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Oscillator problem

  1. Sep 2, 2007 #1
    1. The problem statement, all variables and given/known data
    An air-track glider attached to a spring oscillates with a period of 1.50 s. At t=0s the glider is 4.50 cm left of the equilibrium position and moving to the right at 32.6 cm/s.find the phase constant.


    2. Relevant equations
    w=2pi/t=2pi/1.5=4.189
    x=Acos(wt+phi)
    v=-awsin(wt+phi)


    3. The attempt at a solution
    i tried a systems of equations approach with time equals 0, so the w part drops out, and i keep getting the wrong answer. is this the right approach?
     
    Last edited: Sep 2, 2007
  2. jcsd
  3. Sep 2, 2007 #2

    learningphysics

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    What did you get for a and phi?
     
  4. Sep 2, 2007 #3
    i plugged in and got 32.9=-4.189(4.5/cos(phi))(sin(phi)) and phi=-1.049, which was incorrect
     
  5. Sep 2, 2007 #4
    sorry should say 32.6, but either way it is still wrong
     
  6. Sep 2, 2007 #5
    I get 1.5535, is that correct?
     
  7. Sep 2, 2007 #6
    i dun have any 4.5 in my equation though
     
  8. Sep 2, 2007 #7
    Your answer seems correct to me. Maybe the equation for motion is

    [tex]x=A \sin \omega t[/tex]

    instead. Then [tex]\Delta \phi = 0.522[/tex]. All is a matter of convention.
     
  9. Sep 2, 2007 #8
    no that is wrong too, i only have 2 chances left to get this right.
     
  10. Sep 2, 2007 #9
    I simply used this eq:
    d = (a).sin(m[t] + p)
    v = (a.m).cos(m[t]+p)

    and didn't give consideration to the signs
     
  11. Sep 2, 2007 #10
    Also you may consider the fact that the glider is in the right, and moving to the left, so velocity might be negative, but it depends on axis orientation.
     
  12. Sep 2, 2007 #11
    oops, I used 450 for 4.5
    so now i get phi = 0.5242
     
  13. Sep 2, 2007 #12
    i used the same equations but the one i recieved has cosine in the distance formula and sine in the velocity since velocity is the derivative of the distance function
     
  14. Sep 2, 2007 #13
    .52 is also incorrect
     
  15. Sep 2, 2007 #14

    learningphysics

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    You should have used -4.5 in your calculation...
     
  16. Sep 2, 2007 #15

    learningphysics

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    Do they want the phase in degrees?
     
  17. Sep 2, 2007 #16
    wait for someone else, I will try to find the mistake.

    maybe, that's why! lol
     
  18. Sep 2, 2007 #17
    no radians in the range:

    -pi rad < phi < pi rad
     
  19. Sep 2, 2007 #18
    I think that's the only option left,
    but why its -4.5?

    yes, because d(cos t) dt = -sin t~!~!! :D

    mine weren't correct because that value was for sine functions.
     
  20. Sep 2, 2007 #19

    learningphysics

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    OK... I'm getting phi = 1.0465 and A = -8.98966

    Are you sure the distance is in the form of Acos(wt + phi) and not Asin(wt + phi) ?
     
  21. Sep 2, 2007 #20
    yes, I also got that too for phi
     
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