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

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A user is seeking assistance in finding a general mathematical function that represents a periodic curve with specific characteristics, including symmetry about the y-axis and infinite decay. The function must remain non-negative and start at zero, with an increasing period where the distance between local maxima becomes significantly larger as the curve progresses. The user emphasizes that the first local maxima should be very close together, while subsequent maxima should be spaced further apart. They are open to sharing additional drawings for clarification and request a smaller version of the attached image for better visibility. The discussion highlights the complexity of defining such a function mathematically.
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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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