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    Oscillation and escape velocity of a particle

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    The potential energy function of a particle of mass is V = cx/(x^2 + a^2), where c and a are positive constants. Sketch V as a function of x. Find the position of stable equilibrium, and the period of small oscillations about it. Given that the particle starts from this points with velocity v, find the ranges of values of v for which it (a) oscillates, (b) escapes to - infinite, and (c) escapes to + infinite.

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    https://brainmass.com/physics/energy/linear-motion-the-potential-energy-function-of-a-particle-of-mass-m-is-210499

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    This solution provides calculations for the oscillations and escape velocity of a particle.

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