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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 \( +\alpha \) 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 \( x \).
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