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Wavelength of particle motion

  1. Nov 1, 2007 #1
    I have two parametric equations for the speed of a particle in a plane:

    [tex]\dot{x}(t) = A \left( 1 - cos{\Omega t} \right)[/tex]
    [tex]\dot{y}(t) = A sin{\Omega t}[/tex]

    The period is equal to [itex]\Omega[/itex]. How do I find the wavelength of the motion?

    The wavelength is just [itex] \lambda = \Omega v [/itex], where [itex]v = \sqrt{\dot{x}^2 + \dot{y}^2}[/itex] is the speed, right? But then the wavelength is not time invariant. Could my answer

    [tex]\lambda = \Omega A \left( 2 - 2cos{\Omega t} \right)^{1/2}[/tex]

    really be correct?
  2. jcsd
  3. Nov 2, 2007 #2


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    Homework Helper

    Here omega is not the period, but the angular velocity = 2pi/T where T is the period.
  4. Nov 2, 2007 #3
    I thought about that too, but it's stated in the problem that the motion is periodic with period [itex]\Omega[/itex]. Anyway, my question still remains.
  5. Nov 2, 2007 #4


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    Staff Emeritus
    Science Advisor

    Is this problem in a text book, or was it given by a professor or teacher?

    [itex]\Omega[/itex] as a period would seem to be incorrect since normally the arguments of sine and cosine are dimensionless, which is consistent with rl.bhat's comment.
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