Using the ODE Architect, or some other solver, plot the solution curves of y'' = -y + cy^3, y(0) = 1, y'(0) = 0 for c = 0, -0.1, 0.1 and 0<=t<= 7 on the same screen. Do this by using three variables y, v and c in your solver with the extra question c' = 0. Interpret your results in terms of particular types of springs. Look for example at the values of the different solutions at time t = 7. Discuss also any variations that you notice in v. Expalin how these results confirm your intuitive understanding of these springs.