Using atomistic models and molecular dynamics simulations, interlayer corrugation and resistant force in a biwalled carbon nanotube are shown to be strongly dependent upon the morphology combination of the bitube. Consequently, energy dissipation in a commensurate (e.g., armchair/armchair or zigzag/zigzag) bitube oscillator is found to be much larger than that in an incommensurate (e.g., zigzag/armchair) oscillator, resulting in a decay of oscillation amplitude within a few nanoseconds in the commensurate bitube and several tens of nanoseconds in the incommensurate bitube.