Scatter plot of the normal mode periods of the systems considered a function of the number of strands, N_s = 1, 5, 10, 20, 30, 40, 50, 60, and 100. Each period is drawn as a small horizontal line except the case of N_s = 1 where an asterisk is used. The horizontal dotted line is the period of oscillation of an individual strand, P_s  =  5 min. Both horizontal dashed lines are the analytic approximate expressions for P_H and P_L from Eq. (13). In all the situations the number of modes increases with the proximity to P_s and the plot looks like a continuous dark band. In the case of 100 strands, there is a gap associated with a numerical issue in the T-method. Near the central frequency, the T-matrix becomes singular and the method fails near the singularity.