Define Periodic , Oscillatory and Vibratory Motion: Definitions, Differences, Examples

Learn Periodic Motion, Oscillatory Motion, and Vibratory Motion with complete Class 11 Physics notes. Understand definitions, characteristics, differences, examples, equilibrium position, restoring force, time period, frequency, FAQs, MCQs, true/false questions, fill in the blanks, and exam-oriented questions in one comprehensive guide. Suitable for NCERT, CBSE, State Boards, and competitive exams - Physicskund

Periodic Motion

A motion that repeats itself after equal intervals of time is called Periodic Motion. The interval after which the motion repeats is known as the time period. In periodic motion, the body returns to the same position and state of motion after every fixed interval of time.

Periodic motion does not necessarily involve motion along the same path or about a fixed point. It may be circular, rotational, linear, or oscillatory. Therefore, the existence of an equilibrium position is not compulsory for periodic motion.

Characteristics of Periodic Motion

The motion repeats after equal intervals of time.
It has a fixed time period.
The path of motion may be circular, rotational, linear, or oscillatory.
An equilibrium position is not necessary.
A restoring force is not required.
Every oscillatory motion is periodic, but every periodic motion is not oscillatory.

Examples of Periodic Motion

Revolution of the Earth around the Sun.
Rotation of the Earth about its axis.
Rotation of a ceiling fan.
Motion of the hands of a clock.
Rotation of the blades of a wind turbine.
Motion of a satellite around the Earth.

Time Period

The time period is the time taken by a body to complete one full cycle or one complete repetition of motion. It is represented by the symbol T.

If a body completes one oscillation, one revolution, or one cycle in a time T, then T is called the time period of that motion.

SI Unit

Second (s)

Importance of Time Period

It tells how quickly a periodic motion repeats itself.
A smaller time period means the motion repeats more rapidly.
A larger time period means the motion repeats more slowly.

Frequency

Frequency is the number of complete oscillations or cycles performed by a body in one second. It is represented by the symbol f.

The SI unit of frequency is hertz (Hz).

Relation Between Time Period and Frequency

The time period and frequency are reciprocal to each other.

\[ f=\frac{1}{T} \]

\[ T=\frac{1}{f} \]

where,

f = Frequency (Hz)
T = Time Period (s)

If the frequency increases, the time period decreases. Similarly, if the time period increases, the frequency decreases. Thus, frequency and time period are inversely proportional to each other.

Oscillatory Motion

Oscillatory motion is a special type of periodic motion in which a body moves repeatedly to and fro about a fixed position called the equilibrium position or mean position.

During oscillatory motion, the body moves alternately on both sides of the equilibrium position. After reaching one extreme position, it returns through the equilibrium position to the opposite extreme position. This process repeats continuously.

Characteristics of Oscillatory Motion

The motion is always to and fro.
It occurs about a fixed equilibrium position.
A restoring force always acts towards the equilibrium position.
It repeats after equal intervals of time.
Every oscillatory motion is periodic.
The displacement changes continuously with time.

Examples of Oscillatory Motion

Simple pendulum.
A child on a swing.
A mass attached to a spring.
A ball oscillating inside a bowl.
Oscillation of a floating cork on water.

Vibratory Motion

Vibratory motion is a special type of oscillatory motion in which a body moves rapidly to and fro about its equilibrium (mean) position. In general, vibrations have a very small amplitude and a high frequency. Since vibratory motion repeats itself after equal intervals of time, it is also a periodic motion.

The terms oscillation and vibration are often used interchangeably because there is no significant scientific difference between them. Generally, low-frequency to-and-fro motion is called oscillation, whereas high-frequency to-and-fro motion is called vibration.

Characteristics of Vibratory Motion

It is a rapid to-and-fro motion about the equilibrium position.
It has a comparatively high frequency.
Its amplitude is usually very small.
A restoring force always acts towards the equilibrium position.
Every vibratory motion is oscillatory.
Every vibratory motion is periodic.

Examples of Vibratory Motion

Vibration of a tuning fork.
Vibration of a guitar or violin string.
Vibration of the diaphragm of a loudspeaker.
Vibration of a mobile phone in vibration mode.
Vibration of a stretched wire.
Vibration of the prongs of an electric bell after striking.

Difference Between Periodic Motion and Oscillatory Motion

Periodic Motion	Oscillatory Motion
A motion that repeats itself after equal intervals of time.	A to-and-fro motion about the equilibrium (mean) position.
It may be linear, circular, rotational, or oscillatory.	It is always a to-and-fro motion along the same path.
An equilibrium position is not necessary.	An equilibrium position is always present.
A restoring force is not necessary.	A restoring force always acts towards the equilibrium position.
Every periodic motion is not oscillatory.	Every oscillatory motion is periodic.
Examples: Revolution of the Earth, rotation of a fan, motion of the hands of a clock.	Examples: Simple pendulum, swing, mass attached to a spring.

Difference Between Oscillation and Vibration

Oscillation	Vibration
General to-and-fro motion about the equilibrium position.	Rapid oscillatory motion about the equilibrium position.
Usually has a lower frequency.	Usually has a higher frequency.
Amplitude may be large.	Amplitude is generally small.
Used for comparatively slow motions.	Used for comparatively fast motions.
Examples: Pendulum, swing.	Examples: Guitar string, tuning fork, loudspeaker diaphragm.

Frequently Asked Questions (FAQ)

1. What is periodic motion?

A motion that repeats itself after equal intervals of time is called periodic motion. The Earth revolving around the Sun and the rotation of a ceiling fan are common examples.

2. What is oscillatory motion?

Oscillatory motion is the repeated to-and-fro motion of a body about its equilibrium position. A simple pendulum is the best example of oscillatory motion.

3. What is vibratory motion?

Vibratory motion is a rapid oscillatory motion about the equilibrium position. It usually has a high frequency and a small amplitude.

4. Is every periodic motion oscillatory?

No. Periodic motion only requires repetition after equal intervals of time. Circular motion is periodic but not oscillatory because it is not a to-and-fro motion.

5. Is every oscillatory motion periodic?

Yes. Every oscillatory motion repeats after equal intervals of time, so every oscillatory motion is periodic.

6. What is an equilibrium position?

The equilibrium position is the position where the net force acting on the body is zero. During oscillation, the body moves on both sides of this position.

7. What is restoring force?

The restoring force is the force that always acts towards the equilibrium position whenever the body is displaced from it.

8. What is the SI unit of time period?

The SI unit of time period is the second (s).

9. What is the SI unit of frequency?

The SI unit of frequency is hertz (Hz).

10. Give one example each of periodic, oscillatory and vibratory motion.

Periodic Motion: Revolution of the Earth around the Sun.
Oscillatory Motion: Simple pendulum.
Vibratory Motion: Vibrating tuning fork.

Multiple Choice Questions (MCQs)

A motion that repeats after equal intervals of time is called
- A) Random Motion
- B) Periodic Motion ✓
- C) Projectile Motion
- D) Rectilinear Motion
Every oscillatory motion is
- A) Circular
- B) Periodic ✓
- C) Random
- D) Rotational
Which of the following is not an oscillatory motion?
- A) Swing
- B) Simple Pendulum
- C) Rotation of a Fan ✓
- D) Spring-Mass System
The SI unit of frequency is
- A) Second
- B) Hertz ✓
- C) Metre
- D) Newton
Vibratory motion generally has
- A) Low Frequency
- B) High Frequency ✓
- C) Zero Frequency
- D) Infinite Time Period
Which force acts during oscillatory motion? Answer: Restoring Force ✓
The motion of a tuning fork is Answer: Vibratory Motion ✓
The Earth revolves around the Sun in Answer: Periodic Motion ✓
A child on a swing performs Answer: Oscillatory Motion ✓
The time taken to complete one cycle is called Answer: Time Period ✓
The reciprocal of time period is Answer: Frequency ✓
The SI unit of time period is Answer: Second ✓
Oscillatory motion occurs about Answer: Equilibrium Position ✓
Every vibration is Answer: Oscillatory Motion ✓
Circular motion is Answer: Periodic but not Oscillatory ✓

True or False

Every periodic motion is oscillatory. False
Every oscillatory motion is periodic. True
Vibrations are high-frequency oscillations. True
Circular motion is oscillatory. False
Oscillatory motion occurs about an equilibrium position. True
Frequency is measured in hertz. True
Time period is measured in seconds. True
A restoring force acts in oscillatory motion. True
A tuning fork performs vibratory motion. True
Every vibration is periodic. True

Fill in the Blanks

Motion that repeats after equal intervals is called Periodic Motion.
The SI unit of frequency is Hertz.
The SI unit of time period is Second.
Oscillatory motion takes place about the Equilibrium Position.
The force acting towards the mean position is called the Restoring Force.
Every oscillatory motion is Periodic.
Vibratory motion generally has High Frequency.
The reciprocal of time period is Frequency.
A pendulum performs Oscillatory Motion.
The Earth revolves around the Sun in Periodic Motion.

Match the Following

Column A	Column B
Simple Pendulum	Oscillatory Motion
Earth around the Sun	Periodic Motion
Tuning Fork	Vibratory Motion
Frequency	Hertz (Hz)
Time Period	Second (s)

Very Short Answer Questions

What is periodic motion?
Periodic motion is the motion that repeats itself after equal intervals of time. For example, the revolution of the Earth around the Sun.
What is oscillatory motion?
Oscillatory motion is the repeated to-and-fro motion of a body about its equilibrium (mean) position.
What is vibratory motion?
Vibratory motion is a rapid oscillatory motion of a body about its equilibrium position. It generally has high frequency and small amplitude.
What is the time period?
The time period is the time taken by a body to complete one full cycle or one oscillation. Its SI unit is second (s).
What is frequency?
Frequency is the number of complete oscillations or cycles performed in one second. Its SI unit is hertz (Hz).
Write the relation between frequency and time period.
\[ f=\frac{1}{T} \] or \[ T=\frac{1}{f} \] where f is frequency and T is time period.
What is the equilibrium (mean) position?
The equilibrium position is the position where the net force acting on the body is zero. During oscillatory motion, the body moves on both sides of this position.
What is restoring force?
The restoring force is the force that acts towards the equilibrium position whenever the body is displaced from it.
Is every periodic motion oscillatory?
No. Circular motion is periodic but not oscillatory because it is not a to-and-fro motion.
Is every oscillatory motion periodic?
Yes. Every oscillatory motion repeats after equal intervals of time; therefore, every oscillatory motion is periodic.

Short Answer Questions

1. Explain periodic motion with examples.

A motion that repeats itself after equal intervals of time is called periodic motion. The body returns to its initial position and repeats the same motion after a fixed time interval known as the time period. Periodic motion may be circular, rotational, linear, or oscillatory. It does not necessarily require an equilibrium position or a restoring force.

Examples:

Revolution of the Earth around the Sun.
Rotation of a ceiling fan.
Motion of the hands of a clock.

2. Explain oscillatory motion with examples.

Oscillatory motion is the repeated to-and-fro motion of a body about its equilibrium position. The body moves alternately on both sides of the equilibrium position due to the action of a restoring force. Oscillatory motion is always periodic.

Examples:

Simple pendulum.
Child on a swing.
Mass attached to a spring.

3. What is vibratory motion? Give examples.

Vibratory motion is a rapid oscillatory motion of a body about its equilibrium position. It usually has a high frequency and a small amplitude. Vibrations are commonly observed in musical instruments and electronic devices.

Examples:

Vibrating tuning fork.
Guitar string.
Loudspeaker diaphragm.
Mobile phone vibration motor.

4. Explain the relationship between time period and frequency.

Time period and frequency are reciprocal quantities. The time period is the time required to complete one oscillation, whereas frequency is the number of oscillations completed in one second.

\[ f=\frac{1}{T} \]

\[ T=\frac{1}{f} \]

If frequency increases, the time period decreases. Similarly, if the time period increases, the frequency decreases.

5. Why is every oscillatory motion periodic but every periodic motion is not oscillatory?

Every oscillatory motion repeats after equal intervals of time, so it is periodic. However, every periodic motion is not oscillatory because periodic motion does not always involve a to-and-fro motion about an equilibrium position. For example, the revolution of the Earth around the Sun is periodic but not oscillatory.

6. What is the importance of the equilibrium position?

The equilibrium position is the central position about which oscillatory motion occurs. At this position, the net force acting on the body is zero. When the body is displaced from this position, a restoring force acts to bring it back.

7. Explain restoring force.

Restoring force is the force that always acts towards the equilibrium position whenever the body is displaced from it. This force is responsible for producing oscillatory motion.

For simple harmonic motion,

\[ F=-kx \]

where F is the restoring force, x is the displacement from the mean position, and k is the force constant. The negative sign indicates that the force acts opposite to the displacement.

8. Distinguish between oscillation and vibration.

Oscillation refers to the general to-and-fro motion about the equilibrium position, whereas vibration refers to rapid oscillatory motion with comparatively high frequency and small amplitude. Scientifically, vibration is considered a special type of oscillation.

9. Give three real-life applications of oscillatory and vibratory motion.

Pendulum clocks for time measurement.
Vehicle suspension systems for reducing shocks.
Musical instruments for producing sound.

10. Give three differences between periodic motion and oscillatory motion.

Periodic motion simply repeats after equal intervals of time, whereas oscillatory motion is a to-and-fro motion about an equilibrium position. Periodic motion may or may not require a restoring force, but oscillatory motion always requires a restoring force. Every oscillatory motion is periodic, but every periodic motion is not oscillatory.

Long Answer Questions

1. Define periodic motion. Explain its characteristics and give suitable examples.

Periodic motion is the motion that repeats itself after equal intervals of time. The fixed interval after which the motion repeats is called the time period. A periodic motion may be circular, rotational, linear, or oscillatory. It does not necessarily have an equilibrium position or a restoring force.

Characteristics

Repeats after equal intervals of time.
Has a fixed time period.
May be circular, rotational, linear, or oscillatory.
Restoring force is not compulsory.
Equilibrium position is not necessary.

Examples

Earth revolving around the Sun.
Rotation of a ceiling fan.
Hands of a clock.

2. Explain oscillatory motion in detail with characteristics and examples.

Oscillatory motion is the repeated to-and-fro motion of a body about its equilibrium position. The body continuously moves on both sides of the mean position due to the restoring force. Oscillatory motion is always periodic because it repeats after equal intervals of time.

Characteristics

To-and-fro motion.
Occurs about the equilibrium position.
Requires restoring force.
Repeats after equal intervals of time.
Every oscillatory motion is periodic.

Examples

Simple pendulum.
Swing.
Spring-mass system.
Ball in a bowl.

3. Differentiate between periodic motion, oscillatory motion and vibratory motion.

Periodic motion is any motion that repeats after equal intervals of time. Oscillatory motion is a special type of periodic motion in which the body moves to and fro about its equilibrium position. Vibratory motion is a rapid oscillatory motion with comparatively high frequency and small amplitude. Thus, every vibration is an oscillation, and every oscillation is periodic, but every periodic motion is not oscillatory.

4. Explain the concepts of time period, frequency, equilibrium position and restoring force.

The time period is the time required to complete one oscillation, while frequency is the number of oscillations completed in one second.

\[ f=\frac{1}{T} \]

The equilibrium position is the position where the net force on the body is zero. When the body is displaced from this position, a restoring force acts towards the equilibrium position to produce oscillatory motion.

5. Prove that every oscillatory motion is periodic, but every periodic motion is not oscillatory.

Oscillatory motion always repeats after equal intervals of time and therefore satisfies the definition of periodic motion. Hence, every oscillatory motion is periodic. However, a periodic motion only needs to repeat after equal intervals of time and does not necessarily involve to-and-fro motion about an equilibrium position. For example, the Earth revolves around the Sun periodically, but it does not oscillate. Therefore, every periodic motion is not oscillatory.