With no wind and a stiff chain the flag is a uniform rod hanging from the pole; for small swings its period is T = 2 pi sqrt(2L / 3g). The check releases it 6 degrees from vertical and times five crossings.

The flag is a chain of 26 point masses with distance constraints (position-based Verlet) pinned at the pole, plus second-neighbour constraints that act as bending stiffness. Gravity pulls every node down; the wind force on a node is a linear drag on the velocity of the air relative to the cloth, taken along the local normal: F = k (u_air - v) . n n. The component along the cloth is ignored, as for a thin sheet.

Flutter appears above a critical wind speed when the aerodynamic load can no longer be balanced by gravity and bending: the tip then oscillates. Zero crossings of the tip height are counted to estimate the flapping frequency.

Simplifications: a 1D chain (a real flag is a 2D sheet with wake vortices), no added mass and no vortex-shedding feedback. Educational, not a CFD result.