I know that $$\text{net work} = \text{work done by conservative forces} + \text{work done by non-conservative forces}.$$ and $$\begin{split}\text{net work} & = \text{change in kinetic energy} + \text{change in potential energy} - \text{change in potential energy} \\& = \text{change in kinetic energy}\end{split}.$$
I also know that elastic potential energy is $k x^2/2$.
Therefore, my question is that for example if you compress a spring by $x$, then aren't you doing work on the spring? Therefore, how do we incorporate it as part of the work-energy equation?
