 # Periodic Motion

## What is periodic motion?

We generally describe the motion of bodies in the way they move. If an object moves such that it repeats its path regularly after equal intervals of time, it's motion is said to be periodic. Such motion is characterized by the angular frequency, where the body displaces by some angle at some speed called the angular speed given by,

Here, Ω = 2 πf,  Ω  is the angular speed and f is the frequency. This motion can be represented by a sinusoidal wave as shown below:

You have seen in schools that each lecture is allotted a fixed interval of time. This fixed interval of time is called the time period however the teacher coming and leaving your class daily is the periodic motion of your teacher.

### Periodic Motion Definition

If a body recurs its motion along a definite path, about a certain point after a fixed interval of time is called the periodic motion. The fixed interval of time after which the motion is repeated is called the period of motion. The requirement that the motion of a body or an object must satisfy to be periodic is that it possesses a definitive period where the least interval of time after which the periodic motion of a body repeats itself is called the period T.

### Give Two Examples of Periodic Motion

• The motion of the hands of a clock. The period of motion of an hour’s hand is 12 hrs, of a minute’s hand is 1 hour and of the second’s hand of a clock is 1 minute.

• A simple pendulum, when pulled from its rest position to one side and released, makes to and fro motion (oscillatory motion) is said to be periodic.

### Non - Periodic Motion

The type of motion in which the object repeats its motion but not in a fixed interval or period of time. Let’s take the example of a taxi service that provides the inter-city services to the public but there are plenty of taxis to drop the passengers. Each taxi isn’t having a fixed interval of time and not even sure of which taxi would come to pick the passengers at a stop. Such a condition where the pattern isn’t fixed, the motion of these taxis is said to be in non-periodic motion.

### Non-periodic motion examples

• The running of the batsman between the wickets.

• The swinging of the branches of the tree.

The periodic motion and non-periodic motion differ from each other in their way of existence in nature, that are as follows:

## Difference Between Periodic and Non-Periodic Motion

 Parameters Periodic Motion Non-Periodic Motion Motion Repeated motion Non-repetitive motion Time The occurrence of periodic motion is totally related to the time interval. The non-periodic motion doesn’t have such a relevance. Time period It has a time period It has a time of motion. Type of motion Vibratory or oscillatory motion. Displacement of an object Example The motion of a girl sitting in the swing.The motion of the needle of the sewing machine functioning at a constant speed.When the load attached to the spring is pulled once a little from its mean position and left to itself starts vibrating.Mercury in a U-tube.The motion of the tuning fork.The motion of a muller in a motor when operated manually.The motion of the moon around the Sun. An apple falling under the tree.The motion of a bouncing ball under the action of gravity and friction.Clouds gathering on the sky and their motion.The motion of the vehicle at varying speed.Writing on the paper.A footballer running in the field.A ball rolling down in the ground.Performing any activity.Walking on the road.Playing a game.

### Do you now?

• The period of revolution of the earth around the sun is one year.

• The period of rotation of the earth about its polar axis is one day.

• The period of rotation of the moon around the earth in 27.3 days.

• 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.

• The time period of a simple pendulum of infinite length is equal to the radius of the earth i.e. 84.6 minutes.

• The time period of a pendulum clock in a lift falling freely under gravity is infinity.

Q1: What Causes Periodic Motion?

Ans: According to Newton’s first law i.e. the law of inertia states that a body moves in a straight line unless a force is applied to it. A similar concept is applicable for the bodies in a periodic motion. 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.

Q2: Why is Harmonic Motion Periodic?

Ans: A harmonic motion can be represented by the sine wave. A spring, when stretched from its mean position, oscillates to and fro about the mean position under a restoring force which is always directed towards the mean position whose magnitude at any moment is proportional to the displacement of the body from the mean position at that instant. In the absence of friction, the motion tends to remain periodic. In such a case the harmonic motion is periodic.

Q3: Can Other Motions be Periodic?

Ans: All oscillatory motions are said to be periodic motion because each oscillation is completed in a fixed interval of time. All the oscillatory motions are not periodic such as the revolution of the earth is periodic but not an oscillatory motion.

Q4: What are Periodic and Non-Periodic Changes?

Ans: The changes that occur at regular intervals of time are called periodic changes such as the occurrence of day and night, change of periods in your school. The changes which do not take place periodically are called the non-periodic changes such as freezing of ice to water.