6. (TeamC) Consider the spring mass ODE 2 d$+2bd:+a2 dt2 d $20 where the mass of the system is 1, the damping coefcient is 2b and the Hooks constant is a2. Suppose b 2 0 and a > 0. (a) Convert the second order ODE into a rst order system I w y y' a2:r 2by with critical point (0,0). 0 1 (b) Let A_ [-02 _2b (c) For each of the following cases, classify the critical point and determine its stability in each of the following cases. (i) b = 0; (ii) 0 a . Include a description of the corresponding motion of the mass in your solution. 1 . Find the characteristic equation for A (Le, det(A AI) = 0)