Given that oC 1 e-atu(t) ~ --, s+a ffi-e{ s} > ffi-e{- a}, determine the inverse Laplace

Chapter 9, Problem 9.9

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QUESTION:

Given that

\(e^{-a t} u(t) \stackrel{\mathscr{L}}{\longleftrightarrow} \frac{1}{s+a}, \quad \operatorname{Re}\{s\}>\operatorname{Re}_{e}\{-a\},\)

 determine the inverse Laplace transform of

\(X(s)=\frac{2(s+2)}{s^{2}+7 s+12}, \quad \operatorname{Re}_{e}\{s\}>-3\)

Questions & Answers

QUESTION:

Given that

\(e^{-a t} u(t) \stackrel{\mathscr{L}}{\longleftrightarrow} \frac{1}{s+a}, \quad \operatorname{Re}\{s\}>\operatorname{Re}_{e}\{-a\},\)

 determine the inverse Laplace transform of

\(X(s)=\frac{2(s+2)}{s^{2}+7 s+12}, \quad \operatorname{Re}_{e}\{s\}>-3\)

ANSWER:

Step 1 of 2

The given equation can be written as,

                                                   

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