Potential Energy & Conservation

Gravitational: $$ U_g = m g h $$
Spring: $$ U_s = \frac{1}{2} k x^2 $$
Conservation: $$ K_i + U_i = K_f + U_f $$ (if only conservative forces)
Potential energy depends on position. $$h$$: height, $$x$$: spring deformation, $$k$$: spring constant. Mechanical energy conserved when no non-conservative forces act.