Energy of a spring? 1

[DDP]

For some reason I cant get this to work out. If you have a spring and you apply a P weight in the axial direction, the strain energy in the spring is

Us = 1/2 Px (or 1/2 kx^2)

But the work done by gravity is

W = P x

But Us does not equal W? Maybe this does not account for the effect of someone gently lowering the weight to the equilibrium position instead of just letting the weight instantaneously fall?

 

[prex]

Your last sentence is the answer to your question: if you leave the mass to fall down, an harmonic oscillation will be started with amplitude 2x, that will last forever in the absence of losses.

prex

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