# Solve Laplace Transform of t sinwt w/ Theorem 1.31

• JSBeckton
In summary, The problem at hand is to determine the Laplace transform of t sinwt using theorem 1.31, which is the general differentiation method. The corresponding equations for this method can be found on the provided link, however the link is currently broken. The suggested solution is to transform the sin function, then apply the corresponding Laplace function of t to the transformed sin function. However, it is mentioned that there may be easier theorems to use for this problem, but the instructor specifically wants this method to be used.
JSBeckton

## 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]

[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?

Last edited by a moderator:

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 theorm 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...

## What is the Laplace Transform of t sinwt?

The Laplace Transform of t sinwt is equal to (w/(s^2 + w^2))^2.

## What is Theorem 1.31?

Theorem 1.31 is a mathematical theorem that states the Laplace Transform of t sinwt is equal to (w/(s^2 + w^2))^2. It is commonly used in solving differential equations.

## How is Theorem 1.31 applied in solving differential equations?

Theorem 1.31 is used to transform the time domain representation of a function into the frequency domain representation, making it easier to solve differential equations involving that function.

## Can Theorem 1.31 be used for functions other than t sinwt?

Yes, Theorem 1.31 can be applied to any function that can be expressed in the form of t sinwt, such as t coswt or t^2 sinwt.

## Is Theorem 1.31 a commonly used tool in scientific research?

Yes, Theorem 1.31 is a fundamental tool in the field of engineering and physics, where Laplace Transform is commonly used to solve differential equations and analyze systems in the frequency domain.

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