In Class Presentation 12 :
1. Team 1 : Problem 6.1
2. Team 2 : Problem 6.13
3. Team 3 : Problem 6.14
4. Team 4 : A hoop of mass m1 is free to rotate in its own plane under the influence of gravity about a point P on its edge which is held fixed as shown in the Figure. A bead of mass m2, located at point B, is constrained to move only on the hoop. The point C is the center of the hoop. The angles α and β are measured with respect to the vertical lines passing through P and C.
(a) Find the Lagrangian for the system in terms of the two angles.
(b) Approximate L so that the problem reduces to that of small oscillations.
(c) Find the eigenfrequencies and eigenvectors corresponding to the normal modes. You need not normalize the eigenvectors.
(d) Depict the normal modes with arrows.
