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We present a model of frequency-changeable carbon-nanotube (CNT) oscillator and its dynamic properties are investigated via classical molecular dynamics simulations. The operating frequency of the CNT oscillator can be changed by manipulating the intertube gap. The oscillations of the coretubes were found in two modes; the coretube oscillated between two outertubes or in only one outertube. When the gap is small and the kinetic energy of the coretube is high, the coretube oscillates between two outertubes. When the gap is large and the kinetic energy of the coretube is low, the coretube oscillates in only one outertube. The changes of the gap dominantly influenced the frequency rather than the changes of the initial velocities of the coretube. The bandwidths by intertube gap engineering can be enhanced more than the bandwidths achieved by initial velocity engineering by several tens of gigahertzs.