# Lagrangian and Hamiltonian dynamics of a particle

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A particle of mass m moves in one dimension under the influence of a force:

F(x, t) = (k/x^2)*e^(-t/T)

Where k and T are positive constants.

a) Compute the Lagrangian and Hamiltonian Functions

b) Compare the Hamiltonian and the total energy.

c) Discuss the conservation of energy for the system.

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The solution is a detailed explanation on Lagrangian and Hamiltonian dynamics of a particle which moves in one dimension under the influence of a force. The Lagrangian and Hamiltonian functions of the particle are calculated. Furthermore, the conservation of energy of the system is discussed.

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A particle of mass m moves in one demension under the influence of a force:

F(x, t) = (k/x^2)*e^(-t/T)

Where k and T are positive constants.

a) Compute ...

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