How Do You Correct the Coefficient in an Inverse Laplace Transform Calculation?

This is because when you expand the second term, you get ((398/85))/((s+3)^2+9), which simplifies to (398/85)/((s+3)^2+9), which is the same as (1370.5/595)/((s+3)^2+9). Therefore, the coefficient of the second term should be (307/510). In summary, the issue is with the second term of the problem ((s/s^2+4)+s+5))/(s^2+6s+18). The correct coefficient for this term is (307/510), which can be obtained by dividing the numerator and denominator by 2. This is due to the simplification of
  • #1
Derill03
63
0
ok I am given the problem ((s/s^2+4)+s+5))/(s^2+6s+18) I use the expand function of my ti-89 and get
((163/70)*s)/((s+3)^2+9) + ((398/85))/((s+3)^2+9) + ((7/170)*s)/(s^2+4) + (6/85)/(s^2+4)
1st term--------------------2nd term-----------------3rd term-------------4th term

ok my issue is with the second term when i do the translation i get -2741/1190 I then want it to be 3 because of k so i get a coefficient of (2741/3570) but my calculator says it should be
(307/510)?

All the other terms are correct just this coefficient on second term

Any help?
 
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  • #2
The coefficient of the second term should be (307/510). To get this, divide both the numerator and denominator by 2. That is, 2741/2 = 1370.5 and 1190/2 = 595. Then, 307/510 is the same as 1370.5/595.
 

FAQ: How Do You Correct the Coefficient in an Inverse Laplace Transform Calculation?

1. What is an inverse laplace transform?

An inverse laplace transform is a mathematical operation that is used to find the original function from its laplace transform. It is the reverse of the laplace transform.

2. What is the importance of inverse laplace transform?

The inverse laplace transform is important in engineering, physics, and other fields as it allows us to solve differential equations and analyze systems in the time domain.

3. How is inverse laplace transform calculated?

To calculate the inverse laplace transform, we use a table of laplace transforms to find the corresponding function and then use techniques such as partial fractions or contour integration to find the inverse.

4. What are the applications of inverse laplace transform?

Inverse laplace transform has many applications, including solving differential equations, analyzing electrical circuits, and studying control systems.

5. Are there any limitations to inverse laplace transform?

Yes, there are certain functions that do not have a laplace transform or an inverse laplace transform. In these cases, other methods must be used to solve the problem.

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