We performed molecular dynamics simulation of double walled carbon nanotube (DWCNT) oscillators under constant energy and constant temperatures with various commensurations and nanotube lengths. We clarify and resolve questions and differences raised by previous simulation results of similar systems. At constant energy, sustained oscillation is available for a wide range of initial temperatures. But low initial temperature is advantageous for DWCNTs to sustain oscillation under constant energy. We observed sustained oscillation at constant energy for both commensurate and incommensurate DWCNTs. On the other hand, under constant temperatures, both high and low temperatures are disadvantageous to sustain DWCNT oscillations. At constant low temperature, neither commensurate nor incommensurate DWCNTs can maintain oscillation. At appropriate constant temperatures, the oscillatory behavior of incommensurate nanotubes is much more sustained than that of commensurate tubes. The oscillatory frequency of DWCNTs depends significantly on the length of tubes. The initial oscillatory frequency is inversely proportional to the DWCNT lengths. The oscillation frequency of DWCNTs is insensitive to the initial temperatures at constant energy, but slightly dependent on the temperature at constant temperatures.