  We investigate the sensitivities of searches for exotic spin-dependent
interactions between the polarized nuclear spins of $^3$He and the particles of
unpolarized or polarized solid-state masses using the frequency method and the
resonance method. In the frequency method, the spin-dependent interactions act
as an effective static magnetic field, causing the frequency shift to the spin
precession of $^{3}$He. In the resonance method, proposed by Arvanitaki and
Geraci [Phys. Rev. Lett. 113, 161801 (2014)] for the significant improvement of
the experimental sensitivities on the spin-dependent interactions, the mass
movement is modulated at the Larmor frequency of $^3$He. This results in the
modulating spin-dependent interactions inducing an effective oscillatory
magnetic field, which can tilt the $^3$He spins, similarly as an oscillatory
magnetic field in nuclear magnetic resonance. We estimate the sensitivities of
the searches using a room-temperature $^3$He target for its extremely long
relaxation time. New limits on the coupling strengths of the spin-dependent
interactions can be set in the interaction length range below $10^{-1}$ m.
