So the UK exam board specifications (AQA GCSE) clearly state "...the work done on the spring and the elastic potential energy stored are equal" Here's my problem,
So work done = Force x displacement
Force = Spring constant x extension
Elastic potential energy = 0.5 x spring constant x extension squared
Extension = displacement for a strecthed spring
However if I take some sample values and calculate the work done on the spring, and then the elastic potential energy stored. The Elastic potential is always exactly half the work done. This contradicts the statement in the specifications.
I have looked all over the place but can't find a satisfactory answer to this question. What am I missing? I get that elastic potential energy is equal to area under the Fx graph but why does that not equal the work done?