**Period vs. Mass Data for a Mass-Spring System**This section analyzes four different graphs (A, B, C, and D) showing the relationship between the period (T) and mass (m) of a vibrating system at equilibrium. Each graph represents a distinct mathematical fit for the data.---**Graph A:**- **Equation:** \( y = 3.222x - 0.3793 \)- **Coefficient of Determination (R²):** 0.9895Graph A shows a linear relationship, with a relatively high R² value indicating a strong correlation between mass and period.---**Graph B:**- **Equation:** \( y = 0.4766x^{1.7} \)- **Coefficient of Determination (R²):** 0.9417Graph B represents a power law fit, suggesting that the period increases at a rate proportional to the mass raised to the power of 1.7. The R² value is moderate, indicating a less ideal fit compared to Graph A.---**Graph C:**- **Equation:** \( y = 1066x^4 - 9600x^3 + 3226.7x^2 - 39.167x - 0.55 \)- **Coefficient of Determination (R²):** 1Graph C uses a polynomial fit of degree 4, with an R² value of 1, implying a perfect fit to the data. However, overfitting may be a concern.---**Graph D:**- **Equation:** \( y = 2.5078x^{0.502} \)- **Coefficient of Determination (R²):** 0.9374Graph D displays another power law fit, with the period proportional to the mass raised to approximately 0.502. While this has a lower R² value compared to graph A, it still describes a significant portion of the variation.---**Analysis:**When determining the best line fit for the data, consider both the simplicity of the model and the R² value. Graph A, with its linear equation and high R², offers a straightforward and highly predictive fit. In contrast, Graph C, while perfect in R², might overcomplicate the model.

Name: **Period vs. Mass Data for a Mass-Spring System**This section analyze
Uploaded: 2024-03-20T06:58:04.000Z
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Description: **Period vs. Mass Data for a Mass-Spring System**This section analyzes four different graphs (A, B, C, and D) showing the relationship between the period (T) and mass (m) of a vibrating system at equilibrium. Each graph represents a distinct mathema