What is `S.H.M.` ? Give one example .

Answer

### Step-by-Step Solution:

1. **Definition of Simple Harmonic Motion (S.H.M.):**
Simple Harmonic Motion (S.H.M.) is defined as a type of periodic motion where an object oscillates around a central point, known as the mean position. The motion is characterized by two main features: it is periodic and oscillatory.

2. **Characteristics of S.H.M.:**
- **Periodic Motion:** This means that the motion repeats itself after a fixed time interval, denoted as \( T \) (the time period).
- **Oscillatory Motion:** This refers to the to-and-fro movement of the object around the mean position. The object moves away from the mean position to a maximum displacement and then returns back.

3. **Mathematical Representation:**
The restoring force \( F \) acting on the object in S.H.M. can be expressed mathematically as:
\[ F = -kx \]
where:
- \( F \) is the restoring force,
- \( k \) is the spring constant,
- \( x \) is the displacement from the mean position.
This equation indicates that the force is proportional to the displacement and acts in the opposite direction, which is a key characteristic of S.H.M.

4. **Example of S.H.M.:**
A common example of simple harmonic motion is a **spring-mass system**. When a mass is attached to a spring and displaced from its equilibrium position, it experiences a restoring force that pulls it back towards the mean position. This results in oscillatory motion, where the mass moves back and forth around the mean position.

5. **Mean Position in S.H.M.:**
In the spring-mass system, the mean position is where the restoring force is zero, which occurs when the spring is neither compressed nor extended. At this point, the forces acting on the mass are balanced.