# Periodic Motion Vs Simple Harmonic Motion: Detailed Explanation

A body is acknowledged to be in motion if it changes its position with respect to its encompassing in a given time.

Periodic motion vs simple harmonic motion can be explained as, A body is said to be in periodic motion if it continuously Repeats its motion on a particular path in a certain period of time. While on the contrary, simple harmonic motion can be acknowledged as the simplest form of vibratory or oscillatory motion.

## Periodic Motion

Periodic motion can be understood by motion which we observe on a daily basis. In periodic motion, it is not necessary that the displacement that occurred in the body is in the direction of the restoring force.

For instance, the earth completes its one rotation on its own axis in 1 day. The motion of the moon is also a periodic motion as we know that the moon completes one revolution around the earth in approx. 27 days.

Similarly, the motion of hands in our clock is also a periodic motion. These all motions keep on repeating themselves in a particular path and in a certain period of time.

## Simple Harmonic Motion

Simple harmonic motion can be understood as the periodic motion oneself because simple harmonic motion is a type of oscillatory motion. Where a vibratory motion or oscillatory motion is assumed as a body, which is performing periodic motion and moves along the definite path back and forth about a definite position (fixed position), then the motion of the body is known as ‘vibratory motion’ or ‘oscillatory motion.’

In the above-given figure, we can see that that the body is moving back and forth from the fixed position. Here the body oscillates from the fixed point O to the other side, covering maximum displacement to A, and then comes back to position fixed position O and then goes to another side A’ covering maximum displacement. From point A’ body comes forth to fixed point O again. this back and forth motion done by a body is said to complete ‘1 vibration’ or ‘1 oscillation’.

However, it is proved that each oscillatory motion is automatically a periodic motion, but each periodic motion is not a vibratory or oscillatory motion. For instance, the earth rotates on its own axis but does not move back and forth about a certain point along a path (this is an essential condition for an oscillatory motion that is not followed in the given case.).

Simple harmonic motion has a sine wave waveform of amplitude vs time.

In the above-given figure, the time-displacement curve of a body oscillating back and forth about its fixed position is shown. The displacement y is measured from the fixed position, and the time t is measured from the point when the body passes through its fixed position. One oscillation is completed from point O to point A, and the time T taken for one oscillation is the periodic time of the body.

The maximum value of displacement y in the given figure will be a. this maximum displacement is known as amplitude. The total number of oscillations that a body performs in a time period of 1 second is known as frequency. The frequency (n)is the reciprocal of the time period.

When a body vibrates, its position and direction of motion vary with time. The phase of a vibrating body at any point of time shows the motion of the body at that point of time. At any point in time, two vibrating bodies are passing simultaneously through their equilibrium positions in the same direction, then at that instant, they are in the same phase, and if they are passing in opposite directions, then they are in opposite directions.

Irrespective of periodic motion, Simple harmonic motion needs certain conditions to be satisfied:-

• For simple harmonic motion, the body should be in a straight line moving back and forth about a fixed position
• The restoring force acting on the body should always be proportional to the displacement of the body from the point.

Restoring force is when a body takes the place of its stable position. Now a recurrent force acts upon it, which is directed towards the stable position. It is due to this force that acceleration is produced in the body, and it starts vibrating back and forth

This force is given by :

F= -kx

when restoring force is proportional to the dislocation of the body from the stable position, then the rate of change of velocity of the body is also proportional to the dislocation of the body, and it vibrates, performing the simple harmonic motion.

Where k is force constant and x is displacement and – sign indicates that the body is displaced in the opposite direction.

The force should always be directed towards the fixed point.

Simple harmonic motion can be explained through the following examples. A body attached to a spring in a horizontal plane produces vibrations which are simple harmonic in nature, oscillations by a simple pendulum, the motion of a body dropped in an imaginary tunnel across the earth, oscillations of a body floating in liquid, newton cradle, swings, oscillation of a body in the neck of an air chamber.

We can conclude the difference between periodic motion vs simple harmonic motion on the basis of restoring force that acts on the body performing oscillations which are supposed to be proportionate to the dislocation of the body, whereas periodic motion repeats itself continuously without any given conditions.