1. The system shown below consists of two blocks (each of mass m) attached to a light rigid beam of length I which is supported by two springs with stiffnesses k and nk as shown. x1 m (b) [m L 2 (a) Determine the equations of motion for this system using Newton's laws. Use the coordi- nates and indicated above. No marks will be given if any other coordinate system is used. (b) If n = 4, the equations of motion can be written 3k 2k [-]{3}-[**{3}-{8} ++ + k m-m P = 0.618 P2 = 1.618 {nk Determine the natural frequencies and mode shapes for this system. Clearly sketch the resulting mode shapes and specify the locations of any nodes. (a) [ 18+G+1 *10-0 m L 2 m m {1} = {-1.618) (2) = {0.618) X2