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Phase Constant and glider

  1. Jul 13, 2008 #1
    1. The problem statement, all variables and given/known data
    An air-track glider attached to a spring oscillates with a period of 1.5s. At t = 0s the glider is 5.0 cm left of the equilibrium position and moving to the right at 36.3 cm/s.

    What is the phase constant, [tex]\Phi[/tex]0?

    2. Relevant equations

    x = Acos ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {1}

    Vx = -Vmax ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {2}

    3. The attempt at a solution
    I tried to rearrange equation two for the phase constant, but I am missing A (amplitude). I have tried using vmax = [tex]\varpi[/tex] A but that only works with maximum velocity which I do not have. Maybe I am not seeing something clearly. Can anyone help me out please?
  2. jcsd
  3. Jul 13, 2008 #2


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    Homework Helper

    Hi BioCore,

    This equation is missing the trig function. Is that just a typo?

    They did not give a numerical value for [itex]v_{\rm max}[/itex], but it's in the equation you need to work with, so by using that relationship you can eliminate one of the unknowns from your two equations.

    You'll find the answer by solving the x and v equations together. Based on what the problem gives you, how can you do that to find [itex]\phi[/itex]?
  4. Jul 13, 2008 #3
    Yes sorry it was a typo. Ok so when I solved the formula's together I get:

    [tex]\phi[/tex] 0 = tan-1 ([tex]\frac{Vx }{-\varpi x}[/tex])

    Which when I solve for I get -60 degrees or pi/3. Now the answer they got is -2pi/3 or -120 degrees.

    I can't seem to explain to myself how to it is -120 degrees although I think I know why they say that.
  5. Jul 13, 2008 #4


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    When you find an inverse trig function with a calculator, you only get one of the two possible answers. So when you get your answers of 60 degrees (your post said -60 but you meant 60, right?) you'll actually need to determine if the answer is 60 degrees or 180 degrees away from that, which would be the -120 degrees.

    There are several ways to find out, but probably the quickest way is to see which one solves the original equations you wrote down (for x and v) with the data you got from the problem.
  6. Jul 14, 2008 #5
    Yeah sorry I meant +60 degrees, I am just very tired right now and I think I will go get some rest. But thanks a lot for the help and understanding the answer. Appreciate it a lot.
  7. Jul 14, 2008 #6


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    Sure, glad to help!
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