  We discuss the influence of external forces on the motion of the tip in
dynamic atomic force microscopy (AFM). First, a compact solution for the
steady-state problem is derived employing a Fourier approach. Founding on this
solution, we present an analytical framework to describe the transient behavior
of the tip after perturbations of tip-sample forces and the excitation signal.
The static and transient solutions are then combined to obtain the baseband
response of the tip, i.e., the deflection signal demodulated with respect to
the excitation. The baseband response generalizes the amplitude and phase
response of the tip, and we use it to find explicit formulas describing the
amplitude and phase modulation following the influence of external forces on
the tip. Finally, we apply our results to obtain an accurate dynamic model of
the amplitude controller and phase-locked loop (PLL) driving the cantilever in
a frequency modulated AFM setup. A special emphasis is put on discussing the
tip response in environments of high damping, such as ambient or liquid.
