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