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Creating a Function with Oscillating Discontinuity

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Create one example of a function within the context of a real-world science application (i.e., physics, biology, chemistry, etc.) that contains an oscillating discontinuity,

    2. Relevant equations

    y=sin (1/x)

    3. The attempt at a solution

    I would like to use the simple equation y=sin (1/x) as my function with oscillating discontinuity and understand that the point of discontinuity will occur at x=0 because the point of discontinuity occurs when the denominator is equal to zero, but I am stuck on writing a "SCIENCE Function Equation, in which the graph of the function would look the same as this. Please help!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 20, 2010 #2

    berkeman

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    Staff: Mentor

    It sounds like the question is asking for a real-world example. Do you have a real-world example where that equation comes up and goes to infinity?

    I can think of some real-world situations where periodic discontinuities come up. Can you?
     
  4. Jan 21, 2010 #3
    No, that is my problem, I do not know the physics end of the equation to be able to come up with a function "real world example". That is what I am asking for help with. If I had an idea of one, then i'd be able to customize the sin 1/x problem for the example.
     
  5. Jan 21, 2010 #4
    does this make sense? Two physics students are attempting an experiment where they are standing on opposite sides of a wall where they are both equidistant at 10 feet from the wall. The students are attempting to meet at the wall by taking their distance from the wall and moving half that distance each step closer. On their first steps they move half of the distance to the wall, 5ft. Then move half again, 2.5ft. Then half that again, 1.25ft. They find that no matter how many times they attempt this, they can never actually reach the wall but that they will get closer to it each time. Their steps (wavelenghs) are getting smaller and more frequent as it approaches the wall yet still never reaches.

    Y = sin (10/x)
     
  6. Jan 21, 2010 #5

    berkeman

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    Staff: Mentor

    No, sorry, that doesn't make sense to me. Think about what you can do with a laser beam and a mirror, for example....
     
  7. Jan 21, 2010 #6
    No I'm sorry that does not help me. Can you explain how that is an oscillating process
     
  8. Jan 21, 2010 #7

    berkeman

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    Staff: Mentor

    I gave you a pretty big hint. Think about it for a while. Heck, pull out your laser pointer and a small mirror, and experiment some...
     
  9. Jan 21, 2010 #8
    Thanks for your help and tips. I do not have a laser pointer but will try to google it somehow. I'm in a math program entirely online and reading math books isn't quite helping. Science is not my subject and this is frustrating.
     
  10. Jan 21, 2010 #9

    berkeman

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    Staff: Mentor

    When you go to the grocery store, how do they record what you've purchased... ?
     
  11. Jan 21, 2010 #10
    You use a barcode scanner, laser.... I know that. It doesn't look like this kind of help is working for me, but i appreciate your time.
     
  12. Jan 21, 2010 #11

    berkeman

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    Staff: Mentor

    Correct. Do you think it might apply to your original question?
     
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