Consider two particles of masses m1 and m2. Let m1 be confined to move on a circle of radius a in the z = 0 plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius b in the z = c plane, centered at x = y = 0. A light (massless) spring of spring constant k is attached between the two particles.
(a) Find the Lagrangian for the system.
(b) Solve the problem using Lagrange multipliers and give a physical interpretation for each multiplier.
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