1
EXPERIMENT M0, PHY 158
Error Analysis
Please note:
This lab exercise was created after the last publication of the lab manual, and therefore is not
contained in the manual.
There are also significant changes to nearly every lab, and these changes are
documented in the Manual Addendum for each lab.
You must read both the Addendum and the manual, and
where there is disagreement between the two you must follow the Addendum.
I. Objectives:
i.
Become acquainted with the notion of the average value and the standard deviation of a series of
measurements of a parameter (period T of a simple pendulum)
ii.
Measure the elongation x of a spring as function of applied force F. Use the method of least squares
to determine the spring constant k
iii.
Become acquainted with the notion of error propagation.
iv.
Become familiar with the use of Microsoft EXCEL
II. Equipment:
stand, spring, mass holder, masses, meter stick, pendulum bob, string, stopwatch
III. Introduction:
STOP:
Read the “Data Analysis” section of your lab manual!!!
When we measure any physical parameter such as length, time, mass, etc an uncertainty in the parameter
value is involved.
We know that this is true because if we repeat the same measurement several times we
get slightly different values.
There are several factors that contribute to uncertainty in a measurement.
One
source is the measuring instrument itself.
Consider a length measurement of an object using a meter stick
whose smallest division is one millimeter (1 mm) as shown in fig.1. Each length measurement will have an
uncertainty between 0.3 mm and 0.7 mm.
The second factor is the person who is carrying out the
measurement.
A person with sharp eye sight will be able to measure with uncertainty 0.3 mm (the smallest
value our meter stick allows).
A person with less sharp eyes will have a larger uncertainty.
A third factor
that contributes to uncertainty is the measuring procedure.
In the measurement of fig.1 for example the use
of a magnifying glass will help us keep the uncertainty to a low 0.3 mm.
Another detail is the position of
the observer’s eye during the measurement (see fig.2).
If the observer views the ruler at right angles
(position A in fig.2) this minimizes the uncertainty in the measurement.
On the other hand, placing the
observer’s eye at an angle (positions B and C in fig.2) results in a larger uncertainty.
This phenomenon is
known as
parallax
.
Measurement errors fall into two broad categories:
Random and systematic.
It is the random errors that
cause your measured value to vary from measurement to measurement, and we assume that these random
errors cause your measurements to be scattered around the “true” value that we are measuring.
In other
words, we expect about half of our measurements to be above the “true” value and the other half to be

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*