We study oscillations of a one-dimensional (1D) column of N slightly inelastic particles, produced by a piston vibrating at one end of a closed tube. It is found that for large enough vibrational amplitudes of the piston, the column oscillates periodically with the period equal to the vibrational period. The oscillation patterns are governed by the shock waves propagating across the column. The averaged kinetic energy per particle is shown to be proportional to the square of the vibrational frequency, ω. This energy also strongly depends on the vibrational amplitude. The maximal value of this kinetic energy achievable by these external vibrations is found to be of order [Formula Presented] where L is the total volume (length) of the tube free of particles. The above results on the column resonance oscillations are also predicted by a 3D hydrodynamic model of an inelastic granular gas.