Consider an isotropic harmonic oscillator whose potential is given by V(r) = 1 kr?
(a) Calculate the force F(r) and make plots of both V(r) and F(r)
(b) Make a plot of effective potential for a particle of mass m moving with energy E and angular momentum L. Describe the motion of a particle without solving the equations of motion.
(c) Find the values of E and L for a circular orbit.
(d) Calculate the frequency of revolution for the circular orbit and the frequency of small radial oscillations.
(e) Explain the nature of the orbit that differs slightly from a circular orbit.