The position as a function of time x(t) of a simple harmonic oscillator is given by: x(t) = A cos(wt) where A is the amplitude and w is the angular velocity. a) What is the range of possible values of x permitted for this oscillator? b) Derive the probability density function of p(x) for this oscillator. c) Validate that p(x) is normalized.

The position as a function of time x(t) of a simple harmonic oscillator is given by: x(t) = A cos(wt) where A is the amplitude and w is the angular velocity. a) What is the range of possible values of x permitted for this oscillator? b) Derive the probability density function of p(x) for this oscillator. c) Validate that p(x) is normalized.