Question

Problem 6 2.20 Displacement distribution of random oscillators The displacement x of a classical simple harmonic oscillator as a func- tion of the time t is given by x A cos (wt + φ) where w is the angular frequency of the oscillator, A is its amplitude of oscilla- tion, and ф is an arbitrary constant which can have any value in the range φ<2π. Suppose that one contemplates an ensemble of such oscillators all of which have the same frequency w and amplitude A, but which have random phase relationships so that the probability that ф lies in the range between ф and ф + dp is given simply by dp/(2n). Find the probability P(x)dx that the displacement of an oscillator, at any given time t, is found to lie in the range between x and x + dx.

Answer 1

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