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The high gradient quadrupole magnets being developed by the US-LHC Accelerator Project for the LHC Interaction Regions have stringent field quality requirements. The field quality of these magnets will be measured using a rotating coil system presently under development. Mechanical vibrations of the coil during field quality measurements are of concern because such vibrations can introduce systematic errors in measurement results. This paper presents calculations of the expected influence of vibrations on field quality measurements and a technique to measure vibrations present in data acquired with standard "tangential-style" probes. Measured vibrations are reported and compared to simulations. Limits on systematic errors in multipole measurements are discussed along with implications for probe and measurement system design.