Syllabus Of B.Sc Physics Punjab University

I am pursuing B.Sc (H.S.) Physics from Punjab University, Chandigarh and I loss my old syllabus and my exams are near so I have not enough time to purchase it from market so can you please provide me the syllabus, if possible provide me it in a pdf file?

Hello sir, I’m pursuing B.Sc from Punjab University. Now I’m looking for the syllabus of b.Sc physics subject in Punjab University. Is there any one has presented the syllabus then please provide me?

[Raman Vij]

I was founded syllabus and schemes of physics paper in b.sc course. In Punjab university provides its B.Sc.(Physics) Part-II ( IIIrd and IVth Semester) scheme for session 2012-13, 2013-14, 2014-15.

So here I’m providing you Semester IV Paper I Statistical Physics And Thermodynamics-II:


SECTION-A

Statistical definition of entropy, Change of entropy of a system, Additive nature of entropy, Law of increase of entropy, Reversible and irreversible process and their examples. Work done in a reversible process. Examples of increase of entorpy in natural processes, Entropy and disorder, Brief review of terms and laws of thermodynamics, Carnot’s cycle, Entropy changes in Carnot cycle. Applications of thermodynamics to thermoelectric
effect. Change of entropy along a reversible path in a P.V. diagram, Entropy of a perfect gas, Equation of state of an ideal gas from simple statistical consideration, Heat death of the universe.

SECTION-B

Derivation of Maxwell’s thermo dynamical relations, Cooling produced by adiabatic streching, Adiabatic compression, Change of internal energy with volume, specific heat at constant pressure and constant volume, Expression for Cp -Cv , Change of state and Clayperon equation, Thermo dynamical treatment of Joule-Thomson effect, Use of Joule-Thomson effect, liquefiction of helium, Production of very low temperature by adiabatic demagnetization.


Here I’m also attaching a file for syllabus of Syllabus Of B.Sc Physics Punjab University:

syllabus of Syllabus Of B.Sc Physics Punjab University 2012-2015


SEMESTER III

PAPER I : STATISTICAL PHYSICS AND THERMODYNAMICS-I

Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections A, B and C . There will be four questions from Sections A and B each and each question will carry 08 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


Section A

Basic ideas of statistical physics. Scope of statistical physics. Basic ideas about probability, distribution of four distinguishable particles in two compartment of equal size. Concept of macro states. microstates, thermodynamic probability, Effects of constraints on the system, Distribution of n particles in two compartments, Deviation from the state of maximum prabability, equilibrium state of dynamic system, Distribution of distinguishable n particles in k compartments of unequal sizes.

SECTION-B

Phase space and its division into elementary cells, Three kinds of statistics. The basic approach in the three statistics. Maxwell Boltzman (MB) statistics applied to an ideal gas in equilibrium. Experimental verification of Maxwell Boltzman law of distribution of molecular speeds, Need for quantum statistics-Bose-Einstein (B.E.) statistics, Derivation of Planck’s law of radiation, Deduction of Wien’s displacement law and Stefan’s law from Planck’s law, Fermi-Dirac (F.D.) statistics, Comparison of M.B., B.E. and F.D. statistics.

TEXT BOOKS

1. Statistical Physics and Thermodynamics, V.S. Bhatia (Sohan Lal
Nagin Chand, Jalandhar)
2. Statistical Physics and Thermodynamics, A.K. Sikri (Pardeep
Publication, Jalandhar)
3. A Treatise on Heat, M.N. Saha & B.N. Srivastava, (The Indian
Press pvt. Ltd., Allahabad) 1965.

REFERENCE BOOKS

1. Statistical Mechanics : An Introductory Text, Bhattacharjee, J.K.
(Allied Pub., Delhi) 2000.
2. Statistical Physics, Bhattacharjee, J.K. (Allied Pub., Delhi) 2000.
3. Statistical Mechanics, B.B. Laud (Macmillan India Ltd), 1981.



PAPER II : OPTICS

Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections.: A, B and C . There will be four questions from Sections A and B each and each question will carry 08 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


SECTION-A

Interference :Concept of coherence, Spatial and temporal coherence. Coherence time, Coherence length, Area of coherence,Conditions for observing interference fringes, Interference by wave front division and amplitude division, Michelson’s interferometer—working, Principle and nature of fringes, Interference in thin films, Role of interference
in anti-reflection and high reflection dielectric coatings. Multiple beam intereference, Fabry-Perot interferometer, Nature of fringes, Newton Rings.

SECTION-B

Diffraction : Huygens-Fresnel theory, half-period zones, Zone plates, Distinction between Frensel and Fraunhofer diffraction, Fraunhofer diffraction at rectangular and circular apertures, Effects of diffraction in optical imaging, resolving power of telescope. The diffraction grating, its use as a spectroscopic element and its resolving power, Polarization :
Concept and analytical treatment of un-polarized, plane polarized and elliptically polarized light. Double refraction, Nicol prism, Sheet polarizer, Retardation plates, Production and analysis of polarized light (quarter and half wave plates).



TEXT BOOKS

1. Fundamentals of Optics, F.A. Jenkins and Harvery E. White (McGraw Hill) 4th edition, 2001.

2. Optics, Ajoy Ghatak (McMillan India) 2nd edition, 7th reprint 1997.

3. Introduction to Atomic Spectra, H.E. White (McGraw Hill Book Co.

REFERENCE BOOK

1. Optics, Born and Wolf (Pergamom Press), 3rd edition, 1965.






PAPER III : QUANTUM MECHANICS-I

Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections.: A, B and C . There will be four questions from Sections A and B each and each question will carry 08 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


SECTION-A

Formalism of Wave Mechanics : Brief introduction to need and development of quantum mechanics, Wave-particle duality, de-Broglie hypothesis, Complimentarity and uncertainty principle, Gaussian wave-packet, Schrodinger equation for a free particle, operator correspondence and equation for a particle subject to forces. Normalization and probability
interpretation of wave function, Super position principle, Expectation value, probability current and conservation of probability, Admissibility conditions on the wave function. Ehrenfest theorem, Fundamental postulates of wave mechnics, Eigen functions and eigen values. Operator formalism, Orthogonal systems, Expansion in eigen functions, Hermitian operators. Simultaneous eigen functions. Equation of motion.

SECTION-B

Problems in one and three dimensions : Time dependent Schrodinger equation. Application to stationary states for one dimension, Potential step, Potential barrier, Rectangular potential well, Degeneracy,Orthogonality, Linear harmonic oscillator, Schrodinger equation for spherically symmetric potential, Spherical harmonics. Hydrogen atom energy levels and eigen functions. Degeneracy, Angular momentum.



TEST BOOKS

1. Quantum Mechanics by V.K. Thankappan.

2. A Text Book of Quantum Mechanics, P.M. Mathews and K.
Venkatesan, (Tata McGraw Hill Pub. Co. Delhi), 2002.

3. Quantum Mechanics,J.L. Powell and B. Crasemann (Narosa
Pub. House, N. Delhi) 1997.


Semester- III

PAPER- IV PRACTICAL
Maximum Marks: 30 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 60


1. The student will be asked to perform one experiment out of the experiments mentioned in the syllbus.

2. The distribution of marks is as follows :
(i) One full experiment requiring the student to take some data, analyse it and draw conclusions-(candidates are expected to state their results with limits of error. (20)
(ii) Viva-Voce (05)
(iii) Record(Practical File) (05)

3 There will be one session of 03 hours duration. The paper will consist of 08 experiments out of which an examinee will mark 06 experiments and one of these is to be alloted by the external examiner.

4 Number of candidates in a group for practical examination should not exceed 12.

5. In a single group no experiment be allotted to more than three students in any group.

6. The student should determined Std Deviations and probable error in the calculations whereas needed.

LIST OF EXPERIMENTS
1 Adiabatic expansion of a gas
2 Thermal expansion of crystal using interference fringes
3 Probability distribution using coloured dice coins.
4 To determine the refractive index of liquid using spectrometer
5 To determine the Cauchy’s constants
6 To study the refractive index of doubly refracting prism
7 To determine the wave length of a given light using bi-prism
8 To determine the resolving power of a telescope
9 To determine the principal points of a lens system
10 Study the photoelectric effect and determine the value of Planck’s constant
11 To study the gas discharge spectrum of hydrogen
12 To determine the angle of wedge using interference method
13 Calculation of days between two dates of a year
14 To check if triangle exists and the type of the triangle.

TEXT AND REFERENCE BOOKS
1. A Laboratory Manual of Physics for Undergraduate Classes, D.P.
Khandelwal.

2. B.Sc. Practical Physics, C.L. Arora.

3. Computer Programming, R.C. Verma, V.K. Mittal & S.C. Gupta
(Vishal Pub.), 2003.

4. FORTRAN 77 and Numerical Methods, C. Xavier (New Age Int.
Pvt. Ltd., N. Delhi), 1996.

5. Computer Oriented Numerical Methods, V. Rajaraman (Prentice Hall
of India., N. Delhi), 1998.

SEMESTER IV

PAPER I : STATISTICAL PHYSICS AND THERMODYNAMICS-II

Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections.: A, B and C . There will be four questions from Sections A and B each and each question will carry 08 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


SECTION-A

Statistical definition of entropy, Change of entropy of a system, Additive nature of entropy, Law of increase of entropy, Reversible and irreversible process and their examples. Work done in a reversible process. Examples of increase of entorpy in natural processes, Entropy and disorder, Brief review of terms and laws of thermodynamics, Carnot’s cycle, Entropy changes in Carnot cycle. Applications of thermodynamics to thermoelectric
effect. Change of entropy along a reversible path in a P.V. diagram, Entropy of a perfect gas, Equation of state of an ideal gas from simple statistical consideration, Heat death of the universe.

SECTION-B

Derivation of Maxwell’s thermo dynamical relations, Cooling produced by adiabatic streching, Adiabatic compression, Change of internal energy with volume, specific heat at constant pressure and constant volume, Expression for Cp -Cv , Change of state and Clayperon equation, Thermo dynamical treatment of Joule-Thomson effect, Use of Joule-Thomson effect, liquefiction of helium, Production of very low temperature by adiabatic demagnetization.

TEXT BOOKS

1. Statistical Physics and Thermodynamics, V.S. Bhatia (Sohan Lal
Nagin Chand, Jalandhar)
2. Statistical Physics and Thermodynamics, A.K. Sikri (Pardeep
Publication, Jalandhar)
3. A Treatise on Heat, M.N. Saha & B.N. Srivastava, (The Indian
Press pvt. Ltd., Allahabad) 1965.

REFERENCE BOOKS

1. Statistical Mechanics : An Introductory Text, Bhattacharjee, J.K.
(Allied Pub., Delhi) 2000.
2. Statistical Physics, Bhattacharjee, J.K. (Allied Pub., Delhi) 2000.
3. Statistical Mechanics, B.B. Laud (Macmillan India Ltd), 1981.

PAPER-II LASERS
Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections.: A, B and C . There will be four questions from Sections A and B each and each question will carry 08 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


SECTION-A

Laser Fundamentals : Derivation of Einstein’s relations. Concept of stimulated emission and population inversion. Broadening of spectral lines, natural, collision and Doppler broadening. Line width, Line profile, Absorption and amplification of a parallel beam of light passing through a medium. Threshold condition, Introduction of three level and four level
laser schemes, elementary theory of optical cavity, Longitudinal and transverse modes.

SECTION-B

Laser Systems : types of lasers, Ruby and Nd: YAG lasers, He-Ne and CO2 lasers-construction, mode of creating population inversion and output characterstics. Semiconductor lasers, Dye lasers, Q-switching, Mode locking, Applications of lasers–a general outline. Basics of holography.



TEXT BOOKS

1. Laser Fundamentals, W.T. Silfvast (Foundation Books), New Delhi,
1996.
2. Lasers and Non-linear Optics, B.B. Laud (New Age Pub.), 2002.

REFERENCE BOOK

1. Lasers, Svelto (Plenum Press), 3rd Ed., New York.




PAPER III : QUANTUM MECHANICS-II

Maximum Marks: 40 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 40


Instruction for the Paper Setter

The question paper will consist of Three Sections.: A, B and C . There will be four questions from Sections A and B each and each question will carry 06 marks. Section C will consist of one compulsory question having eight parts of short answer type covering the whole syllabi. Each part will carry one mark.

Instruction for the candidates

1) Candidates are required to attempt two questions each from Section A and B of the question paper. Section C is compulsory.

2) Use of non programmable calculator is allowed in the examination centre but this will not be provided by the University/College.


SECTION-A

One Electron Atomic Spectra : Excitation of atom with radiation. Transition probability, Spontaneous transition. Selection rules and life time. Spectrum of hydrogen atom. Frank Hertz Experiment, Line structure, Normal Zeeman effect, Electron spin, Stern Gerlach experiment, Spin orbit coupling (electron magnetic moment, total angular momentum),Hyperfine structure, Examples of one electron systems, Anomalous,Zeeman effect, Lande-g factor (sodium D-lines).

SECTION-D

Many Electron System Spectra :Exchange symmetry of wave functions, exclusion principle, Shells, Sub shells in atoms, atomic spectra (Helium), L.S. coupling, Selection rules, Regularities in atomic spectra, Interaction energy, X-ray spectra, Mosley law, Absorption spectra. Auger effect. Molecular bonding, Molecular spectra, Selection rules, Symmetric structures, Rotational, vibrational electronic level and spectra of molecules,
Raman spectra.



TEXT BOOKS

1. Concepts of Modern Physics, Arthur Beiser (McGraw Hill Pub.
Co., Delhi, 9th ed.), 1995.

2. Elements of Modern Physics, S.H. Patil (McGraw Hill), 1998.

REFERENCE BOOKS

1. Quantum Mechanics, E. Merzbacher (John Wiley, 2nd ed.)
2. Fundamental of Molecular Spectroscopy, C.N. Banwell (Tata
McGraw Hill Pub. Co., Delhi), 2001.
3. Atomic Spectra, H.G. Kuhn (Longmans), 2nd ed., 1969.
4. Introduction to Quantum Mechanics, L. Pauling and E.B. Wilson
(Tata McGraw Hill Pub. Co., Delhi), 2002.
5. Quantum Mechanics, W. Greiner (Springer Verlag), 1994.

Semester- IV

PAPER IV PRACTICAL
Maximum Marks: 30 Time Allowed: 3 Hours
Pass Marks: 35 % Total Teaching Lectures: 80


1. The student will be asked to perform one experiment out of the experiments mentioned in the syllbus.

2. The distribution of marks is as follows :
(i) One full experiment requiring the student to take some data, analyse it and draw conclusions-(candidates are expected to state their results with limits of error. (20)
(ii) Viva-Voce (05)
(iii) Record(Practical File) (05)

3 There will be one session of 03 hours duration. The paper will consist of 08 experiments out of which an examinee will mark 06 experiments and one of these is to be alloted by the external examiner.

4 Number of candidates in a group for practical examination should not exceed 12.

5. In a single group no experiment be allotted to more than three students in any group.

6. The student should determined Std Deviations and probable error in the calculations whereas needed.

LIST OF EXPERIMENTS
1. Thermal conduction in poor conductor (variation with geometry) by Lee’s method
2. Thermo e.m.f. calibration comparison
3. Total radiation law, temperature dependence of radiation
4. Study of rotation of plane of polarization with a polarimeter.
5. Set up Newton’s rings to determine wave length of sodium light
6. To determine the wave length and dispersive power using plane diffraction grating (Use Hg source)
7. To determine the resolving power of a grating
8. To measure an inaccessible height using sextant
9. To determine the divergence and wave length of a given laser source.
10. To study the absorption spectra of iodine vapours
11. To determine the ionization potential of mercury
12. Study of variation of light intensity using photovoltaic cell/inverse square law
13. To determine the angle of wedge using interference method
14. Calculation of days between two dates of a year
15. To check if triangle exists and the type of the triangle.
TEXT AND REFERENCE BOOKS
1. A Laboratory Manual of Physics for Undergraduate Classes, D.P.
Khandelwal.
2. B.Sc. Practical Physics, C.L. Arora.
3. Computer Programming, R.C. Verma, V.K. Mittal & S.C. Gupta
(Vishal Pub.), 2003.
4. FORTRAN 77 and Numerical Methods, C. Xavier (New Age Int.
Pvt. Ltd., N. Delhi), 1996.
5. Computer Oriented Numerical Methods, V. Rajaraman (Prentice Hall
of India., N. Delhi), 1998.


PHYSICS (HONOURS) Part-II ( IIIrd and IVth Semester)
SCHEME

SESSION 2012-13, 2013-14, 2014-15

TITLE OF PAPER MAX MARKS NO OF LECTURES

SEMESTER -III
Paper A MATHEMATICAL PHYSICS –I
50 40

Paper B CLASSICAL MECHANICS -I 50 40



SEMESTER -IV
Paper A MATHEMATICAL PHYSICS –II
50 40

Paper B CLASSICAL MECHANICS -II 50 40


PHYSICS (HONOURS) (Semester-III)

PAPER I : MATHEMATICAL PHYSICS-I

Max. Marks : 50 Total Teaching Periods : 40
Pass Marks : 35% in the subject Time Allowed : 3 Hours

INSTRUCTIONS FOR THE PAPER-SETTER

The question paper will consist of three sections : A, B &C .
Section A, B will have four questions from the respective sections
of the syllabus and will carry 10 marks each. Section C will consist of 10
short answer type questions which will cover the entire syllabus uniformly
and will carry 10 marks in all.

INSTRUCTIONS FOR THE CANDIDATES

1. Candidates are required to attempt two question each from sections
A, B of the question paper and section C. is compulsory.

2. Use of non programmable calculator is allowed in the ExaminationCentre,
but this will not be provided by the university/College.

SECTION-A
Three dimensional vector algebra and vector calculus using kronecker
and levi-c vita symbols; linear dependence, linear transformations and
summation convention, Definition of a tensor and its rank. Symmetric
and antisymmetric tensors, Invariant tensors, outer product, contractions
and inner product of tensors, the quotient law of tensors, conjugate
tensors.
SECTION-B
Partial Differential equations and Boundary value problems
Introduction : Basic theory of homogenous and nonhomogenous linear
differential equations. Singular points power series solution and Frch's
theorem.


BOOKS RECOMMENDED

1. L. A. Pipes and L. R. Harwill : Applied Mathematics for Engineer and
Physics.
2. A. W. Joshi : Matrices and Tensors in Physics.


Semester-III

PAPER II : CLASSICAL MECHANICS-I

Max. Marks : 50 Total Teaching Periods : 40
Pass Marks : 35% in the subject Time Allowed : 3 Hours

INSTRUCTIONS FOR THE PAPER-SETTER

The question paper will consist of three sections : A, B &C .
Section A, B will have four questions from the respective sections
of the syllabus and will carry 10 marks each. Section C will consist of 10
short answer type questions which will cover the entire syllabus uniformly
and will carry 10 marks in all.

INSTRUCTIONS FOR THE CANDIDATES

1. Candidates are required to attempt two question each from sections
A, B of the question paper and section C. is compulsory.

2. Use of non programmable calculator is allowed in the ExaminationCentre,
but this will not be provided by the university/College.

SECTION-A
Survey of Elementary principles; Kinematical preliminaries Basic
theorems of classical mechanics, Principle of virtual work, Alembert's
Principle, Lagrange's equations, General solution of one-dimensional
motion, Extension of basic concepts to a system of particles; generalized
coordinates, classification of constraints.

SECTION-B

Lagrangian function for a single particle and a system of particles.
Variational formulation of mechanics; Calculus of variation, Derivation
of Lagrange's equations from Hamilton's Principle.

BOOKS

1. Goldstein : Classical Mechanics.


SEMESTER-IV

PAPER II : MATHEMATICAL PHYSICS-II

Max. Marks : 50 Total Teaching Periods : 40
Pass Marks : 35% in the subject Time Allowed : 3 Hours

INSTRUCTIONS FOR THE PAPER-SETTER

The question paper will consist of three sections : A, B &C .
Section A, B will have four questions from the respective sections
of the syllabus and will carry 10 marks each. Section C will consist of 10
short answer type questions which will cover the entire syllabus uniformly
and will carry 10 marks in all.

INSTRUCTIONS FOR THE CANDIDATES

1. Candidates are required to attempt two question each from sections
A, B of the question paper and section C. is compulsory.

2. Use of non programmable calculator is allowed in the ExaminationCentre,
but this will not be provided by the university/College.

SECTION-A
Partial differential equations of physics, separation of variables;
diffusion and conduction equation. The wave equation, ideal vibrating
string problem.

SECTION-B

Legendre functions, and Legendre polynomials, generating functions,
Rodrigue's formula, Recurrence relations, parity and Orthogonality,
Expansion of functions in Legendre series, Applications, Associated
Legendre Functions. First and Second kind. Generating function of first
kind, Recurrence relations, orthogonality, Modified Bessel functions
and their recurrence relations application.

BOOKS RECOMMENDED

1. L. A. Pipes and L. R. Harwill : Applied Mathematics for Engineer and
Physics.

2. A. W. Joshi : Matrices and Tensors in Physics.

Semester-IV

PAPER II : CLASSICAL MECHANICS-II

Max. Marks : 50 Total Teaching Periods : 40
Pass Marks : 35% in the subject Time Allowed : 3 Hours

INSTRUCTIONS FOR THE PAPER-SETTER

The question paper will consist of three sections : A, B &C .
Section A, B will have four questions from the respective sections
of the syllabus and will carry 10 marks each. Section C will consist of 10
short answer type questions which will cover the entire syllabus uniformly
and will carry 10 marks in all.

INSTRUCTIONS FOR THE CANDIDATES

1. Candidates are required to attempt two question each from sections
A, B of the question paper and section C. is compulsory.

2. Use of non programmable calculator is allowed in the ExaminationCentre,
but this will not be provided by the university/College.

SECTION-A
Equivalent one dimensional problem and the classification of orbits, the Kepler problem and Rutherford's scattering. The Independent coordinates of rigid body, orthogonal transformation, Formal properties of the transformation matrix.

SECTION-B
Euler angles, Euler theorem on the motion of a rigid body. Infinite rotations, Infinitesimal rotations, rate of change of a vector. The Coriolis force. Angular momentum and kinetic energy of rotation about a point. Tensors and dyadics. The inertia tensor and moment of inertia.

BOOKS

1. Goldstein : Classical Mechanics.