Use the first transfer function given and add each of the nonlinearities indicated in the problem separately to the system in simulink. Assume proportional control with k=1.
If you observe a limit cycle in the solution, stop.
If not, then continue to the second and third transfer functions.
For the case where you found a limit cycle, plot the describing function and Nyquist contour and show they intersect at the point corresponding to approximately the frequency and magnitude of oscillation. For a case where you did not observe a limit cycle, plot the Nyquist contour and describing function to show that they do not intersect.