This work presents the results of modeling the ion dynamics in the ART-MS (Autoresonant Trap Mass Spectrometry) device in the quasi-static approximation. This instrument utilizes an anharmonic, purely electrostatic trap for ion confinement and a radio frequency (RF) voltage source with decrementally varying frequency for selective ion extraction. The autoresonant interaction between the oscillatory motion of the ion and the RF voltage increases the amplitude of some confined ions, allowing their selective extraction. Numerical modeling shows that the extraction of ions with a given mass occurs not only at the fundamental frequency but also at its harmonics. This effect reduces the selective properties of devices of this type because along with the main mass component for a given frequency, it is possible to enter the detector channel of ions with another mass, for which this frequency corresponds to the second or higher harmonics, even a superposition of some of these harmonics of different ions.