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If you place a weight on a spring and it is an equilibrium, then you have this equation:
$mg = kx$
you would solve for k and get:
$k = mg/x$
but, if we used conservation of energy, assuming that when the mass is on the spring it is at x = 0, we would get:
$1/2kx^2 = mgx $
we would get $k = 2mg/x$
What assumption am I making that is false? How would the k value be different with two correct statements?