Choose the correct statement:

Options

A. Every osillatory motion is periodic in nature.
B. Every periodic motion is oscillatory in nature.
C. The motion of a pendulum bob is periodic in nature ( within its small amplitude)
D. Both (a) and ( c)

Explanation

To solve the question, we need to analyze the statements related to oscillatory and periodic motion. Let's break down the statements one by one.

### Step-by-Step Solution:

1. **Understanding Oscillatory Motion:**
- Oscillatory motion is defined as motion that repeats itself in a regular cycle around a central point (mean position).
- An example of oscillatory motion is a pendulum swinging back and forth.

**Hint:** Oscillatory motion involves a mean position and movement away from it in both directions.

2. **Statement Analysis:**
- **Statement A:** "Every oscillatory motion is periodic in nature."
- This statement is true. Since oscillatory motion repeats itself after a fixed interval of time, it is periodic.

**Hint:** If a motion repeats itself regularly, it is periodic.

3. **Statement B:** "Every periodic motion is oscillatory."
- This statement is false. A periodic motion does not necessarily have to be oscillatory. For example, a vehicle moving in a circular path is periodic (it returns to the starting point after a fixed time) but does not oscillate back and forth.

**Hint:** Not all periodic motions involve back-and-forth movement.

4. **Statement C:** "The motion of a pendulum bob is periodic in nature within its small amplitude."
- This statement is true. The motion of a pendulum bob does repeat itself at regular intervals, especially when the amplitude (the maximum distance from the mean position) is small.

**Hint:** Pendulum motion is a classic example of periodic motion.

5. **Conclusion:**
- Based on the analysis, the correct statements are A and C. Therefore, the answer to the question is that both statements A and C are correct.

### Final Answer:
The correct statements are:
- A: Every oscillatory motion is periodic in nature.
- C: The motion of a pendulum bob is periodic in nature within its small amplitude.