Well, I was looking for and explanation of how two different ways of deriving k gave two different answers, not a derivation of the PE of a spring. You still have not explained why k derived through PE is not the same as k derived by force.
AlephZero, would it be correct then to say that...
Consider the following question: a woman of mass m steps onto a vertical spring and compresses it a distance d. What is the value of the spring constant k?
The dilemma is that I found what I believe are two valid ways of solving this problem, but the two results for k are not equal!
If...