NOTES
The ellipse in the previous chart is a graphical representation of the attractor towards which the motion of the pendulum will go, regardless of initial conditions. If you want to know “why” the final oscillation has a particular magnitude or phase, or period, you don't need to know anything about the initial conditions - the system has no history.
Engineers love this kind of system and historically got so used to analyzing and designing for this kind of system that other behavior was treated as misbehavior - and the system would be altered until it stopped doing that!