Find a General Function for a Periodic Curve with Symmetry and Infinite Decay"

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Discussion Overview

The discussion revolves around finding a general mathematical function that describes a specific periodic curve characterized by symmetry, infinite decay, and specific properties related to its maxima and minima. The focus is on theoretical exploration rather than practical application or homework assistance.

Discussion Character

  • Exploratory

Main Points Raised

  • One participant seeks a function that is periodic, symmetric about the y-axis, and has non-negative values, with the requirement that it decays as it approaches infinity.
  • The participant specifies that the distance between the first local maxima on either side of the y-axis should be very small, while the distance between subsequent maxima should increase significantly.
  • There is an indication of a need for visual aids, as the participant mentions posting drawings to clarify their request.
  • Another participant requests a smaller version of the image provided, indicating a concern with the size of the visual aid shared.

Areas of Agreement / Disagreement

The discussion does not present any consensus or resolved disagreements, as it primarily consists of a request for assistance and logistical comments regarding image size.

eqm
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Hi! This is my first ever post on PF. Thanks in advance for anyone who helps me out on this!

I'm trying to find a general function that describes the curve in the attached image. As you can see, it is periodic and decays as it approaches infinity. y ≥ 0 at all times; f(0)=0; symmetric about y axis.

The period should increase as well - the distance between the first local maxima on the each side of the y-axis should be very small (nearly 0) but increases at a very large rate. For example, set the highest local maximas as p and p' and the second highest as q and q'. Well the distance between p and p' <<<< than the distance between p and q (similarly p' and q').

I'll post more drawings if need be. Thank you very much to whoever helps me out with this.
 
Last edited by a moderator:
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Didn't realize the picture would be huge... Sorry!
 
Can you post a smaller version of the image you posted? It should be around 900 px X 600 px or so. Yours was way larger than that.
 
hu15iq.jpg


That's what I thought, sorry :/
 

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