In cardiovascular applications of Doppler ultrasound, oscillating structures are at times within the sample volume of the transducer. When the period of oscillation is shorter than the time window of the Fourier transform, the velocities of the structure are not resolved in time by the frequency analyzer. The resulting display can differ considerably from that obtained from structures with linear velocities. The investigation characterizes this phenomenon with the use of theoretical relations, mechanical model experiments and patient data. The results demonstrate that the representations of rapidly oscillating structures on the Doppler display can be interpreted in terms of frequency of oscillation and also, to some extent, in terms of maximum displacement of the structure.