What is meant by `S.H.M.` ?

Answer

### Step-by-Step Solution

1. **Definition of Simple Harmonic Motion (S.H.M.)**:
- Simple Harmonic Motion (S.H.M.) is a type of periodic motion where an object moves back and forth around a central point (mean position).

2. **Characteristics of S.H.M.**:
- **Periodic Motion**: The motion repeats after a fixed interval of time, denoted as \( T \) (the time period).
- **Oscillatory Motion**: The motion involves oscillation, meaning the object moves to and fro about a fixed position.

3. **Mean Position**:
- In S.H.M., the central point around which the motion occurs is called the mean position. The object moves away from this position and then returns back, creating a to-and-fro motion.

4. **Mathematical Representation**:
- The force acting on the object in S.H.M. can be expressed by the equation:
\[ F = -kx \]
where:
- \( F \) is the restoring force,
- \( k \) is a constant (spring constant),
- \( x \) is the displacement from the mean position.
- The negative sign indicates that the force is directed towards the mean position, opposing the displacement.

5. **Condition for Oscillatory Motion**:
- For the motion to be oscillatory, the force equation must be of the form \( F = -kx^n \) where \( n \) is an odd integer (1, 3, 5, ...). The simplest case is when \( n = 1 \), which leads to the definition of S.H.M.

### Summary
Simple Harmonic Motion is characterized by periodic and oscillatory motion around a mean position, with a restoring force that is proportional to the displacement from that position.