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Graphs relating to simple harmonic motion

  1. May 7, 2016 #1
    1. The problem statement, all variables and given/known data

    untitled1.jpg Untitled 2.jpg
    2. Relevant equations
    None.

    3. The attempt at a solution
    Hi everyone. Apparently 5 is the right answer, although I chose D.

    Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong?

    Thanks!
     
  2. jcsd
  3. May 7, 2016 #2

    TSny

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    Please explain how you got your answer.
     
  4. May 7, 2016 #3
    Velocity can also be negative...
     
  5. May 7, 2016 #4

    haruspex

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    True, but that does not rule out any of the graphs. There is no claim that the graph represents an entire cycle. There is a better reason for choosing 5. What would the graph of velocity actually look like?

    Edit: please do not post an answer to that on this thread, at least not until RoboNerd has had a chance to answer it.
     
  6. May 7, 2016 #5
    Hi everyone, robonerd is back, of course.

    I know that at xmin and max, the velocity [with kinetic energy] = 0 instantaneously. Thus, I narrow down to B and D.
    However, I know that with a variable spring force giving a variable acceleration, I will not have the velocity changing in a linear manner [constant acceleration with constant slope], so I rule out B. D is thus a potential answer. Why is D wrong?
     
  7. May 7, 2016 #6

    haruspex

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    Can you write an equation relating velocity and x?
     
  8. May 7, 2016 #7
    Yes. Using conservation of energy I have:

    ( 1 / 2 ) * k * A^2 = a constant value = (1 / 2) * m * v^2 + ( 1/ 2) * k * x^2
     
  9. May 7, 2016 #8

    haruspex

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    Good. Can you recognise that form as a common shape? (Think of v as the y coordinate.)
     
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