PHYS 211 2013 Exam 3
Your name:_ _
Each problem is worth 10 points. Return this sheet with your solutions.
You will only get complete credit for a problem if you fully explain your answers.
Problem 1
A long string of mass 1.0 g cm-1 is joined to a long st
PHYS 211 2013 Exam 2
Your name:_Solutions_
You will only get complete credit for a problem if you fully explain your answer.
Problem 1 - Forced oscillations
A mass m is connected to a horizontal spring with spring constant k. The other end of the spring i
PHYS 211 Exam 1
Your name:_Solutions_
Each problem is worth 10 points. Return this sheet with your solutions.
You will only get complete credit for a problem if you fully explain your answer.
Problem 1
A mass of 0.5 kg is attached to a spring with a sprin
Use of the Fourier series
We would like to study the behavior of a damped harmonic oscillator that is driven by a force F(t) as
shown in figure 1. Unfortunately, we have only learned how to solve this type of problem for a driving
force of the form F ( t
Assignment 6 report
Text book problems
5.3. (a) Show that the following are solutions to the one-dimensional wave equation
(i) y = A sin 2 (t x / v), (ii) y = A sin ( 2 ) ( x + vt ), (iii) y = A sin 2 ( x t T ),
(iv) y = Aei (t + kx ) , and (v) y = Acos(1
Coupled oscillations
Consider two masses connected as shown below by springs. The left end of the leftmost spring is
attached to a rigid immovable wall. There is no dissipation. The springs have equal strength but the
masses are different.
k
k
m
M
x1
x2
Assignment 5 report - Coupled oscillations
The equations of motion for the two masses shown in figure 1 are
Mx1 = kx1 + k ( x2 x1 ) = k ( x2 2 x1 ) ,
mx2 = k ( x2 x1 ) .
(1.1)
Figure 1. System of two unequal masses connected by springs to a rigid support
Assignment 4 report - Text book problems
3.1. A mass of 0.03 kg rests on a horizontal table and is attached to one end of a spring of spring constant
12 N m-1. The other end is of the spring is attached to a rigid support. The mass is subjected to a harmo
A numerical study of the damped harmonic oscillator
The aim of this project is to use Origins numerical differentiation and integration abilities to check that
for a damped harmonic oscillator the power of the damping force is equal to the rate of change
A numerical study of the damped harmonic oscillator
We have a damped harmonic oscillator with the following properties
1) The mass, m, is 200 g.
2) The damping constant, = 1 s-1.
3) The oscillation frequency, = 20 rad s -1.
4) In the absence of damping, t
Assignment 2 report
Text book problems
1.8. We might assume that the period of a simple pendulum depends on the mass m, the length l of the
string and g the acceleration due to gravity, i.e. T m l g , where , and are constants. Consider
the dimensions of
Looking at some of trigonometric functions from the trigonometric
exercises
1. Make a graph (using Origin) that contains the functions sin4 t , sin7 t and sin4 t sin7 t over
the interval 0 t 1 .
2. Make a graph that contains the functions sin2 4 t and cos
Assignment 1 report
f(t) = sin(4t)
f(t) = sin(7t)
f(t) = sin(4t)sin(7t)
1.0
sin ( 7 t ) , and their product sin ( 4 t ) sin ( 7 t ) . From
0.5
careful inspection of figure 1 (or by plotting to t = 2),
we see that the product has period, P = 2. This can be