1. Team 1 : Problem 3.31
2. Team 2 : Problem 3.4
3. Team 3 : Problem 3.18
4. Team 4 : A particle moves inside of a praboliod with equation z = br², where b > 0 is a contant, r is the distance from the z axis. The surface of the paraboloid exerts no friction. The acceleration due to gravity has magnitude g and acts in the negative z direction. Find the condition for circular orbits to occur and determine their stability. What is the period of such orbits.