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By virtue of its direct association with the cardiovascular (CV) functions and compatibility to unobtrusive measurement during daily activities, the limb ballistocardiogram (BCG) is receiving an increasing interest as a viable means for ultra-convenient CV health and disease monitoring. However, limited insights on its physical implications have hampered disciplined interpretation of the BCG and systematic development of the BCG-based approaches for CV health monitoring. In this study, a mathematical model that can predict the limb BCG in responses to the arterial blood pressure (BP) waves in the aorta was developed and experimentally validated. The validated mathematical model suggests that (i) the limb BCG waveform reveals the timings and amplitudes associated with the aortic BP waves; (ii) mechanical filtering exerted by the musculoskeletal properties of the body can obscure the manifestation of the arterial BP waves in the limb BCG; and (iii) the limb BCG exhibits meaningful morphological changes in response to the alterations in the CV risk predictors. The physical insights garnered by the analysis of the mathematical model may open up new opportunities toward next generation of the BCG-based CV healthcare techniques embedded with transparency, interpretability, and robustness against the external variability.