For a mass on a spring (vertical set up) why is potential energy U defined as 1/2 kx^2? This is just the elastic potential energy. Shouldn't it be U = 1/2 kx^2 + mgh? Both the elastic AND potential energy? Also, for a simple pendulum at a very low amplitude, the potential energy is all gravitational, right? By the way, if U = 1/2 kx^2 + mgh, then the relationship ω = √(k/m) becomes invalid, since U = 1/2 mω^2 x^2 is always valid and equating this to both elastic and gravitational potential energy gives us a different expression for ω.