(d) Investigate how the solution changes as n increases. What happens as n 00? The solution ---Select--- V for n = 0, since the nth tern ---Select--- proach zero. does dditional Materials does not A computer algebra system is recommended. Consider the initial value problem y" + y = f(t), y(0) = 0, y'(0) = 0, where f(t) Molt) + 2 (-1)*uka(t). k = 1 (a) Draw the graph of f(t) on an interval such as osts 6. f(t) f(t) 1.04 5 10 15 -0,5 0.5 -1.0 110 15 -1.5 -0.5 0-2.0 f(t) f(t) 1.0 5 10 15 0.5 -0.5 - 1.0 5 110 15 -0.5 -1.5 0-10 0-2.04 (b) Find the solution of the initial value problem. y(t) = 1 - sin t + 2 (-1)\[1 sinct k)]uka(t) k = 1 n y(t) = = 1 - cost + 2 (-1)\[1 cos(t KAT)]4kz(t) k = 1 O yt) = 1 + cost 2 (-1)\[1 cos(t krt)]uka(t) k = 1 O y(t) = 1 cost + (+1)*[1 sinct kn)]uka(t) k = 1 O y(t) = 1 + sin t- (+1)*[1 sinct kn)]uka(1) k = 1 (c) Let n = 15 and plot the graph of the solution for Osts 60. t) ) 20 101 101 -101 -10 -20 -20 -30 y) 30 20 10 -10 -10 -20 -20 0-30 Describe the solution and explain why it behaves as it does. For Ost