Hello i would like some help with laplace transforms.

In summary, we discussed the Laplace transform of -3e^{9t}+9 sin(9t) and its representation in a math program, providing two possible solutions: -3/(s - 9) + 9/(s^2 + 81) and -3(s^2 + 81)/(s - 9)(s^2 + 81). We also clarified the correct Laplace transform for sin(9t) as 9/(s^2 + 81).
  • #1
stephan2124
1
0
hello if someone could please tell me if i am incorrect and where , and how to type it into a math program so it can understand it many thanks stephan2124

L -3e^{9t}+9 sin(9t)
L-3e^{9t}+L 9 sin (9t)
-3 Le^{9t}+9 L sin(9t)
-3 (1/s-9) +9 (9/(s^2+9^2))
-3 (1/s-9) +9 (9/(s^2+81))

into a math program
-3*(1/(s-9)+9*(9/s exp +81)
 
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  • #2
We have no way of knowing what your math program will accept as an answer!

Yes, the Laplace transform of [tex]-3e^{9t}+ 9 sin(9t)[/tex] is -3 times the Laplace transform of [tex]e^{9t}[/tex] plus 9 times the Laplace transform if [tex]sin(9t)[/tex]. Yes, the Laplace transform of [tex]e^{9t}[/tex] is [tex]\frac{1}{s- 9}[/tex] and the Laplace transform of [tex]sin(9t)[/tex] is [tex]\frac{1}{s^2+ 9^2}= \frac{1}{s^2+ 81}[/tex] so the Laplace transform of
[tex]-3e^{9t}+ 9 sin(9t)[/tex] is [tex]\frac{-3}{s- 9}+ \frac{9}{s^2+ 81}[/tex].

Now, if your math program does not accept that, perhaps it wants the two fractions added: [tex]\frac{-3(s^2+ 81)}{(s- 9)(s^2+ 81)}+ \frac{9(s- 9)}{(s- 9)(s^2+ 81)}= \frac{-3s^2- 243}{(s- 9)(s^2+ 81)}+ \frac{9s- 81}{(s- 9)(s^2+ 81)}= \frac{-3s^2+ 9s- 324}{(s- 9)(s^2+ 81)}= \frac{-3s^2+ 9s- 324}{s^3- 9s^2+ 81s- 729}= -\frac{3s^2- 9s+ 324}{s^3- 9s^2+ 81s- 729}[/tex].

Any one of those is a correct answer.
 
  • #3
HallsofIvy said:
the Laplace transform of [tex]sin(9t)[/tex] is [tex]\frac{1}{s^2+ 9^2}= \frac{1}{s^2+ 81}[/tex]

Actually it's $\displaystyle \frac{9}{s^2 + 81} $.

so the Laplace transform of
[tex]-3e^{9t}+ 9 sin(9t)[/tex] is [tex]\frac{-3}{s- 9}+ \frac{9}{s^2+ 81}[/tex].


Actually it's $\displaystyle -\frac{3}{s - 9} + \frac{81}{s^2 + 81}$.To enter it in Weblearn you will need to write:

-3/(s - 9) + 81/(s^2 + 81)
 

FAQ: Hello i would like some help with laplace transforms.

1. What are Laplace transforms?

Laplace transforms are mathematical tools used to solve differential equations. They transform a function of time into a function of complex frequency, making it easier to solve complex problems.

2. Why are Laplace transforms useful?

Laplace transforms are useful because they can simplify complex problems involving differential equations, making them easier to solve. They are also used in engineering and physics to model and analyze systems.

3. How do you perform a Laplace transform?

To perform a Laplace transform, you first need to express the function in terms of time. Then, you use the Laplace transform formula to convert the function into a function of complex frequency. Finally, you can solve the transformed function using algebraic methods.

4. What are some applications of Laplace transforms?

Laplace transforms have various applications in engineering, physics, and mathematics. They are used to solve problems involving differential equations in control systems, electrical circuits, and heat transfer. They are also used in signal processing and data analysis.

5. Are there any limitations of Laplace transforms?

While Laplace transforms are a powerful tool for solving differential equations, they have some limitations. They may not work for all functions, and they can be challenging to use for functions with discontinuities or singularities. Additionally, they may not always give a unique solution to a problem.

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