Consider the mechanical system shown in Figure 1: where qi (i = 1,2) are the displacement of masses, m; are the masses, and ki are the values of the stiffness of spring. ma1 + (ki + k)91 - K292 = 0 m292 k2q1 +k292 = 0 91 1. Represent the dynamics as i Ar where the state-variable is z = 92 91 [92 2. What are the eigen-values of A when m = m = 1, 9 92 = 1. (you can certainly use Matlab command eig) 3. Using command expm(A) one can find e^. Can you comment on what will be q (2), and 42 (2) when initial condition is r(0) = k mor m 19 voo m (1) 19 Figure 1: Mechanical System for Problem 1