Two sets of experiments have been performed which show that the damping of an oscillating body in a fluid is small, for example damping ratios of 0.01 or less. A method for calculating the damping is examined that uses the shear forces in the boundary layer. The shear forces depend on the amplitude of the vibration and change in character as the amplitude is increased. For very large amplitudes separation of the boundary layer is expected and this can lead to larger values of damping. The behaviour of the boundary layer with amplitude is investigated so that the amplitude needed to produce significant damping is identified.