l. A bead of mass m slides without friction on a rotating wire hoop of radius (1 whose axis of rotation is through a vertical diameter as shown in Fig.2.l7. The constant angular velocity of the hoop is a). (a) Write the Lagrangian for the system and nd any constants of the motion that may exist. (b) Locate the positions of equilibrium of the bead fora) we ,where Which of these positions of equilibrium are stable and unstable? (c) Calculate the oscillation frequencies of small amplitude Vibrations about the points of stable equilibrium