  (Abridged) We study the gravitational radiation from gravitational collapses
of rapidly rotating neutron stars induced by a phase-transition from normal
nuclear matter to a mixed phase of quark and nuclear matter in the core of the
stars. The study is based on self-consistent three dimensional hydrodynamic
simulations with Newtonian gravity and a high resolution shock capturing
scheme, and the quadrupole formula of gravitational radiation. The quark matter
of the mixed phase is described by the MIT bag model and the normal nuclear
matter is described by an ideal fluid equation of state (EOS). 1. We determined
the magnitudes of the emitted gravitational waves for several collapse
scenarios. 2. We determined the types and frequencies of the fluid oscillation
modes excited by the process. In particular, we find that the gravitational
wave signals produced by the collapses are dominated by the fundamental
quadrupole and quasi-radial modes of the final equilibrium configurations. In
some collapse scenarios, we find that the oscillations are damped out within a
few dynamical timescales due to the growth of differential rotations and the
formation of strong shock waves. 3. We showed that the spectrum of the
gravitational wave signals is sensitive to the EOS, implying that the detection
of such gravitational waves could provide useful constraints on the EOS of
newly born quark stars. 4. For the range of rotation periods we have studied,
we found no sign of the development of nonaxisymmetric dynamical instabilities
in the collapse process.
