This research focuses on enhancing the accuracy and performance of piezoelectric sensors, particularly in vibratory analysis. The study examines the physical behavior of piezoelectric sensors and derives a mathematical formula that relates sensor accuracy to relative movement or vibratory displacement. The model is validated through simulations and experimental tests. By optimizing the damping rate, the research aims to improve the sensor's parameters and advance vibratory analysis techniques. The findings contribute to better design and implementation of piezoelectric sensors, enhancing their accuracy and effectiveness in capturing and analyzing vibratory movements. The study also highlights the importance of piezoelectric materials in various applications, such as ultrasonic sensors and low-power electronics. The research concludes with a new formula for sensor accuracy and the identification of an optimal damping rate (0.68) to achieve 99.7% accuracy. The developed model is validated through experimental validation and simulation, demonstrating its practical utility in vibratory analysis.This research focuses on enhancing the accuracy and performance of piezoelectric sensors, particularly in vibratory analysis. The study examines the physical behavior of piezoelectric sensors and derives a mathematical formula that relates sensor accuracy to relative movement or vibratory displacement. The model is validated through simulations and experimental tests. By optimizing the damping rate, the research aims to improve the sensor's parameters and advance vibratory analysis techniques. The findings contribute to better design and implementation of piezoelectric sensors, enhancing their accuracy and effectiveness in capturing and analyzing vibratory movements. The study also highlights the importance of piezoelectric materials in various applications, such as ultrasonic sensors and low-power electronics. The research concludes with a new formula for sensor accuracy and the identification of an optimal damping rate (0.68) to achieve 99.7% accuracy. The developed model is validated through experimental validation and simulation, demonstrating its practical utility in vibratory analysis.