1. Write the effective potential for the particle.

2. Sketch a graph of the effective potential, Ueff(r), and indicate on your graph where

bound orbits and circular orbits are possible.

3. Find the radii of the possible circular orbits with this potential. (You may leave your

answers in terms of the fourth power of each radius).

4. Which of the possible circular orbits that you found above is stable? Hint: Think

about the case L = 0.

5. Suppose the particle is initially moving along the stable circular orbit. The trajectory

of the particle is perturbed slightly. Find the angular frequency of small oscillations

around the radius of the circular orbit.