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Homework Help: Parabolic Bowl

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider a particle moving back and forth on a frictionless parabolic bowl, y = ax2, where a = 1.460 m-1
    If the particle is released from rest at the point on the
    bowl at b = 0.43 m, find the period of the oscillations.

    I have an equation for velocity(as a function of x). What i was thinking is that i could integrate this from -b to +b, and call this value 'v(x)*d', (it having units of m2/s.
    since v=d/t, v(x)*d=d2/t.
    thus t=d2/'v(x)*d'.
    making the period, T=2*(d2/'v(x)*d'),
    where d is the arc length of y(x), from -b to +b.

    I realize this may be the least elegant and very possibly "physically incorrect", but it actually gave me a period very close to that obtained by the 'small angle approximation' (however, incorrect)

    Can anybody comment on this method?
     
  2. jcsd
  3. Sep 27, 2010 #2
    i guess the crux of my argument is whether the area under the v(x) curve can be used in this manner, comments?
     
  4. Sep 28, 2010 #3
    The acceleration and velocity are not at all constant, so the method is, mathematically speaking, completely wrong.
     
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