[Physics Class Notes] on Oscillation Pdf for Exam

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{2pi 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{2pi 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-

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.

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.

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. 

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. 

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.