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Homework Help: Find the period of the particle and the amplitude

  1. May 14, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle moves with SHM through two points p and q 1.2 metres apart. It takes 3 seconds to move from p to q and 3 seconds to move from q to q, i.e. passing q the next time.
    Find the period of the particle and the amplitude.


    2. Relevant equations
    x = ACos(wt + a)
    v = w(A^2-x^2)^1/2
    a = -w^2x

    3. The attempt at a solution
    I drew a diagram, and tried associated circular motion, but the problem is I have no idea where to start the motion, or if I can take the point half way between p and q as being equilibrium.
     
  2. jcsd
  3. May 14, 2010 #2

    rl.bhat

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    Let O be the equilibrium position, and A and B are the extreme position. The particle takes 1.5 s to go from O to q and 1.5 s to go from q to B. So it takes 3 s to go from O to B. This interval is T/4. Hence T = 12 s.
    If you measure the displacement from the equilibrium, then
    x = Asin(2πt/T)
    Here x = 0.6 m, T = 12 s and t = 1.5 s.
    Now find A.
     
  4. May 14, 2010 #3

    ehild

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    Are the period and amplitude different if you start to measure the time later or sooner? You can take he phase constant equal to zero, a=0.

    ehild
     
  5. May 15, 2010 #4
    It's never specified that it takes 1.5 seconds to go from O to q, just that it takes 3 seconds to gor from q to B to q. How did you come up with this?

    Your answers are correct, though.
     
  6. May 15, 2010 #5

    rl.bhat

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    In the problem two quantities are unknown. To find them, you must have two data. One data is time to move from q to q back. If p and q are any two points you cannot use 1.2 m in 3 s data for the solution. The problem is poorly worded.
     
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