Identify the corret definition

Options

A. If after every certain interval of time, particle repeats its motion then motion is called periodic motion
B. To and fro motion of a particle over the same path is called oscillatory motion
C. Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion
D. All of these

Answer

To solve the question of identifying the correct definition of oscillatory motion, we will analyze each provided definition step by step.

### Step 1: Analyze the First Definition
**Definition A:** "If after every certain interval of time particle repeats its motion then the motion is called periodic."

- **Explanation:** This definition describes periodic motion, which is indeed a characteristic of oscillatory motion. In oscillatory motion, the system returns to its initial state after a fixed time interval, which is the essence of periodicity.

### Step 2: Analyze the Second Definition
**Definition B:** "To and fro motion of a particle over the same path is called oscillatory motion."

- **Explanation:** This definition accurately describes oscillatory motion. Oscillation involves a particle moving back and forth around a central point, retracing the same path. Therefore, this definition is also correct.

### Step 3: Analyze the Third Definition
**Definition C:** "Oscillatory motion described in terms of single sine and cosine function is called simple harmonic motion."

- **Explanation:** This definition is correct as well. Simple Harmonic Motion (SHM) is a specific type of oscillatory motion that can be represented mathematically using sine and cosine functions. The motion is periodic and has a defined amplitude and frequency.

### Conclusion
After analyzing all three definitions, we can conclude that:

- **Definition A** is correct as it defines periodic motion.
- **Definition B** is correct as it describes oscillatory motion.
- **Definition C** is correct as it defines simple harmonic motion.

Thus, the most accurate answer to the question is:
**Option D:** All of these definitions are correct.