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A particle of mass, m, in an isolated environment moves along a line with speed v...

A particle of mass, m, in an isolated environment moves along a line with speed v whilst experiencing a force proportional to its distance from the origin.

a) Determine the Langrangian of the system

b) Determine the Hamiltonian of the system

c) Write down Hamilton’s equations of motion for the particle d) Show that the particle executes simple harmonic motion

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