Consider the following initial value problem: y" + 25y = f(t); f(t) = { y(0) = 0, y'(0) = 5; 5, 0≤t < 3³ 3π 0, 35 ≤ t <∞ (a) Sketch the graph of the forcing function on an appropriate interval. 10+ 9 8 7 6 5 4 3 2 1 3 4 6 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where uc(t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. y(t) =
Consider the following initial value problem: y" + 25y = f(t); f(t) = { y(0) = 0, y'(0) = 5; 5, 0≤t < 3³ 3π 0, 35 ≤ t <∞ (a) Sketch the graph of the forcing function on an appropriate interval. 10+ 9 8 7 6 5 4 3 2 1 3 4 6 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by ue(t) where uc(t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. y(t) =
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 1YT
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Transcribed Image Text:Consider the following initial value problem:
y" + 25y = f(t); _y(0) = 0, y'(0) = 5;
f(t)
y(t) =
=
=
7
6
5
4
3
2
5, 0≤t <3³
5
{
(a) Sketch the graph of the forcing function on an appropriate interval.
10
3π
0, 3≤ t <∞
5
Ť
(b) Find the solution of the given initial value problem.
NOTE: Denote the Heaviside function by ue(t) where uc(t) = 1 if t > c and 0 otherwise.
Indicate separately the value of c.
3
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