What is inverse oflaplace (12)/(0.5s^2+4s+5) ?

The answer to inverse oflaplace (12)/(0.5s^2+4s+5) is 4sqrt(6)e^{-4t}sinh(sqrt(6)t)

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inverse oflaplace (12)/(0.5s^2+4s+5)

inverse laplace

\frac{12}{0.5 s ^{2} + 4 s + 5}

46 e^{- 4 t} sinh (6 t)

Solution steps

L^{- 1} {\frac{12}{0.5 s ^{2} + 4 s + 5}}

Expand

\frac{12}{0.5 s ^{2} + 4 s + 5} : 24 \cdot \frac{1}{( s + 4 ) ^{2} - 6}

= L^{- 1} {24 \cdot \frac{1}{( s + 4 ) ^{2} - 6}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= 24 L^{- 1} {\frac{1}{( s + 4 ) ^{2} - 6}}

L^{- 1} {\frac{1}{( s + 4 ) ^{2} - 6}} : e^{- 4 t} \frac{1}{6} sinh (6 t)

= 24 e^{- 4 t} \frac{1}{6} sinh (6 t)

Refine

24 e^{- 4 t} \frac{1}{6} sinh (6 t) : 46 e^{- 4 t} sinh (6 t)

= 46 e^{- 4 t} sinh (6 t)

What is inverse oflaplace (12)/(0.5s^2+4s+5) ?
The answer to inverse oflaplace (12)/(0.5s^2+4s+5) is 4sqrt(6)e^{-4t}sinh(sqrt(6)t)