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When a particle of mass m moves on the x-axis in a potential form , it performs simple harmonic motion. The corresponding time period is proportional to , as can be seen easily using dimensional analysis. However, the motion of a particle can be preiodic even when its potential energy increases on both sides of x=0 in a way different from and its total energy is such taht the particle does not escape to infinity. consider a particle of mass m moving on the x -axis. its potential energy is for |x| near the origin and becomes a constant equal to for |x|
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If the total energy of the particle is E, it will perform periodic motion only if

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Question Text
When a particle of mass m moves on the x-axis in a potential form , it performs simple harmonic motion. The corresponding time period is proportional to , as can be seen easily using dimensional analysis. However, the motion of a particle can be preiodic even when its potential energy increases on both sides of x=0 in a way different from and its total energy is such taht the particle does not escape to infinity. consider a particle of mass m moving on the x -axis. its potential energy is for |x| near the origin and becomes a constant equal to for |x|

If the total energy of the particle is E, it will perform periodic motion only if