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Data Table for Part C- Testing the Empirical Model Calculated Period Total Mass Time for 20 cycles Measured On Spring m (kg] 0.05 Amplitude Period % Difference x. [m] T»Isec] T[sec] T(sec] 0.05 11.63 1 0.1 0.05 18.21 0.2 0.05 22.07 29.01 4 0.4 0.05 0.02 0.05 12.81

Data Table for Part C- Testing the Empirical Model Calculated Period Total Mass Time for 20 cycles Measured On Spring m (kg] 0.05 Amplitude Period % Difference x. [m] T»Isec] T[sec] T(sec] 0.05 11.63 1 0.1 0.05 18.21 0.2 0.05 22.07 29.01 4 0.4 0.05 0.02 0.05 12.81

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Fill in the blank in the chart.

The Spring constant is 7.8(N/m).

**Data Table for Part C – Testing the Empirical Model** This table presents data collected for testing an empirical model in a spring-mass system. The parameters observed include the total mass on the spring, amplitude, and the time taken for 20 oscillation cycles. The measured and calculated periods are compared to find the percentage difference. | Total Mass on Spring (m [kg]) | Amplitude (x₀ [m]) | Time for 20 cycles (T₂₀ [sec]) | Measured Period (T [sec]) | Calculated Period (T [sec]) | % Difference | |-------------------------------|--------------------|-------------------------------|---------------------------|-----------------------------|--------------| | 0.05 | 0.05 | 11.63 | | | | | 0.1 | 0.05 | 18.21 | | | | | 0.2 | 0.05 | 22.07 | | | | | 0.4 | 0.05 | 29.01 | | | | | 0.02 | 0.05 | 12.81 | | | | **Explanation:** - **Total Mass on Spring (m [kg])**: The mass attached to the spring, in kilograms. - **Amplitude (x₀ [m])**: The maximum displacement from the equilibrium position, in meters. - **Time for 20 cycles (T₂₀ [sec])**: The total time taken for 20 complete oscillations, in seconds. - **Measured Period (T [sec])**: The actual period measured from the oscillations. - **Calculated Period (T [sec])**: The period determined theoretically from calculations. - **% Difference**: The percentage difference between the measured and calculated periods, highlighting discrepancies. The data entries for the measured and calculated periods as well as the percentage difference are missing. Further measurements and calculations are needed to complete the analysis.
Transcribed Image Text:**Data Table for Part C – Testing the Empirical Model** This table presents data collected for testing an empirical model in a spring-mass system. The parameters observed include the total mass on the spring, amplitude, and the time taken for 20 oscillation cycles. The measured and calculated periods are compared to find the percentage difference. | Total Mass on Spring (m [kg]) | Amplitude (x₀ [m]) | Time for 20 cycles (T₂₀ [sec]) | Measured Period (T [sec]) | Calculated Period (T [sec]) | % Difference | |-------------------------------|--------------------|-------------------------------|---------------------------|-----------------------------|--------------| | 0.05 | 0.05 | 11.63 | | | | | 0.1 | 0.05 | 18.21 | | | | | 0.2 | 0.05 | 22.07 | | | | | 0.4 | 0.05 | 29.01 | | | | | 0.02 | 0.05 | 12.81 | | | | **Explanation:** - **Total Mass on Spring (m [kg])**: The mass attached to the spring, in kilograms. - **Amplitude (x₀ [m])**: The maximum displacement from the equilibrium position, in meters. - **Time for 20 cycles (T₂₀ [sec])**: The total time taken for 20 complete oscillations, in seconds. - **Measured Period (T [sec])**: The actual period measured from the oscillations. - **Calculated Period (T [sec])**: The period determined theoretically from calculations. - **% Difference**: The percentage difference between the measured and calculated periods, highlighting discrepancies. The data entries for the measured and calculated periods as well as the percentage difference are missing. Further measurements and calculations are needed to complete the analysis.
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