  We examine the reasons for discrepancies between two alternative approaches
to modeling small-amplitude tides in binary systems. The 'direct solution' (DS)
approach solves the governing differential equations and boundary conditions
directly, while the 'modal decomposition' (MD) approach relies on a normal-mode
expansion. Applied to a model for the primary star in the heartbeat system
KOI-54, the two approaches predict quite different behavior of the secular
tidal torque. The MD approach exhibits the pseudosynchronization phenomenon,
where the torque due to the equilibrium tide changes sign at a single,
well-defined and theoretically predicted stellar rotation rate. The DS approach
instead shows 'blurred' pseudosynchronization, where positive and negative
torques intermingle over a range of rotation rates.
  We trace a major source of these differences to an incorrect damping
coefficient in the profile functions describing the frequency dependence of the
MD expansion coefficients. With this error corrected some differences between
the approaches remain; however, both are in agreement that
pseudosynchronization is blurred in the KOI-54 system. Our findings generalize
to any type of star for which the tidal damping depends explicitly or
implicitly on the forcing frequency.
