Notices
(Assignments and Other Information)
Homework
- Ch. 3: #1-5, 7m 8 13, 17. (Due: Monday, Jan. 7)
- Ch. 2: #7, 9, 12. (Due: Friday, Jan. 4)
Lab Assignments
- Additional Lab Experiments
(Choose two from the following list; due Monday, Jan. 21)
- Determining the Value of G Using a Torsional Pendulum
- Determining the Value of h Using LED's
- Determining the Value of e/m with Electron beam in Helmholtz Coils
- Determining the Value of g Using the Kater Pendulum
- Observing Hysteresis of a Magnetic Field in an Iron Rod
- Analyzing a Complex Sound Wave
- Radioactivity and Sheilding
- Oscillating Spring and Mass
This lab will explore the behavior of an under-damped harmonic oscillator.
The goal is to match a sine wave to the data with an exponential decay
associated with the amplitude. Collecting the data will be fairly simple,
but the data analysis (using Mathematica) will be fairly complicated
and time-consuming.
Attach a 500-g or a 1-kg mass to one of the good springs available in the
lab. Position it vertically from a rod fastened to the lab bench. Pull the
mass down some additional extension (but not an additional distance greater
than what the mass already extended the spring) and release it. Place the
Vernier motion detector on the floor and start collecting data when the
system seems stable. Then export the data from LoggerPro by copying
and pasting it into Excel (from which it can then be exported as a
text file) or by exporting it from LoggerPro as a text file
After reading your data into Mathematica and centering it about the
y=0 axis and starting it at t=0, look only at 100 or so data points and fit
a sine wave to them. Here is the Mathematica code to do this.
----------------------------------
In[19]:=
<<Statistics`NonlinearFit`
In[20]:=
fitfunc2 = NonlinearFit[data1,a Sin[(2 [Pi]/1.66) t+ b],t,{a,b}]
----------------------------------
The form of input for the NonlinearFit function is to give the data, the
mathematical model, the variable(s), and the parameter(s). Here, data1 is my
data, "a Sin[ (2 Pi/T) t +b" (using the actual Greek letter for Pi) is my
model (with my period being 1.66 s as figured from a plot of the first 100
points or so of data), "t" is the variable, and "a" and "b" are the
parameters in the model. While the NonlinearFit function should fit the data
with three variables, I discovered that if I gave it a good guess of the
period, then it would converge nicely to the expected sine wave. The period
may have to be tweaked to make the fit work well.
Finally, find the fit to four or five 100-point segments of your data and
use the amplitude of your fit sine equation as data to fit a exponential
envelope to your first fit sine wave model. Finally show a graph with both
the original data and the fit function.
- Reading a file into Mathematica.
- Acceleration Due to Gravity at Our Location (Due: Wednesday, Jan.
16)
Use the Vernier sonic range finder to collect
position and time data for a metal ball rolling down a long wooden board.
Export the data from Logger Pro for statistical analysis by Excel and
Mathematica. The data needs to be truncated at the beginning to get
rid of starting noise in the data. Curve-fitting will then be done to
extract the value of g from the data. The experiment should be repeated for
a total of five sets of data.
- Average Ending Density of the Game of Life in a Variety of Small
Universes (Due: Monday, Jan. 7).
Note that what we are investigating
is the density of the ending generation for a random beginning population as
a function of the universe size and the boundary conditions used. In pairs,
you should study at least four different sizes of 2-D universes for at least
two different boundary conditions. A good project will actually expand upon
this minimum. For example, use more sizes or explore how many generations
does it take for a particular population to reach its ending state, or one
could measure what the actual beginning population density is and see if it
affects the outcome.
My suggestion is to do some fun exploration
to begins with. Then define a plan of action, submit it to me for approval,
and then carry out the investigation. One day next week, we will spend a
session where each team reports their findings, so keep that in mind.
Also, what are the average, standard
deviation, and standard deviation of the average of the ending density for
each size and boundary condition set for which you collected observations?
And is there an observable central tendency?
Wednesday, January 2, 2008
- Welcome to PHYS 345 Experimental Physics. I hope you are as
eager as I am to explore some more advanced experiments in physics, which
will be more like mini-research projects. --Dr. R. Bowman
Created and maintained by: Richard L. Bowman
(last updated: 15-Jan-08)
