  Using a recently introduced mapping between a scalar elastic network tethered
at its boundaries and a diffusion problem with permanent traps, we study
various vibrational properties of progressively tethered disordered fractals.
Different scaling forms are proposed for different types of boundary tethering
and numerical investigation of the scaling is performed by the approximate
diagonalization of the corresponding large, sparse transition probability
matrices. Rather different localization behaviors are found for the leading
modes depending on the types of tethering.
