Which of the following x-t graphs does not represent periodic motion?

Options

A.
B.
C.
D.

Explanation

To determine which of the given x-t graphs does not represent periodic motion, we will analyze each option based on the definition of periodic motion. Periodic motion is characterized by the repetition of motion after a fixed interval of time, known as the time period (T).

### Step-by-Step Solution:

1. **Understand the Definition of Periodic Motion**:
- Periodic motion is when an object returns to its initial position after a certain time interval (T). This means the graph must show a repeating pattern.

2. **Analyze Each Graph**:
- **Option 1**: Check if the graph shows a repeating pattern.
- If the graph has a consistent shape and returns to the same position after a certain time, it is periodic.
- **Option 2**: Check if the graph shows a repeating pattern.
- If the graph does not return to the same position or does not have a consistent shape, it is not periodic.
- **Option 3**: Check if the graph shows a repeating pattern.
- Similar to option 1, if it repeats consistently, it is periodic.
- **Option 4**: Check if the graph shows a repeating pattern.
- Again, if it returns to the same position after a certain time, it is periodic.

3. **Identify the Non-Periodic Graph**:
- After analyzing all options, identify which graph does not exhibit periodic behavior.
- In this case, upon examining the graphs, **Option 2** does not show any periodicity and does not return to the same position after a fixed time.

4. **Conclusion**:
- Therefore, the graph that does not represent periodic motion is **Option 2**.

### Final Answer:
Option 2 is the correct answer as it does not represent periodic motion.