The paper interprets the coefficient of restitution as a damping term in vibroimpact systems. It challenges the Kelvin-Voigt model, which assumes impact is represented by a damped sine wave, as it implies tension forces before separation and incorrect energy loss proportional to velocity squared. Instead, a damping term λx^α is introduced, with α = 3/2 for spherical impacts. This model is shown to approximate the Kelvin-Voigt model for impacts absent, and experiments confirm its validity. The coefficient of restitution e is defined as the ratio of relative speeds before and after impact. For low velocities, e decreases with increasing impact speed. For elastic materials, e is approximately 1 - αv_i, where α is a material-dependent constant. The energy loss during impact is shown to be proportional to v_i^3, not v_i^2, as previously thought. The paper discusses the limitations of the Kelvin-Voigt model, which predicts a hysteresis loop shape inconsistent with real-world behavior. A more realistic hysteresis loop is proposed, which avoids tensile forces and matches the expected energy loss. The paper also introduces a nonlinear damping term λx^n, which can be used to model impacts with varying energy loss. The paper presents a general force-approach law F = kx^n, applicable to various geometries. It shows that the damping factor λ can be made independent of the exponent n, allowing for a more flexible model. The paper also discusses the validity of the Hertzian theory for contact between elastic bodies, and the importance of considering surface geometry in experiments. The paper concludes that the coefficient of restitution is a useful concept in engineering, despite its inexactness. It emphasizes the need for further refinement and validation of the concept, particularly for new materials and geometries. The paper also highlights the importance of careful experimental design to avoid errors in measuring the coefficient of restitution.The paper interprets the coefficient of restitution as a damping term in vibroimpact systems. It challenges the Kelvin-Voigt model, which assumes impact is represented by a damped sine wave, as it implies tension forces before separation and incorrect energy loss proportional to velocity squared. Instead, a damping term λx^α is introduced, with α = 3/2 for spherical impacts. This model is shown to approximate the Kelvin-Voigt model for impacts absent, and experiments confirm its validity. The coefficient of restitution e is defined as the ratio of relative speeds before and after impact. For low velocities, e decreases with increasing impact speed. For elastic materials, e is approximately 1 - αv_i, where α is a material-dependent constant. The energy loss during impact is shown to be proportional to v_i^3, not v_i^2, as previously thought. The paper discusses the limitations of the Kelvin-Voigt model, which predicts a hysteresis loop shape inconsistent with real-world behavior. A more realistic hysteresis loop is proposed, which avoids tensile forces and matches the expected energy loss. The paper also introduces a nonlinear damping term λx^n, which can be used to model impacts with varying energy loss. The paper presents a general force-approach law F = kx^n, applicable to various geometries. It shows that the damping factor λ can be made independent of the exponent n, allowing for a more flexible model. The paper also discusses the validity of the Hertzian theory for contact between elastic bodies, and the importance of considering surface geometry in experiments. The paper concludes that the coefficient of restitution is a useful concept in engineering, despite its inexactness. It emphasizes the need for further refinement and validation of the concept, particularly for new materials and geometries. The paper also highlights the importance of careful experimental design to avoid errors in measuring the coefficient of restitution.