Solve Laplace Transform of t sinwt w/ Theorem 1.31

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SUMMARY

The discussion focuses on solving the Laplace Transform of the function t sin(wt) using Theorem 1.31, which pertains to the General Differentiation method. Participants express confusion regarding the application of this theorem due to the multiplication of two functions rather than a single function raised to a power. The original poster seeks clarification on how to properly apply the theorem despite the existence of simpler methods for this problem.

PREREQUISITES
  • Understanding of Laplace Transforms
  • Familiarity with Theorem 1.31 (General Differentiation method)
  • Knowledge of trigonometric functions, specifically sine
  • Basic calculus concepts involving function multiplication
NEXT STEPS
  • Review the application of Theorem 1.31 in Laplace Transforms
  • Study the properties of Laplace Transforms for products of functions
  • Explore alternative methods for solving Laplace Transforms, such as the convolution theorem
  • Practice solving Laplace Transforms involving trigonometric functions
USEFUL FOR

Students studying differential equations, mathematicians focusing on transform methods, and educators teaching Laplace Transforms in advanced mathematics courses.

JSBeckton
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Homework Statement



Determine L{t sinwt} with the aid of therom 1.31 (its the General Differentiation method on this page: "link"[/URL]



[h2]Homework Equations[/h2]

Shown on linked page



[h2]The Attempt at a Solution[/h2]

I do not understand how to start this becasue I do not have a function to a power, I have a multiplication of 2 functions. I know there are better theorms for this porblem but he specifically said we need to use this one, can anyone help me out?

Thanks in advance.
 
Last edited by a moderator:
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That link is broken.
 
transform sin function then apply the corresponding laplace function of t to the transformed sin function.
 
euler_fan said:
transform sin function then apply the corresponding laplace function of t to the transformed sin function.


I don't think that is what this theorem calls for, can you verify from th link?

He said that he wants us to do it this way even though there are easier ways, go figure...
 

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