What is inverse oflaplace 8/(s^2+9) ?

The answer to inverse oflaplace 8/(s^2+9) is 8/3 sin(3t)

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inverse oflaplace 8/(s^2+9)

inverse laplace

\frac{8}{s ^{2} + 9}

\frac{8}{3} sin (3 t)

Solution steps

L^{- 1} {\frac{8}{s ^{2} + 9}}

= L^{- 1} {\frac{8}{3} \cdot \frac{3}{s ^{2} + 3 ^{2}}}

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)}

= \frac{8}{3} L^{- 1} {\frac{3}{s ^{2} + 3 ^{2}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{a}{s ^{2} + a ^{2}}} = sin (a t)

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

= \frac{8}{3} sin (3 t)

\frac{d ^{2}}{d x ^{2}} (\frac{x - 4}{3 x - x ^{2}})

x \to 0 - lim (arcsin (e^{x}))

\frac{\partial}{\partial a} (ab)

\int_{- \infty}^{0} x e^{4 x} d x

\int x^{4} (1 - x^{5})^{7} d x

What is inverse oflaplace 8/(s^2+9) ?
The answer to inverse oflaplace 8/(s^2+9) is 8/3 sin(3t)