Position probability distribution for a pendulum. Consider the classical motion of a pendulum bob which, for small amplitudes of oscillation, moves effectively as a harmonic oscillator along a horizontal axis according to the equation.
x(t) = Asinωt
The probability that the bob will be found within a small distance delta x at x in random observations is proportional to the time it spends in this region during each swing. Obtain a mathematical expression for this probability as a function of x, assuming delta x<