  We study translational, breathing and twisting resonant modes of transverse
magnetic domain walls pinned at notches in ferromagnetic nanostrips. We
demonstrate that a mode's sensitivity to notches depends strongly on the
characteristics of that particular resonance. For example, the frequencies of
modes involving lateral motion of the wall are the ones which are most
sensitive to changes in the notch intrusion depth (especially at the narrower,
more strongly confined end of the domain wall). In contrast, the breathing
mode, whose dynamics are concentrated away from the notches is relatively
insensitive to changes in the notches' sizes. We also demonstrate a sharp drop
in the translational mode's frequency towards zero when approaching depinning
which is found, using a harmonic oscillator model, to be consistent with a
reduction in the local slope of the notch-induced confining potential at its
edge.
