It is common to think of resonance width in steady state terms, but there are two important factors which make this approach inappropriate for field-line resonance (FLR) pulsations in the magnetosphere. First of all, the excitation is short-lived, i.e., decidedly not monochromatic. Second, for excitations of interest, FLR widths diminish with time [Mann et al., 1995>, and the ionospheric damping of these resonances in concert with their short-lived excitation ensures that they are time-limited. The widths most likely to be observed are those corresponding to a time near that of the maximum amplitude of the pulsation. As a consequence, observed FLR widths are greater, sometimes significantly greater, than the steady state equivalent (i.e., the Q width). Each FLR oscillation is the sum of two components; one is an oscillation at the resonant frequency, and the other, which is the transient portion of the response, is at the natural resonant frequency of each flux tube. The latter frequency varies with L. Moreover, as the excitation becomes more short-lived, the shorter is the duration of the FLR in a lossy magnetosphere/ionosphere, and the greater the influence of the transient. The purpose of this paper is to examine the possibility that a random or quasi-random ensemble of short lived excitations of the magnetospheric waveguide over the Pc3--5 range might yield FLR widths sufficiently large in practice for the pulsation signature to be similar to that seen in Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) satellite pulsation data. The latter signature appears to be consistent with each flux tube ringing at several of its natural resonance harmonics. It is found that under some realistic conditions the ensemble of excitations can produce FLR spectral widths which are contiguous or overlap in L, suggesting the possibility of an FLR explanation of AMPTE/CCE pulsation observations. ¿ 1999 American Geophysical Union