Mathematica
For Physics Students
Hatem O. Babaa, 2005
Revised Edition, 2006.
Hatem O. Babaa, 2005
Mathematica For Physics Students.nb
2
1. Introduction
1.1 Physics
Physics is the most fundamental of all natural science, will reveal to us the basic princ
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 1 (August 2001)
(1) Double Pendulum: Consider small planar oscillations of a double pendulum
consisting of two metal bars, the upper bar of mass 2m and length D, and th
Ben Sauerwine
Practice for Qualifying Exams
Thanks to Chip, Diana and Shiang Yong for their help with this solution.
Problem Source: CMU August 2001 Qualifying Exam
A white dwarf star is a dense, spherical start in which there is no longer any
significant
Ben Sauerwine
Practice for Qualifying Exams
Given the Maxwells Equations in differential form (SI units)
v
v
vv
v v B
vv
v v r D
D = E +
= 0 B = 0 H = J +
t
t
(a) Write down these Maxwells Equations in integral form.
v
v
v
D ndS = dV E dl
S
V
C
=
v
B ndS
Ben Sauerwine
Practice for Qualifying Exam
Problem Source: CMU August 2003 Qualifying Exam
The Maxwell equations in SI units are given by:
v
vv
v v B
D = E +
=0
t v
vv
v v v D
B = 0 H = J +
t
Below the plane z = 0 (region 1) is a vacuum with permittivity
Problem Source: CMU Qualification Exam Day 1 (August 2003)
(2) Consider a stretched string of variable density (mass per unit length) (x ) . If
the transverse displacement is u (x, t ) , then in the limit of small displacements
u (x, t ) satisfies the wav
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2004 Qualifying Exam
The Fourier transform f (k ) of a function f ( x ) is defined by
f (k ) =
1
e
2
f ( x )dx
ikx
(a) Show that the Fourier transform of f ' ( x ) =
df
can be express
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 1 (August 2004)
(3) This problem concerns the precession of perihelion predicted by general
relativity and how it might be generated by modifications of the distributio
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU August 2005 Qualifying Exam
(a) A 10 4 kg spacecraft is launched from Earth and is to be radially accelerated
away from the Sun using a circular solar sail. The initial acceleration of the sa
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU Qualification Exam Day 1 (August 2005)
(1) A spherical ball of radius a and mass m which is not uniformly distributed
throughout its volume rolls without slipping down the circular surface of
Ben Sauerwine
Practice for Qualifying Exams
Problem Source: CMU February 2006 Qualifying Exam
A particle of mass m is in a 1-d harmonic oscillator potential
V=
1
m 2 x 2
2
(a) Show that the Hamiltonian can be written as
1
H = h a + a +
2
where a, a + are
MULTIPLE CHOICE QUESTIONS
One Dimensional Kinematics
Copyright 1997, 1999 by Edwin R. Schweber
Distributed on the internet by physicsweb.com
http:/www.physicsweb.com
These questions may only be used by teachers with their own students at public, religious