Inverse Laplace transform

In summary, an inverse Laplace transform is a mathematical operation that converts a function from the Laplace domain back to the time domain. It is important because it simplifies the solution process for differential equations. The Laplace transform and inverse Laplace transform are inverse operations, and the inverse Laplace transform can be calculated using a table or integration techniques. This transform has various applications in engineering, physics, and other scientific fields, including solving differential equations, analyzing circuits, and modeling dynamic systems. It is also used in signal processing and control systems.
  • #1
casper12
11
0

Homework Statement


Determine the inverse Laplace transform

Homework Equations


3s+9.
(s+3)^2+7

The Attempt at a Solution


[/B]
Hi iam new to the forum and still unsure how to make the equations the correct format so hope you can understand what I have typed.

I have Tried to Convert the original equation into the equation below to try and use the partial fractions method but getting nowhere.

3s+9.
s^2+6s+16 I'm Not sure if Iam making the question more difficult, can't seem to put the division side of the equestion into brackets.

Attempt was (s-2)(s+8) but that results in s^2+6s-16 resulting in an incorrect sign. Can't seem to change the signs to make it correct.

Not sure if partial fractions method is the best method or if I'm making it more difficult than it is.

Any advice much appreciated.
 
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  • #2
casper12 said:

Homework Statement


Determine the inverse Laplace transform

Homework Equations


3s+9.
(s+3)^2+7

The Attempt at a Solution


[/B]
Hi iam new to the forum and still unsure how to make the equations the correct format so hope you can understand what I have typed.

I have Tried to Convert the original equation into the equation below to try and use the partial fractions method but getting nowhere.

3s+9.
s^2+6s+16I'm Not sure if Iam making the question more difficult, can't seem to put the division side of the equestion into brackets.

Attempt was (s-2)(s+8) but that results in s^2+6s-16 resulting in an incorrect sign. Can't seem to change the signs to make it correct.

Not sure if partial fractions method is the best method or if I'm making it more difficult than it is.

Any advice much appreciated.
Write your expression as ##\frac{3(s + 3)}{(s + 3)^2 + 7}##
The s + 3 expressions represent a translation to the left of ##\frac{3s}{s^2 + 7}##. If you can recognize what the inverse Laplace Transform of this expression is, and take care of the translation represented by s + 3, you should be able to answer your question.

Regarding using partial fractions, your factorization of (s - 2)(s + 8) is obviously wrong, as this doesn't give you s2 + 6s + 16. This quadratic doesn't factor into linear factors with real coefficients, so that technique is not useful here.
 
  • #3
Thread closed. The original thread is in the Engineering & CS Homework section.
 

1. What is an inverse Laplace transform?

An inverse Laplace transform is a mathematical operation that takes a function in the Laplace domain and converts it back to the time domain. It is essentially the reverse process of a Laplace transform.

2. Why is the inverse Laplace transform important?

The inverse Laplace transform is important because it allows us to solve differential equations in the time domain by transforming them into algebraic equations in the Laplace domain. This makes the solution process simpler and more efficient.

3. What is the relationship between Laplace transform and inverse Laplace transform?

The Laplace transform and inverse Laplace transform are inverse operations of each other. This means that if we apply a Laplace transform to a function and then apply an inverse Laplace transform to the resulting function, we will get back the original function.

4. How is the inverse Laplace transform calculated?

The inverse Laplace transform is calculated by using a table of Laplace transforms or by using integration techniques. The method used depends on the complexity of the function being transformed.

5. What are some applications of the inverse Laplace transform?

The inverse Laplace transform has many applications in engineering, physics, and other areas of science. It is commonly used to solve differential equations, analyze circuits, and model dynamic systems. It is also used in signal processing and control systems.

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