Choose the correct statement.

Options

A. Every oscillatory 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 evaluate the given statements about oscillatory and periodic motion:

### Step-by-Step Solution:

1. **Evaluate Option A**: "Every oscillatory motion is periodic in nature."
- **Explanation**: Oscillatory motion refers to motion that repeats itself at regular intervals. For example, the swinging of a pendulum is oscillatory and occurs in a periodic manner. Therefore, this statement is **correct**.

2. **Evaluate Option B**: "Every periodic motion is oscillatory in nature."
- **Explanation**: Periodic motion refers to motion that repeats at regular intervals, but not all periodic motions are oscillatory. For instance, the revolution of planets around the sun is periodic but not oscillatory. Therefore, this statement is **incorrect**.

3. **Evaluate Option C**: "The motion of a pendulum is periodic in nature within its small amplitude."
- **Explanation**: The motion of a pendulum does repeat itself in a regular time interval, especially when the amplitude is small. This is a characteristic of simple harmonic motion (SHM). Therefore, this statement is **correct**.

4. **Evaluate Option D**: "Both A and C."
- **Explanation**: Since both Option A and Option C are correct, this option is also **correct**.

### Conclusion:
The correct statement is **Option D: Both A and C**.