Suppose the spring in Figure is nonlinear and is described by the cubic force-displacement relation. The equation of motion is
m = c( - ) + k1(y - x) + k2(y - x)3
Where m = 100, c = 600, k1 = 8000, and k2 = 24000. Approximate the unit-step input y(t) with y(t) = 1 - e-t/Ï„, where r is chosen to be small compared to the period and time constant of the model when the cubic term is neglected. Use MATLAB to plot the forced response x(t).