The dynamics of the detailed micromagnetic structure of domain walls in thin films are computed by numerical integration of the Landau-Lifshitz-Gilbert equation. The temporal and spatial variations of wall structure under a suddenly applied in-plane field lying in the plane of the wall are investigated. The structure is substantially changed at in-plane field strengths of only 2% of the anisotropy field, Hk. A critical in-plane field value is reached at about 2.25% of Hk; at this point, the time required for the wall structure to reach equilibrium is a maximum. This settling time is also a function of the damping parameter α. For α≳0.1, the settling time is found to be nearly proportional to α; for α≲0.1, the settling time becomes larger as α decreases due to oscillations of the wall structure. In the language of harmonic oscillators, the micromagnetic structure appears underdamped for α<0.1, critically damped at α≈0.1, and overdamped for α≳0.1.