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We present numerical results from three-dimensional evolutions of scalarperturbations of Kerr black holes. Our simulations make use of a high-orderaccurate multi-block code which naturally allows for fixed adaptivity andsmooth inner (excision) and outer boundaries. We focus on the quasinormalringing phase, presenting a systematic method for extraction of the quasinormalmode frequencies and amplitudes and comparing our results against perturbationtheory.  The amplitude of each mode depends exponentially on the starting time of thequasinormal regime, which is not defined unambiguously. We show that thistime-shift problem can be circumvented by looking at appropriately chosenrelative mode amplitudes. From our simulations we extract the quasinormalfrequencies and the relative and absolute amplitudes of corotating andcounterrotating modes (including overtones in the corotating case). We studythe dependence of these amplitudes on the shape of the initial perturbation,the angular dependence of the mode and the black hole spin, comparing againstresults from perturbation theory in the so-called asymptotic approximation. Wealso compare the quasinormal frequencies from our numerical simulations withpredictions from perturbation theory, finding excellent agreement. Finally westudy under what conditions the relative amplitude between given pairs of modesgets maximally excited and present a quantitative analysis of rotationalmode-mode coupling. The main conclusions and techniques of our analysis arequite general and, as such, should be of interest in the study of ringdowngravitational waves produced by astrophysical gravitational wave sources.Comment: 21 pages, 9 figure

Numerical study of the quasinormal mode excitation of Kerr black holes