  We present an extensive survey for rapid pulsators among Extreme Horizontal
Branch (EHB) stars in omega Cen. The observations performed consist of nearly
100 hours of time-series photometry, as well as low-resolution spectroscopy. We
obtained photometry for some 300 EHB stars. Based on the spectroscopy, we
derive reliable values of log g, Teff and log(N(He)/N(H)) for 38 targets, as
well as estimates of the effective temperature for another nine targets. The
survey uncovered a total of five rapid variables with multi-periodic
oscillations between 85 and 125 s. Spectroscopically, they form a homogeneous
group of hydrogen-rich subdwarf O stars clustered between 48,000 and 54,000 K.
For each of the variables we are able to measure between two and three
significant pulsations believed to constitute independent harmonic
oscillations. In addition to the rapid variables, we found an EHB star with an
apparently periodic luminosity variation of ~2700 s, which we tentatively
suggest may be caused by ellipsoidal variations in a close binary. Using the
overlapping photometry and spectroscopy sample we are able to map an empirical
omega Cen instability strip. This can be directly compared to the pulsation
driving predicted from the Montreal "second-generation" models. We find that
the region where p-mode excitation occurs is bifurcated, and the well-known
instability strip between 29,000-36,000 K where the rapid subdwarf B pulsators
are found is complemented by a second one above 50,000 K. While significant
challenges remain at the quantitative level, we believe that the same
kappa-mechanism that drives the pulsations in hot B subdwarfs is also
responsible for the excitation of the rapid oscillations observed in the omega
Cen variables.
