A 120-lb uniform circular plate is welded to two elastic rods which have fixed ends at supports

Question:

A 120-lb uniform circular plate is welded to two elastic rods which have fixed ends at supports A and B as shown. The torsional spring constant of each rod is 150 lb ft/?? t/rad, and the system is in equilibrium when the plate is vertical. Knowing that the plate is rotated 2? about axis AB and released, determine

(a) The period of oscillation,

(b) The magnitude of the maximum velocity of the mass center G of the plate.