  We perform a detailed analysis of the fundamental $f$-mode frequencies and
damping times of nonrotating boson stars in general relativity by solving the
nonradial perturbation equations. Two parameters which govern the microscopic
properties of the bosonic condensates, namely the self-coupling strength and
the mass of scalar particle, are explored. These two quantities characterize
oscillations of boson star. Specifically, we reexamine some empirical relations
that describe the $f$-mode parameters in terms of mass and radius of the boson
stars. We found it is possible to constrain the equation of state if the
fundamental oscillation mode is observed.
