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a) Find the Laplace transform of the following expression by using transform tables. f (t) = t³ + sin 2t b) Find the inverse Laplace transform of the following expression by using transform tables. F(s) = + s+5 s²+25 c) Use the First Shift Theory to find the Laplace transform of the following expression. e-3t sinh 5t d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e) Use the Multiply by t rule to find the Laplace transform of the following expression. f(t) = t²e5t

a) Find the Laplace transform of the following expression by using transform tables. f (t) = t³ + sin 2t b) Find the inverse Laplace transform of the following expression by using transform tables. F(s) = + s+5 s²+25 c) Use the First Shift Theory to find the Laplace transform of the following expression. e-3t sinh 5t d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e) Use the Multiply by t rule to find the Laplace transform of the following expression. f(t) = t²e5t

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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a) Find the Laplace transform of the following expression by using transform tables. f (t) = t³ + sin 2t b) Find the inverse Laplace transform of the following expression by using transform tables. F(s) s2+25 c) Use the First Shift Theory to find the Laplace transform of the following expression. e-3t sinh 5t d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e) Use the Multiply by t rule to find the Laplace transform of the following expression. f(t) = t²e5t
Transcribed Image Text:a) Find the Laplace transform of the following expression by using transform tables. f (t) = t³ + sin 2t b) Find the inverse Laplace transform of the following expression by using transform tables. F(s) s2+25 c) Use the First Shift Theory to find the Laplace transform of the following expression. e-3t sinh 5t d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e) Use the Multiply by t rule to find the Laplace transform of the following expression. f(t) = t²e5t
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