This paper aims to present a thorough investigation into the mechanics of a $C60$ fullerene oscillating within the center of a carbon nanotube bundle. To model this nanoscale oscillator, a continuum approximation is used along with a classical Lennard–Jones potential function. Accordingly, new semianalytical expressions are given in terms of single integrals to evaluate van der Waals potential energy and interaction force between the two nanostructures. Neglecting the frictional effects and using the actual van der Waals force distribution, the equation of motion is directly solved. Furthermore, a new semianalytical formula is derived from the energy equation to determine the precise oscillation frequency. This new frequency formula has the advantage of incorporating the effects of initial conditions and geometrical parameters. This enables us to conduct a comprehensive study of the effects of significant system parameters on the oscillatory behavior. Based upon this study, the variation of oscillation frequency with geometrical parameters (length of tubes or number of tubes in bundle) and initial energy (potential energy plus kinetic energy) is shown.