Run 1, 2, and 3 are for different masses. Does the frequency, f, appear to depend on the mass used? Run 1 and 4 are for the same mass but with different amplitude. Does the frequency, f,appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion

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  1. Run 1, 2, and 3 are for different masses. Does the frequency, f, appear to depend on the mass used?
  2. Run 1 and 4 are for the same mass but with different amplitude. Does the frequency, f,appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion
**Table of Experimental Data**

**Mass of the iOLab Device**
- \( m = 1.85 \, \text{kg} \)

**Spring Constant**
- \( k = 99.07 \)

| Run # | Total Mass \( m_{\text{tot}} \) (kg) | Time for 4 Cycles (s) | Period \( T \) (s) | Frequency \( f = 1/T \) (Hz) | Angular Frequency \( \omega \) | Theoretical |
|-------|-------------------------------------|------------------------|-------------------|-------------------------------|-------------------------------|-------------|
| 1     | \( m \)                             | 9.41                   | 2.35              | 1.171                         | 2.67                         | 1.165       |
| 2     | \( m + 0.05 \, \text{kg} \)         | 10.48                  | 2.62              | 1.72                          | 2.39                         | 1.149       |
| 3     | \( m + 0.1 \, \text{kg} \)          | 11.30                  | 2.83              | 1.72                          | 2.22                         | 1.34        |
| 4     | \( m \)                             | 9.38                   | 2.34              | 1.71                          | 2.69                         | 1.165       |

**Explanation of Table:**

- **Total Mass \( m_{\text{tot}} \) (kg):** Represents the total mass used in each run.
- **Time for 4 Cycles (s):** The total time taken for 4 oscillation cycles.
- **Period \( T \) (s):** Calculated as the time for 4 cycles divided by 4.
- **Frequency \( f \) (Hz):** The reciprocal of the period \(\left(\frac{1}{T}\right)\).
- **Angular Frequency \( \omega \):** An experimental measurement related to the rate of oscillation.
- **Theoretical:** Predicted values based on theoretical calculations.
Transcribed Image Text:**Table of Experimental Data** **Mass of the iOLab Device** - \( m = 1.85 \, \text{kg} \) **Spring Constant** - \( k = 99.07 \) | Run # | Total Mass \( m_{\text{tot}} \) (kg) | Time for 4 Cycles (s) | Period \( T \) (s) | Frequency \( f = 1/T \) (Hz) | Angular Frequency \( \omega \) | Theoretical | |-------|-------------------------------------|------------------------|-------------------|-------------------------------|-------------------------------|-------------| | 1 | \( m \) | 9.41 | 2.35 | 1.171 | 2.67 | 1.165 | | 2 | \( m + 0.05 \, \text{kg} \) | 10.48 | 2.62 | 1.72 | 2.39 | 1.149 | | 3 | \( m + 0.1 \, \text{kg} \) | 11.30 | 2.83 | 1.72 | 2.22 | 1.34 | | 4 | \( m \) | 9.38 | 2.34 | 1.71 | 2.69 | 1.165 | **Explanation of Table:** - **Total Mass \( m_{\text{tot}} \) (kg):** Represents the total mass used in each run. - **Time for 4 Cycles (s):** The total time taken for 4 oscillation cycles. - **Period \( T \) (s):** Calculated as the time for 4 cycles divided by 4. - **Frequency \( f \) (Hz):** The reciprocal of the period \(\left(\frac{1}{T}\right)\). - **Angular Frequency \( \omega \):** An experimental measurement related to the rate of oscillation. - **Theoretical:** Predicted values based on theoretical calculations.
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