Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: (sin(at), 0≤t<1 {Sit 1
Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: (sin(at), 0≤t<1 {Sit 1
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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I need help with finding y(t)

Transcribed Image Text:Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}:
y" + 4y = (sin(nt),
0<t<1
10,
1≤t
π
1
1
Y (8) = 2 ² ²-4 ( 3² + 4 = 2² +2²2) (1
Y(s)
2
Now find the inverse transform:
y(t) =
Note:
1 + e
-s)
y(0) = 0, y'(0) = 0
Hint: write the right hand side in terms of the Heaviside function.
π
π
1
1
2² + 7²) (2² + 4) = 7² − 4 ( 8² + 4 − R+R)
(s²
-
(Notation: write u(t-c) for the Heaviside step function u(t) with step at t = c.)
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