Math behind Spring Interp

It’s been a while since physics class but, I have some basic knowledge of how stiffness and dampening effects a spring (mostly with the help of visualizations & graphs)

Spring animation

Desmos graph

But, overall I’m having trouble understanding how the values effects the interpolation aspect of this node and it feels like most values I’m playing with are arbitrary.

For example why exactly does have a 0 damping factor which I think leads to constant oscillation like a sin wave lead to the motion being slower?