Difference between Natural (Free) Vibrations and Forced Vibrations

Natural (Free) Vibrations:

1.) The vibrations of a body in absence of any resistive or external force are called natural vibrations.

2.) The frequency of vibration depends on the shape and size of the body.

3.) The frequency of vibration remains Constant.

4.) The amplitude of vibration remains constant with time (in absence of surrounding medium).

Forced Vibrations:

1.) The vibrations of a body in a medium in presence of an external periodic force are called forced vibrations.

2.) The frequency of vibration is equal to the frequency of the applied force.

3.) The frequency of vibration changes with change in the frequency of the applied force.

4.) The amplitude of vibration depends on the frequency of the applied force.

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  • Electric Charge and its properties

  • Comparison between electric charge and mass

  • Coulomb′s law and Application

  • Vector form of Coulomb′s Law

  • Force between multiple charges (Superposition principle of electrostatic forces)

  • Electric Line of Force and its Properties

  • Electric field Intensity (Definition) and Electric field Intensity due to point charge

  • Electric Dipole and Derivation of Electric field intensity at different points of an electric dipole

  • Derivation of torque on an electric dipole in an uniform and a non-uniform electric field


  • Electric potential and derivation of electric potential at a point due to point charged particle

  • Work done by a rotating electric dipole in uniform electric field

  • The electric potential at different points of the electric dipole

  • The electric potential energy of an electric dipole in the uniform electric field

  • The electric potential energy of a system of Charges


  • Gaussian Surface and its Properties

  • Gauss's Law for Electric Flux and Derivation

  • Electric field intensity due to point charge by Gauss's Law

  • Electric field Intensity due to a uniformly charged Spherical Shell

  • Electric field intensity due to the uniformly charged solid sphere(Conducting and Non-conducting)

  • Electric field intensity due to thick hollow non-conducting sphere

  • Electric field intensity due to uniformly charged plane sheet and parallel sheet

  • Electric field intensity due to uniformly charged wire of infinite length


  • Capacitance of an Isolated Spherical Conductor

  • Potential Energy of a Charged Conductor

  • Parallel Plate Air Capacitor and Its Capacitance

  • Capacitance of a Parallel Plate Capacitor Partly Filled with Dielectric Slab between Plates

  • Force between the plates of a Charged Parallel Plate Capacitor

  • Energy Stored in a Charged Capacitor



  • Description dielectric materials and their types



  • Combination of cell in the circuit

  • Relation between electromotive force (E), internal resistance (r) and potential difference (V) in a circuit

  • Relation between electric current and drift velocity

  • Derivation of Ohm's Law

  • Kirchhoff's laws for an electric circuits

  • Wheatstone's Bridge

  • Metre Bridge OR Slide Wire Bridge

  • Principle construction and working of potentiometer

  • Difference between Potentiometer and Voltmeter



  • Biot- Savart's Law

  • Motion of Charged Particles in Uniform Magnetic Field

  • Magnetic Field due to a Straight Current-Carrying Conductor of Finite Length

  • Ampere's circuital Law and its modification

  • Magnetic Field at the axis of a current-carrying circular loop

  • Magnetic Field at the center of a current-carrying circular loop

  • Principle, Construction and Working of Current Carrying Solenoid

  • Derivation of force on current carrying conductor in uniform magnetic field

  • Derivation of Force between two long and parallel current-carrying conductors



  • Magnetic Dipole Moment of Current carrying loop

  • Magnetic potential energy of current-loop in a magnetic field

  • Magnetic dipole moment of a revolving electron

  • Conversion of Galvanometer into an Ammeter

  • Conversion of Galvanometer into a Voltmeter



  • Diamagnetic substances and its properties

  • Paramagnetic substance and its properties



  • Mean Value and Root Mean Square Value of Alternating Current

  • Alternating Current Circuit containing Resistance only (R-Circuit)

  • Alternating Current Circuit containing Inductance only (L-Circuit)

  • Alternating Current Circuit containing Capacitance only (C-Circuit)

  • Circuit containing Inductor and Resistor in Series (L-R Series Circuit )

  • Circuit containing Capacitor and Resistor in Series (C-R Series Circuit )

  • Circuit containing Inductor and Capacitor in Series (L-C Series Circuit )

  • Circuit containing Inductor, Capacitor, and Resistor in Series (L-C-R Series Circuit )

  • Power in Alternating Current Circuit

  • Merits and Demerits of Alternating Current in Comparison to Direct Current



  • Faraday's Laws of Electromagnetic Induction

  • Self Induction and its Coefficient

  • Mutual Induction and its Coefficient



  • Classical world and Quantum world

  • Inadequacy of classical mechanics

  • Drawbacks of Old Quantum Theory

  • Bohr's Quantization Condition

  • Energy distribution spectrum of black body radiation

  • Energy distribution laws of black body radiation

  • The Compton Effect | Experiment Setup | Theory | Theoretical Expression | Limitation | Recoil Electron

  • Davisson and Germer's Experiment and Verification of the de-Broglie Relation

  • Significance of Compton's Effect

  • Assumptions of Planck’s Radiation Law

  • Derivation of Planck's Radiation Law

  • de-Broglie Concept of Matter wave

  • Definition and derivation of the phase velocity and group velocity of wave

  • Relation between group velocity and phase velocity ($V_{g}=V_{p}-\lambda \frac{dV_{p}}{d\lambda }$)

  • Group velocity is equal to particle velocity($V_{g}=v$)

  • Product of phase velocity and group velocity is equal to square of speed of light ($V_{p}.V_{g}=c^{2}$)

  • Heisenberg uncertainty principle

  • Generation of wave function for a free particle

  • Physical interpretation of the wave function

  • Derivation of time dependent Schrodinger wave equation

  • Derivation of time independent Schrodinger wave equation

  • Eigen Function, Eigen Values and Eigen Vectors

  • Postulate of wave mechanics or Quantum Mechanics

  • Quantum Mechanical Operators

  • Normalized and Orthogonal wave function

  • Particle in one dimensional box (Infinite Potential Well)

  • Minimum Energy Or Zero Point Energy of a Particle in an one dimensional potential box or Infinite Well

  • Normalization of the wave function of a particle in one dimension box or infinite potential well

  • Orthogonality of the wave functions of a particle in one dimension box or infinite potential well

  • Eigen value of the momentum of a particle in one dimension box or infinite potential well

  • Schrodinger's equation for the complex conjugate waves function

  • Probability Current Density for a free particle in Quantum Mechanics

  • Ehrenfest's Theorem and Derivation

  • Momentum wave function for a free particle

  • Wave function of a particle in free state

  • One dimensional Step Potential Barrier for a Particle



  • Overview and History of Special Relativity

  • Inertial-frame and Non-inertial frame

  • Galilean Transformation Equations and Failure of Galilean Relativity

  • Derivation of Lorentz Transformation's Equations

  • Consequences of Lorentz's Transformation Equations

  • Concept of Simultaneity in Special Relativity

  • Derivation of Addition of Velocity in Special Relativity

  • Variation of Mass with Velocity in Relativity

  • Einstein’s Mass Energy Relation Derivation



  • Nuclear Force and Its Properties

  • Weak nuclear force or interaction and its properties

  • Radioactive Decay and its types

  • Mass Defect, Binding Energy and Binding Energy per nucleon

  • Nuclear Fission and Nuclear Fusion

  • Binding Energy Curve

  • Construction and Working of Nuclear Reactor or Atomic Pile

  • Safety measures for nuclear power plants



  • Description of Force and their Types

  • Work Energy Theorem Statement and Derivation

  • Conservative force and Non Conservative force

  • Conservation Law of linear momentum and its Derivation

  • Relation between angular velocity and linear velocity

  • Relation between angular acceleration and linear acceleration

  • Definition and Derivation of Centripetal Acceleration

  • Definition and Practical Applications of Centripetal Force

  • Motion of body in a vertical circle and its Practical Applications

  • Principle and Proof of Law of Conservation of Energy

  • Definition of work done and its essential condition

  • Force of Friction | Expression for the acceleration and the work done on inclined rough surface| Advantage and Disadvantage



  • Kepler's Laws of Planetary Motion

  • Newton's law for Gravitational Force

  • Deduction of Newton's Law of gravitation from Kepler's Law

  • Relation between gravitational acceleration and gravitational force

  • Gravitational field, Intensity of Gravitational field and its expression

  • Derivation of Gravitational Potential due to Point mass and on the Earth

  • Derivation of Gravitational Potential Energy due to Point mass and on the Earth

  • Expression for Orbital velocity of Satellite and Time Period

  • Variation of Acceleration Due to Gravity



  • Characteristics of Electromagnetic Wave

  • Displacement Current

  • Derivation of Maxwell first equation

  • Derivation of Maxwell's second equation

  • Derivation of Maxwell's third equation

  • Derivation of Maxwell's forth equation

  • Equation of continuity of electromagnetic wave

  • Equation of continuity for current density

  • Electromagnetic wave equation in free space

  • Solution of electromagnetic wave equations in free space

  • Transverse nature of electromagnetic waves

  • Electric and magnetic field vector are mutually perpendicular to each other in electromagnetic wave

  • Electromagnetic wave equation in non conducting media (i.e. Perfect dielectric or Lossless media)

  • Solution of electromagnetic wave equations in non conducting media

  • Electromagnetic Wave Equation in Conducting Media (i.e. Lossy dielectric or Partially Conducting)

  • Solution of electromagnetic wave equations in conducting media

  • Characteristic impedance of electromagnetic wave

  • Poynting Vector and Poynting Theorem

  • Energy flow in the electromagnetic wave in free space

  • Energy density in electromagnetic waves in free space

  • Momentum of electromagnetic wave

  • Radiation pressure of electromagnetic wave



  • Laser and properties of a Laser beam

  • High Monochromaticity of Laser Light

  • Population of energy level and it thermal equilibrium condition

  • Absorption, Spontaneous Emission and Stimulated Emission of Radiation

  • Derivation of Einstein Coefficient Relation

  • Two Level Pumping in Laser

  • Three level pumping in Laser

  • Four level pumping in Laser

  • Application of Lasers

  • Brief Description of Liquid Lasers

  • Principle, Construction and Working of the Ruby Laser

  • Characteristics, Advantages, Disadvantages and Applications of Ruby Laser

  • Distinction between Spontaneous and Stimulated Emission of Radiation

  • Light Detection And Ranging (LIDAR)



  • Light and its properties

  • Refraction of light and its Properties

  • Refraction of light through concave spherical surface

  • Refraction of light through convex spherical surface

  • Refraction of light through a thin lens Or Lens maker's formula

  • Combined focal length and power of two thin lenses in contact



  • Principle Construction, Working and Angular Magnification of Simple Microscope

  • Principle Construction, Working and Angular Magnification of Compound Microscope



  • Analytical expression of intensity for constructive and destructive interference due to Young's double slit

  • Interference of light due to thin film

  • Interference of light due to a wedge shaped thin film

  • Fringe width of wedge shaped thin film for normal incidence

  • Newton's rings in reflected monochromatic light



  • Difference between Fraunhofer and Fresnel diffraction

  • Fraunhofer diffraction due to a single slit

  • Fraunhofer diffraction due to a double slit

  • Missing Order in double slit diffraction pattern

  • Diffraction due to a plane diffraction grating or N- Parallel slits

  • Dispersive power of plane diffraction grating and its expression

  • Difference between interference and diffraction

  • Difference Between Prism Spectra and Grating Spectra

  • Resolving Power of Optical Instrument | Rayleigh Criterion of Resolution



  • Numerical Aperture and Acceptance Angle of the Optical Fibre

  • Comparison of Single Mode and Multimode Index Fibres

  • Comparison of Step Index and Graded Index Fibres

  • Attenuation of optical signal in optical fibre

  • Principle of optical fibre communication



  • Fluid and it's important characteristics

  • Principle of continuity in fluid

  • Bernoulli's Theorem and Derivation of Bernoulli's Equation

  • Principle, Construction and Working of Venturimeter

  • Viscosity, Viscous force and Coefficient of Viscosity



  • Difference between sound waves and light waves

  • Difference between Natural (Free) Vibrations and Forced Vibrations

  • Difference between Natural Vibrations and Damped Vibrations

  • Difference between Forced Vibrations and Resonant Vibrations

  • Intensity of a wave



  • Bohr's Model of Atom

  • Bohr's Theory of Hydrogen-Like Atoms

  • Limitations of Bohr's Model

  • Spectrum of Hydrogen Atom



  • Laws of Photoelectric Emission

  • Failure of wave theory in explaining photoelectric emission effect

  • Einstein Photoelectric Emission



  • Basics and types of nanomaterials

  • Synthesis of Nanomaterials

  • Preparation of Nanostructured Particles By Sol-Gel Method

  • Nanoparticles and Its Properties



  • Difference between Heat and Temperature

  • Difference between Heat Capacity and Specific Heat Capacity

  • Comparison of Isothermal and Adiabatic Processes for an Ideal Gas



  • Concept of Perfect Gas

  • Kinetic theory of ideal gases



  • Superconductor and its properties



  • Origin of Biomedical Signals



  • Basics of Semiconductor Materials

  • Basics of Third Generation Solar Cells and Their Types



  • Renewable Energy Sources



  • Limitations of Dimensional Analysis

  • Description of Errors in Measurement

  • Finding Significant Figures in a Measurement


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