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f It) = a e 71 f Sin 4t + 5 cos 4t

f It) = a e 71 f Sin 4t + 5 cos 4t

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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Question
Determine Laplace transform
f It) a e3* sin 4t * cos 4t
Transcribed Image Text:f It) a e3* sin 4t * cos 4t
Expert Solution
Step 1

Laplace Transform:

Given a function Ft defined for all real t≥0, the Laplace transform of Ft is a function of new variable s given by

LFt=fs=∫0∞e-stFtdt

First shifting or first translation theorem:

If LFt=fs, then 

LeatFt=fs-a,

where a is any real or complete constant.

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