A particle, which is constrained to move along the -axis, is subjected to a force in the same direction which varies with the distance of the particle from the origin as Here and are positive constants. For , the functional form of the potential energ

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A particle, which is constrained to move along the $x$ -axis, is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin as $F (x) = - k x + a x^{3} .$ Here $k$ and $a$ are positive constants. For $x \geq 0$ , the functional form of the potential energy $U (x)$ of the particle is [2002]

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