Displacement amplitude over time in the loop anti-node (z = 0). The values are normalized to the initial displacement. For the top plots (A = 0.01, left: l = 0.1R, right: l = 0.5R), the Gaussian and exponential profiles from Eq. (3) obtained by fitting Eq. (5) are plotted. For the bottom plots (A = 0.05, left: l = 0.1R, right: l = 0.5R), the Gaussian of Eq. (3) is fitted for the whole data and plotted, as well as the exponential resulting from fitting Eq. (6).