Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 8
Due date: Wednesday, Nov. 28, 5 pm. No late homework will be accepted; I intend to promptly
post the solutions, so that you can study them before
Physics 351: Problem Set 8 Solutions
1. Normal Modes of a Gas Filled Pipe:
(a) We are given Youngs modulus as:
Y =
F/A
.
/
We want to relate this quantity to the pressure and volume of the gas cylinder.
We are given a way to relate force and area to press
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 7
Due date: Wednesday, Nov. 21, 5pm. No late homework will be accepted, due to the Thanksgiving break.
Reading: French Chapters 5-6.
Note: This prob
Physics 351, Fall 2007, Prof. Parthasarathy
Problem Set 7 Solutions
1. CO2 :
(a) This problem requires the same treatment as PS6 no. 2 but with a dierent set
of dierential equations. The forces acting on masses 1, 2, and 3 are:
F1
F2
F3
= k (x1 x2 )
= k (
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and
Waves
Problem Set 6: SOLUTIONS
(1)
Phase Space.
Two methods:
(i)
We know that for a simple harmonic oscillator, x(t ) = A cos(t ) and x = A sin(t ) .
The equation for
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 5
Due date: Thursday, Nov. 1, noon. (Turn in the assignment to the box outside my door.)
So that I can distribute the solutions immediately: NO LATE
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and
Waves
Problem Set 5: SOLUTIONS
(1)
The bouncing man.
(a) We need to find 0, which we know from earlier work equals (k/m). What is the spring constant, k?
Then the man
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 4
Due date: Friday, Oct. 26, 5 pm.
Reading: French Chapter 3; start Chapter 4.
(1, 3 pts.) A Tuning Fork. A tuning fork rings at A above middle C, a
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 4: SOLUTIONS
(1)
A Tuning Fork.
(a) The tuning fork is underdamped (or else we couldnt hear a continuous tone, because there wouldnt be
any oscillat
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 2
Due date: Friday, Oct. 12, 5pm.
Reading: French Chapter 2 and Chapter 3 through page 54
(1, 3 pts.) French, Problem 2-3.
(2, 4 pts. total) A verti
(3) A rolling ball.
(a) As x 0, h +, and as x +, h +. Also there is only one value of x for which
1a
dh
a
=
+ b is zero, namely x0 =
3/ 2
2x
dx
2b
2/3
. (From the first observation, or by looking at the second
derivative of h, it should be clear that h
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 1
Due date: Wednesday, Oct. 3, 10 a.m.
Reading: French, Chapters 1-2, Dimensional Analysis notes
Comments. This assignment spans three topics:
(i) S
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and Waves
Problem Set 1: SOLUTIONS
Comment: Think about what ei/2 looks like graphically, in the complex plane a 90 rotation!