Laplace Transform, transfer function

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Homework Help Overview

The discussion revolves around the application of the Laplace transform in analyzing a transfer function, specifically H(s)=s^2+4, and its output in response to a sinusoidal input x(t)=sin(2t). Participants are tasked with determining the time-domain output y(t) and assessing its boundedness.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the inverse Laplace transform of the input and discuss the resulting output. There is confusion regarding the boundedness of the delta function, with participants questioning its properties and definitions.

Discussion Status

The discussion is ongoing, with participants raising questions about the nature of the delta function and its boundedness. Some guidance has been offered regarding the output, but there is no explicit consensus on the definition of boundedness or the implications of the output.

Contextual Notes

Participants are navigating the complexity of the professor's prompt, which is described as "tricky," indicating that there may be underlying assumptions or definitions that need clarification.

sandy.bridge
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Homework Statement


Given transfer function H(s)=s^2+4 and input x(t)=sin(2t), find the ouput y(t) in time domain, and show whether bounded or unbounded.

Okay, so I know L^{-1}[sin(2t)]=2/(s^2+4)=2/[(s+j2)(s-j2)]

and that Y(s)=H(s)X(s)=2

Therefore, y(t)=2\delta{(t)}

However, I am a little bit confused as to how I should show if it is bounded or unbounded.
 
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Is the delta function bounded?
 
I believe it is. However, this question seems rather simple considering the professor stated it was "tricky".
 
What's your definition of bounded?
 

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