What is inverse oflaplace 2/(3s^2+4) ?

The answer to inverse oflaplace 2/(3s^2+4) is 1/(sqrt(3))sin((2t)/(sqrt(3)))

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inverse oflaplace 2/(3s^2+4)

inverse laplace

\frac{2}{3 s ^{2} + 4}

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

Solution steps

L^{- 1} {\frac{2}{3 s ^{2} + 4}}

= L^{- 1} ⎩ ⎨ ⎧ \frac{1}{3} \cdot \frac{\frac{2}{3}}{s ^{2} + ( \frac{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{1}{3} L^{- 1} ⎩ ⎨ ⎧ \frac{\frac{2}{3}}{s ^{2} + ( \frac{2}{3} ) ^{2}} ⎭ ⎬ ⎫

Use Inverse Laplace Transform table:

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

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

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

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

\int cos (2 v) d v

\frac{d}{d x} (x, x)

\frac{d}{d x} (\frac{b}{a} a^{2} - x^{2})

\frac{\partial}{\partial T} (\frac{x}{T})

What is inverse oflaplace 2/(3s^2+4) ?
The answer to inverse oflaplace 2/(3s^2+4) is 1/(sqrt(3))sin((2t)/(sqrt(3)))