Finding area of elliptical ring (phase space)

[mathlete]

To make a long story short, the problem has an elliptical ring from width E to E+dE in phase space (p on y axis, x on x axis). This is a harmonic oscillator, so the standard equations apply (E=p^2/2m + kx^2/2)... now for the question I need to find the total area in the ring of the ellipse in a slice from x to x + dx and divide it by the total area of the ring, but I don't know how to do that. I know the total area of the ring (should be just dE), but I can't seem to find out how to get the area of a narrow slice of this thing without complex integration (which I don't believe is necessary for this). Anyone have any ideas to push me in the right direction?

 

[quasar987]

Hi mathlete,

you might want to keep an eye on this thread: https://www.physicsforums.com/showthread.php?t=132872

;)

Btw, would you mind extrapolating on your idea concerning complex integration?