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7. Two Connected Toy Train Cars. 15 minutes. 10 points Two identical masses m on frictionless and massless wheels are moving

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7. Two Connected Toy Train Cars. 15 minutes. 10 points Two identical masses m on frictionless and massless wheels are moving along the r direction and connected by a spring of force constant k. The equilibrium separation is d. (a) Write the Lagrangian of the system in terms of the positions of the two masses. (b) Transform the Lagrangian to the Hamiltonian, explaining what you do. (c) Obtain Hamilton's equations for this system. You are not asked to solve them.
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2 2 Ym 2 2. M2

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