We performed self-mixing laser Doppler vibrometry on a vibrating oscillator consisting of a rigid-body laser-light-scattering object attached to a piezoelectric element driven by low-frequency AC voltage to evaluate its motion. The sideband spectrum reflecting the motion of the oscillator is observed in the power spectrum of the modulated wave. The time dependence of the intensity of the sideband spectrum is explained by Newton's second law assuming that the oscillator has a mechanical resonance frequency and undergoes simple vibration under the driving force, which depends on the deformation velocity of the piezoelectric element. Our results indicate that the motion of a slowly moving target with sub-nanometer displacement, which is difficult to measure by general laser Doppler vibrometry, can be evaluated with high spatial and frequency resolutions by detecting the sideband signal, which changes periodically at the driving frequency of the piezoelectric element.