# Total mechanical work, solving for x

by Nano-Passion
Tags: mechanical, solving, work
 P: 1,306 1. The problem statement, all variables and given/known data I understand the problem conceptually. I just need help solving for x, which is the hardest part of the problem for me. 1/2mv^2 = 1/2kx^2 + umgx 3. The attempt at a solution Not really sure how to solve this. I tried and tried to separate by x but nothing worked. Here are 1 of the attempts I suppose. I feel pretty stumped here. $$1/2mv^2 = 1/2kx^2 + umgx$$ $$1/2mv^2 - umgx = 1/2kx^2$$ $$\frac{mv^2}{k} - \frac{2umgx}{k} = x^2$$ ???