The system examined in the problem is depicted below: ^^^^^(m1)^^^^^(m2) m1 and m2 are connected by a spring and m1 is connected to the wall by a spring. The spring constant is k. T = m/2 [ x1'^2 +x2'^2 ] kinetic energy of system (x1' is velocity of m1, x2' is velocity of m2) U = 1/2 m k^2 (x1 - b)^2 + 1/2 m k^2 (x2-x1-b)^2 potential energy of system (x1 is position of m1, x2 is position of m2, b is the unstretched length of the spring) Is m the reduced mass? Also, could someone explain how the equation for U is derived? Why is it k^2 and not just k (i.e. potential energy for spring = 1/2 kx^2)? Also, why is there a mass term in the potential energy? Or is this the wrong expression for potential energy altogether? I known then that the Lagrangian for the system is L = T - U. I can then take derivatives and substitute into the Euler-Lagrange equation. I should have two E.L. equations, correct? But what should I solve for -- x1 and x2? Any guidance/hints greatly appreciated!