Question

consider an ensamble of classical one-dim harmonicoscillators.

let the displacement x of an oscillator as a function of time tbe given by x=Acos(wt+θ). Assume that the phase angle θ isequally likely to assume any value in its range 0<θ<2π. Theprobability w(θ)dθ that θ lies in the range between θ and θ + dθ isthen simply w(θ)dθ = (2π)^-1dθ. For any fixed time t, find theprobability P(x)dx that s lies between x and x+dx by summing w(θ)dθover all angles θ for which x lies in this range. Express P(x) interms of A and x.