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The whiteboard in the image discusses **Lab 4: Pendulum Simple**, focusing on determining which variables affect the period \( T \) of a simple pendulum and estimating the gravitational constant \( g \). Below is a breakdown of the key points from the image:

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### Objective:
- **Determine which variables affect the period of a simple pendulum.**
- **Estimate the value of \( g \) using a simple pendulum.**

### Period Formula:
The period \( T \) is the time taken for one complete oscillation.

### Variables to Measure:
1. **Effect of Mass**:
   - Construct two pendulums of the same length but with different masses.
   - Make them oscillate from a small angle \( \theta \).

2. **Effect of Initial Amplitude**:
   - Construct a pendulum and make it oscillate with two different amplitudes (ensuring the angle \( \theta \) is less than 20 degrees).

3. **Effect of Length**:
   - Construct two pendulums with different lengths and masses.
   - Make them oscillate from the same small angle \( \theta \).

### Conclusion:
- Determine which variables truly affect \( T \) (the period).
- Compare the experimental value of \( g \) obtained with the theoretical value of \( g \).

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### Results:
- \( T_1, T_2 \) for varying masses
- \( T_3, T_4 \) for varying amplitudes
- \( T_5, T_6 \) for varying lengths

Each result is measured with its corresponding uncertainty \( \Delta T \).

### Formula to Obtain \( g \):
Using one of the results, the gravitational constant \( g \) is calculated using the formula:

\[
T = 2\pi \sqrt{\frac{L}{g}}
\]

Where \( T \) is the period and \( L \) is the length of the pendulum.

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Would you like more details on any of these points, or an explanation of how to experimentally verify the effect of one of these variables?

Here are some related questions:

1. How does changing the mass affect the period of a pendulum?
2. What is the theoretical derivation of the period \( T \) for a pendulum?
3. Why should the angle \( \theta \) be less than 20 degrees for accurate measurements?
4. How can experimental errors be minimized in a pendulum lab?
5. What are the practical applications of pendulum period measurement in estimating \( g \)?

**Tip:** Always ensure that your pendulum's length is measured accurately from the pivot point to the center of mass of the bob for the most reliable period results.

What variables affect the period of a simple pendulum, and how can the gravitational constant g be estimated using a pendulum experiment?

Learn how to experimentally determine the gravitational constant (g) using a simple pendulum. Explore how variables such as mass, length, and amplitude affect the pendulum's period, with step-by-step guidance for high school and undergraduate students.

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