  In the study of perturbations around black hole configurations, whether an
external source can influence the perturbation behavior is an interesting topic
to investigate. When the source acts as an initial pulse, it is intuitively
acceptable that the existing quasinormal frequencies will remain unchanged.
However, the confirmation of such an intuition is not trivial for the rotating
black hole, since the eigenvalues in the radial and angular parts of the master
equations are coupled. We show that for the rotating black holes, a moderate
source term in the master equation in the Laplace s-domain does not modify the
quasinormal modes. Furthermore, we generalize our discussions to the case where
the external source serves as a driving force. Different from an initial pulse,
an external source may further drive the system to experience new perturbation
modes. To be specific, novel dissipative singularities might be brought into
existence and enrich the pole structure. This is a physically relevant
scenario, due to its possible implication in modified gravity. Our arguments
are based on exploring the pole structure of the solution in the Laplace
s-domain with the presence of the external source. The analytical analyses are
verified numerically by solving the inhomogeneous differential equation and
extracting the dominant complex frequencies by employing the Prony method.
