4 The displacement a of a mass on a spring changes according to the second order differential equation at2 + w x = 0. a Write this as a coupled system of first order differential equations. b Write this system in the matrix form x = Ax. A more realistic model for a mass on a spring includes damping due to air resistance. The displacement a can be modelled using dt2 + k + wax = 0 where k > 0 is the level of damping. a Write this as a coupled system of first order differential equations. b Write this system in the matrix form x = Ax. c Show that the eigenvalues of A are -ktyk2 - 4w2 2 d If k = 0, the spring is undamped. State the nature of the equilibrium point and its significance in this case. e Suppose 0