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We discuss quantum measurements of position and repeated-measurement schemes for monitoring free-mass position to an arbitrary accuracy. Using these schemes, weak classical forces can be monitored to an arbitrary accuracy. To illustrate various measurement uncertainties and intrinsic uncertainties, we consider the case of a Michelson interferometer. In the low-intensity limit, two measurement uncertainties, photon counting error and radiation pressure error, are independent of the intrinsic uncertainty. The uses of squeezed states and number eigenstates are discussed.