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 identify the correct definition of periodic motion, oscillatory motion, and simple harmonic motion, we can break down the definitions provided in the video transcript step by step.

### Step 1: Understanding Periodic Motion
- **Definition**: Periodic motion is defined as the motion of a particle that repeats itself after a certain interval of time. For example, if a body returns to the same position after a fixed time \( T \), it is said to be in periodic motion.
- **Example**: The motion of planets around the sun is periodic because they follow the same path and return to the same position after a fixed time.

### Step 2: Understanding Oscillatory Motion
- **Definition**: Oscillatory motion refers to the to-and-fro motion of a particle over the same path. This motion occurs around a central position (mean position).
- **Example**: A simple pendulum exhibits oscillatory motion. When displaced from its mean position and released, it swings back and forth around that mean position.

### Step 3: Understanding Simple Harmonic Motion (SHM)
- **Definition**: Simple Harmonic Motion is a specific type of oscillatory motion where the displacement of the particle is described by a sine or cosine function. The general equations for SHM can be expressed as:
- \( x = a \sin(\omega t) \)
- \( x = a \cos(\omega t) \)
where \( a \) is the amplitude and \( \omega \) is the angular frequency.
- **Example**: The motion of a mass on a spring or a pendulum can be modeled as simple harmonic motion when the displacements are small.

### Step 4: Evaluating the Options
- **Option 1**: Correctly describes periodic motion.
- **Option 2**: Correctly describes oscillatory motion.
- **Option 3**: Correctly describes simple harmonic motion.
- **Option 4**: Since all previous options are correct, this option is the right answer.

### Final Answer
The correct answer is **Option 4**, as all the statements provided in the options are correct.

---