Find f(t) if L(f) = 6(1-e^(-πs))/(s^2+9)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find f(t) if L(f) = 6(1-e^(-πs))/(s^2+9)

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The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as 0e-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. If F(s) or L[f(t)] is the Laplace transform of the function f(t), then f(t) is called the inverse Laplace transform of F(s).

According to the definition of Heaviside function, the value of the function uc(t) is equal to 1 if tc and equal to 0, if t<0. The Laplace transform of the function in the form Luc(t)f(t-c)=e-csF(s).

 

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