Restoring Force

Q.

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 $F\left(x\right)=-kx+a{x}^3$. Here k and a are positive constants. For $x\ge 0$, the functional from of the potential energy $U_{\left(x\right)}$of the particle is [IIT JEE 2002]

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Q.

The potential energy of a system is represented as shown in the figure. The force acting on the system will be represented by

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