The potential energy for a conservative force system is given by `U=ax^(2)-bx`. Where a and b are constants find out (a) The expression of force (b) Potential energy at equilibrium.

Explanation

(a) For conservative force
`F = -(dU)/(dx) = -(2ax - b) = - 2ax + b`
(b) At equilbrium ` F = 0 Rightarrow - 2ax + b = 0,`
`x = (b)/(2a)`
(c)` U = a((b)/(2a))^(2) - b((b)/(2a)) = (b^(2))/(4a) - (b^(2))/(2a) = b^(2)/(4a)`