- #1

indianaronald

- 21

- 0

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In summary, the conversation discusses the process of finding the inverse Laplace of 1/s using different methods such as integral and formula-based approaches. The use of MATLAB and Mathematica is also mentioned. The correct property for finding the inverse is also clarified.

- #1

indianaronald

- 21

- 0

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- #2

antibrane

- 38

- 0

[tex]

\mathcal{L}^{-1}\left\{s\right\} = \frac{d}{dt}\delta(t)

[/tex]

- #3

indianaronald

- 21

- 0

16180339887 said:derivativeof the delta function, in other words:

[tex]

\mathcal{L}^{-1}\left\{s\right\} = \frac{d}{dt}\delta(t)

[/tex]

Hey yeah, figured that out. It's actually by this property:

inverse( df/dt)= s F(s) where laplace(f) = F(s)

laplace ( dirac delta )=1 ( known property )

laplace( d(diracdelta)/dt ) = s*(1)

hence, inverse( s) = d(diracdelta)/dt

- #4

jfgobin

- 90

- 2

Almost, be careful that:

[itex]\mathcal{L}\left\{ \frac{\mathrm{d}f}{\mathrm{dt}} \left(t\right)\right\}=s\mathcal{L}\left\{f\left(t\right)\right\}[/itex]

Not the inverse as you mentioned it.

- #5

indianaronald

- 21

- 0

jfgobin said:

Almost, be careful that:

[itex]\mathcal{L}\left\{ \frac{\mathrm{d}f}{\mathrm{dt}} \left(t\right)\right\}=s\mathcal{L}\left\{f\left(t\right)\right\}[/itex]

Not the inverse as you mentioned it.

yeah yeah. That's what I meant. Typo.

The formula for finding the inverse Laplace of 1s is 1/s, where s is the Laplace variable.

To use the formula, simply plug in the value of s and then perform the necessary arithmetic operations to find the inverse Laplace of 1s.

Yes, the formula can be used for any value of s, as long as it is a constant and not a function of time.

The inverse Laplace of 1s is a fundamental formula in mathematics and is used in various applications such as signal processing, control systems, and differential equations.

Yes, there are alternative methods such as using tables, partial fraction decomposition, and contour integration. However, the formula-based solution is the most straightforward and commonly used method.

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