The resonant frequency of the collective electron oscillations in a conductive nanofiber is calculated. The friction force acting on the oscillating collective electrons from the side of the ions is taken into account. Due to the action of this force, the phase shift between the phase of the applied external homogeneous alternative electric field and the phase of the oscillating movement of the collective electrons appears. This phase shift is also calculated. Measured resonant frequency, phase shift, and/or resonant amplitude could be used to calculate the relaxation time $\tau$ responsible for the friction.