Kink motions with (a) S​_x and (b) A_x patterns in a two-elliptic-tube configuration with an x-major orientation. Plotted are the time sequences of the x speed sampled at the left tube center (v_x(−d/2, 0; t), the solid curves) for a number of ratios of the semi-major to semi-minor axis (a/b) distinguished with different colors. A fitting procedure was performed for each sequence, over the duration encompassing the six extrema, starting with the one denoted by an asterisk. The best-fit damping envelope is plotted for the entire sequence, but only for a/b = 2.5 to avoid overcrowding the plots. The computations pertain to a fixed combination, $[{\rho }_{\mathrm{i}}/{\rho }_{\mathrm{e}}=3,\overline{l}=0.4,d/b=5,kb=\pi /30]$.