  Filament longitudinal oscillations have been observed on the solar disk in
H$\alpha$. We intend to find an example of the longitudinal oscillations of a
prominence, where the magnetic dip can be seen directly, and examine what is
the restoring force of such kind of oscillations. We carry out a
multiwavelength data analysis of the active region prominence oscillations
above the western limb on 2007 February 8. Besides, we perform a
one-dimensional hydrodynamic simulation of the longitudinal oscillations. The
high-resolution observations by Hinode/SOT indicate that the prominence, seen
as a concave-inward shape in lower-resolution Extreme Ultraviolet (EUV) images,
actually consists of many concave-outward threads, which is indicative of the
existence of magnetic dips. After being injected into the dip region, a bulk of
prominence material started to oscillate for more than 3.5 hours, with the
period being 52 min. The oscillation decayed with time, with the decay
timescale being 133 min. Our hydrodynamic simulation can well reproduce the
oscillation period, but the damping timescale in the simulation is 1.5 times as
long as the observations. The results clearly show the prominence longitudinal
oscillations around the dip of the prominence and our study suggests that the
restoring force of the longitudinal oscillations might be the gravity.
Radiation and heat conduction are insufficient to explain the decay of the
oscillations. Other mechanisms, such as wave leakage and mass accretion, have
to be considered. The possible relation between the longitudinal oscillations
and the later eruption of a prominence thread, as well as a coronal mass
ejection (CME), is also discussed.
