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Consider the following initial value problem: y" + 4y = f(t); y(0) = 0, 3(0) = 2; { S 2, 0 c and 0 otherwise. Indicate separately the value of c. y(t): where c = (c) Use a graphing utility to view the graph of the solution.

Consider the following initial value problem: y" + 4y = f(t); y(0) = 0, 3(0) = 2; { S 2, 0 c and 0 otherwise. Indicate separately the value of c. y(t): where c = (c) Use a graphing utility to view the graph of the solution.

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: 3y" + 4y = f(t); y(0) = 0, 3/ (0) = 2; S 2, 0st< f(t) = 0, <t< 0 (a) Sketch the graph of the forcing function on an appropriate interval. 9 7 5 2 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 ift> c and 0 otherwise. Indicate separal the value of c. 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. During 0 <t <. 37 the solution is periodic with period 2 and amplitude and centered at which is the particular solution for the equation over that interval. At t = 2 the external force is removed. For t > the solution is purely 2' periodic with period and amplitude
Transcribed Image Text:Consider the following initial value problem: 3y" + 4y = f(t); y(0) = 0, 3/ (0) = 2; S 2, 0st< f(t) = 0, <t< 0 (a) Sketch the graph of the forcing function on an appropriate interval. 9 7 5 2 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 ift> c and 0 otherwise. Indicate separal the value of c. 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. During 0 <t <. 37 the solution is periodic with period 2 and amplitude and centered at which is the particular solution for the equation over that interval. At t = 2 the external force is removed. For t > the solution is purely 2' periodic with period and amplitude
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