Good point. And that does validate my simulation, more or less.Case 1 limiting value would be 30∘ below the horizontal as per physics of an oblique elastic collision between 2 equal masses.
Unfortunately the simulation breaks down there. In a simple simulation of SHM, there's a tendency for the energy to grow exponentially. There are probably some standard tricks for taming this, but I haven't managed to find one.could you perhaps set the string's spring constant to 100 times that of ball pair system ?