Vibration:

A vibration is a kind of motion that changes the direction of sense and after a regular interval of time. It is also a to and fro motion.

 

Free Vibration:

A closed vibratory system is given and initial excitation and is allowed to vibrate without further influence executes free vibration.

 

Criteria of Vibration

a) It has restoring force

b) It has inertia of motion

c) It has also initial excitation

 

Simple Harmonic Motion:

When a body moves such that its acceleration is proportional to its displacement from its equilibrium position or any other fixed point at its path and be always directed towards that point then the motion of the body is called simple harmonic motion. 

Characteristics of S.H.M. / Criteria of S.H.M.

a) The motion is periodic motion in a particular case

b) the acceleration of the body is proportional to its displacement from its equilibrium position

c) The acceleration of the body is directed towards a certain fixed point

d) The motion is isochronous because the expression for the time period  is independent of the amplitude of the motion

e) The equation does not conclude the motion of the particle along the circle

f) Acceleration varies directly as its distance from the equilibrium point.