I have this complicated function given by:
$$y(x)=c-\sqrt{(g^2-4\omega^4x^2)}-g\log(\sqrt{(g^2-4\omega^4x^2)}+g$$
This looks sort of like a cycloid for different values of the constants $\omega,g$ and $c.$
You check out it's shape on desmos (online graphing tool): https://www.desmos.com/calculator/gtpkp9agxl
My question is, of course, is it a cycloid?