There are many new nanomechanical devices created based on carbon nanostructures among which gigahertz oscillators have generated considerable interest to many researchers. In the present paper, the oscillatory behavior of ellipsoidal fullerenes inside single-walled carbon nanotubes is studied comprehensively. Utilizing the continuum approximation along with Lennard–Jones potential, new semi-analytical expressions are presented to evaluate the potential energy and van der Waals interaction force of such systems. Neglecting the frictional effects, the equation of motion is directly solved on the basis of the actual force distribution between the interacting molecules. In addition, a semi-analytical expression is given to determine the oscillation frequency into which the influence of initial conditions is incorporated. Based on the newly derived expression, a thorough study on the various aspects of operating frequencies under different system variables such as geometrical parameters and initial conditions is conducted. Based on the present study, some new aspects of such nano-oscillators have been disclosed.