The Lab Experience
Part II: The Experiment, Low Bandwidth Version
In this experiment, we are measuring the position
of a physical pendulum as it swings back and
forth as a function of time.
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The data acquisition for this experiment
makes use of a potentiometer which converts the physical
displacement of the rigid pendulum into a voltage
signal which can be "understood" and stored
by electronic instrumentation. The voltage is proportional
to the angular displacement of the pendulum and can
be scaled to +/- 10 volts. Using an analog-to-digital
converter, the voltage of the potentiometer is recorded
at small fixed time intervals, called the sampling
period. The voltage measurements at each time step
are also digitized into a binary code in order for
the information to be efficiently stored by the computer.
We are taking a snapshot in time of the
amplitude of the pendulum as it swings every 20th of
a second, so when we plot the amplitude as a function
of time, we have an accurate time base.
By using a protractor, the angle will
be measured at 40 degrees when first pulled back.
When the program prompts:
What sampling rate in Hertz do you want?
It is asking us how many recordings should
be made and stored on the computer every second. We
want a reading every 0.05 seconds, so we say 20
readings in a second.
The next parameter prompted for by
the data acquisition program is:
How many points do you want to take?
We will take 200 readings, so we'll say
we want 200 points. This means that over a 10
second period, there will be 200 reading precisely .05
seconds apart.
On our screen, we see a plot
with time plotted in the X direction (abscissa), and
amplitude in the Y direction (ordinate).
A period is defined as the time it takes
to go from one maximum to the next, or one minimum to
the next. Each dot is .05 seconds apart. By counting
the number of dots from one maximum to the next, we
get an estimate of the period, the time it took the
pendulum to go through one complete swing. There are
26 dots, taken 20 per second. This tells us:
The period is 26 divided by 20,
or 1.30 seconds
The amplitude has decreased over time.
The period stays the same, to the accuracy of our measurement,
even as the amplitude has gotten smaller.
In order to analyze the data,
it is stored and viewed on another graphing program.
The voltage signal has been converted into angular displacement
measured in degrees. Here it is plotted as a function
of time. First it goes down to -23 degrees, then up
to 20 degrees, and then down to -20, and so on. We can
see the amplitude dying out or decaying.
All real pendulums come to rest because
of energy losses. We see this in the decreasing amplitudes
of each oscillation displayed on the computer screen.
Dissipation or damping of energy is an important part
to understanding real world physics and engineering.
Adding energy to the pendulum by pushing on it compensates
for the energy that is dissipated from the pendulum
system by forces such as air resistance and friction.
Part of the brilliance of the early scientists was to
be able to extract out "idealized" motion from observations
of the motion of real objects in the real world which
are always operating with such dissipative forces and
energy sources.
Now that you have observed the lab experiment,
you will now open a Data Analysis Lab Notebook with
the results from this lab experience. Just like the
Introductory Experiment, the Data Analysis Lab Notebook
is embedded in a Microsoft Word document. This time,
instead of entering your own data you will answer
the questions for analysis based on the data captured
with the analog-to-digital converter during Dr. Weigman's
pendulum experiment. After you have anwered the questions,
save your file to disk, and then proceed on to the
next section, Understanding Mathematical Models.
