Course

Unit 1

Small oscillations in bound systems: Harmonic approximation, linearity, superposition principle; damped, over damped and critically damped oscillations, relaxation time, use of complex variables; steady-state response of a damped spring-mass system under sinusoidal forces, phase lag, resonance, Q-value, absorption bandwidth, amplification, impedance in mechanical and electrical systems. [8+2] (Ref.1, 5)

Unit 2

Transverse oscillations: small oscillation approximations; Free oscillations of systems with two degrees of freedom – 2D harmonic oscillator, longitudinal or transverse oscillations two coupled masses or coupled pendulums, normal modes. Linear chain of coupled pendulums: semi-Propagation of undamped free waves, dispersion relation, mechanical band-pass filter. (Ref.4, 5) [6+2]

Unit 3

Free oscillations in systems with many degrees of freedom: Transverse waves in strings, wave equation, boundary conditions, standing waves, harmonics, wave velocity, wave number, and dispersion relation; general motion and Fourier series. (Ref.4) [3+1]

Travelling solutions, superposition of waves, beats, phase and group velocities, bandwidth theorem (without proof). Forced oscillations and characteristic impedance of a travelling wave, boundary conditions for reflection and transmission; reflection and transmission coefficients (results only); energy flux, reflection and transmission of energy – intensity coefficients (results only); impedance matching and its importance in electrical circuits. (Ref.5) [6+2]

Unit 4

Geometrical Optics: Fermat’s principle and Snell’s laws, total internal reflection, prisms, general theory of image formation, plane and spherical mirrors, thick and thin lenses and lens combinations, aberrations, cardinal points, optical systems. [8+2]

Unit 5

Interference: coherence, interference by division of wave front: Young’s double slit, Fresnel’s bi- prism; interference by division of amplitude: Thin-films, Newton’s rings, basic ideas of Michelson and Fabry-Perot interferometers. Fraunhofer diffraction; Rayleigh criterion and resolving power; diffraction gratings. Polarization: linear and circular polarization; double refraction and optical rotation, polarizers and quarter waveplate, Malus law. [7+3]

Description: Building upon the first introductory course on mechanics, this course is the first part of the two courses that introduces advanced techniques in mechanics covering topics of vector kinematics and dynamics, energy methods, momentum and angular momentum, central force and damped and forces oscillatory motion, coupled oscillations and mechanical waves in elastic media from an intermediate level book on mechanics.

Course Outcomes: After successful completion of this course, students shall be able to

1. Apply the principles of simple harmonic motion to simple physical systems,
2. Apply principles of mechanics to derive equations of coupled oscillations and mechanical waves.
3. Apply principles of mechanics to arrive at wave equations in a string and deduce its behaviour and associated properties
4. Apply principles of ray optics to calculate images formation in mirror and lens systems and other related parameters of optical systems.
5. Apply the concepts in interference and diffraction to calculate interference fringe pattern parameters in Newton’s rings and other optical systems, calculate diffraction intensity patterns, the
   resolving power of a few optical systems, apply the concepts of polarization to intensities of light passing through polarizers, optical rotation and other related parameters

Evaluation Pattern: As in the rules for Assessment Procedure (R.14)

Skills and Employability: The entire contents of this course, tutorials and assignments lays conceptual/theoretical foundation for application of laws of physics to problems of scientific interest and builds skills required for a career as an educator/academician in schools, colleges, universities and coaching centres, as a professional researcher in government/industrial research organizations, and as a communicator of science in general.

1. Vibrations and Waves, A.P. French
2. Berkeley Physics Vo. 3, Waves. Wiley India.
3. H.J. Pain, Vibrations and Waves, 6th Edition.
4. EM waves & Optics: Ch. 34-37 of Halliday, Resnick, & Walker, Fundamentals of Physics, 10th Ed. Or equivalent material in Eugene Hecht.
5. Ajoy Ghatak, Optics, 7th Ed., TMH