Module-I Oscillations and Waves Free Oscillations: Definition of SHM, derivation of equation for SHM, Mechanical simple harmonic oscillators (mass suspended to spring oscillator), complex notation and phasor representation of simple harmonic motion. Equation of motion for free oscillations, Natural frequency of oscillations. Damped and forced oscillations: Theory of damped oscillations: over damping, critical & under damping, quality factor. Theory of forced oscillations and resonance, Sharpness of resonance. One example for mechanical resonance. Shock waves: Mach number, Properties ofShock waves, control volume. Laws of conservation of mass, energy and momentum. Construction and working of Reddy shock tube, applications of shock waves. Numerical problems MODULE-II Elastic properties ofmaterials: Elasticity: Concept of elasticity, plasticity, stress, strain, tensile stress, shear stress, compressive stress, strain hardening and strain softening, failure (fracture/fatigue), Hooke's law, different elastic moduli: Poisson's ratio, Expression forYoung's modulus (Υ), Bulk modulus (Κ) and Rigidity modulus (η) in terms of and β. Relation between Υ, η andK, Limits ofPoisson's ratio. Bending ofbeams: Neutral surface and neutral plane, Deήvation of expression for bending moment. Bending moment of a beam with circular and rectangular cross section. Single cantilever, derivation of expression for Υ oung's' modulus. Torsion of cylinder: Expression for couple per unit twist of a solid cylinder (Derivation), Torsional pendulum-Expression for peήod of oscillation. Numerical problems. MODULE-III Maxwell's equations, ΕΜ waves and Optical fibers Maxwell's equations: Fundamentals of vector calculus. Divergence and curl of electric field and magnetic field ( static ), Gauss' divergence theorem and Stokes' theorem. Descήption of laws of electrostatics, magnetism and Faraday's laws of ΕΜΙ. Current density & equation of Continuity; displacement cuπent (with deήvation) Maxwell's equations in vacuum. ΕΜ Waves: The wave equation in differential form in free space (Derivation of the equation using Maxwell's equations), Plane electromagnetic waves ιη vacuum, their transverse nature, polarization ofEM waves ( Qualitative). Optical fibers: Propagation mechanism, angle of acceptance. Numerical aperture. Modes of propagation and Types of optical fibers. Attenuation: Causes of attenuation and Mention of expression for attenuation coefficient. Discussion of block diagram of point to point communication. Merits and demeήts Numerical problems. MODULE-IV Quantum Mechanics and Lasers Quantum mechanics: Introduction to Quantum mechanics, Wave nature of particles, Heisenberg's uncertainty principle and applications (ηοη confinement of electron in the nucleus), Schrodinger time independent wave equation, Significance ofWave function, Normalization, Particle in a box, Energy eigen values of a particle in a box and probability densities. Lasers: Review of spontaneous and stimulated processes, Einstein's coefficients ( deήvation of expression for energy density). Requisites of a Laser system. Conditions for laser action. Pήnciple, Construction and working ofCO2 and semiconductor Lasers. Application of Lasers in Defense (Laser range finder) and Engineering (Data storage). Numerical problems MODULE-V Material science Quantum Free electron theory of metals: Review of classical free electron theory, mention of failures. Assumptions of Quantum Free electron theory, Mention of expression for density of states, Ferrni-Dirac statistics ( qualitative ), Ferrni factor, Ferrni level, Derivation of the expression for Ferrni energy, Success ofQFET. Physics of Semiconductor: Ferrni level in intrinsic semiconductors, Expression for concentration of electrons in conduction band, Hole concentration in valance band (only mention the expression), Conductivity of semiconductors(deήvation), Hall effect, Expression for Hall coefficient ( derivation) Dielectric materials: polar and non-polar dielectήcs, internal fields in a solid, Clausius-Mossotti equation(Deήvation), mention of solid, liquid and gaseous dielectrics with one example each. Application of dielectήcs in transforrners. Numeήcal problems.
