A particle performing harmonic oscillation 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 \( \dfrac{dP}{dx} \) depends on \(x\). Here \(dP \) denotes the probability of particle falling within the interval from \(x\) to \(x+ \, dx \).

Plot \( \dfrac{dP}{dx} \) and \(P\) as a function of \(x\).

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