What is inverse oflaplace (8.2)/(4.2x^2+4x+5) ?

The answer to inverse oflaplace (8.2)/(4.2x^2+4x+5) is 1.98879…e^{-0.47619…t}sin(0.98169…t)

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inverse oflaplace (8.2)/(4.2x^2+4x+5)

inverse laplace

\frac{8.2}{4.2 x ^{2} + 4 x + 5}

1.98879 \dots e^{- 0.47619 \dots t} sin (0.98169 \dots t)

Solution steps

L^{- 1} {\frac{8.2}{4.2 x ^{2} + 4 x + 5}}

Expand

\frac{8.2}{4.2 x ^{2} + 4 x + 5} : 1.95238 \dots \cdot \frac{1}{( x + 0.47619 \dots ) ^{2} + 0.96371 \dots}

= L^{- 1} {1.95238 \dots \cdot \frac{1}{( x + 0.47619 \dots ) ^{2} + 0.96371 \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)}

= 1.95238 \dots L^{- 1} {\frac{1}{( x + 0.47619 \dots ) ^{2} + 0.96371 \dots}}

L^{- 1} {\frac{1}{( x + 0.47619 \dots ) ^{2} + 0.96371 \dots}} : e^{- 0.47619 \dots t} \frac{1}{0.98169 \dots} sin (0.98169 \dots t)

= 1.95238 \dots e^{- 0.47619 \dots t} \frac{1}{0.98169 \dots} sin (0.98169 \dots t)

Simplify

1.95238 \dots e^{- 0.47619 \dots t} \frac{1}{0.98169 \dots} sin (0.98169 \dots t) : 1.98879 \dots e^{- 0.47619 \dots t} sin (0.98169 \dots t)

= 1.98879 \dots e^{- 0.47619 \dots t} sin (0.98169 \dots t)

\frac{s ^{2}}{( s ^{2} - 1 ) ^{2}}

\frac{10}{x ^{2}}

n = 0 \sum \infty \frac{6}{n ( n + 3 )}

f (t) = \frac{1}{t ^{2}}

f (x) = \frac{1}{1 + e ^{x}}, at x = 1

What is inverse oflaplace (8.2)/(4.2x^2+4x+5) ?
The answer to inverse oflaplace (8.2)/(4.2x^2+4x+5) is 1.98879…e^{-0.47619…t}sin(0.98169…t)