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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
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)

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.)
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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