1. The problem statement, all variables and given/known data Given the system in the image below, I need to find the equation of motions for the coupled system. The surface where the block moves is frictionless. The red line is position where the block is at equilibrium. At equilbrium x1 and x2 = 0. After finding the equation of motion for the coupled system, I need to find the normal modes which I can do but I'm having trouble finding first part. Also the angle is small angle approximation. http://imgur.com/JPzK1Jn http://imgur.com/JPzK1Jn 2. Relevant equations F= ma sinθ = tanθ = θ = [x2 - x1]/L 3. The attempt at a solution Ok so taking the horizontal and vertical forces of each: Block: Fx1 = -kx1 - Tsinθ Fy1 = N - mg - Tcosθ Mass on Pendulum: Fx2 = Tsinθ ************** Fy2 = mg - Tcosθ *****I feel like the spring should add a force here, but I'm not sure how. If I proceed adding a -kx1 to Fx2 and solving for the equations of motion using the small angle approximation I get a1 = -k/mx1 + T/Lm(x2 - x1) and a2 the same which is wrong. Also I cannot get rid of T. I am not so concerned over the normal modes because I can do that after. We did not do any langrange stuff so I am not allowed to use it. Also because of the small angle, I asked if I was allowed to approximate the vertical displacement for the pendulum to be zero, but I cannot so I have to find another way.