Using the radial eqtn. of motion, we can derive an equation for small oscillations of the system when the orbit deviates a little bit from circular (actually we can do it for small oscillations around any closed orbit, but this is a little harder). we do this here for 2 different potentials consider a central field with a newtonian potential, such that v(r) ="v_0/r. find first of all, when the system has a given angular momentum l, what is the value r_0 of the radius for which the orbit is circular; and determine also the orbital period of this orbit (ie., for the angular motion). then make a taylor expansion of the radial potential up to 2nd order in the deviations of r from r_0 and use this to find the frequency of harmonic oscillations of r around r_0. how does this frequency compare with the frequency of orbital motion when r = r_0? now do exactly the same for the 2 - d harmonic potential, where v(r) = kr62/2\ ie., first find r_0 for circular orbits, then find the period of revolution around the z axis, and finally find the frequency of small oscillations around r-0