Conservation of Energy
If all forces are conservative forces (i.e. path independent, like weights and linear springs) (no friction!), then we can apply the Principle of Conservation of Energy.
Any decrease in potential energy V is accompanied by an equivalent increase in kinetic energy, and vice versa.
Kinetic Energy T = 1/2 mv2 Gravitational Potential Energy V = Wy Elastic Potential Energy V = 1/2 kx2