# Probability and oscillations

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 $$x$$.

Note by Rishabh Deep Singh
2 years, 5 months ago

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