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
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: 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: 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
(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: SOLUTIONS
Comment: Think about what ei/2 looks like graphically, in the complex plane a 90 rotation!
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351 Vibrations and
Waves
Programming #P7: Solution
(a) For the exact (analytic) solution:
The general solution x(t) = A sin(t - ). The initial x(t=0) = 0, so = 0. v(t=0) = A cos(t) = v0
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
Physics 351
Computer Programming: A Brief Introduction
SOLUTIONS: Exercises P1-P3
P1. Chang et al., retract the conclusions of several of their recent papers, stating that their results are
inc
Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
SOLUTIONS
NAME:
Physics 351 Vibrations and Waves
M IDTERM EXAMINATION
Format: Closed book; no calculators. Four problems.
Time: 50 minutes. (Suggested times: #1, 5 min; #2, 10 min., #3 & #4, ea