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Take the Laplace transform of the following initial value and solve for X(s) = L{x(t)}: S sin(nt), 0

Take the Laplace transform of the following initial value and solve for X(s) = L{x(t)}: S sin(nt), 0

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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Take the Laplace transform of the following initial value and solve for X(s) = L{x(t)}: S sin(nt), 0 <t <1 0, x" + 16x x(0) = 0, a'(0) = 0. 1<t X(s) = help (formulas) Hint: First write the right hand side of the ODE in terms of the Heaviside function Now find the inverse trai orm to find x(t) = help (formulas) Use u(t – a) for the Heaviside function shifted a units horizontaly. Note: 1 1 (s2 + n² )(s² + 16) - 16 \ s2 + 16 s2 + 72
Transcribed Image Text:Take the Laplace transform of the following initial value and solve for X(s) = L{x(t)}: S sin(nt), 0 <t <1 0, x" + 16x x(0) = 0, a'(0) = 0. 1<t X(s) = help (formulas) Hint: First write the right hand side of the ODE in terms of the Heaviside function Now find the inverse trai orm to find x(t) = help (formulas) Use u(t – a) for the Heaviside function shifted a units horizontaly. Note: 1 1 (s2 + n² )(s² + 16) - 16 \ s2 + 16 s2 + 72
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