  Eccentric compact binaries pose not only a challenge for gravitational wave
detectors, but also provide a probe into the nuclear equation of state if one
of the objects is a neutron star. At the short pericenter passage, tidal
interactions excite f-modes on the star, which in turn emit their own
gravitational waves. We derive an analytic waveform for these stellar
oscillations within the effective fly-by framework, modeling the emission to
leading post-Newtonian order. At this order, the f-mode response can be written
in a Fourier decomposition in terms of orbital harmonics, with the amplitudes
of each harmonic depending on Hansen coefficients. Re-summing the harmonics of
the f-mode results in a simple decaying harmonic oscillator, with the amplitude
now determined by a Hansen coefficient of complex harmonic number. We compute
the match between the re-summed f-mode and numerical integrations of the tidal
response, and find ${\cal{M}} > 0.98$ for systems with high orbital
eccentricity $(e > 0.8)$ and low semi-latus rectum $(p < 15M)$ for three
equations of state. We further compare our model to modes generated from
subsequent pericenter passages under the effect of radiation reaction, and
develop an accurate model to time pericenter passages. We show how the timing
model can be used to specify initial conditions to accurately track the f-mode
excitation across multiple pericenter passages.
