Verlet.

Points that remember where they were. Links that pull them back. Nothing else.

Solver iterations12
Gravity1400
Wind0
Extra air drag0.6%
Tears at strainoff

Drag the cloth with the Grab tool. Cut slices links you draw across. Pin nails a point in place or frees it.
Keys: 1 to 4 scenes, G C P tools, space pause, S step, R reset.
Air drag set to zero is not undamped: projecting a position back onto its constraint costs energy by itself, about 12% of a swing per period at 60 steps a second, and less the smaller the step. Measured, not folklore.