Three particles of identical mass m are constrained to move on a frictionless horizontalhoop as shown in the below Figure. The identical springs obeying Hooke's Law withspring constant k connect the three particles of mass m. The small displacements of thethree particles from their equilibrium positions are x₁, x2, and x3 as also shown in theFigure.X3kkX₁X2ka) Determine the total force acting along the hoop on each of the three particles.b) Write down the potential energy for the system and verify by differentiation that theexpression obtained above for the forces is consistent.c) Write down the equations of motion for the three particles.

(a) We can write the potential of the system V=1/2k(x2-x1)2+1/2k(x3-x2)2+1/2k(x3-x1)2

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