1. The problem statement, all variables and given/known data Hi guys, I'm struggling to figure out how the solution in the picture that I posted was able to get rid of their mg factors and then come up with a factor of k for x_1 in their eigenvalue equation. You can see that in the second equation of motion there is no k*x_1 but it shows up in the eigenvalue equation. I thought you could just drop those mg factors when you went to figure out eigenvalues since they only effect the equilibrium positions. Thanks a bunch of any help. 2. Relevant equations Lagrangian for two springs and two hanging masses. Change of variables. 3. The attempt at a solution I've tried to work out what the change of variables would be or how you would calculate it but not such luck yet. Any help would be greatly appreciated. Thank you.