determine a function f(t) that has the given Laplace transform F(s)=frac{4s+5}{s^{2}+9}

determine a function f(t) that has the given Laplace transform F(s)=frac{4s+5}{s^{2}+9}

Question
Laplace transform
asked 2020-12-17
determine a function f(t) that has the given Laplace transform
\(F(s)=\frac{4s+5}{s^{2}+9}\)

Answers (1)

2020-12-18
Step 1
Given Laplace transform is \(F(s)=\frac{4s+5}{s^{2}+9}
The function can be obtained as follows. \(f(t)=L^{-1}\left\{F(s)\right\}
\(=L^{-1}\left\{\frac{4s+5}{s^{2}+9}\right\}
\(=L^{-1}\left\{\frac{4s}{s^2+9}\right\}+L^{-1}\left\{\frac{5}{s^2+9}\right\}
Step 2 On further simplifications, \(f(t)=4L^{-1}\left\{\frac{s}{s^2+3^{2}}\right\}+\frac{5}{3}L^{-1}\left\{\frac{3}{s^2+3^{2}}\right\}
\(=4\cos(3t)+\frac{5}{3}\sin(3t)\)
0

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