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The above is a result I got using Mathematica for my research.

Assume that $l$ is fixed, and $\Theta\in[-0.005,0.005]$. I found that there is always a threshold $t_0\in(0.59,0.63)$ such that: The output on the right decreases to $-\infty$ as $t\to t_0^-$ and increases to $+\infty$ as $t\to t_0^+$. Also, $t_0$ decreases as $\Theta$ increases.

I want to draw a graph of $t_0$ versus $\Theta$ using Mathematica. But I have no idea how to determine $t_0$ accurately. Any suggestion or help will be much appreciated!

IntegralLover
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  • Assuming you have a list of points $(t_0,\theta)$, you can compute the discrete derivative of the set for neighboring points and pick the maximum value of the resulting array of numbers. This should approximate the position of the singularity. – DinosaurEgg Jan 16 '23 at 19:40
  • Actually, that is what I'm trying to get. If I can get a list of such points, then it's easy for me to plot them. – IntegralLover Jan 16 '23 at 19:50
  • Well if you have the functional relation between these quantities, just evaluate it at isolated points instead of using manipulate? – DinosaurEgg Jan 16 '23 at 20:03

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