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# Periodic Motion

## Definition

Periodic motion can be best described as the motion in which a body moves. If an object or body moves in such a way that its position or motion regularly repeats at equal intervals, then the motion of that object or body is said to be periodic. Periodic motion is characterized by angular frequency. In this, the body displaces at some angle at a particular speed termed as angular speed. Angular speed is given by-
Ω = 2 π f,
where Ω is the angular speed, and f is the frequency.

• Periodic motion – The body recurs its motion about a certain point along a concrete path at fixed time intervals.
• Period of motion – Periodic motion’s fixed interval after which the body repeats its path is known as the period of motion.
• Time period – The least time interval after which the periodic motion is repeated is the time period. It is denoted by T.
• Frequency – The number of times a motion is repeated in one second is known as frequency. The unit of frequency is Hertz and is denoted by f.
f = 1/T

Examples of periodic motion
1. The clock in every house works in a periodic motion. The hour hand, minute hand, and the second hand repeat their paths after every 60 units in the clock.
2. A pendulum goes to one side and then to another in a to and fro motion, known as oscillatory motion. The movement of a pendulum is periodic.
3.The classes in schools are also an example of periodic motion as they happen after regular intervals. Moreover, the weekly timetable follows the periodic motion.

Non-periodic motion – The type of motion that does not repeat itself in a fixed interval of time is known as non-periodic motion. For example, a man was walking on the road. If he walks on the road, motion occurs. But that motion is not periodic until and unless the same man walks on the road at regular time intervals daily with the same speed.

Examples of non-periodic motion
1. Swimming in a pool
2. Running a taxi on a highway
3. Completing homework
4. A bowler taking wickets
5. A footballer hitting goals

## Difference between periodic and non-periodic motion

 Parameters Periodic Motion Non-Periodic Motion Motion It is a repeated motion. It is a non-repetitive motion. Time The occurrence of periodic motion is totally related to the time interval. The non-periodic motion is not related to time. Time period It has a time period. It has a time of motion. Type of motion Vibratory or oscillatory motion. Displacement of an object

## Facts on periodic motion

• The period of rotation of the moon around the earth is 27.3 days.
• The time period of a simple pendulum of infinite length is equal to the earth's radius, i.e., 84.6 minutes.
• The period of revolution of the earth around the sun is one year.
• The time period of a pendulum clock in a lift falling freely under gravity is infinite.
• The period of rotation of the earth about its polar axis is one day.
• The oscillatory motion can be expressed in sine or cosine waves or their combinations. It is due to the reason that the oscillatory motion is called harmonic motion.

## Frequently asked questions on periodic motion

Ques 1: How does periodic motion occur?
Newton's third law of motion, the law of inertia, states that a body moves as it is unless and until subjected to a force that can change its course of inertia. A similar concept is applicable for the bodies in a periodic motion. For example, a simple pendulum, when pulled (pulling is a kind of force) from its resting position, starts moving to and fro and tends to oscillate till we continue to apply the force to the pendulum.

Ques 2: How is harmonic motion periodic?
A sinusoidal wave can represent a harmonic motion. Therefore, it is a periodic motion. Take an example of spring. When a spring is stretched, its mean position changes, and it oscillates towards its extreme position. During this motion, it restores force and tries to come back to its original position. This magnitude of the force is equal to the displacement that the spring has to undergo to reach its original position. As a result, we can say that a harmonic motion is a periodic motion.

Ques 3: What are the other examples of periodic motion?
All oscillatory motions move in a fixed time interval. Hence, they are periodic in nature. However, all oscillatory motions are not periodic, like the revolution of the earth. Therefore, it is periodic but not oscillatory.

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