# Uniformly distributed phase of oscillators -> probability for special displacement

1. Apr 11, 2010

### Derivator

1. The problem statement, all variables and given/known data
Assume, you have an ensemble of linear harmonic oscilators, all having the same frequency $$\omega$$ and amplitude $$a$$:

$$x = a\cos(\omega t + \phi)$$​
.

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

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...)

--derivator

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