4. A particle of mass m moves in a central field of attractive force that has a magnitude () eat, where kand a are constants, t is the time, and ris the distance of m from the force's center. Find the Lagrangian and Hamiltonian functions. Compare the Hamiltonian and the total energy of the system and discuss the conservation of energy for the system.

4. A particle of mass m moves in a central field of attractive force that has a magnitude () eat, where kand a are constants, t is the time, and ris the distance of m from the force's center. Find the Lagrangian and Hamiltonian functions. Compare the Hamiltonian and the total energy of the system and discuss the conservation of energy for the system.

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