Undergrad Laplace transform of an expression using transform tables

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The discussion focuses on finding the Laplace transform of a specific expression using conversion formulas. The initial interpretation of "1" as a unit step function with a Laplace transform of 1/s is acknowledged. However, errors in algebra were identified, particularly in the numerator of the expression. After corrections were made, the final result was confirmed as correct. The conversation emphasizes the importance of careful algebraic manipulation in obtaining accurate Laplace transforms.
PainterGuy
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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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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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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
 
You make the same mistake in the numerator, now at the beginning of the second line.
 
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
 
Correct!
 
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