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Introductory examples include
connecting certain force laws to the corresponding potential energy:
F(spring,particle) --> PE(spring,particle)
F(gravity,particle) --> PE(gravity,particle)
and you can equally well start from an energy principle and go the other
direction
PE(spring,particle) --> F(spring,particle)
PE(gravity,particle) --> PE(spring,particle)
and the choice of direction is mostly a matter of taste.