  The No Hair theorem in classical general relativity predicts that rotating
black holes are specified by the Kerr metric, which is uniquely identified by
the mass and spin. However, as a pioneering study beyond general relativity,
the rotating hairy black hole has been proposed, which encompasses the Kerr
black hole as a special case. In these black holes, there are extra hair which
could appear due to the additional surrounding sources such as dark matter or
dark energy. In this work, we study the phenomenology of the rotating hairy
black hole in terms of gravitational perturbations. In particular, the
supperradiance and the quasinormal modes. Using the matching-asymptotic method,
we derive the amplification factor and the superradiance conditions. We also
calculate the quasinormal modes using the continued fraction method. The
results are in very good agreement with previous studies in the Kerr limit. We
also show how the amplification and quasinormal modes will shift in response to
variations in the hairy parameters, black hole spin, and quantum numbers.
