INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 1
29.8.2007
A two-dimensional autonomous dynamical system in continuous time is specied
by a pair of rea
Chapter 4
Oscillations
In this chapter we will discuss oscillatory motion. The simplest examples of such
motion are a swinging pendulum and a mass on a spring, but it is possible to make
a system more
Chapter 5
Conservation of energy and
momentum
Conservation laws are extremely important in physics. They are enormously
helpful, both quantitatively and qualitatively, in figuring out what is going on
148
Conservation of energy and momentum
V(x)
Example: A particle moves under the influence of the potential V (x) =
A/x2 B/x, where A, B > 0. Find the frequency of small oscillations around the
equili
Cylindrical Polar Co-ordinates (,z)
r
Position vector is r = e + z e z
r
d r = d e + d e + dz e z
r
v = & e + & e + z&e z
r
& & + &)e + &
a =(& & 2 ) e + (2
z e z
z
P
z
x
dz d
d
Area Vector
r
r
r
Az
DEPARTMENT OF PHYSICS
INDIAN INSTITUTE OF TECHNOLOGY, MADRAS
PH101 Physics I
18.10.2002
Particle Motion in a Central Force
Contents: Particle kinematics in cylindrical and spherical polar coordinates;
35
Physics I Course Material
y
ey
e
e
P
A new basis of unit vectors (
e , e ) is defined along the directions of increasing and
increasing respectively. From Fig. 6.2, it
is obvious that
ex
e = cos ex
11/20/2013
Recap: Gradient
Vector field from Scalar fields
The gradient of a scalar function at any point indicates the
direction In which the function has largest rate of increase
Note: Not every vec
5.9 Problems
5.9
173
Problems
Section 5.1 Conservation of energy in one dimension
5.1. Minimum length *
The shortest configuration of string joining three given points is the one
shown in the first se
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 4
17.10.2007
1. (a) The probability density of the xcomponent of the velocity of a molecule
of mass m in
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 3
12.9.2007
1. We have seen that canonical transformations (CTs) are symplectic transformations in the f
INDIAN INSTITUTE OF TECHNOLOGY MADRAS
DEPARTMENT OF PHYSICS
PH350 Classical Physics
Problem Set 2
1.9.2007
1. Indicate whether the statements in quotation marks are true or false.
(a) The Lagrangian o
NPTEL COURSE ON CLASSICAL PHYSICS
V. Balakrishnan
Department of Physics, Indian Institute of Technology Madras
Chennai 600 036, India
Two-dimensional Autonomous Dynamical Systems
A two-dimensional (2D
684
Appendix B
B.4 Gradient
Given a function f (x, y, z) (well work mainly with three variables from now on),
we can form the vector whose components are the partial derivatives of f , namely
(f /x, f