What would the laplace inverse of a laplace be?

We will, in fact, be interested in the inverse transform, finding a function from its Laplace transform.In summary, the conversation discusses the definition of the Laplace transform and its inverse. The Laplace transform of a function of t is a function of s, and the inverse transform allows us to find a function from its Laplace transform.
  • #1
Jim wah
6
0
For example:
If F(s) = L{t3e-16tcos(3t)sin2(t)}

What would L-1{F(s)} be?
 
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  • #2
Jim wah said:
For example:
If F(s) = L{t3e-16tcos(3t)sin2(t)}

What would L-1{F(s)} be?

If ##\mathcal{L}[f(t)] = F(s)##, then ##\mathcal{L}^{-1}[F(s)] = \mathcal{L}^{-1}[\mathcal{L}[f(t)]] = f(t)##
 
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  • #3
[itex]F(s)= L[t3e^{-16t}cos(3t)sin^2(t)][/itex] seem perfectly reasonable to me. A standard definition of the Laplace transform is
[tex]F= \int_0^\infty e^{-st}f(t)dt[/tex]
so that the Laplace transform of a function of t is a function of s.
 
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Related to What would the laplace inverse of a laplace be?

1. What is the Laplace inverse of a Laplace?

The Laplace inverse of a Laplace is the original function that would produce the given Laplace transform when put through the Laplace transform equation.

2. Can the Laplace inverse of a Laplace be calculated?

Yes, the Laplace inverse of a Laplace can be calculated using the inverse Laplace transform equation.

3. How is the Laplace inverse of a Laplace used in science?

The Laplace inverse of a Laplace is commonly used in science to solve differential equations and analyze systems in physics, engineering, and mathematics.

4. Are there any limitations to finding the Laplace inverse of a Laplace?

There may be certain functions for which the Laplace inverse cannot be calculated, or the calculation may be very complex and time-consuming. Additionally, the Laplace inverse may not exist for some Laplace transforms.

5. Is the Laplace inverse of a Laplace unique?

Yes, the Laplace inverse of a Laplace is unique, meaning that for a given Laplace transform, there is only one original function that would produce it.

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