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Consider the following initial value problem: y" + 4y = sint − u2(t) sin(t — 2π); y(0)=0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. -1 y(t): m/4 = P (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. where c = 5/4 3/2 7/4 2 9/4 5/2 1/4 3 X X X

Consider the following initial value problem: y" + 4y = sint − u2(t) sin(t — 2π); y(0)=0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. -1 y(t): m/4 = P (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. where c = 5/4 3/2 7/4 2 9/4 5/2 1/4 3 X X X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following initial value problem: y" + 4y = sint - u2(t) sin(t – 2π); y(0) = 0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. 1 y(t): 4 m/2 3/4 m 5/4 3m/2 7/4 2 9/4 5/2 1/4 3 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. = where c = X X X
Transcribed Image Text:Consider the following initial value problem: y" + 4y = sint - u2(t) sin(t – 2π); y(0) = 0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. 1 y(t): 4 m/2 3/4 m 5/4 3m/2 7/4 2 9/4 5/2 1/4 3 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. = where c = X X X
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