How would I take the laplace transform of f(t)= te^tsin^2(t)?

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Discussion Overview

The discussion revolves around the process of taking the Laplace transform of the function f(t) = te^t sin²(t). Participants explore the challenges and methods involved in computing this transform, including potential techniques and formulas that may be applicable.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant initially asks how to take the Laplace transform of f(t) = te^t sin²(t).
  • Another participant suggests that the function might be misinterpreted as t e^t sin(2t) and questions what the specific problem is.
  • Clarification is provided that the function is indeed te^t sin²(t), prompting further discussion.
  • Some participants assert that this is a standard case and mention that it can be approached using integration by parts.
  • There is a suggestion to first compute the transform of sin²(t) and then apply the theorem for e^t and t.
  • One participant notes that they have not seen the transform of sin²(t) in any table and recommends computing it directly using the definition of the Laplace transform.
  • Another participant mentions the need to use the half-angle formula for integrating sin²(t) in the transformation integral.

Areas of Agreement / Disagreement

Participants express differing views on the approach to take, with some suggesting integration by parts while others emphasize the need to compute the transform directly. There is no consensus on the best method to proceed.

Contextual Notes

Participants reference the potential complexity of the function and the need for specific mathematical techniques, such as the half-angle formula, without resolving the overall approach to the Laplace transform.

Jim wah
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How would I take the laplace transform of f(t)= te^tsin^2(t)?
 
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You mean t et sin(2t)? What's causing you the problem? It is pretty straight-forward application of the definition case.
 
DevacDave said:
You mean t et sin(2t)? What's causing you the problem? It is pretty straight-forward application of the definition case.
No the equation is f(t)= te^tsin^2(t)
 
Still, it's a standard case (I have a vague recall of this exact function class being important in telecommunication). Perfectly doable via integration by parts. Is this where you got stuck?
 
DevacDave said:
Still, it's a standard case (I have a vague recall of this exact function class being important in telecommunication). Perfectly doable via integration by parts. Is this where you got stuck?
Kinda, Is there anyway to figure out the transform of sin^2(t) then use the theorem for the e^t and t?
 
I don't know of having seen that in a table anywhere, it doesn't look like an elementary form, so what you need to do is compute the transform directly using the Laplace transformation definition.
Jim wah said:
Kinda, Is there anyway to figure out the transform of sin^2(t) then use the theorem for the e^t and t?

For integrating the sin2(t) in the transformation integral you need to use the half-angle formula: http://www.sosmath.com/trig/douangl/douangl.html
 
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jack476 said:
I don't know of having seen that in a table anywhere, it doesn't look like an elementary form, so what you need to do is compute the transform directly using the Laplace transformation definition.For integrating the sin2(t) in the transformation integral you need to use the half-angle formula: http://www.sosmath.com/trig/douangl/douangl.html
Thank you so much!
 

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