The following suspension system has two support structures-a spring and a rubber pad. Vertical force F (N) acts on the moveable plate. The spring has a spring constant of k1 = 1000 N/m. The rubber pad has a spring constant of k2 = 20000 N/m. The rubber pad starts touching the moving plate when the plate has moved down by a distance of a = 4 cm from the unloaded position. Define a function m-file that calculates the displacement x for given inputs of F, k1, k2, and a. Using the function, calculate the displacement for F = 0, 20, 40, 60, 80, 100 N. Plot these in F-x coordinates (F-horizontal, x-vertical) using solid lines and square markers. Annotate the figure.
Hint: the suspension system becomes stiffer for F > 40 N = F k1*a. When the plate is supported only by the spring, the force is F = k1*x, whereas when the plate is supported by the spring and the rubber pad, the force is F = k1*x + k2*(x-a).