I am trying to answer the following question: Two equal masses are constrained by the spring-and-pulley system shown (the pulley has no mass and the surface is frictionless). Determine the equation of motion for the system in terms of x, the extension of the spring from its unstretched length. Solve for x as a function of time with the boundary conditions x = dx/dt = 0 at t = 0. I have attached a word document with the diagram for the system. All that I've added to the diagram so far is T1, T2 and mg for the mass dangling over the edge. Now, the last part of the question (solving for x with the boundary conditions) I can solve easily once I've actually figured out the equation of motion. The problem I'm having is getting to the point where I have a second-order differential that I can solve. I'm not entirely sure how to choose my coordinate system (should I have an x and y coordinate system?) and I'm also not sure about the forces involved. Are the tensions (T1 and T2) that I've drawn in correct, and what do they equal? Is it just T1 = T2 = -kx + mg , or am I missing something? I'd really appreciate it if someone can point me in the right direction here.