Which one of the following statements regarding motion is correct?

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Which one of the following statements regarding motion is correct?

All the periodic motions are necessarily simple harmonic
All the simple harmonic motions are necessarily periodic motions
There is no co-relation between the simple harmonic motions and the periodicity of motion
The relation between the simple harmonic motion and periodic motion depends upon the mass of object undergoing the motion
This question was previously asked in
UPSC CAPF – 2020
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All the simple harmonic motions are necessarily periodic motions.
Periodic motion is defined as any motion that repeats itself in a regular interval of time. Simple Harmonic Motion (SHM) is a special type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts towards the equilibrium. Since SHM repeats itself at regular intervals (its period), it is always a periodic motion. However, not all periodic motions are SHM (e.g., a simple pendulum with large amplitude is periodic but not SHM; a uniform circular motion is periodic but not oscillatory/SHM).
SHM is characterized by a sinusoidal variation of displacement, velocity, and acceleration with time. Examples include the oscillation of a mass on a spring (Hooke’s Law) or the small-angle oscillations of a simple pendulum.

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