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Consider the following initial value problem: y" + 4y = f(t); f(t) = where c = (a) Sketch the graph of the forcing function on an appropriate interva 10+ 9 8 7 659 y(0) = 0, y'(0) = 2; 4 3 2 2, 0

Consider the following initial value problem: y" + 4y = f(t); f(t) = where c = (a) Sketch the graph of the forcing function on an appropriate interva 10+ 9 8 7 659 y(0) = 0, y'(0) = 2; 4 3 2 2, 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1E
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Consider the following initial value problem: y" + 4y = f(t); y(t) (a) Sketch the graph of the forcing function on an appropriate interval 10+ 9 8 7 6 = where c = f(t) = (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by u(t) where ue(t) = 1 if t≥c and 0 otherwise Indicate separately the value of c. y = y(0) = 0, y'(0) = 2; 5 4 3 2 2, 0<t<3 0, 3 ≤ t <∞ (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. 3π During 0 ≤ t ≤ the solution is periodic with period 2' periodic with period and amplitude the external force is removed. For t 6 3π particular solution for the equation over that interval. At t = 2 3π 2' and amplitude and centered at which is the the solution is purely
Transcribed Image Text:Consider the following initial value problem: y" + 4y = f(t); y(t) (a) Sketch the graph of the forcing function on an appropriate interval 10+ 9 8 7 6 = where c = f(t) = (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by u(t) where ue(t) = 1 if t≥c and 0 otherwise Indicate separately the value of c. y = y(0) = 0, y'(0) = 2; 5 4 3 2 2, 0<t<3 0, 3 ≤ t <∞ (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. 3π During 0 ≤ t ≤ the solution is periodic with period 2' periodic with period and amplitude the external force is removed. For t 6 3π particular solution for the equation over that interval. At t = 2 3π 2' and amplitude and centered at which is the the solution is purely
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