The dynamic force distance control for scanning near-field optical microscopy on the basis of a tuning fork as piezoelectric force sensor is remarkably sensitive. In order to gain a better understanding of this sensitivity the vibrational properties of the tuning fork are modelled within the framework of two coupled harmonic oscillators. As a result, the effective force constant of the tuning fork at resonance frequency is determined. Furthermore, the influence of the additional mass by the attachment of the near-field probe is investigated.