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

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SUMMARY

The discussion centers on finding a general mathematical function that represents a periodic curve with symmetry and infinite decay, specifically one that remains non-negative (y ≥ 0) and symmetric about the y-axis. The user seeks a function where the period increases significantly, with the distance between local maxima decreasing rapidly. The challenge includes defining the relationship between the first and second local maxima, denoted as p, p', q, and q', with a focus on their respective distances.

PREREQUISITES
  • Understanding of periodic functions and their properties
  • Knowledge of symmetry in mathematical functions
  • Familiarity with concepts of decay in mathematical modeling
  • Basic graphing skills to visualize functions and their characteristics
NEXT STEPS
  • Research mathematical functions that exhibit periodic behavior, such as sine and cosine functions
  • Explore the concept of infinite decay in functions, focusing on exponential decay
  • Investigate the properties of symmetric functions and their applications
  • Learn about the mathematical modeling of curves and their graphical representations
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Mathematicians, students studying calculus or advanced mathematics, and anyone interested in modeling periodic phenomena with specific decay characteristics.

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.
 
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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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