Give three definitions of conservative force.

(N/A) $(1)$ $A$ force $F$ is conservative if the work done by it on a particle moving between two points depends only on the initial and final positions,not on the path taken.
$(2)$ $A$ force $F$ is conservative if the work done by it in moving a particle around any closed path is zero.
$(3)$ $A$ force $F$ is conservative if it can be expressed as the negative gradient of a scalar potential energy function $U$,such that $F = -\nabla U$.