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

Question

determine a function f(t) that has the given Laplace transform

F (s) = \frac{4 s + 5}{s^{2} + 9}

Answer 1

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

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

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