A restoring force is a must for a body to execute `S.H.M` Explain, why

Answer

### Step-by-Step Solution:

1. **Definition of Simple Harmonic Motion (S.H.M)**:
- Simple Harmonic Motion is defined as a type of oscillatory motion where a particle moves back and forth around a central or mean position. The motion is periodic and can be described mathematically by sine or cosine functions.

2. **Understanding Restoring Force**:
- A restoring force is a force that acts to bring a system back to its equilibrium or mean position. In the context of S.H.M, this force is directed towards the mean position whenever the particle is displaced from it.

3. **Role of Restoring Force in S.H.M**:
- For a body to execute S.H.M, it must experience a restoring force that is proportional to its displacement from the mean position. This means that if the particle is displaced to the right (positive direction), the restoring force will act to the left (negative direction), and vice versa.

4. **Oscillatory Motion Requirement**:
- The essence of oscillatory motion is the to-and-fro movement about a mean position. If there is no restoring force, once the particle is displaced, it will not return to the mean position. Instead, it will continue moving in the direction of the displacement, leading to a non-oscillatory motion.

5. **Conclusion**:
- Therefore, a restoring force is essential for a body to execute S.H.M. Without it, the motion cannot be periodic or oscillatory, which are key characteristics of simple harmonic motion.