The noncovalent interaction energy as a function of the core extension in double-walled carbon nanotubes (DWCNT) was accurately calculated in the frame of density functional theory, considering dispersion correction and without resorting to adjustable parameters. A linear correlation between the change of the noncovalent energy and core displacement was established for the first time through a pure quantum mechanics approach; hence, the force needed to pull out the DWCNT core was accurately calculated. This force was found to be in good agreement with experimental values reported in the literature. Furthermore, the effect of the DWCNT edges was considered in the calculation of the potential energy profile, and the frequency, associated with the oscillation of core inlet, was calculated for the first time through a quantum approach. This frequency falls in the low infrared region, and it depends on the chemical nature of the oscillator edges. The work highlights that the noncovalent H···π interaction controls the inner shell oscillation and it should be considered, beyond the stacking between inner and outer walls, as a driving force for the activation of the telescopic process. As a result, this noncovalent interaction can be tuned for the design of nano-dynamometers with well-defined force constants.