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Ellipse and a sine curve

  1. Oct 23, 2007 #1
    1. The problem statement, all variables and given/known data
    an ellipse whose semi axes have lengths a and b rolls without slipping on the curve y =c sin (x/a), find the relationship between a, b, and c. Assume that the ellipse completes one revolution per period of the sine curve.

    The answer is b^2 = a^2 + c^2 and you find it by requiring that the arclengths be the same for one period.

    Why is it wrong to just require that a = c and b = pi a /2 ? That would seem natural to me because then one half of the ellipse would fit perfectly into one "hump" of the sine curve?

    2. Relevant equations

    3. The attempt at a solution
    Last edited: Oct 23, 2007
  2. jcsd
  3. Oct 23, 2007 #2
    do people understand the problem?
  4. Oct 23, 2007 #3
    should I draw a picture?
  5. Oct 23, 2007 #4


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    An ellipse does not fit perfectly into a sine curve. I don't know what you are talking about.
  6. Oct 23, 2007 #5
    My approach was to make the ellipse have minor axis equal to half the period of the sine curve and a semi-major axis equal to the amplitude of sine curve. All I want to know is why that approach produces ellipses that are different from the ones in the answer.
  7. Oct 23, 2007 #6


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    Because they don't fit. The profile of an ellipse only resembles a sine curve. It's not an exact match.
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