0.2 4 6. 8 10 12 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise. Indicate separately the value of c....

Extracted text: 0.2 4 6. 8 10 12 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise. Indicate separately the value of c. %3D y(t) = where c = (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. After an initial transient, the solution Choose one

c and 0 otherwise. %3D Indicate separately the value of c. y(t) = 2. "/>
Extracted text: Consider the following initial value problem: y(4) + 41y" + 400y = 1 – u(t); y(0) = 0, y'(0) = 0, y"(0) = 0, y"(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. 1 0.8 0.6 0.4 0.2 4 6. 10 12 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t > c and 0 otherwise. %3D Indicate separately the value of c. y(t) = 2.