    library logged me off, i will finish later
  2. jcsd
  3. Aug 10, 2006 #2
    Nevermind I figured it out. I made mistake in my method before.

    s = r Z

    r = 1/k where k is the curvature.
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