Select the correct statements

Options

A. A simple harmonic motion is necessarily periodic
B. a simple harmonic motion is necessarily oscillatory
C. an oscillatory motion is necessrily periodic
D. a periodic motion is necessarily oscillatory

Answer

To solve the question of selecting the correct statements regarding simple harmonic motion (SHM), we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- SHM is a type of periodic motion where an object moves back and forth around a central point (mean position) in a regular time interval.
- The motion is characterized by its oscillatory nature, meaning it moves to and fro.

2. **Analyzing Option 1**:
- **Statement**: "A simple harmonic motion is necessarily periodic."
- **Explanation**: In SHM, the object returns to its mean position after a fixed time interval, making it periodic.
- **Conclusion**: This statement is **correct**.

3. **Analyzing Option 2**:
- **Statement**: "A simple harmonic motion is necessarily oscillatory."
- **Explanation**: SHM involves oscillation about a mean position, which is the essence of oscillatory motion.
- **Conclusion**: This statement is **correct**.

4. **Analyzing Option 3**:
- **Statement**: "An oscillatory motion is necessarily periodic."
- **Explanation**: Oscillatory motion can be periodic (like SHM) or non-periodic (like a damped oscillator that eventually stops). An example is a ball in a frictional bowl that oscillates but does not return to the same position in a fixed time.
- **Conclusion**: This statement is **incorrect**.

5. **Analyzing Option 4**:
- **Statement**: "A periodic motion is necessarily oscillatory."
- **Explanation**: Periodic motion can be oscillatory (like SHM) or non-oscillatory (like uniform circular motion). In uniform circular motion, the motion repeats at regular intervals but does not oscillate about a mean position.
- **Conclusion**: This statement is **incorrect**.

### Final Selection of Correct Statements:
- The correct statements are:
- Option 1: A simple harmonic motion is necessarily periodic.
- Option 2: A simple harmonic motion is necessarily oscillatory.