Problem 4.9

A particle performs harmonic oscillations along the \(x\) axis according to the law \(x=a \cos \omega t\). Assuming the probability \(P\) of the particle to fall within an interval from \(-a\) to \(+a\) to be equal to unity, find how the probability density \(d P / d x\) depends on \(x\). Here \(d P\) denotes the probability of the particle falling within an interval from \(x\) to \(x+d x\). Plot \(d P / d x\) as a function of \(x\).