Section 8.4 presents a second-order differential equation that can be used to analyze the unforced oscillations of an automobile shock absorber. Given m = 1.2 x 10⁶ g, c = l x 10⁷ g/s, and k =l.25 x l0⁹ g/s², use a numerical method to solve for the case where x(0) = 0.4 and dx(0) dt = 0.0. Solve for both displacement and velocity from t = 0 to 0.5 s.