Finding Laplace Transform Limits for Periodic Functions

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Discussion Overview

The discussion revolves around finding the limits of the Laplace transform for periodic functions, specifically focusing on the behavior of the transform as the variable s approaches infinity and zero. The scope includes mathematical reasoning and technical explanation related to Laplace transforms and periodic functions.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant asks how to find the limits of the Laplace transform function for periodic functions.
  • Another participant seeks clarification on what is meant by the "limits" in this context.
  • A third participant provides the formula for the Laplace transform of a periodic function and specifies the limits to be evaluated as s approaches infinity and zero.
  • A later reply suggests that understanding the integral of e^{-st}f(t) is necessary before determining the limits, recommending a case-by-case approach after integrating.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are clarifying the question and exploring different aspects of the limits without agreeing on a specific method or conclusion.

Contextual Notes

Participants have not fully defined the assumptions regarding the periodic function f(t) or the specific conditions under which the limits are evaluated, leaving some aspects unresolved.

orange22
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How would you go about finding the limits of the general laplace transform function for periodic functions?
 
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Could u clarify the question?
More specifically what are these *limits* that u talk abt?
 
If the laplace transform of f for a periodic function is given by

L(f)(s)=

1/(1-e^{-sT})) *integral from 0 to T of (e^{-st}f(t)dt))


then how do you find
lim_{s→∞}L(f)(s) and lim_{s→0}L(f)(s).
 
You need to know what the integral of e-stf(t) looks like before you can do that. First integrate to get your function of s, then handle it on a case by case basis.
 

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