For an oscillating pendulum of fixed length, which of the following is true ?

Options

A. Frequency depends on amplitude of oscillation
B. Frequency and time period are not related.
C. Time period depends on amplitude of oscillation.
D. Frequency and time period are related and do not depend on amplitude of oscillation.

Explanation

To solve the question regarding the behavior of an oscillating pendulum of fixed length, we need to analyze the options provided and understand the principles of pendulum motion.

### Step-by-Step Solution:

1. **Understand the Pendulum Motion**: A pendulum oscillates back and forth due to the force of gravity. The length of the pendulum affects its period of oscillation.

2. **Identify Key Terms**:
- **Frequency (f)**: The number of complete oscillations per unit time, measured in Hertz (Hz).
- **Time Period (T)**: The time taken for one complete oscillation, measured in seconds. The relationship between frequency and time period is given by the formula:
\[ f = \frac{1}{T} \]

3. **Analyze Each Option**:
- **Option 1**: "Frequency depends on amplitude of oscillation."
- This is incorrect for a simple pendulum of fixed length, as the frequency does not change with amplitude for small angles.

- **Option 2**: "Frequency and time period are not related."
- This is incorrect because frequency and time period are inversely related as shown in the formula above.

- **Option 3**: "Time period depends on amplitude of oscillation."
- This is also incorrect for small angles. For small amplitude oscillations, the time period remains constant and does not depend on amplitude.

- **Option 4**: "Frequency and time period are related and do not depend on amplitude of oscillation."
- This is correct. For a simple pendulum of fixed length, the frequency and time period are related, and they do not change with the amplitude of oscillation for small angles.

4. **Conclusion**: The correct answer is **Option 4**: "Frequency and time period are related and do not depend on amplitude of oscillation."