machanics and waves oscillations
UNIT-1
1. Mechanics of Particles
Review of Newton’s Laws of Motion, Motion of variable mass system, Motion of a rocket, Multistage rocket, Concept of impact parameter, scattering cross-section, Rutherford scattering-Derivation.
2. Mechanics of Rigid bodies
Rigid body, rotational kinematic relations, Equation of motion for a rotating body, Angular momentum and Torque Moment of inertia tensor, Euler equations, Precession of a spinning top, Gyroscope, Precession of the equinoxes
Unit-II
3. Motion in a Central Force Field
Central forces, definition and examples, characteristics of central forces, conservative nature of central forces, Equation of motion under a central force, Kepler’s laws of planetary motion- Proofs, Motion of satellites, Basic idea of Global Positioning System (GPS), weightlessness, Physiological effects of astronauts
UNIT-III
4. Relativistic Mechanics
Introduction to relativity, Frames of reference, Galilean transformations, Michelson-Morley experiment, negative result, Postulates of Special theory of relativity, Lorentz transformation, time dilation, length contraction, variation of mass with velocity, Einstein’s mass-energy relation
Unit-IV
5. Undamped, Damped and Forced oscillations: (07 hrs) Simple harmonic oscillator and solution of the differential equation, Damped harmonic oscillator, Forced harmonic oscillator – Their differential equations and solutions, Resonance, Logarithmic decrement, Relaxation time and Quality factor.
6. Coupled oscillations
Coupled oscillators-Introduction, Two coupled oscillators, Normal coordinates and Normal modes- N-coupled oscillators and wave equation
Unit-V
7. Vibrating Strings
Transverse wave propagation along a stretched string, General solution of wave equation and its significance, Modes of vibration of stretched string clamped at ends, Overtones and Harmonics,Melde’s strings.
8. Ultrasonics
Ultrasonics, General Properties of ultrasonic waves, Production of ultrasonics by piezoelectric and magnetostriction methods, Detection of ultrasonics, Applications of ultrasonic waves, SONAR