Category: Physics Notes PPT

After understanding the electric field it becomes essential to understand what are the effects of the electric field on the source charge. The electrostatic potential or electric potential plays a vital role in electrostatics. The electrostatic potential is the amount of work required in bringing a point charge from a reference point to a specific position against the effect of the electric field. The concept of electric potential is used to demonstrate the effect of the electric field of a source charge in terms of the position within the limits of the electric field. In this article, we will look upon the electric potential formula and detailed information on the electric potential difference equation.

Potential Difference Formula

To understand the potential difference formula, we must be aware of the concepts such as electrostatic potential energy. Before jumping into the potential difference formula let us have a look at the concept of what is potential energy or electric potential energy.

Electric Potential Energy Formula

Whenever an object or a particle is placed in a certain position or configuration, then the external work done on the object will be stored in the form of potential energy. Therefore, in general, potential energy is a form of stored energy. If the work done required to change the position or configuration of an object is more then the potential energy stored in the object will also be more. The magnitude of the potential energy is directly proportional to the external work done on the object.

Let us consider an example, assume that an object of mass m is placed on the ground. To displace the object from the ground to a height of h we need to apply an external force which is equal to mg. Then the work done in bringing the object from ground level to height h will be equal to mgh and it is known as the gravitational potential energy. Thus, the work done on the object from one point to another will be equal to the difference in objective potential energies.

Now, what is electric potential energy? The electrostatic potential energy is almost similar to the gravitational potential energy. We discuss the electric potential energy formula concerning the gravitational potential energy concept. When an electric charge is subjected to an external electric field, then the external work done on the electric charge will be stored in the form of electric potential energy or electrostatic potential energy. Therefore, the electric potential energy is defined as the external work done by an agent in bringing a charge or system of charges from infinity to the required position without accelerating the charge.

Consider a positive charge q placed in an external electric field, let a test charge + [q_{0}] be placed at a point A (say). Due to the electric field around the charge +q, the test charge + [q_{0}] will experience an electrostatic force [F_{e}] directed away (or outward direction) from the charge. Since both the charges are of the same nature the force exerted will be repulsive i.e., [F_{ext} = -F_{e}]

Let the potential energy of the charge + [q_{0}] at point A be UAand it is displaced by a distance dr towards the charge +q. The magnitude of an external force acting on the test charge will be equal to the electrostatic force.

The work done in displacing the test charge from point A to dr distance, we write:

[ Rightarrow  dw = F_{ext} . dr …(1)]

If we want to displace the test charge from point A to point B, then the total work done is given by:

[Rightarrow int_{A}^{B} dw = int_{A}^{B} F_{ext} . dr …(2) ]

We know that Fext=-Fe, therefore equation (2) changes to,

[Rightarrow W = – int_{A}^{B} F_{e} . dr …(3)]

Therefore the total potential energy stored in the charge is equal to the difference in potential energies at point A and point B respectively. So, the electrostatic potential energy formula can be derived by calculating the potential difference at two points.

What is Electrostatic Potential Difference?

Now, let us have a look at what is electrostatic potential and electric potential difference formulas. The electrostatic potential is defined as the electric potential energy per unit charge. The external work done per unit charge is equal to the change in potential of a point charge. Consider an electric charge q and if we want to displace the charge from point A to point B and the external work done in bringing the charge from point A to point B is W_AB  then the electrostatic potential is given by:

[Rightarrow Delta V = V_{A} – V_{B} = frac{W_{AB}}{q} ….(1)]

Where,

[W_{AB}] − The external work done in bringing charge from point A to B. 

Equation (1) is known as the electric potential difference equation or electrostatic potential equation. If the initial position of the charge is at infinity we know that the potential at infinity will be zero therefore we write,

[Rightarrow Delta V = V_{infty} – V_{B} = frac{W_{infty B}}{q}]

[Rightarrow V_{B} = frac{W_{infty B}}{q} … (2)]

Equation (2) is known as the electric potential equation. Therefore, the electrostatic potential is defined as the total external work done in bringing the point charge from infinity to the required position.

Example

1. Calculate the electrostatic potential due to a point charge placed at a distance r.

Ans: The electric potential at a point in an electric field is defined as the amount of external work done in moving a unit positive charge from infinity to that point along any path(i.e., it is path independent) when the electrostatic forces are applied.

Suppose that a positive charge is placed at a point P in a given external electric field. The charge placed at that point will exert an external force due to the presence of an electric field. The electric potential at any point at a distance r from the positive charge +q is given by:

[Rightarrow  Vfrac{kq}{r} …(1)]

Where,

K – is the coulomb constant and is equal to [ frac{1}{4pi epsilon theta}]

r – The position vector.

When external work is done in moving a charge of 1 coulomb from infinity to a particular point due to an electric field against the electrostatic force, then it is said to be 1 volt of the electrostatic potential at a point.

Importance of Electrostatic Potential

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Conclusion

After rea
ding this write-up you have understood the meaning of electrostatic potential and associated concepts like its formulas, work done, and a lot more. It can be seen how these entities vary with distance. One can also use the analogy of electric potential to some extent to understand this concept. 

This concept along with the concept of the electric field will help you in understanding further topics like capacitance better. Questions from these are always expected thus studying these topics is inevitable for any exam, may it be board exams, engineering entrance exams, or medical entrance exams.

Introduction to Entropy Thermodynamic

Students should understand the importance of entropy law as it is very helpful for studying physics. Entropy can be explained in numerous ways. The applications of entropy are useful in thermodynamic stages.  

In 1850, Rudolf, a German physicist, named its entropy. Entropy is a measurement of disorder or randomness found in a system. Many definitions are associated with entropy. In this article, we will know about two definitions of entropy, such as thermodynamic definition as well as statistical definition. 

Entropy Law and Thermodynamics

We will now understand the three laws associated with thermodynamics. 

• The first law of thermodynamics relating to entropy

• The second law of thermodynamics in terms of entropy

• The third law of thermodynamics in terms of entropy

1. First Law of Thermodynamics

This law states that heat is one type of energy that cannot be produced or neither be ruined. Well, thermodynamic processes are there that always consider a state i.e., conservation of energy.

However, heat can be transferred from one place to another, and this sort of energy is only convertible from one form to another. 

Some miscellaneous facts on the first law of thermodynamics

• We notice a surge of entropy when there is a change of state of the mater.

• Also, we encounter the rise of entropy when the number of moles of gaseous products rises more than reactants.

2. Second Law of Thermodynamics

Some specific points are there that can illustrate the entropy and second law of thermodynamics.

• Natural or spontaneous processes are irreversible in terms of thermodynamics.

• Entropy second law of thermodynamics states that the transfer of heat into work is not possible without wasting a certain amount of energy.

• The entropy level for the universe is surging continuously.

• 2nd law of thermodynamics entropy: ∆Stotal =∆Ssurroundings+∆Ssystem >0

The overall sum of the entropy of the system and the surrounding will be above zero.

3. Third Law of Thermodynamics

When the temperature of any solid crystalline has an absolute temperature, then the entropy will appear towards zero. This happens only due to a perfect order that exists in a crystal at absolute zero.

This law has a limitation that it is only applicable for the solid substances which do not have zero entropy at absolute zero such as glassy solid, solid containing a mixture of isotopes.

Entropy Statistical Mechanics

When you talk about the entropy of vaporization, the definition for it can be given as the upsurge of entropy due to the change of a liquid into vapours. 

This phenomenon is happening only due to the rise of molecular movement. This behaviour manifests randomness of motion.

The entropy of vaporization can be stated as the ratio of the enthalpy of vaporization and its boiling point. 

It can be represented as ∆vap S = ∆vap H / Tb 

Spontaneity

Chemical reactions that have Exothermic behaviour possess Spontaneity because ∆Ssurr is positive. This allows the value ∆Stotal to remain positive.

Some of the Endothermic reactions are spontaneous. 

It happens due to ∆Ssystem is positive only. Though ∆Ssurroundings is negative but complete ∆Stotal is positive.

The standards for the change in Free energy are always there for forecasting spontaneity. This concept is superior to entropy change criteria.

This is due to some important requirements that stand only for the free energy change of the system. However, some of the free energy also needs entropy change of both system and surroundings.

Do you know?

Entropy evolves numerous ideas when it comes to nature tending from order to disorder states. It means, the right-hand-side box of molecules existed before the left-side molecules

Conclusion 

Entropy is one of the thermodynamic properties that help us to measure the disorder of a system in detail. We can conclude that when we notice any heat transfer from higher to the lower temperature, the magnitude of entropy decreases. However, in the opposite case, the entropy value increases.

Everything including planets, moons, asteroids, and comets revolve around the sun in their orbits. Our solar system consists of eight planets. The Sun is the only star in our solar system. There are millions of stars in this universe and planets revolving around these stars. The planets revolving outside the solar system revolving around a star other than the sun is called an exoplanet. Scientists have discovered many exoplanets using various methods. These methods used to detect the planets outside the solar system are discussed in detail here.

What is an Exoplanet or Extrasolar Planet?

The term exoplanet comes from combining the words exo meaning external and the planet. The word exo and planet are combined to produce the word exoplanet meaning planets outside the solar system. Any planet outside the solar system which is revolving around stars other than the sun is called an exoplanet. The exoplanets are also called extrasolar planets. These exoplanets orbit their own stars with some being part of entire planetary systems. The exoplanets are made up of the same elements by which the planets in our solar system are made up of. Based on the composition and the structure, each exoplanet differs from the others.

The exoplanets are classified into four types. The different categories of exoplanets are as follows:

The giant or Neptune-like planets are large gaseous exoplanets like the gaseous planets in our solar system. Hot Jupiters are other gaseous exoplanets that closely orbit their stars. Since hot Jupiters are closely orbiting their respective sun, the surface temperature of these hot Jupiters is high. Super earth is another category of exoplanets. Super earth is larger than our earth but smaller than the gas giants. Super earth is terrestrial and is made up of primarily rocky or icy materials. The fourth category of exoplanets is earth analogs. As the name suggests, earth analogs are similar to earth in various ways. The similarities of the earth analogs with our earth include size, composition, and distance from the star.

Methods of Detection of Exoplanets

It is very difficult to detect the exoplanets directly. The main reason that makes the exoplanet unable to detect or identify directly is that exoplanets are very faint to detect. This is because of the brightness of the stars that exoplanets are orbiting around. There are various methods used to detect the exoplanets. Scientists use radial velocity methods to detect and study the exoplanet. Let us learn some methods used by astronomers to detect the exoplanet in detail. We will also discuss the principle behind each method.

Radial Velocity Method

Through radial velocity, an exoplanet can be identified outside the solar system. The radial velocity method measures the motion of the host star in response to the gravitational tug by their planets. The first planet discovered outside the solar system is 51 Pegasi b in 1995. The great discovery was made by Swiss astronomers Michel Mayor and Didier Queloz. They were given the Nobel prize in Physics for their discovery. 

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The exoplanet and the star exert equal amounts of gravitational force according to Newton’s law of gravitation. Even though the exoplanets are small compared to the stars, the gravitational pull of the exoplanet on the star causes the star to wobble. Suppose we are observing the exoplanet orbiting the star. When the position of the exoplanet is between the star and the observer at a particular instant of its orbital motion, the exoplanet pulls the star slightly towards us. When the exoplanet is behind the star, then the exoplanet pulls the star away from us. This causes the wobbling of the star back and forth due to the gravitational tug of the exoplanet on the star. The astronomers look for the wobbling of the stars to identify the exoplanet. 

The astronomers use a spectrograph and powerful telescope to identify the wobbling of the stars. The lights coming from distant stars are examined in a spectrograph. The spectrograph contains dark lines or small dark gaps due to the absorption of light by the atmosphere of the star when the light passes through it. When the star moves toward us due to the gravitational tug, these dark lines shift towards the blue region of the spectrum. When the star moves away from us due to the gravitational pull of the exoplanet, the dark lines shift towards the red end of the spectrum. Therefore, this is how astronomers check if any exoplanet is orbiting a distant star by examining the light spectrum of the star. Through the radial velocity method, astronomers can find the size and shape of the orbits of the extrasolar planet orbiting the star.

Transit Method

The transit method uses the concept of shadows to identify the exoplanet. If we are observing a star from the earth which is orbited by an exoplanet, then the exoplanet will regularly pass through the position between the observer and the star. When the position of the exoplanet is between the star and the earth or the observer from the earth, the exoplanet will block a tiny amount of light coming from the star and reaching the observer. Hence the intensity of light from the star is slightly reduced for a period of time due to the current transit of planets. 

The current transit of planets and their effects is similar to the case of the solar eclipse. A solar eclipse happens when the position of the moon is in between the sun and the earth. The moon will block a certain amount of light coming from the sun from reaching the earth. Similarly, for a brief period of time, the star looks dimmer. This will help the astronomers to identify that an exoplanet is orbiting the star. If the brightness of the distant star is decreased regularly and repeatedly for a brief period of time, it could be due to the reason that the exoplanet is transiting the star. THis is the principle behind the transit method to identify the exoplanet.

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The transit method is also called transit photometry. Through this method, astronomers can measure the size of the exoplanets as well as the time period of the exoplanet orbiting around the star. Astronomers combine the radial velocity method and transit photometry to obtain accurate measurements of the mass of the exoplanets. The density of the exoplanet can also be measured which helps to identify the composition of the exoplanets. The spectroscopy studies of the transit exoplanets help to identify the gases such as hydrogen, sodium, and methane in the upper atmosphere of giants. In 1999, the exoplanet HD 209458b was identified using transit photometry. The exoplanets orbiting close to the stars are identified easily using the transit photometry method.

Gravitational Microlensing Method

Through gravitational microlensing, exoplanets are identified by astronomers. When one celestial body passes in front of another celestial body from our point of view, The close objects’ gravity can bend and magnify the light of a more distant object. This causes the distant object to appear brighter than normal for a short period of time. This is called gravitational microlensing. This gravitational microlensing is a form of gravitational lensing. Gravitational lensing is a physical phenomenon that occurs when a massive body bends the light coming from the source with respect to the observer. A gravitational lens bends the light by the gravity of the massive body. If the bending of light  due to bodies like stars, planets or blackholes, then it is called microlensing.

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If one star passes in fron
t of another distant star, the distant star will temporarily appear brighter for a short period of time. The brightness of the distant star returns to normal once the closer star passes it. But if the star that is passing by is accompanied by an exoplanet, then the brightness of the distant star increases temporarily for the second time as the planet passes in front of it. Therefore astronomers can identify the presence of an exoplanet by observing the distant star’s brightness to intensify twice.

Astrometry Method

Astrometry is the science of precisely measuring the position of an object in the sky. As we have discussed earlier, when an exoplanet is orbiting the star, the exoplanet will exert a gravitational pull on the star which causes the star to slightly move toward the observer on the earth as well as away from the observer depending on the position of the exoplanet. This causes the star to wobble due to the gravitational pull of the exoplanet. So, there is a small relative movement of the star with respect to other stars. This movement with a periodic rhythm can be observed using a powerful telescope. Thereby, astronomers can identify the presence of exoplanets orbiting the star.

 

Direct Imaging Method

Taking a picture of an exoplanet is the most difficult way because of the reason that exoplanets are outshined by the bright stars. The presence of the exoplanet’s faint glow is very very difficult to detect in the bright lights from the stars. In spite of this, astronomers use this technique to discover any exoplanets out there. Astronomers use a black mask called a coronagraph to cover up the star and most of the light coming from the star. If the planet is nearby to the star and is not covered by the coronagraph, then a powerful telescope might be able to detect the reflected light from the exoplanet. This is how the direct imaging technique works.

Exoplanets or extrasolar planets are planets outside the solar system which are orbiting a star other than the sun. Due to the faint glow of these exoplanets in the presence of bright stars, exoplanets are very difficult to identify. Therefore astronomers use different methods to identify the presence of exoplanets. There are five different methods astronomers use to detect and study exoplanets. 

The radial velocity method is the most successful method so far to detect the exoplanet. Astronomers can measure the mass of the exoplanets accurately by combining the radial velocity method and the transit photometry method. There are many exoplanets similar to our earth. The study about exoplanets helps us to find out if there is any possibility of planets having extraterrestrial life outside the solar system.

Energy in quantum mechanics is a complicated affair and is different from how energy is perceived in terms of light energy, thermal energy, etc. in Physics. An example of such a form of energy is Fermi energy. Let’s understand more about Fermi energy and topics related to it, in this article.

The concept of Fermi energy derives its name from the 20th-century Italian physicist, Enrico Fermi, who defined a measure of energy to understand the point at which the electrons in a solid are at their most loosely bonded. Some solids are tighter and are more strongly held together than others, and the difference between the extent to which each one is held together is called the Fermi level. If one were to understand it generally, Fermi level is the highest kinetic energy that can be achieved by an electron at an absolute zero temperature.

More specifically, at absolute zero temperature, the highest kinetic energy that an electron can achieve, i.e. the difference in energy between the highest and lowest states of fermions in a quantum system, is called Fermi energy.

How to Calculate Fermi Energy?

To put a number to the Fermi energy in a system, every state that has equal energy should be organized into sets. These sets shall be in an increasing order, where single particles are added continuously and state with the lowest energy are gradually filled up. The energy in the highest state is how one arrives at the Fermi energy quantity.

 

Here is a simpler way to understand it. The particles are cooled down to absolute zero or at zero Kelvin, and this essentially removes all potential energy from the metal. But when the energy is removed, electrons still continue to move around freely. The ones that move fastest in terms of velocity are moving at Fermi energy.

What is a Fermi Level?

There is a minor difference between Fermi level and Fermi energy, even though in most instances they are used as one and the same. The Fermi level refers to the highest energy level an electron experiences at 0 Kelvin. This “level” is the Fermi level. But the Fermi level would be different from Fermi energy in temperatures that are not absolute. This is why both the terms are necessary.

What are Fermions?

Based on the Fermi-Dirac statistics, when a group of subatomic particles have angular momentum that is odd and have half-integral movement ([ frac{1}{2} or frac{3}{2} spin ]), each of these particles In the system is known as fermions. Leptons, baryons, nuclei of odd mass number, are some examples of particle classes that are classified as fermions by the definition above. Here, it is important to discuss Pauli’s Exclusion Principle. According to it, one quantum state cannot be occupied by more than one particle of this form and type.

Boltzmann Constant

Named after the Austrian physicist Ludwig Boltzmann, the Boltzmann Constant is a physics constant that is found in basic as well as quantum physics in Statistical Mechanics. The constant is symbolized as “k” and has the value of [1.380649 times 10^{-23}] joules per kelvin (K). The constant is relevant to Fermi levels as the constant k allows one to calculate the amount of energy or heat generated in correspondence with random thermal motions of a particle in a substance.

Bonus Information – Band Theory

The Band Theory is an inseparable fundamental theory in solid-state electronics, as it helps a student note the electrical and thermal nature of various solids. The Theory organizes electrons and their behavior in specific states into bands, which represents a range of allowed energies. Every brand has a specific level at which it conducts, and this Fermi level at each band is an important part of the theory and has various practical applications.

Did You Know?

The Band of Solid Theory helps to explain the quantum state that an electron attains inside a solid metal. Each molecule is made up of different discrete energy levels and how an electron function within a molecule is described appropriately in this theory. Fermi level is an important part of this theory which states about the top of the available electron energy levels at low temperatures. The position of the Fermi level for the conduction band is a vital parameter in determining the electrical properties.

The term that is fluid mechanics is in the branch of physics which is concerned with the mechanics of fluids that are the liquids, and the gases, and plasmas as well and the forces on them. It has applications as well in a range which is wide of disciplines, which are including mechanical, and civil, as well as the chemical and biomedical engineering.

We will learn more about the topic that is fluid mechanics in further this article.

What is Fluid Mechanics

The fluid mechanics which is the science that is concerned with the response of fluids to forces exerted upon them. It is said to be a branch which is of classical physics with applications as well of great importance in hydraulic and aeronautical engineering, along with the chemical engineering, and meteorology, and zoology too.

The fluids that are the most familiar is of course water and an encyclopaedia that is said to be of the 19th century which is probably have dealt with the subject under the separate headings of hydrostatics that is the science of water at rest,and hydrodynamics also. The science that is said to be of water that too in motion. The scientist Archimedes founded hydrostatics in about 250 BC which is when according to legend he leapt out of his bath and ran naked through the streets of Syracuse crying “Eureka!” isn’t it funny that it has undergone rather little development since. The foundations of theorem of hydrodynamics that is on the other hand we can say were not laid until the 18th century when mathematicians such as Leonhard Euler and Daniel Bernoulli as well began to explore the consequences that is for a virtually continuous medium like water that is of the principle that is dynamic that Newton had enunciated for systems composed of discrete particles. Their work was said to be continued in the 19th century by several  physicists and mathematicians of the first rank notably G.G. Stokes and William Thomson.

By the end of the century the explanations which had been found for a host of intriguing phenomena that is said to be having the flow of water through tubes and orifices the waves that ships moving through level which is behind them that is the raindrops on window panes and the like. There was still no understanding or we can say proper understanding however that is of problems as fundamental as that of water which is flowing past a fixed obstacle and exerting a force which is drag upon it that is the theory of flow of the potential which generally worked so well in other contexts that resulted yielded that at relatively high flow rates were grossly at variance with experiment. This problem was not properly understood until 1904 when the physicist who was german Ludwig Prandtl introduced the concept of the boundary layer.

The carrier of the Prandtl’s continued into the period in which the first manned aircraft that were developed. We can say that since that time the air flow has been of as much interest to the physicists and the engineers as the water flow. And the hydrodynamics that has as a consequence generally become the dynamics of the fluid. The term which is fluid mechanics that is as used here which generally embraces both the dynamics of fluid and the subject still generally referred to as hydrostatics.

All About Fluid Mechanics

The term that is said to be the fluid mechanics is the study of the behaviour of fluid that is the liquids, the gases, human blood and plasmas which are at rest and in motion. The fluid mechanics that generally has a wide range of applications in mechanical and engineering that is the chemical engineering which is in the system which is biological. And in the subject like astrophysics. In this chapter which is said to be of fluid mechanics and its application as well in the system of biology are presented and discussed. At first that the fluid mechanics term governing the equations and blood properties are explained as well. In the following section which are the different models for blood as a fluid that is non-Newtonian are presented. In addition we can say that the blood flow in three important parts of the human system of cardiovascular arteries, and vein, and capillaries is generally studied and the equations which are presented. Finally we can say that the pulsatile blood flow in the body is introduced.

The term that is fluid mechanics is the study of fluids which is at rest and in motion. A fluid is generally  defined as a material that continuously deforms under a constant load. There are five relationships that are most useful in the problem of fluid mechanics that are named as: the kinematic, the stress, the conservation, the regulating, and the constitutive. The analysis of fluid mechanics can be altered depending on the choice of the system of interest and the volume of interest. which we can say is governed by the simplification of vector quantities. By assuming that a fluid is said to be a continuum we make the assumption that there are no inhomogeneities within the fluid. The term that is viscosity relates the shear rate to the stress which is the shear stress. The definition of a fluid is as Newtonian depends on whether the viscosity is constant at various shear rates.

 

The fluids of the Newtonian have constant viscosities which are said to be fluid non-Newtonian that have a nonconstant viscosity. For most of the applications of biofluid we assume that the fluid is Newtonian.

The studies of the fluid mechanics the systems with fluid such as gas or liquid under static and loads of dynamic. The mechanics that is the fluid mechanics is a branch of continuous mechanics that is in which the kinematics and mechanical behavior of materials are modeled as a continuous mass which is said to be rather than as discrete particles. The relation of fluid mechanics and continuous mechanics has been discussed by Bar-Meir which was in 2008. In the mechanics of fluid mechanics the continuous domain does not hold certain shapes and geometry like for example solids, and in many applications as well, the density of various fluids varies with time and position. Observations have shown some common problems involved in fluid mechanics. 

Have you ever wondered how radio plays a channel of a selected frequency or why the voice of an opera singer shatters a wine glass? Well, it all happens due to the phenomenon of forced oscillation and resonance. Under normal conditions, when there is no external damping or driving force, a system will generally oscillate at its natural frequency. But, when a driving force is applied to the system periodically, some energy is put into the system at a frequency different from the system’s natural frequency of oscillation. The system will now be “forced” to vibrate with the frequency of the external periodic force, giving rise to forced oscillations. The difference between the natural frequency of the system and that of the driving force will determine the amplitude of the forced vibrations; a larger frequency difference will result in a smaller amplitude.

Oscillation can be described as the repetitive motion of an object between two different points or states. The word Oscillation is derived from the Latin term Oscillate which means “to swing”. In simple words, when a body is in to and fro motion with respect to a central axis or point, it is termed as oscillation. You can understand the concept of oscillation very easily by observing the motion of a pendulum. The vibration of the string in instruments like the guitar is also an example of oscillation.

How are Free and Forced Oscillations Different?

Free oscillations differ from forced oscillations in the following respects:

• Free oscillations or vibrations occur in the absence of an external force. But forced oscillations take place under the influence of an external driving force.

• While the frequency of free oscillations depends solely on the source of vibrations, the frequency of forced oscillations is affected by the source of vibration and the frequency of the applied driving force.

• In the case of free oscillations, the frequency of vibration remains constant throughout. However, the frequency of forced oscillations can be altered by changing the frequency of the driving force.

• The amplitude of the vibrations remains constant for free oscillations. But in the case of forced oscillations, the amplitude may increase, decrease, or remain constant.

What is Resonance? 

So what gives rise to resonance oscillation? Resonance is a particular case of forced oscillation. When the frequency difference between the system and that of the external force is minimal, the resultant amplitude of the forced oscillations will be enormous. However, when the two frequencies match or become the same, resonance occurs. Thus, at resonance, the amplitude of forced oscillation is maximal, and the natural oscillating frequency of the system is equal to the frequency of the periodic driving force. 

The following diagram illustrates forced oscillations and resonance:

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Displacement – Time Graphs for Different Oscillations

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Types of Resonance

Resonance can be of the following types:

• Mechanical Resonance: A mechanical system tends to absorb more energy when the natural frequency of vibration of the system matches the frequency of its oscillations. The phenomenon of mechanical resonance may result in extreme vibrations leading to wild swaying motions and often, the collapse of structures like buildings, bridges, trains, and aircraft.

• Acoustic Resonance: The mechanical vibrations that occur in the audible range of the human ear constitute acoustic resonance. It is a branch of mechanical resonance that deals with the vibrations produced within the frequency range of 20 Hz to 20 kHz. Acoustic resonance is a crucial factor for building instruments that use resonators, like the body and strings of a violin, the length of a fluted tube, or the tension of a drum membrane.

• Electrical Resonance: The phenomenon of electrical resonance is observed in electrical circuits. It is used to transmit and receive wireless communication as in cell phones, television, and radio.

• Optical Resonance: Optical resonators or resonant optical cavity is widely used in lasers. It comprises an arrangement of optical components that enables the circulation of a beam of light in a closed path. 

• Orbital Resonance: This is a concept related to celestial mechanics. In the case of orbital resonance, two orbiting bodies mutually exert a periodic and regular gravitational force. As a result, the mutual gravitational effect of the bodies is greatly enhanced.

• Atomic Resonance: The concept of resonance in particle physics pertains to particular quantum mechanical properties observed in an atomic nucleus under the influence of an externally applied magnetic field. Nuclear Magnetic Resonance (NMR) finds application in several scientific techniques like spectroscopy and Magnetic Resonance Imaging (MRI); NMR spectroscopy can be used to study molecules, crystals, and non-crystals, whereas MRI is used in medical imaging procedures.