1. The problem statement, all variables and given/known data Hey guys, I have been making progress in classical mechanics but I'm having a tough time figuring out how to solve for the normal frequencies for this set of equations of motion: http://imgur.com/nQKPNsu In order to account for the mass gravity term here the book suggests setting new primed variables to create new simpler equations of motion like so http://imgur.com/vQBGInD I'm comfortable with everything here except that I really don't know how or why the defined those primed variables the way they did. I don't know how they fit in to the new equations of motion or resemble the old unprimed ones. Any help here would be aweomse. Thank you. 2. Relevant equations http://imgur.com/nQKPNsu http://imgur.com/vQBGInD 3. The attempt at a solution I tried adding the old equations of motion together to try and figure out if they found a relationship between the y variables and then exploited it when defining the primed ones but I had no luck there.