Consider a three dimensional harmonic oscillator with a nonlinear force such that the potential

a) calculate the force.
b) what is the lagrangian for this system?
c) what are the euler-lagrange equations?
d) find the effective potential.
e) what kind of orbits are possible-consider both small angular momentum and large angular momentum.
f) when they exist, find the radii of possible circular orbits as a function of the angular momentum.
g) which, if any of these orbits are stable?
h) for stable orbits, what is the frequency of small oscillations.