Name of the University : Mahatma Gandhi University
Department : Applied Physics
Degree : M Sc Physics
Subject Code/Name : AP1C04/Classical Mechanics and Nonlinear Dynamics
Paper : IV
Sem : I
Website : mgu.ac.in
Document Type : Model Question Paper
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/mgu.ac.in/5209-CMS%20Classical%20CMS.pdf
Classical Mechanics & Nonlinear Dynamics :
M.Sc. Degree (PGCSS) Examination :
Faculty of Science :
First Semester :
Related : MGU APH1C02 Thermal and Statistical Physics M.Sc Model Question Paper : www.pdfquestion.in/5208.html
Applied Physics :
AP1C04 Classical Mechanics and Nonlinear Dynamics :
[For 2012 admission Students]
Time: Three Hours
Maximum Weight: 30
Part A :
(Answer any SIX questions. Each question carries a weightage of ONE)
1. What do you mean by inertia tensor?
2. What are normal coordinates and normal modes?
3. Show that Hamiltonian is a constant of motion if Lagrangian does not depend on time explicitly.
4. Why are direction cosines not considered as generalized co-ordinates?
5. What is meant by velocity-dependent potential?
6. What are canonical transformations? What is its importance?
7. Explain the significance of Lagrangian Density.
8. Distinguish between time dependent perturbations and time independent perturbations quoting an example each.
9. State and explain KAM theorem?
10. What do you understand by chaos? Explain with examples. (6 x 1 = 6 weights)
Part B :
(Answer any FOUR questions. Each question carries a weightage of TWO)
11. The Langrangian of two coupled oscillators of mass m each is
L = m x& + x& – mw x + x + mw µ x x . Find out the equations of motions and the normal modes of the system.
12. Show that infinitesimal rotation will commute.
13. Obtain the Langrangian, Hamiltonian and equations of motion for a projectile near the surface of the earth.
14. Show that the transformation Q = 1/p and P = qp2 is canonical.
15. Show that angular acceleration is the same in fixed and rotating co-ordinate systems.
16. Discuss the Kepler problem within the framework of the classical perturbation theory.
(4 x 2 = 8 weights)
Part C :
(Answer any ALL questions. Each question carries a weightage of FOUR)
17. (a) Discuss the theory of a spinning symmetrical top under gravity.
OR
(b) Develop the dynamics of a crystal lattice in one dimension having a diatomic basis. Hence explain acoustic and optical phonon modes
18. (a) Formulate the Hamilton’s least action principle. Derive Lagrange’s equation from Hamilton’s principle.
OR
(b) Define Poisson bracket. Show that (i) invariant under canonical transformations
(ii) Poisson bracket of two constants of motion is itself a constant of motion.
19. (a) Outline the Lagrangian formulation of a continuous system and discuss sound vibrations in a gas.
OR
(b)What are Einstein’s field equations? Explain their importance.
20. (a) Discuss the formulation of canonical perturbation theory. Apply the same to the case of a simple pendulum with finite amplitude.
OR
(b)Using logistic map as an example, explain the route to chaos in dissipative system. (4 x 4 = 16 weights)
Model Question Paper :
V Semester :
PH5B01U- Classical Mechanics And Quantum Mechanics
Instructions :
1. Time allotted : 3 hrs
2. Answer all questions in part A. This contains 4 bunches of 4 objective questions. For each bunch, grade A will be awarded if all the 4 answers are correct, B for 3, C for 2. D for 1 and E for 0. Answer any 5 questions from part B, any 4 from part C and any 2 from part D.
3. Candidates can use ……………………( type of calculator/tables)
Part A : (Objective type- weight 1 each)
Bunch I.
1. The force of constraint (F) does no work in producing virtual displacement (S) because
(a) F and S are parallel (b)F and S are perpendicular
(c) S=0 (d) F=0
2. Einstein’s photoelectric equation is based on the law of conservation of
(a) Momentum (b) charge
(c ) Mass ( d) Energy
3. The conservative nature of a given force F can be tested using
(a) grad F=0 (b) curl F=0
(c) div F=0 (d) F=ma
4 .A system consisting of 3 particles is described in a three dimensional cartesian co- ordinate system. If there are 3 constraints, the number of degrees of freedom of the system is
(a) 3 (b) 6
(c) 9 (d) 12
Bunch II :
5. The physical meaning of normalization of wave function of a particle is that
(a) the wave function is continuous everywhere
(b) the particle exists somewhere in space
(c) the wave function is single valued
(d) the wave function has no significance
6. The wave function of a particle encountering a finite potential step behaves inside the step as if
(a) it is oscillatory
(b) it is exponentially decaying
(c) it is stationary
(d) vanishes at the boundary