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labie TT 2. 3. Make the calculations to fill the empty cells in table # 2. Table # 2: Determination of the period and frequency of the simple harmonic motion Mn (g) = MT= Mh+ Msw MT Msw (g) 200 220 240 0.0240 Frequency when Msw=200 g. 1 Note: fexp = T MT (kg) t10 (s) 200 0000 4.16 6.416 226 0.0220 4.5.6 0.456 240 5.880.580 exp Texp Mh: Mass of the weight hanger Msw: Mass of added slotted weights MT: Total Mass = t10 10 Texp (s) Th=27₁ Tth (s) QUESTIONS: 1. How does the period change with increasing mass? MT K t10: Time for 10 oscillations Texp: Experimental period Tth: Theoretical period fexp: Experimental frequency π = 3.14 % dif in T

labie TT 2. 3. Make the calculations to fill the empty cells in table # 2. Table # 2: Determination of the period and frequency of the simple harmonic motion Mn (g) = MT= Mh+ Msw MT Msw (g) 200 220 240 0.0240 Frequency when Msw=200 g. 1 Note: fexp = T MT (kg) t10 (s) 200 0000 4.16 6.416 226 0.0220 4.5.6 0.456 240 5.880.580 exp Texp Mh: Mass of the weight hanger Msw: Mass of added slotted weights MT: Total Mass = t10 10 Texp (s) Th=27₁ Tth (s) QUESTIONS: 1. How does the period change with increasing mass? MT K t10: Time for 10 oscillations Texp: Experimental period Tth: Theoretical period fexp: Experimental frequency π = 3.14 % dif in T

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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How do I find the T th (s) I'm confused on it how to get the an

### Determination of the Spring Constant (K) - Educational Content **Table #1: Determination of the Spring Constant (K)** --- The objective of this experiment is to measure the spring constant (K) by analyzing the displacement of the spring (x) with various masses (M). Below is a detailed table representing the data collected during the experiment. --- ### Symbols and Units - **M<sub>t</sub> (kg):** Total mass (weight hanger plus slotted weights) - **M<sub>sw</sub> (g):** Mass of added slotted weights - **M<sub>th</sub> (g):** Mass of the weight hanger - **M<sub>t</sub> (g):** Total Mass - **x<sub>0</sub> (cm):** Position of the spring’s bottom (unstretched) - **x<sub>i</sub> (cm):** Position of the spring’s bottom (stretched) - **Δx (m):** Elongation of the spring - **F (N):** Force exerted by the masses - **K (N/m):** Force constant of the spring ### Data Table | M<sub>sw</sub> (g) | M<sub>t</sub> (kg) | M<sub>t</sub> (g) | x<sub>0</sub> (cm) | x<sub>i</sub> (cm) | Δx (m) | F (N) | K (N/m) | |------------------|-------------------|------------------|-------------------|-------------------|----------|----------|---------| | 50 | 0.065 | 65 | 5.0 | 6.1 | 0.011 | 0.637 | 57.91 | | 100 | 0.115 | 115 | 5.0 | 7.1 | 0.021 | 1.127 | 53.67 | | 150 | 0.165 | 165 | 5.0 | 8.2 | 0.032 | 1.617 | 50.53 | | 200 |
Transcribed Image Text:### Determination of the Spring Constant (K) - Educational Content **Table #1: Determination of the Spring Constant (K)** --- The objective of this experiment is to measure the spring constant (K) by analyzing the displacement of the spring (x) with various masses (M). Below is a detailed table representing the data collected during the experiment. --- ### Symbols and Units - **M<sub>t</sub> (kg):** Total mass (weight hanger plus slotted weights) - **M<sub>sw</sub> (g):** Mass of added slotted weights - **M<sub>th</sub> (g):** Mass of the weight hanger - **M<sub>t</sub> (g):** Total Mass - **x<sub>0</sub> (cm):** Position of the spring’s bottom (unstretched) - **x<sub>i</sub> (cm):** Position of the spring’s bottom (stretched) - **Δx (m):** Elongation of the spring - **F (N):** Force exerted by the masses - **K (N/m):** Force constant of the spring ### Data Table | M<sub>sw</sub> (g) | M<sub>t</sub> (kg) | M<sub>t</sub> (g) | x<sub>0</sub> (cm) | x<sub>i</sub> (cm) | Δx (m) | F (N) | K (N/m) | |------------------|-------------------|------------------|-------------------|-------------------|----------|----------|---------| | 50 | 0.065 | 65 | 5.0 | 6.1 | 0.011 | 0.637 | 57.91 | | 100 | 0.115 | 115 | 5.0 | 7.1 | 0.021 | 1.127 | 53.67 | | 150 | 0.165 | 165 | 5.0 | 8.2 | 0.032 | 1.617 | 50.53 | | 200 |
### Table #2: Determination of the Period and Frequency of Simple Harmonic Motion This table is used to document the findings from an experiment designed to determine the period and frequency of a simple harmonic motion system. #### Parameters: - **MT**: Total Mass (kg) - **M_h**: Mass of the weight hanger (kg) - **M_sw**: Mass of added slotted weights (kg) - **f_exp**: Experimental frequency, calculated as \( f_{\text{exp}} = \frac{1}{T_{\text{exp}}} \) - **T_exp (s)**: Experimental period - **T_th (s)**: Theoretical period, calculated as \( T_{\text{th}} = 2\pi \sqrt{\frac{MT}{K}} \) - **MT (kg)**: Total Mass - **t_{10} (s)**: Time for 10 oscillations The table includes constants and derived values such as the experimental and theoretical periods, frequencies, and the percentage difference in the periods. #### Recorded Data: | MT (kg) | M_sw (g) | t_{10} (s) | T_exp (s) | f_exp (Hz) | |---------|----------|------------|-----------|------------| | 0.200 | 200 | 8.20 | 0.820 | 1.22 | | 0.200 | 220 | 8.48 | 0.848 | 1.18 | | 0.200 | 240 | 9.06 | 0.906 | 1.10 | | 0.200 | 260 | 9.66 | 0.966 | 1.03 | \(\pi\) = 3.14 #### Equations Used: 1. \( f_{\text{exp}} = \frac{1}{T_{\text{exp}}} \) 2. \( T_{\text{th}} = 2\pi \sqrt{\frac{MT}{K}} \) #### Questions: 1. How does the period change with increasing mass? --- The table above provides a comprehensive dataset that includes the mass of added weights, the time taken for 10 oscillations, and the calculated periods and frequencies for each total mass configuration. This information
Transcribed Image Text:### Table #2: Determination of the Period and Frequency of Simple Harmonic Motion This table is used to document the findings from an experiment designed to determine the period and frequency of a simple harmonic motion system. #### Parameters: - **MT**: Total Mass (kg) - **M_h**: Mass of the weight hanger (kg) - **M_sw**: Mass of added slotted weights (kg) - **f_exp**: Experimental frequency, calculated as \( f_{\text{exp}} = \frac{1}{T_{\text{exp}}} \) - **T_exp (s)**: Experimental period - **T_th (s)**: Theoretical period, calculated as \( T_{\text{th}} = 2\pi \sqrt{\frac{MT}{K}} \) - **MT (kg)**: Total Mass - **t_{10} (s)**: Time for 10 oscillations The table includes constants and derived values such as the experimental and theoretical periods, frequencies, and the percentage difference in the periods. #### Recorded Data: | MT (kg) | M_sw (g) | t_{10} (s) | T_exp (s) | f_exp (Hz) | |---------|----------|------------|-----------|------------| | 0.200 | 200 | 8.20 | 0.820 | 1.22 | | 0.200 | 220 | 8.48 | 0.848 | 1.18 | | 0.200 | 240 | 9.06 | 0.906 | 1.10 | | 0.200 | 260 | 9.66 | 0.966 | 1.03 | \(\pi\) = 3.14 #### Equations Used: 1. \( f_{\text{exp}} = \frac{1}{T_{\text{exp}}} \) 2. \( T_{\text{th}} = 2\pi \sqrt{\frac{MT}{K}} \) #### Questions: 1. How does the period change with increasing mass? --- The table above provides a comprehensive dataset that includes the mass of added weights, the time taken for 10 oscillations, and the calculated periods and frequencies for each total mass configuration. This information
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