Consider the following initial value problem: y" +9y = sint - U2(t) sin(t - 2π); y(0) = 0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval 0 π/4 л/2 3л/4 5/4 3/2 7/4 2 where c = (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by u(t) where ue(t) = 1 ift≥c and 0 otherwis Indicate separately the value of c. y(t) = 9/4 5/2 11n/43 (c) Use a graphing utility to view the graph of the solution. (d) Explain how the graphs of the forcing function and the solution are related. When the external force is on, the solution is periodic with a period Choose one ▾ and an amplitude When the external force is removed, the solution Choose one

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