The time period of a simple pendulum depends only on ___________

Options

A. length of the string
B. amplitude
C. oscillation
D. frequency

Answer

To answer the question, "The time period of a simple pendulum depends only on ___________", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Time Period**:
- The time period (T) of a simple pendulum is defined as the time taken to complete one full oscillation or swing.

2. **Identifying the Factors**:
- The time period of a pendulum can be influenced by several factors, including the length of the string (L), the mass of the bob (m), and the acceleration due to gravity (g).

3. **Time Period Formula**:
- The formula for the time period of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Here, \(L\) is the length of the string, and \(g\) is the acceleration due to gravity.

4. **Analyzing the Formula**:
- From the formula, we can see that the time period (T) is directly related to the square root of the length (L) of the pendulum and inversely related to the square root of the acceleration due to gravity (g).

5. **Constant Factors**:
- On the surface of the Earth, the acceleration due to gravity (g) is approximately constant (about 9.81 m/s²). Therefore, for a simple pendulum, the only variable that significantly affects the time period is the length of the string (L).

6. **Conclusion**:
- Thus, we conclude that the time period of a simple pendulum depends only on the length of the string (L).

### Final Answer:
The time period of a simple pendulum depends only on the **length of the string (L)**.

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