Is there a mathematical function you can think of to model this behavior?

Question

Could someone give me an idea on how I can model one period of this function where I am able to control the width of this dip at the middle ($W_m$) and the width separation at the top ($W_t$). It should be a smooth curve at the bottom.

Answer 1

In this post I described a family of curves called superconics that are generally described by

$$f(X) = b(1-|X/a|^q)^{1/p}$$

When $p$ and $q$ are large you can achieve the shape that you are looking for. The large values of these parameters will assure that the curve is smooth at the bottom. The figure below shows an example for the case of $a=b=1 \text{ & } p=q=10$. There are sufficient parameters here to fit your curve nicely.