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A particle free to move along the x axis has potential energy given by U...

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A particle free to move along the x axis has potential energy given by U K 1 exp x for x 0 where K is a positive constant of appropriate dimensions Then 1 At points away from the origin the particle is in unstable equilibrium 2 For any finite non zero value of x there is a force directed away from the origin 1 K 2 3 If its total mechanical energy is it has minimum kinetic energy at the origin 4 For small displacements from x 0 the motion is simple harmonic

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