  It is shown that the equation of state of nuclear matter can be determined
within the mean-field theory of $\sigma \omega$ model provided only that the
nucleon effective mass curve is given. We use a family of the possible nucleon
effective mass curves that reproduce the empirical saturation point in the
calculation of the nuclear binding energy curves in order to obtain
density-dependent effective coupling constants. The resulting density-dependent
coupling constants may be used to study a possible equation of state of nuclear
system at high density or neutron matter. Within the constraints used in this
paper to $M^*$ of nuclear matter at saturation point and zero density, neutron
matter of large incompressibility is strongly bound at high density while soft
neutron matter is weakly bound at low density. The study also exhibits the
importance of surface vibration modes in the study of nuclear equation of
state.
