Periodic Motion:
(i) When a body moves on a definite path and repeats its motion again and again after a definite interval of time, then its motion is called periodic motion.
The constant time interval after which it repeats its motion called its time period of motion, T.
Example : Motion of earth around Sun ( T=365.25 days), Motion of minutes hand in clock (T= 1hour), Motio of a simple pendulum in free space, etc.
So, for motion of a body to be periodic,
* Body must move on a definite path.
* It must repeat its motion after a definite time interval.
Oscilatory Motion:
When a body makes to and fro motion about a fixed point, on a almost straight line path and repeats its motion after a definite time interval, then the motion of the body is a vibratory motion or oscillatory motion
* It must have periodic motion
* The body must move to & fro about a fixed point on a almost straight line path.
The point about which the body makes to and fro motion is called its mean position.
Example:
(i) Motion of a bob of a simple pendulum if displacement is small, (ii) Motion of a mass attached to a spring,
(iii) Motion of a block, moving with constant speed, on a smooth horizontal floor between two rigid walls.
* Every oscillatory motion must be a periodic motion but every periodic motion is not oscillatory.
Simple Harmonic Motion
When a body makes oscillatory motion about a fixed mean position such that the acceleration of the body at any instant is directly proportional to its displacement from the mean position & is always directed towards the mean position
a ∝ –x
or a = – ω2 x ……………….. (1)
Where, ω (const) = angular frequency
According to Newtons second law –
F = ma
or F = –mω2x
F = –k x ……………….. (2)
i.e. F ∝ –x
Where, k = Force constant
Since, the force is always directed towards the mean position it is called restoring force.
- Note :The necessary and sufficient condition for a motion of a particle to be S.H.M. that, force acting on it must be directed towards a fixed point called mean (equilibrium) position and magnitude of the force must be proportional to the displacement of the particle from the equilibrium position.
- Note: For SHM F = –k x
Introduction to SHM Video [In HINDI+ENGLISH Mix Language]
