6. " In this problem, we'll look at the effect of a periodic external force on the pendu- lum, using the model 0" + 0.050' + sin 0 = 0.3 cos wt (D.5) (cf. Problems 3-5). We have chosen a value for the damping coefficient that is more typical of air resistance than the values in the previous problem. Prepare Simulink models for (D.5) and its linear approximation 0" + 0.050' + 0 = 0.3 cos wt. The right-hand side can be produced by a Sine Wave block (which is in the Sources Library). When you install this block and left-click on it to bring up the Block Parameters menu, you will see an Amplitude box in which to insert the parameter 0.3 and a Frequency box in which to insert the parameter w. Note that since we have a cosine, not a sine, you also have to adjust the Phase (to }, since coset = sin(wt + 5 )). Your Simulink models should: . Plot the numerical solution of this differential equation with initial conditions #(0) = 0, #'(0) = 0, from t = 0 to t = 60. . Do the same for the linear approximation. Compare the nonlinear and linear models for the following values of the frequency w: 0.6, 0.8, 1, 1.2. Which frequency moves the pendulum farthest away from its equi- librium position? For which frequencies do the linear and nonlinear equations have173 widely different behaviors? Which forcing frequency seems to induce resonance- type behavior in the pendulum? Graph that solution on a longer interval and decide whether the amplitude goes to infinity