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We consider the tidal excitation of modes in a binary system of arbitraryeccentricity. For a circular orbit, the modes generally undergo forcedoscillation with a period equal to the orbital period ($T$). For an eccentricorbit, the amplitude of each tidally excited mode can be written approximatelyas the sum of an oscillatory term that varies sinusoidally with the modefrequency and a `static' term that follows the time dependence of the tidalforcing function. The oscillatory term falls off exponentially with increasing$\b$ (defined as the ratio of the periastron passage time to the mode period),whereas the `static' term is independent of $\b$. For small $\b$ modes ($\b\approx 1$), the two terms are comparable, and the magnitude of the modeamplitude is nearly constant over the orbit. For large $\b$ modes ($\b \gta$ afew), the oscillatory term is very small compared to the `static' term, inwhich case the mode amplitude, like the tidal force, varies as the distancecubed. For main sequence stars, $p$, $f$, and low order $g$-modes generallyhave large $\b$ and hence small amplitudes of oscillation. High overtone$g$-modes, however, have small overlap with the tidal forcing function. Thus,we expect an intermediate overtone $g$-mode with $\b \sim 1$ to have thelargest oscillation amplitude. The dependence on mode damping and the stellarrotation rate is considered, as well as the effects of orbital evolution. Weapply our work to the two binary pulsar system: PSR J0045-7319 and PSRB1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures  available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars