Find the probability density function f(x) for the position x of a particle which is executing simple harmonic motion on (-a, a) along the x axis. (see chapter 7, section 2, for a discussion of simple harmonic motion.) hint: the value of x at time t is x a cos wt. find the velocity da/dt; then the probability of finding the particle in a given dax is proportional to the time it spends there which is inversely proportional to its speed there. don't forget that the total probability of finding the particle somewhere must be 1