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  • $\begingroup$ Okay I have done what you said (I usually do exactly what you said and only use symbols rather than numbers) and I have gotten the right answer. I think that my main issue was redefining my coordinate system mid problem. This clearly wont work for potential energies. The equation that got me there $$mg\left(y_0+\frac{mg}{k}+A\right)=\frac{1}{2}k\left(\frac{mg}{k} +A\right)^2$$ Where $y_0$ is initial height above spring, $mg/k$ the distance from unstretched to equilibrium, and $A$ the resulting amplitude. $\endgroup$ Commented Apr 12 at 4:58