1. The problem statement, all variables and given/known data A mass M is confined to move on a smooth, flat, two-dimensional surface. Label the locations on this surface using the Cartesian coordinates (x,y). The mass is attached to two identical springs, each of length l and spring constant k. One spring has one end fixed to the point (-L, 0) and the other spring has one end fixed to the point (L, 0) 1) Find the normal modes of this system when l<L. 2) At t=0, the mass is released at rest from the point (0.1L, -0.2L). What is the position of the mass for all subsequent times? 2. Relevant equations 3. The attempt at a solution I used the Lagrangian method to find the equations of motion (see attachment). I'm sure there is something I could do to simplify these two equations by making some sort of approximation. But I'm not sure what to do. Any help would be appreciated. Thanks!