Consider two equal masses m connected by three springs in a triangular conguration, as shown in the sketch. The masses are constrained to move along the coordinate axes, i.e. the left mass moves only in the ydirection and the right mass only in the X direction. The two identical springs attached to the origin have force constant k and equilibrium length L. The third (diagonal) spring has force constant k'and equilibrium length \\/Z L. A. Write the Lagrangian for this system, using Xand you the diagram as generalized coordinates. (10 pts) Assume that the system stays near equilibrium, so that Xandyare much smaller than L. [The binomial approximation (1 + X)\" z 1 + HX will be useful in writing the potential energy in this approximation] B. Find the equations of motion and rewrite them in the standard form M 55 = K it. to identify the matrices M and K. (5 pts) C. \\What are the normal frequencies 0'1 and associated normal modes {i for this coupled oscillator? Describe the motion in the two normal modes. (10 pts)