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Dynamics and Hamiltonians : Hamilton's Equations

A dynamical system, with one degree of freedom has Hamiltonian (see attachment for equation)

? Write down the Hamilton's equations governing the motion of this system, and deduce that H remains constant during the motion.
? Solve Hamilton's equations with initial conditions (see attachment) and show that q(t) and p(t) both tend to zero as t tends to infinity.


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Hamilton equations are investigated. The solution is detailed and well presented.