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13. In this problem, we consider the long-term behavior of solutions of the initial value problem day +0.244 y + y = 0.3 cos(wt), y(0) = 0, 7/0) = 0 ' (D.8) dt2 dt for various frequencies w in the forcing term. Plot a numerical solution of (D.8) from t = 0 to t = 100 for each of the eight frequencies w=0.8,0.9,...,1.4,1.5. Describe and compare the different long-term behaviors you see. Due to the forcing term, all solutions will oscillate, but pay particular attention to the magnitude of the oscillations and to whether or not there is a periodic pattern to them. Are there any similarities between your results for this nonlinear system and the phenomenon of resonance for linear systems with periodic forcing