Probability is equal to the time spent in interval (x,x+dx) normed to total time it takes mass to run through entire available x space ( from -A to A, A is amplitude ). So you haveHow to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?
Which is what we started with ( dp = 2 dt/T ), with normalization added: P(-infinity < x < +infinity) = 1dx=vdt so P =2 int(dt)/T = 1.
Thats seems to be about right, although I don't understand how you got there :)Maybe Asin(ωt) = A[1-cos2(ωt)]1/2 = A[1-x2/A2]1/2, so you obtain v(x)?