1
PHY481 - Midterm II (2009)
Time allowed 50 minutes. Do all questions - to get full credit you must show your working.
Problem 1. a) Write down the integral and dierential forms of Maxwells equations
PHY 203: Solutions to Problem Set 3
October 16, 2006
1
Problem 7.7
Assigning coordinates of the double pendulum in the usual way we have
x1 = l sin 1
(1)
y1 = l cos 1
(2)
x2 = l(sin 1 + sin 2 )
(3)
y2
PHYSICS 140B : STATISTICAL PHYSICS
PRACTICE MIDTERM SOLUTIONS
Consider a four-state ferromagnetic Ising model with the Hamiltonian
H = J1
Si Sj H
Si Sj J 2
i
ij
ij
Si ,
where the rst sum is over all n
PHY 203: Solutions to Problem Set 4
October 24, 2006
1 Buoy Dropped from an Airplane
From energy conservation the buoy hits the surface of the water with a velocity
120 = x/2gh. The equation of motion
PHYSICS 140A : STATISTICAL PHYSICS
MIDTERM EXAM : DO ANY TWO PROBLEMS
(1) For each of the following situations, explain clearly and fully why it is or is not thermodynamically possible.
(a) Energy fun
PHYSICS 140B : STATISTICAL PHYSICS
MIDTERM EXAM SOLUTIONS
Consider a four-state ferromagnetic Ising model with the Hamiltonian
H = J
Si Sj H
Si ,
i
ij
where the rst sum is over all links of a lattice
INTRODUCTION TO DIFFERENTIAL EQUATIONS, FINAL EXAM
Sections 13-16, Fall 2002
Section meeting time Name 8 o \ A ( 0n )
Instructions. You are allowed to use three 8 1/2 X 11 inch sheets of paper of note
PHY 203: Solutions to Problem Set 1
September 30, 2006
1
Firing Shells at Constant Speed
Here we would like to nd the set of all points that lie on some trajectory of
a shell red with xed speed v0 , b
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 3
Sections 13—16, Fall 2002
Section meeting time Name
Instructions. You are allowed to use one 8 1/2 x 11 inch sheet of paper of notes. No
calculators, PDA
PHY 203: Solutions to Problem Set 2
October 9, 2006
1
Laser Beam in Refractive Medium
Here we nd the path of a light ray using Fermats principle. The travel time is
T=
n0
ds
=
v
c
1 + (y )2 (1 + ky )d
PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #2 SOLUTIONS
(1) Consider a d-dimensional ideal gas with dispersion (p) = A|p| , with > 0. Find the
density of states D(E), the statistical entropy S(E
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 2
Sections 13—16, Fall 2002
Section meeting time _ Name _——
Instructions. You are allowed to use one 8 1/2 X 11 inch sheet of paper of notes. No
calculator
\3 E:
-t1. BS kWlc
7, '-11
.:,
-;>
f
~
-:!
"-
- :/
13 ~ 153+36k rnl
. )
-;,
9 (E ~ v x B/
'f\.o+\.,~n~& con1ri bVl+~
a.,) \J": 0 s oB tktt does
-:.J
f :=:9 E
~
\
1
h') v -= 6, y. J0 6~
I
\5)
D0
Math 38
Spring 2011
Midterm Exam 2 with Solutions
1. (15 points): Use the method of undetermined coecients to nd a particular solution
of the equation
x + x 2x = 18te2t .
Solution: The characteristic
INTRODUCTION TO DIFFERENTIAL EQUATIONS, TEST 1
Sections 13-16, Fall 2002
Section meeting time _-_ Name
Instructions. You are allowed to use one 8 1/2 x 11 inch sheet of paper of notes. No
calculators