The potential energy of a conservative force field is given by `U=ax^(2)-bx` where, a and b are positive constants. Find the equilibrium position and discuss whether the equilibrium is stable, unstable or neutral.

The potential energy of a conservative force field is given by `U=ax^(

1.	The potential energy of a conservative force field is given by `U=ax^(2)-bx` where, a and b are positive constants. Find the equilibrium position and discuss whether the equilibrium is stable, unstable or neutral.
Answer» `U=alphax^2-betax` `(dU)/(dx)=2alphax-beta` For equilibrium,`F=-(dU)/(dx)=0` `2alphax=betaimpliesx=(beta)/(2alpha)` `(d^2U)/(dx^2)=2alpha` (positive), i.e., `U` is minimum. At `x=(beta)/(2alpha)`, equilibrium is stable.

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The potential energy of a conservative force field is given by `U=ax^(2)-bx` where, a and b are positive constants. Find the equilibrium position and discuss whether the equilibrium is stable, unstable or neutral.

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