We provide all the information for the forward problem in two forms. First, the masses, lengths and tensions can be read directly from the given tables. For convenience we also provide *.mat files containing this same information. This is contained in the structure info, which has the following fields:

• m - The masses of the beads in kilograms sequentially left to right.
• ell - The distance between the center of the beads in meters.
• tension - Tension in the string in Newtons.

With these spectra plots we have also included gray bars; the left and right ends containing estimates of the eigenvalues assuming negligible and non-negligible bead lengths.

D0132 dataset problem m = 17.804 17.804 g l = 25.7 61 25.7 cm  D0134 dataset problem m = 17.804 17.804 g l = 33.3 45.7 33.3 cm  D0166 dataset problem m = 30.783 30.783 g l = 30.8 50.8 30.8 cm  D0139 dataset problem m = 30.783 17.804 17.804 30.783 g l = 25.7 20.3 20.3 20.3 25.7 cm  D0142 dataset problem m = 30.783 17.804 17.804 30.783 g l = 15.6 30.5 20.3 30.5 15.6 cm  D0144 dataset problem m = 30.783 17.804 17.804 30.783 g l = 15.6 25.4 30.5 25.4 15.6 cm  D0146 dataset problem m = 30.783 17.804 17.804 30.783 g l = 10.5 30.5 30.5 30.5 10.5 cm  D0148 dataset problem m = 17.804 9.097 9.097 17.804 g l = 25.7 20.3 20.3 20.3 25.7 cm  D0149 dataset problem m = 17.804 9.097 9.097 17.804 g l = 15.6 30.5 20.3 30.5 15.6 cm  D0151 dataset problem m = 17.804 9.097 9.097 17.804 g l = 15.6 25.4 30.5 25.4 15.6 cm  D0152 dataset problem m = 17.804 9.097 9.097 17.804 g l = 15.6 30.5 20.3 30.5 15.6 cm        