Question

A system exhibiting S.H.M must possess
(A).Inertia only
(B).Elasticity as well as inertia
(C).Elasticity inertia and an external force
(D).Elasticity only

Answer 1

S.H.M means Simple Harmonic Motion. The Simple Harmonic Motion is a kind of oscillation. For example, the Simple Harmonic Motion is the spring attached with mass m. If force is given to the Simple Harmonic Motion system, then the system starts oscillating (i.e., back and forth motion). We already know about the spring system, it has some elasticity and as well as inertia to the spring system.

Complete answer:

Option (A)
Inertia is a kind of property of matter. If any system would like to continue in the existing state of rest or a motion. If any external force is applied to the system, then only the state of the system will be changed. Or inertia means a natural tendency of a system to resist the change in its state of motion. From this simple harmonic system, the mass m has inertia. So inertia is part of the reason for Simple Harmonic Motion. So option A is wrong.
Option (C)
The external force is not the reason for a Simple Harmonic Motion. In starting, we apply some external force to the system then only it makes simple harmonic motion. After that, we didn’t apply external force continuously to keep the system in Simple Harmonic Motion. So the option C is wrong.
Option (D)
The Simple Harmonic System has the spring. So here the elasticity is also part of the reason for Simple Harmonic Motion. Elasticity only is not the reason for the Simple Harmonic motion. So the option D is wrong.
Option (B)
There are some basic conditions for executing a simple harmonic motion. The first reason is the elastic force or elastic restoring force, and the second reason is the system must have inertia. So option B is correct.

Option (B) is the answer.

Additional Information:
The inertia and elasticity are not only a reason for the Simple Harmonic motion. The acceleration (a) is directly proportional to the displacement of the mass. The proportionality is also a reason for executing a Simple Harmonic Motion.

Note:
The above picture represents the SHM in the horizontal plane. The mass has always touched the ground, if we consider it’s a smooth plane means, then only the Simple harmonic motion will oscillate a long time concerning the applied force. If it's not a smooth plane, the friction will reduce an oscillation, or otherwise, it's called a damped oscillation. The SHM motion in a vertical direction also. In the vertical direction, only air resistance and gravity will be caused to reduce an oscillation. But air resistance is negligible.