Periodic Motion - Definition, Examples, FAQs

Edited By Vishal kumar | Updated on Nov 30, 2024 11:42 AM IST

Periodic motion is a fundamental concept that undergoes regular repetition over a cycle. It is involved in many objects of the natural world and human-made devices from the swinging of a pendulum to the blades of a fan. Knowledge of periodic motion helps to consider such issues as sound waves and light waves or the motion of celestial objects.

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What is Periodic Motion?
Characteristics of Periodic Motion
Types Of Periodic Motion
Examples of Periodic Motion

Periodic Motion - Definition, Examples, FAQs

What is Periodic Motion?

Periodic Motion occurs when a system or an object repeats its motion after a fixed interval of time, called as Period (denoted by T). Periodic motion is observed in multiple forms and scales, from microscopic particles to macroscopic mechanical systems.

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Periodic motion in Physics is governed by Newton's laws of motion and can often be described by differential equations. For instance, the equation of motion for a simple harmonic oscillator is:

$$
m \frac{d^2 x}{d t^2}+k x=0
$$

where $m$ is the mass, and $k$ is the spring constant.

Characteristics of Periodic Motion

Below points shows the measurable characteristics of Periodic Motion which helps in its analysis:

Period (T): The time taken for one complete cycle of motion.
Frequency ( f ): The number of cycles per unit time, given by $f=\frac{1}{T}$.
Amplitude (A): The maximum displacement from the equilibrium position.
Phase: Indicates the position and direction of the oscillating object at a specific instant.

Types Of Periodic Motion

Periodic motion is majorly divided into five basic types. Let's discuss each type:

Simple Harmonic Motion (SHM)
Oscillatory Motion
Circular Motion
Rotational Motion
Wave Motion

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Simple Harmonic Motion (SHM): Motion in which restoring force is directly proportional to the displacement and acts in the opposite direction, then it is called as simple harmonic motion.

Simple harmonic motion can be mathematically represented as:

$$
x(t)=A \cos (\omega t+\phi)
$$

where $\omega=2 \pi f$ is the angular frequency.

Oscillatory Motion: Motion that moves back and forth about an equilibrium position is called as Oscillatory Motion.

Example- Seasaw

Circular Motion: When an object moves in a circular path with a constant angular velocity, its projection on any axis shows periodic motion.

Example- Rotation of Earth

Rotational Motion: Motion that involves rotation of an earth's object around a fixed axis is called as rotational motion.

Example- Blades of a fan

Wave Motion: A periodic disturbance that transfers energy through a medium or space.

Example- Sound waves, electromagnetic waves.

Related Topics

Examples of Periodic Motion

The revolution of the hands of a wall clock. The periodic time of an hour’s hand of a clock is 12 hrs, of a minute’s hand of a clock is 1 hour, and of the second’s hand of a clock is 1 minute.
A pendulum hung from the wall when pulled from its mean position to one side and loose free makes the pendulum make to and fro motion (oscillatory motion) is said to be periodic.
Oscillating balance wheel
rotating chair
Earth's rotation
Earth's rotation around its axis
Moon's rotation around Earth
Diapason
The blade of the propeller
Hand of the clock
Heart rate

Difference between Periodic and Non-Periodic Motion

Parameters	Periodic Motion	Non-Periodic Motion
Motion	Repeated motion	Non-repetitive motion
Time	The rate of periodic motion is totally dependent on the time interval.	The non-periodic motion doesn’t have such 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	Movement of a girl sitting on a swing. The needle movement of the sewing machine runs at a constant speed. When the load attached to the spring is pulled once from its middle position and to the left, the spring begins to oscillate. Mercury in a U-tube Tubular movement. Movement of the mill in the motor during manual operation. The rotation of the moon around the sun.	Motion of a ball under the action of gravity and friction when throne from some distance Clouds gather in the sky and their movements. Vehicle movement at variable speed. Write on paper. A soccer player is running on the grass. A ball rolls on the ground. Perform any activity. Walking on the street. Play games.

Do you know?

• The earth's rotation around the sun is one year.

• The earth's rotation around its polar axis is one day.

• The period of revolution of the moon around the earth is 27.3 days.

• Oscillating motion can be expressed as sine or cosine waves or a combination thereof. It is due to the oscillating motion known as harmonic motion.

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

• The length of time the pendulum clock in the elevator is in free fall under the influence of gravity is infinite.

Frequently Asked Questions (FAQs)

1. What causes periodic motion?

According to Newton's first law, the law of inertia, if no force is applied to an object, the object moves in a straight line. A similar concept applies to objects that move periodically. A simple pendulum, when pulled out of its resting position (tension is a force), starts to move back and forth and tends to swing until we continue to apply force to the pendulum.

2. Why is simple harmonic motion periodic?

A harmonic motion can be represented by a sinusoidal wave motion. When the spring extends from the middle position, it swings back and forth around the middle position under the action of a restoring force that always points to the middle position. The size of the spring is proportional to the displacement of the object from the middle position at any position. This moment in time. There is no friction, and the movement remains periodic. In this case, the harmonic motion is periodic.

3. Can other actions be periodic?

All swing motions are called periodic motions, because each swing is completed in a fixed time interval. All oscillating motions are not periodic, just like the rotation of the earth is periodic, but not oscillating.

4. What are periodic and non-periodic changes?

The changes that occur regularly are called cyclical changes, such as the occurrence of day and night, and changes in the time of your school. Changes that do not occur periodically are called non-periodic changes, such as B. freezing into water.

5. Soldiers walking on the drawbridge are advised to leave the stairs. Why?

It is recommended that soldiers marching on the suspension bridge leave the steps, because in this case, the frequency of the marching steps corresponds to the natural frequency of the suspension bridge, and resonance occurs, which can greatly increase the vibration.

6. The vibrator of the harmonic oscillating single pendulum is made of ice. How will the rotational cycle change as the ice begins to melt?

The period of oscillation of a simple pendulum will remain constant until the position of the center of gravity of the pendulum remaining after the ice melts remains at the fixed position of the suspension. If the center of gravity of the iceberg is upward after melting, the effective length of the pendulum decreases and, therefore, the period of oscillation decreases. Likewise, if the center of gravity shifts downward, the time interval increases.