The conservative force in one dimension is the negative slope of the potential energy curve: $F_{x} = -\frac{dU(x)}{dx}$

Sum the potential energies of all pairs of interacting objects: $U_{total} = U_{12} + U_{13} + U_{23} + ...$

1. Find the slope of the potential energy curve at the point of interest. 2. Take the negative of that slope: $$F_{x} = -\frac{dU(x)}{dx}$$.

Sum the potential energies of all pairs of interacting objects: U_total = U_12 + U_13 + U_23 + ...

The change in potential energy (ΔU) is equal to the negative work done by conservative forces: $$\Delta U = - \int_{a}^{b} \vec{F}_{cf}(r) \cdot d\vec{r}$$

Conservative: Work is path-independent, net work in a closed loop is zero, potential energy exists (e.g., gravity). Non-conservative: Work is path-dependent, energy is dissipated (e.g., friction).

Stable: Local minimum of potential energy, system returns to equilibrium after disturbance. Unstable: Local maximum of potential energy, system moves away from equilibrium after disturbance.