This is the first quarter of a three quarter course. This quarter and
the first half of winter quarter will be devoted to vibrations and waves
of all kinds, including matter waves. The second part of winter quarter
and then spring quarter are devoted to thermal physics. We will try to
develop practical applications of the material.
- Sept. 26.
- Read: Chapter 1 of Pain, through section
titled "Energy".
- Be sure to go over the section at the end of chaper 1 entitled "Some
Useful Mathematics" (Euler's notation).
- Problem set 1 is due Monday,
Oct. 3 and can be found here. (Problems 5&6 deferred until week 2)
- Oct. 3. Mostly Euler's Notation/Complex math
- Read section 6 of "Oscillators" (class notes from
last year, download below); Pain Ch.1 "Some Useful Mathematics"
- Start on Pain, Ch.2, Damped oscillations
- Problem Set 2 (due Monday, Oct. 10) can be found here.
- Oct. 10. Damped and driven oscillators
- Read Pain, Ch.2, Damped oscillations, Ch. 3, Forced oscillations
- Problem Set 3 (due Monday, Oct. 17) can be found here.
- Oct. 17
- Homework 4 and reading is posted here.
- Oct. 24
- Read Ch. 3 of Pain and "Oscillators" notes on driven damped
oscillators
- In class, I will try to explain the difference in notation between
Pain and the lecture--there is a reason!
- Homework 5, due Monday, Oct. 31, is posted here.
- Oct. 31. Coupled oscillators
- Read Ch. 4 Pain p 79-87.
- Note: for adding oscillations, "beat frequencies", etc. read p 12-15
(Ch. 1 Pain)
- Homework 6: problems 4.1, 4.2, 4.3 and 4.4 in Pain.
- Nov. 7. Wave equation
- Read Ch. 4 Pain p. 90-97; Ch. 5 107-155; "Waves" notes from
previous terms (download link below)
- For problem 4.11 in Pain (vibrational damping), a nice overview may
be found here (pdf file).
- Homework
7 is posted here.
- Nov. 14. Wave equation
- Read Ch. 4 Pain p. 90-97; Ch. 5 107-155; "Waves" notes from
previous terms (download link below)
- Homework 8 is posted here. (not to turn
in)
- Midterm II Friday, Nov. 18, through reflection and transmission
coefficients.
- For discussions of these coefficients, see problem 2 on
homework 8, "Waves" notes pp. 4-6, Pain pp. 117-119.
- Nov. 21. Energy transmission, Sound waves
- Reading Pain p. 117-124, 148-149 (Summary), 151-165 (Sound)
- "Waves" notes has treatment of energy transmission
- Homework 9 is posted here. Due Monday, Nov. 28
- Nov. 28. Sound and Light
- Reading Pain p. 151-165 (Sound), 200-208 (Light)
- Homework 10 is posted here. Not required,
but extra credit will be granted equivalent to one homework problem
set.
Note: I encourage students to work together
on the homework. I don't want you to just copy from someone else's work
because you
won't learn anything that way. However, if you work out the solution jointly
with someone else or with a group, that's fine. Please write up the solution
independently! This policy is an exception to the normal
university rule about doing your work, but much of science is teamwork. Of
course, on exams, your work
has to be entirely your own.
Homework and exam solutions (PDF files)
Available lecture notes, also material from previous terms in .pdf
format:
Reference Materials
Available Mathematica notebooks:
- NDsolve.nb Solution for problem 12.1
-
samples.nb Some additional examples of Mathematica commands
- programming.nb Some examples of loops,
function definitions,
branches, etc. used for simple Mathematica programs
- Euler.nb Euler's method for numerical solution of
differential equations, with application to spring and mass.
- RungeKutta2.nb
Runge-Kutta method for numerical solution of differential equations,
with application to the simple pendulum and the simple harmonic
oscillator, with friction if desired.
- chaos_pop.nb Population growth model with predation
and showing
chaotic behavior
We will use Mathematica from time to time, especially for
numerical problems. That's partly because it is a useful tool to help
us understand the subject and partly because students in
science ought to learn how to use computers to do science.
Mathematica was picked as a tool because it gives us all a common reference point.
The university has a site license and copies of the program are installed on many
of the computers in the labs. If anyone wants to use Maple, Basic, Fortran or C++,
that's fine.
Exams:
- Midterm Exam: Friday 21 October (in class).
- Midterm Exam: Friday 18 November (in class).
- Final Exam: Wednesday 7 December at 10:15.
Grading:
Overall course scoring: 25% homework, 20% each midterm, 35% final
Tentative schedule:
- Oscillations (Weeks 1-4; 12 days)
- (2 days) Free vibrations.
- (1 day) Complex numbers.
- (2 days) Free vibrations in physics.
- (1 day) Damping.
- (1 day) Damping in physics.
- (1 days) Forced vibrations.
- (1 day) Forced vibrations in circuits.
- (1 day) Review.
- (1 day) Exam, Friday 21 October.
- Waves in one dimension (Weeks 5-7; 9 days)
- (2 days) Wave equation and solution.
- (2 day) Sound waves.
- (1 days) Reflection and transmission at a boundary.
- (1 day) Energy transmission.
- (1 day) Review.
- (1 day) Exam, Friday 19 November
- Waves in three dimensions and optics (Weeks 8-10; 8 days)
- (1 day) Light waves.
- (2 days) Reflection and refraction.
- (4 days) Formation of images.
- (1 day) Review.
