  We apply the dynamical generator coordinate method (DGCM) with a conjugate
momentum to a nuclear collective excitation. To this end, we first discuss how
to construct a numerically workable scheme of the DGCM for a general one-body
operator. We then apply the DGCM to the quadrupole vibration of $^{16}$O using
the Gogny D1S interaction. We show that both the ground state energy and the
excitation energies are lowered as compared to the conventional GCM with the
same number of basis functions. We also compute the sum rule values for the
quadrupole and monopole operators, and show that the DGCM yields more
consistent results than the conventional GCM to the values from the double
commutator. These results imply that the conjugate momentum is an important and
relevant degree of freedom in collective motions.
