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Help on Oscillation problem

  1. Feb 9, 2007 #1
    I'm not quite sure on what I did wrong. Can anyone please help me with this?

    1. The problem statement, all variables and given/known data

    An air-track glider attached to a spring oscillates with a period of 1.50sec . At the glider is 4.60cm left of the equilibrium position and moving to the right at 33.4cm/s.
    What is the phase constant , if the equation of the oscillator is taken to be ? Give an answer in the range -pi < Q < pi.

    2. Relevant equations
    phase constant = Q
    Amplitude = A
    angular frequency = w
    x(t) = Acos(wt+Q)
    v(t) = -Awsin(wt + Q)
    w = (2pi)/period

    3. The attempt at a solution
    4.6 = Acos(Q)
    33.4 = -Awsint(Q)

    Q = atan(.334/(.046*(2pi/1.5))
  2. jcsd
  3. Feb 10, 2007 #2
    It appears that this is close to the right answer, but I'm missing some "additive constant". I probably posted this in the wrong section just by judging by the number of responses on this. If someone would kindly help me, I'd really appreciate it. :frown:
  4. Feb 10, 2007 #3
    I think you might have missed a constant in your calculation there, but is there a way that you can figure out, t, at these instant where you're given x and v.

    The term w*t seems to have disappeared, from the argument of both trig functions, not sure you can do this, or at least can't call it Q unless you're at t=0 or some integral number of cycles after that. In otherwords, you neet to solve for A and Q both if I'm not mistaken. You can get A from the approacch you were using once you know the angle. See it that leads anywhere
  5. Feb 10, 2007 #4
    The term w*t is no longer present b/c it was a function of time, and at the instance when t =0 or time = 0sec, w * t or (2pi/period) *t became 0. I then solved for A (Amplitude) from the first equation then substituted that into the second eqaution. If I'm not mistaken, isn't that the way to solve for two variables using two equations?
    Last edited: Feb 10, 2007
  6. Feb 10, 2007 #5


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    The displacement is 4.6 cm and the velocity 33.4 cm/s at some time t different from 0. As denverdoc mentioned, you can write those equations but with a value different then Q and solve for A.
    Once you know A, you can solve for Q.
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