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Popular >

inverse oflaplace 2/(3(s-3)^2+12)

Solution

inverse laplace

\frac{2}{3 ( s - 3 ) ^{2} + 12}

Solution

e^{3 t} \frac{1}{3} sin (2 t)

Solution steps

L^{- 1} {\frac{2}{3 ( s - 3 ) ^{2} + 12}}

Apply inverse transform rule:

if

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {F (s - a)} = e^{a t} f (t)

For

\frac{2}{3 ( s - 3 ) ^{2} + 12} : a = 3, F (s) = \frac{2}{3 s ^{2} + 12}

= e^{3 t} L^{- 1} {\frac{2}{3 s ^{2} + 12}}

L^{- 1} {\frac{2}{3 s ^{2} + 12}} : \frac{1}{3} sin (2 t)

= e^{3 t} \frac{1}{3} sin (2 t)

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Frequently Asked Questions (FAQ)

What is inverse oflaplace 2/(3(s-3)^2+12) ?
The answer to inverse oflaplace 2/(3(s-3)^2+12) is e^{3t} 1/3 sin(2t)