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

In a conservative field
`F=-(dU)/(dx)=-(d)/(dx)(ax^(2)-bx)=-(2ax-b)`
`therefore F-b-2ax`
For equilibrium `F=0`
or `b-2ax=0 " "therefore x=(b)/(2a)`
From the given equation we can see that
`(d^(2)U)/(dx^(2))=2a` (positive), i.e., U minimum.
Therefore, `x=(b)/(2a)` is the stable equilibrium position.