2 A, 3 masses (20 points) Consider the pictured 3-dof system: m 2m m Three masses slide on a frictionless table, connected by four identical springs. a) Find the M and K matrices for this set of masses and identical springs. (6 pts) b) Find the allowed frequencies of vibration, w, the associated mode shapes, , and write down the general solution. (6 pts) c) Sketch the mode shapes illustrating the relative motions. Identify all nodes on your sketches, and confirm that the first mode has no nodes, the second mode has one node, and the third mode has two nodes. (4 pts) d) Given the initial conditions (4 pts) 1(0) x2( == [1(0)] 12(0) = 2 (1) [3 (0)] find the subsequent motion of the carts. Show that the second mode is not excited by these initial conditions (A2 = 0 and B = 0).