  We use the formalism of Fermi coordinates to describe the interaction of a
plane gravitational wave in the proper detector frame. In doing so, we
emphasize that in this frame the action of the gravitational wave can be
explained in terms of a gravitoelectromagnetic analogy. In particular, up to
linear displacements from the reference world-line, the effects of the wave on
test masses can be described in terms of a Lorentz-like force equation. In this
framework we focus on the effects on time measurements provoked by the passage
of the wave, and evaluate their order of magnitude. Eventually, we calculate
the expression of the local spacetime metric in cylindrical coordinates adapted
to the symmetries of the gravitational field and show its relevance in
connection with the helicity-rotation coupling.
