# Oscillation

## What is Oscillation?

The repeated back and forth movement between two positions or states of an object is known as oscillation. It can also be referred to as the periodic motion that has the tendency to repeat itself in a regular cycle. For example- a sine wave, with a side-to-side pendulum swing, or the up-down motion with a weight of a spring. The oscillating movement takes place around an equilibrium point or a mean value. This motion is also referred to as the periodic motion. A single oscillation is considered to be a completed movement over a period of time whether it is a side to side movement or an up-down movement.

The motion of the body is said to be oscillatory or vibratory motion if it moves back and forth (to and fro) about a fixed position or point after a regular interval of time. The fixed point about which the body oscillates is called mean position and equilibrium position. Every oscillatory motion is periodic but every periodic motion is not oscillatory. Some of the examples of oscillatory motion are Vibration of wire of sitar and oscillation of the mass suspended from spring.

### Oscillation- Examples

The tides in the sea and the movement of a simple pendulum of the clock are some of the most common examples of oscillations. The vibrations caused by the guitar strings and the other instruments having strings are also examples of oscillations. The movements caused by oscillations are referred to as oscillating movements. For example, oscillating movements in a sine wave or a spring when it moves up and down.

In Oscillating movements, the maximum distance covered or the height in which the oscillations take place is known as the amplitude. In order to complete one complete cycle the time taken is known as the time period of the oscillation. The number of oscillating cycles completed in one second is referred to as the frequency which is the reciprocal of the time period.

$Frequency = \frac{1}{Time}$

### Simple Pendulum

If a heavy point mass is suspended by a weightless, inextensible, and perfectly flexible string from rigid support then this arrangement is called a simple pendulum.

Expression for time period:

For an angular momentum,  sin θ, so that

F = -mgsin θ

= -mgθ

= -( mg/l )y = -Ky

Because Y = lθ, thus the time period of the simple pendulum is: T=2π√L/g. This equation is valid only when the length of a simple pendulum (l) is negligible as compared to the radius of the earth.

If a simple pendulum of density rho is made to oscillate in a liquid of density rho then its time period will increase as compared to that of air and is given by:

$T = \frac{2\pi \sqrt{L}}{1-(\frac{{\sigma }}{\rho})}$

If the bob of a simple pendulum has positive charge q and the pendulum is placed in a uniform electric field E which is in a vertically downward direction then the time period decreases.

$T = \frac{2\pi \sqrt{L}}{g} + \frac{qe}{m}$

Compound Pendulum

Any rigid body which is free to oscillate in a vertical plane about a horizontal axis passing through a point is defined as a compound pendulum

### Oscillation- Types

Oscillation can be classified into the following types which are as follows-

• Free Oscillation

When the body, in an oscillating movement, vibrates with a frequency of its own, the oscillation is known as free oscillation. It has a constant amplitude and period to set the oscillation without any external force. Examples of free oscillation include the vibrations caused by a tuning fork.

• Damped Oscillation

Most of the free oscillations, due to the ever-present damping forces in the surrounding, eventually die out. The type of oscillation that is decreased with time is known as damped oscillation. The damping is caused due to external factors which include friction or air resistance which further reduces the amplitude of the oscillation with time and this results in the loss of energy in the system. Examples of damped oscillation include decaying oscillations of a pendulum.

• Forced Oscillation

When an external period force influences something to oscillate it is known as forced oscillation. In this case, the amplitude experiences damping but due to external energy supplied to it, it remains constant. Examples of forced oscillation include feet moved by a child in order to move the swing.

When the frequency of a driving system is equal to its natural frequency then the phenomenon is known as resonance. The amplitude of the forced oscillations is higher as the damping of the system is less near resonance. A broader reaction is received to drive various frequencies as more damping is there.

• Resonance

When the frequency of external force (driver) is equal to the natural frequency of the oscillator (driven), then this state of driven and driven is known as the state of resonance. In the state of resonance there occurs maximum transfer of energy from driven to the driver. Hence the amplitude of motion becomes maximum. In the state of the resonance frequency of the driver is known as the resonant frequency.

• Coupled Oscillation

A system of two or more oscillations linked together in such a way that there is a mutual exchange of energy between them is called a coupled system. The oscillations of such a system are called coupled oscillations. The examples of coupled systems are as under:

• Two masses are attached to each other by three springs between two rigid supports. The middle spring can be viewed as a coupling between the driven system and the driving system.

• Two simple pendulums hang from the same rigid support with their bobs attached to each other by a spring.

FAQs on Oscillation

1. What are some of the properties of oscillation?

Some of the properties of oscillations are listed below-

• The maximum displacement of an oscillator from the equilibrium position is defined as the amplitude (A).

• The number, per unit time, of one complete oscillation, is defined as the frequency (F).

• The taken, in seconds, for one complete oscillation is defined as the time period (T).

• Time and frequency possess a reciprocal relationship which is F=1/T

2. What is meant by a simple harmonic motion?

When the restoring force in an oscillatory motion acts in the opposite direction of displacement of the object, the motion is known as simple harmonic motion. Using the sine and cosine functions, the simple harmonic motion can be described. It is the most common type of periodic motion. It is used in modeling various systems whether the mass is oscillated about an equilibrium point, for example, a mass on a pendulum or a spring.

3. What is meant by oscillators?

The devices exhibiting motion around an equilibrium point are known as oscillators. For example, in a clock pendulum with each swing the potential energy changes to kinetic energy. The potential energy is maximum at the top of the swing and as it falls that energy is converted into kinetic energy and is driven up back to the other side. Then again the kinetic energy is dropped to zero and the potential energy gets high which powers the return of the swing. The frequency is translated via gears of the swing to mark the time. If the clock is not corrected by the spring, the pendulum will lose energy over time to friction.

4. What is meant by oscillating waves?

When in an extended medium the oscillation process occurs, it is known as an oscillating wave. There are a vast amount of oscillating particles in an extended medium, all of which are interconnected. When an oscillation pulse is received in one of these particles, it becomes the center of a propagating wave movement. A wave can be described as the spatial and temporary periodic process where only energy is transported without any transportation of matter.

5. What are the factors affecting the periods of oscillation?

The period of oscillation is, most primarily, directly proportional to the length of the arm and it is also inversely proportional to gravity. When there is an increase in the length of the arm of the pendulum, there is a subsequent increase in the period. When there is a decrease in the length of the arm, the period also decreases. If the gravitational acceleration is stronger, the smaller the period.

6. Define the term oscillation?

The motion of the body is said to be oscillatory or vibratory motion if it moves back and forth (to and fro) about a fixed position or point after a regular interval of time. The fixed point about which the body oscillates is called mean position and equilibrium position. Every oscillatory motion is periodic but every periodic motion is not oscillatory. Some of the examples of oscillatory motion are Vibration of wire of sitar and oscillation of the mass suspended from spring.

7. Explain the different types of motion?

The different types of motion are discussed below:

• Periodic Motion: Any motion which repeats itself after a regular interval of time is called periodic motion or harmonic motion. The constant interval of time after which motion is repeated is called the time period.

• Oscillatory Motion: The motion of the body is said to be oscillatory and vibratory motion if it moves back and forth about a fixed point after a regular interval of time.

• Simple Harmonic Motion: It is the simplest form of vibratory motion. It is of various types like:

1. Linear Simple Harmonic Motion

2. Angular Simple Harmonic Motion

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