What is inverse oflaplace 8/(0.65s+1) ?

The answer to inverse oflaplace 8/(0.65s+1) is 12.30769…e^{-1.53846…t}

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inverse oflaplace 8/(0.65s+1)

inverse laplace

\frac{8}{0.65 s + 1}

12.30769 \dots e^{- 1.53846 \dots t}

Solution steps

L^{- 1} {\frac{8}{0.65 s + 1}}

= L^{- 1} {12.30769 \dots \cdot \frac{1}{s + 1.53846 \dots}}

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)}

= 12.30769 \dots L^{- 1} {\frac{1}{s + 1.53846 \dots}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s + 1.53846 \dots}} = e^{- 1.53846 \dots t}

= 12.30769 \dots e^{- 1.53846 \dots t}

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What is inverse oflaplace 8/(0.65s+1) ?
The answer to inverse oflaplace 8/(0.65s+1) is 12.30769…e^{-1.53846…t}