  In a continuous measurement scheme a spin-1/2 particle can be measured and
simultaneously driven by an external resonant signal. When the driving is weak,
it does not prevent the particle wave-function from collapsing and a detector
randomly outputs two responses corresponding to the states of the particle. In
contrast, when driving is strong, the detector returns a single response
corresponding to the mean of the two single-state responses. This situation is
similar to a motional averaging, observed in nuclear magnetic resonance
spectroscopy. We study such quantum system, being periodically driven and
probed, which consists of a qubit coupled to a quantum resonator. It is
demonstrated that the transmission through the resonator is defined by the
interplay between driving strength, qubit dissipation, and resonator linewidth.
We demonstrate that our experimental results are in good agreement with
numerical and analytical calculations.
