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Simple Harmonic Motion: Displacement after s seconds

  1. Aug 12, 2012 #1
    The question is:

    A 56.0 kg bungy-jumper hangs suspended from her bungy-cord, at rest. She is displaced from this position by 15.0 m downward, and then released. She bounces up and down, with a period of 5.800 s. Assume the woman undergoes simple harmonic motion, described by
    y(t) = X cos(2 π t / T + φ)

    Where is the woman after 43.20 s of bouncing? (enter a negative value if she is below her rest position).

    The answer is 14.2m.

    I've been using x=Xcos(2*pi*t/T) --> 15cos(2pi43.2/5.8) = 10.27m. This equation was in my book. What did I do wrong? Am I supposed to use y(t) = X cos(2 π t / T + φ? In that case, I don't know what φ is...
     
  2. jcsd
  3. Aug 12, 2012 #2

    Doc Al

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    Staff: Mentor

    Are you using your calculator properly? (Radians, not degrees.)
     
  4. Aug 12, 2012 #3
    Oooh, thanks. I did not know you had to use radians. So do you have to always have to use radians when dealing with simple harmonic motion?
     
  5. Aug 12, 2012 #4

    Doc Al

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    Generally, yes. But you can always convert from one to the other.

    Note what's going on in the equation y(t) = X cos(2 π t / T). That ratio t/T tells you what fraction of a period you are dealing with. The 2π tells you that you are dealing with radians, since one complete period is 2π radians.
     
  6. Aug 12, 2012 #5
    Oh, that make sense. Thanks, that was really helpful. =)
     
  7. Jun 5, 2013 #6
    how do you know if the woman is above or below her rest position?
     
  8. Jun 5, 2013 #7

    Doc Al

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    Set up properly, the equation will tell you.

    Or you can just see what fraction of a full period she ends up at.
     
  9. Jun 5, 2013 #8
    Do you mean by using this equation ?y(t) = X cos(2 π t / T + φ)
    btw what isφ
     
  10. Jun 5, 2013 #9

    Doc Al

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    Yes.

    φ is a phase factor. But since the motion starts at maximum displacement below the rest position, you may not need it.

    What final equation would you use to describe the position as a function of time?
     
  11. Jun 5, 2013 #10
    simply using y(t) = X cos(2 π t / T) ?
    is that right
     
  12. Jun 6, 2013 #11

    Doc Al

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    Since she starts out below the rest position, I'd put a minus sign in front of that. Then you'd be fine.
     
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