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Homework Help: Uniformly distributed phase of oscillators -> probability for special displacement

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Assume, you have an ensemble of linear harmonic oscilators, all having the same frequency [tex]\omega[/tex] and amplitude [tex]a[/tex]:

    [tex]x = a\cos(\omega t + \phi)[/tex]​

    The phase [tex]\phi[/tex] is uniformly distributed in the inteval [tex][0,2\pi)[/tex]. What ist the probability [tex]w(x)dx[/tex] to find the displacement of one oscillator in the interval [tex][x,x+dx][/tex]? (for constant [tex]t[/tex])

    2. Relevant equations

    3. The attempt at a solution
    I have looked in all my books and in the internet, but I absolutely have no idea how to start...

    A little hint would be great!

    (I don't want a solution from you, I just want to know, what formula/concept I have to look at, to have at least a chance to solve this exercise...)

  2. jcsd
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