  We have studied the dynamics of quartz tuning fork resonators used in atomic
force microscopy taking into account mechanical energy dissipation through the
attachment of the tuning fork base. We find that the tuning fork resonator
quality factor changes even for the case of a purely elastic sensor-sample
interaction. This is due to the effective mechanical imbalance of the tuning
fork prongs induced by the sensor-sample force gradient which in turn has an
impact on the dissipation through the attachment of the resonator base. This
effect may yield a measured dissipation signal that can be different to the one
exclusively related to the dissipation between the sensor and the sample. We
also find that there is a second order term in addition to the linear
relationship between the sensor-sample force gradient and the resonance
frequency shift of the tuning fork that is significant even for force gradients
usually present in atomic force microscopy which are in the range of tens of
N/m.
