4. (20 pts) Three beads of equal mass m, which are free to slide on a frictionless hoopJ are connected b identical springs of spring constant. k. Assume that. the springs are Hookjan. (a) \"That. are the equations of motion for the three degrees of freedom 51, 32, 33? (b) What are the normal angular frequencies? Express your answers in terms of mo = q/k/m. (c) Describe the normal modes. Show your work and justify your descriptions mathematically