We study the effects of piezoelectric hysteresis and relaxation induced by a weak constant electric field in ferroelectric ceramics. Using the piezoelectric resonance analysis method and program, precision measurements of the impedance spectra for thickness and radial vibrations of thin piezoceramic disks were performed for various polarities of the applied constant electric field and polarization of the piezoceramic. An analysis of the field and time dependences of the complex piezoelectric constants of piezoceramics obtained by processing sequentially measured impedance spectra is carried out, and a physical interpretation of the results is proposed.