Laplace transform of an expression using transform tables

In summary, the conversation was about finding the Laplace transform of a given expression and correcting errors in the resulting transformation. The person asking for help made mistakes in the algebraic calculations but was able to fix them with guidance.
  • #1
PainterGuy
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TL;DR Summary
I was working to find Laplace transform using the table and wanted to know that if my final result is correct
Hi,

I 'm trying to find the Laplace transform of the following expression.
1587364477947.png


I used the following conversion formulas.
I think "1" is equivalent to unit step function who Laplace transform is 1/s.
1587364605853.png


I ended up with the following final Laplace transform.
1587364834778.png


Is my final result correct? Thank you for the help!
 
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  • #2
Your Laplace transforms are correct, but not your subsequent algebra. The last term in the first (red) line is where the error appears.
 
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  • #3
DrClaude said:
The last term in the first (red) line is where the error appears.

I tried to fix the error. Could you please give it a look? For some reason, I think that in the numerator I should only get "10" and not "2s+10".

1587371218734.png
 
  • #4
You make the same mistake in the numerator, now at the beginning of the second line.
 
  • #5
DrClaude said:
You make the same mistake in the numerator, now at the beginning of the second line.

Sorry!

It looks good now.
1587372103691.png
 
  • #6
Correct!
 
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FAQ: Laplace transform of an expression using transform tables

What is the Laplace transform and how does it work?

The Laplace transform is a mathematical tool used to convert a function of time into a function of complex frequency. It is often used in engineering and physics to solve differential equations and analyze systems. The transform works by integrating the function over all time and multiplying it by a decaying exponential term.

Why do we use transform tables when finding the Laplace transform?

Transform tables provide a quick and efficient way to find the Laplace transform of common functions. These tables contain a list of functions and their corresponding transforms, making it easier to solve problems without having to go through the integration process every time.

What are some common functions that can be transformed using Laplace transform tables?

Some common functions that can be transformed using Laplace transform tables include polynomials, exponential functions, trigonometric functions, and their combinations. It is important to note that the function must be defined for all values of time in order for the transform to exist.

Can the Laplace transform be used to solve differential equations?

Yes, the Laplace transform can be used to solve differential equations. By transforming both sides of a differential equation, it can be converted into an algebraic equation which is easier to solve. Once the solution is found, the inverse Laplace transform can be applied to obtain the solution in the time domain.

Are there any limitations to using Laplace transform tables?

Yes, there are some limitations to using Laplace transform tables. These tables only contain transforms for common functions and may not cover all possible functions. In addition, the tables may not include transforms for functions with complex or piecewise-defined components. In these cases, the transform must be found through integration or using other methods.

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