The motion of domain walls is influenced by their internal structure and their structural changes during motion. The macroscopic motion is well understood but the internal dynamics during motion have not been experimentally studied in detail. We study vortex domain walls excited by nanosecond long magnetic field pulses in a pinning potential and above the pinning threshold. The dynamic response is imaged by transmission x-ray microscopy and the structural changes are analyzed. From the directly observed inertial behavior of the wall the domain-wall mass equivalent is estimated. During motion, oscillations of both the vortex core around the center of the domain wall and the domain-wall width are observed. The wall shows a fully elastic behavior by compression and overexpansion when being pushed by the field.