Principal Component Analysis on a Spring Mass Dynamic System

This research presents a comprehensive evaluation of the application of Principal Component Analysis (PCA) on data sets from three cameras in the study of the motion of a spring mass dynamic system. The objective of this study is to assess the strengths and weaknesses of the Singular Value Decomposition (SVD) algorithm in extracting the most significant features of the motion of a spring-mass dynamic system. The analysis considers four test scenarios: an ideal vertical oscillation case, a camera vibration with vertical oscillation case, a case with horizontal displacement generating pendulum and vertical oscillation case, and a case with horizontal displacement combined with rotation and vertical oscillation case. The video recorded data from the three cameras is preprocessed through cleaning and normalization procedures. PCA is then employed on the merged data matrix to extract the singular values and corresponding singular vectors via SVD. The projected motion is finally approximated from the lower rank data sets data. The insight gained from applying PCA with SVD algorithms to the motion of the spring-mass system is of immerse value. The findings hold significance for a broad range of real-world cases with multiple camera systems.