Viruses and tumor cells exhibit rapid adaptive mutation, drug resistance, and immune escape under external stress, which represent core issues in life sciences and biomedicine lacking a unified explanatory framework. Existing molecular biological and genetic theories focus mostly on phenomenological description and correlation analysis, and are difficult to reveal the universal physical essence behind these behaviors. Based on first principles of vibration and resonance theory, this paper equates biological functional units as elastic vibration systems and establishes a quantitative model of structure–frequency coupling. Mathematical relationships among structural deformation, stiffness change, and natural frequency shift are derived. Studies show that observable experimental phenomena—including viral capsid conformational remodeling, nucleic acid folding, cell volume compression, cytoskeleton remodeling and regional stiffening, and protein topological entanglement—directly alter the equivalent stiffness of the system, leading to significant shifts in natural frequency. As a result, biological systems move out of the resonance range of external excitation and achieve survival via resonance avoidance. Supported by well-recognized experimental evidence from cryo-electron microscopy, cellular mechanics, drug resistance induction, and mechanical stress response, this paper completes a full closed-loop verification of the theory. For the first time, it unifies the intrinsic mechanisms of viral adaptation and malignant transformation of tumors at the physical level. The proposed structure–frequency coupling law is quantifiable, testable, and falsifiable, providing a novel theoretical paradigm for the application of resonance physics in biomedicine, the development of new physical interventions, and cross-scale biological system research.