In this work, the main focus is on studying the effects of piezoelectric materials and exploring the functionality of piezoelectric sensors. The physical behavior of the sensor is thoroughly examined and a mathematical formula relating the accuracy of the sensor to relative movement or vibratory displacement is derived. The developed model is veri ed through simulations and experimental tests. By carefully selecting the appropriate damping rate, it is possible to enhance the parameters of the piezoelectric sensor and advance the technique of vibratory analysis. Overall, this research aims to enhance our understanding of piezoelectric materials and sensors, and how they can be effectively utilized in various applications involving vibratory analysis. The ndings from this study can contribute to better design and implementation of piezoelectric sensors, improving their accuracy and effectiveness in capturing and analysing vibratory movements.