What is inverse oflaplace ((3+3s))/(s^2+0.5) ?

The answer to inverse oflaplace ((3+3s))/(s^2+0.5) is 4.24264…sin(0.70710…t)+3cos(0.70710…t)

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inverse oflaplace ((3+3s))/(s^2+0.5)

inverse laplace

\frac{( 3 + 3 s )}{s ^{2} + 0.5}

4.24264 \dots sin (0.70710 \dots t) + 3 cos (0.70710 \dots t)

Solution steps

L^{- 1} {\frac{( 3 + 3 s )}{s ^{2} + 0.5}}

Expand

= L^{- 1} {\frac{3}{s ^{2} + 0.5} + \frac{3 s}{s ^{2} + 0.5}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= 3 L^{- 1} {\frac{1}{s ^{2} + 0.5}} + 3 L^{- 1} {\frac{s}{s ^{2} + 0.5}}

L^{- 1} {\frac{1}{s ^{2} + 0.5}} : \frac{1}{0.70710 \dots} sin (0.70710 \dots t)

L^{- 1} {\frac{s}{s ^{2} + 0.5}} : cos (0.70710 \dots t)

= 3 \cdot \frac{1}{0.70710 \dots} sin (0.70710 \dots t) + 3 cos (0.70710 \dots t)

Simplify

3 \frac{1}{0.70710 \dots} sin (0.70710 \dots t) + 3 cos (0.70710 \dots t) : 4.24264 \dots sin (0.70710 \dots t) + 3 cos (0.70710 \dots t)

= 4.24264 \dots sin (0.70710 \dots t) + 3 cos (0.70710 \dots t)

\frac{( cos ( x ) )}{1 - sin ( x )}

\frac{2}{x + 3}

18 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

\frac{\partial}{\partial w} (u v - w)

\int e^{3 l n (x)} d x

What is inverse oflaplace ((3+3s))/(s^2+0.5) ?
The answer to inverse oflaplace ((3+3s))/(s^2+0.5) is 4.24264…sin(0.70710…t)+3cos(0.70710…t)