Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y" + 12y' + 17y= T(t) y(0) = 0, y'(0) = 0 Where T(t) = = 0 ≤ t < 1/2 [1-t, 1/2≤t
Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y" + 12y' + 17y= T(t) y(0) = 0, y'(0) = 0 Where T(t) = = 0 ≤ t < 1/2 [1-t, 1/2≤t
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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Question
![Take the Laplace transform of the following initial value
problem and solve for Y(s) = L{y(t)}:
y" +12y + 17y= T(t)
y(0) = 0, y'(0) = 0
Where
T(t) =
=
St,
0 < t < 1/2
1-t, 1/2 ≤t<1'
T(t+1) = T(t).
Y(s) =
Graph of T'(t) (a triangular wave function):
f](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7154d7d-eae8-44c2-ac46-13a234391d51%2F0197bd1f-0732-4e03-8eee-eabd8c9ee396%2F878x5po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Take the Laplace transform of the following initial value
problem and solve for Y(s) = L{y(t)}:
y" +12y + 17y= T(t)
y(0) = 0, y'(0) = 0
Where
T(t) =
=
St,
0 < t < 1/2
1-t, 1/2 ≤t<1'
T(t+1) = T(t).
Y(s) =
Graph of T'(t) (a triangular wave function):
f
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