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Unformatted text preview: 1 EXPERIMENT M0, PHY 158 Error Analysis 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 observers 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 observers 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 below. In the above example of reading a meter stick, if you make an honest effort to position your eye in the same spot directly overhead with every reading, then the parallax error is random. Sometimes you will be a little to the left of directly overhead, sometimes you will be a little to the right. By taking the average of these measurements, we can, in a sense, cancel out these errors. 2 Sometimes, there exists another type of error, known as systematic errors. These types of errors will not be reduced by averaging, because they act to shift your average value away from the true value. be reduced by averaging, because they act to shift your average value away from the true value....
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- Spring '08