Please see posted question below

2. Consider the 2DOF massspring system shown in the gure. (a) W'rite the equations of motion for this sly-"stem, and put them in matrix form. Find the natural frequencies as a function of n. (b) Find the mode shapes for m. = 11 k = 1_. and n: 1. 111 332 (c) Suppose that each spring also has a damping (e1: (:2: (:3). Find the damping values (c1, (:2, C3) such k at k that the system has proportional damping (i.e. C = - 02M + 5K)