What is inverse oflaplace 3/(s^2+2s+10) ?

The answer to inverse oflaplace 3/(s^2+2s+10) is e^{-t}sin(3t)

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inverse oflaplace 3/(s^2+2s+10)

inverse laplace

\frac{3}{s ^{2} + 2 s + 10}

e^{- t} sin (3 t)

Solution steps

L^{- 1} {\frac{3}{s ^{2} + 2 s + 10}}

Expand

\frac{3}{s ^{2} + 2 s + 10} : 3 \cdot \frac{1}{( s + 1 ) ^{2} + 9}

= L^{- 1} {3 \cdot \frac{1}{( s + 1 ) ^{2} + 9}}

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)}

= 3 L^{- 1} {\frac{1}{( s + 1 ) ^{2} + 9}}

L^{- 1} {\frac{1}{( s + 1 ) ^{2} + 9}} : e^{- t} \frac{1}{3} sin (3 t)

= 3 e^{- t} \frac{1}{3} sin (3 t)

Refine

3 e^{- t} \frac{1}{3} sin (3 t) : e^{- t} sin (3 t)

= e^{- t} sin (3 t)

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

y = 2 C x + C (sin (x) + x cos (x))

\frac{\partial}{\partial x} (\frac{x y}{y - x})

n = 1 \sum \infty (\frac{7}{3})^{n}

\int_{6}^{8} \frac{66}{( x - 6 ) ^{3}} d x

What is inverse oflaplace 3/(s^2+2s+10) ?
The answer to inverse oflaplace 3/(s^2+2s+10) is e^{-t}sin(3t)