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.

Explanation

`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.