This study deals with the mechanical oscillatory behavior of a C60 fullerene tunneling through open carbon nanocones (CNCs) using molecular dynamics simulations. The van der Waals (vdW) interactions between two molecules are modeled by Lennard–Jones (LJ) potential, while the interatomic interactions between carbon atoms are modeled by Tersoff–Brenner (TB) potential. Considering the two nanostructures to be either rigid or flexible, a comparative study is conducted to get an insight into the effects of initial conditions (initial separation distance and initial velocity) and geometrical parameters (length and radii of nanocone) on the oscillatory behavior of C60- open CNC oscillators. It is found out that the fullerene molecule performs a uniform oscillation inside open CNCs in the case of rigid nanostructures, whereas it performs a decaying oscillation inside nanocones with a considerable decrease in amplitude and significant increase in oscillation frequency in the case of flexible nanostructures. It is further shown that the preferred position of system corresponding to rigid nanostructures occurs inside of nanocone and close to its small end. On the contrary, this position related to flexible ones changes during the oscillation and moves toward the wide end of nanocone. This study can be used as a benchmark for the improvement of gigahertz (GHz) oscillators and related potential applications together with future developments in the field by extending to fractal calculus.