Answer:

Simple Harmonic Motion (SHM) is a type of oscillatory motion in which the restoring force is directly proportional to the displacement and acts in the opposite direction to the displacement. SHM is an ideal case of periodic motion and has several characteristics such as a constant period, sinusoidal motion, and constant amplitude.

Option A: An electric dipole placed stably in a uniform electric field and then given a very small regular displacement.

In this case, the electric dipole experiences a restoring torque that is directly proportional to the angular displacement from its equilibrium position. The electric field acts as the restoring force, and the electric dipole experiences SHM. The torque tries to align the dipole with the electric field, and as the dipole is displaced, it experiences a restoring torque that brings it back to its equilibrium position. The motion of the dipole is periodic, with a constant period and sinusoidal variation.

Key Points:
- Electric dipole experiences restoring torque proportional to angular displacement.
- Electric field acts as the restoring force.
- Motion is periodic, with a constant period and sinusoidal variation.

Option B: A simple pendulum with a very small angle of swing.

A simple pendulum is an ideal system that exhibits SHM when the angle of swing is small. The force of gravity acts as the restoring force, and as the pendulum is displaced from its equilibrium position, it experiences a restoring force that brings it back towards the equilibrium. The motion of the pendulum is periodic, with a constant period and sinusoidal variation.

Key Points:
- Force of gravity acts as the restoring force.
- Motion is periodic, with a constant period and sinusoidal variation.

Option C: Shadow of a point mass having uniform circular motion, on the vertical diameter.

The shadow of a point mass undergoing uniform circular motion on the vertical diameter does not exhibit SHM. The motion of the shadow is not periodic, and the restoring force is not directly proportional to the displacement.

Conclusion: Among the given options, only option A represents an ideal case of SHM where an electric dipole placed in a uniform electric field experiences a restoring torque proportional to the angular displacement.

Because simple pendulum is not the case of ideal SHM as it is mention in NCERT
shadow of a point mass having uniform circular motion on the horizontal diameter then it is a case os SHM but as mention in option it is on vertical diameter so the correct option is A