Exercise 3.5.1: Take the equation mx" +cx' + kx-0, with m > 0, c 2 0, k > 0 for the mass-spring system. a) Convert this to a system of first order equations. b) Classify for what m, c, k do you get which behavior. c) Can you explain from physical intuition why you do not get all the different kinds of behavior here? Exercise 3.5.2: What happens in the case when P-ld11? In this case the eigenvalue is repeated and there is only one independent eigenvector What picture does this look like? Exercise 3.5.3: What happens in the case when P we have drawn? ]?Does this look like any of the pictures Exercise 3.5.4: Which behaviors are possible if P is diagonal, that is P] You can assume that a and b are not zero.