How to Find the Probability of a Mass in Oscillatory Motion?

[bemigh]

A Mass is oscillating on a spring, with a normal equation of motion being:
x(t) = xmax sin(wt)
Were also given that the energy equation is E = 0.5mv^2 + 0.5mw^2 x^2
Now, we need to find the probability P(x,deltax) of finding the mass in a small region of size delta x.

I really have no idea where to get started.
I understand that the mass will spend the most time at its endpoints, because it moves the slowest then.
Any idea how to get started?

 

[quasar987]

The idea is to take the ratio in phase space of the volume corresponding to x+dx to the total volume.