Quick question on coupled pendulum kinetic energy

[cmackeen]

I have found that the kinetic energy term for each mass on a coupled (by a spring) pendulum has no $\dot{y}$ terms, as in the the masses do not move in the y direction at all. What am I missing here? I know they are connected, but in the first normal mode, both masses should move like regular pendulums. Regular pendulums have a $\dot{y}$ component in their kinetic energy, so why are there only $\dot{x}$ terms for kinetic energy? Provided link below

http://csirnetphysics.blogspot.com/2012/11/classical-mechanics-question-1.html

In this diagram, x_1 and x_2 correspond to each mass (m_1 and m_2)

 

[mikeph]

I can't see any correspondence between the diagram and your variables. What are x1 and x2? I don't see any mention of y throughout the derivation.