A particle which is constrained to move along the \( x \)-axis, is subjected to a force in the s...

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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 [IIT-JEE (Screening) 2002; DCE 2006]
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