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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

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

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.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 31E
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Consider the following initial value problem: y" +9y = sint - U2π(t) sin(t – 2π); y(0) = 0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval J π/2 3л/4 5/4 3/2 7/4 2 1 (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(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. When the external force is on, the solution is periodic with a period and an amplitude 9/4 5/2 11n/43 Choose one ▾ When the external force is removed, the solution [Choose one ▾
Transcribed Image Text:Consider the following initial value problem: y" +9y = sint - U2π(t) sin(t – 2π); y(0) = 0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval J π/2 3л/4 5/4 3/2 7/4 2 1 (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(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. When the external force is on, the solution is periodic with a period and an amplitude 9/4 5/2 11n/43 Choose one ▾ When the external force is removed, the solution [Choose one ▾
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