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)`
`therefore F = - (d)/(dx) (ax^(2) - bx) = 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 is minimum.
Therefore, x = `(b)/(2a)` is the stable equilirium position.