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Find the Laplace transform L{f(t)} of the following functions. sin(3t) .0 1

Find the Laplace transform L{f(t)} of the following functions. sin(3t) .0 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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Find the Laplace please
Find the Laplace transform L{f(t)} of the following functions. sin(3t) .0 <t < 1 f(t) = telt-1) + sin(3t) ,t > 1
Transcribed Image Text:Find the Laplace transform L{f(t)} of the following functions. sin(3t) .0 <t < 1 f(t) = telt-1) + sin(3t) ,t > 1
Expert Solution
Step 1

The function f(t) is a rule that associates or fixes a number to a particular point t. According to the fundamental theorem of calculus ∫abf(t)dx=F(b)-F(a), where dFdt=f(t).

The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as ∫0∞e-stf(t)dt, since the dimension of s is the same as the reciprocal of the dimension of t, the transform transforms a function into its reciprocal space.

 

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