The authors have studied, using molecular dynamic (MD) simulations, the oscillatory characteristics of a 2C60/CNT oscillator system, in which two C60 fullerenes oscillate inside a single walled carbon nanotube (CNT) in two basic modes, i.e., the symmetric and non-symmetric motions. In the symmetric mode, with each oscillation the two fullerenes move symmetrically from the CNT ends towards the CNT center where they bounce off each other and head back towards the ends. In the non-symmetric mode, the two fullerenes move back and forth inside the CNT crossing the center point of the CNT together with each oscillation. The simulations show that the non-symmetric oscillation mode is stable for the prescribed initial (maximum) velocities up to 300 m/s, while the symmetric oscillation mode however, experiences dynamic instabilities for a prescribed initial (maximum) velocity larger than 250 m/s. The instability takes place as a result of the transfer of energy from the translational to the rotational motion of the fullerenes. This characteristic differentiates 2C60/CNT oscillators from double-walled CNT oscillators. The rotation is primarily caused by the inter-colliding of the two fullerenes, which subjects the fullerenes to large van der Waals repelling forces. These repelling forces are not necessarily aligned perfectly along the CNT axis nor precisely pointing towards the mass centers of the fullerenes. These misalignments cause the fullerenes to rock around the CNT's axis, while their offsets from the mass centers cause the fullerenes to rotate. The rocking motion, being severely confined by the CNT, does not gain much energy itself, but instead, channels energy from translational to rotational motion. The energy channeling is found to be reversed in some very short time intervals, but the rotational motion always gains energies from the translational motion over a time interval that is long enough at the MD time scale. This feature, contrary to our experiences in the macroscopic world, appears to be unique for such nanoscopic mechanical systems.