Order of work

As an example, consider the processing of the results of measurements of the oscillation period of a simple pendulum (mathematical pendulum is called the body suspended on a weightless and inextensible thread, which is much greater than its size).

1. Use the stopwatch to measure the time tі 30 oscillations of a pendulum. The measurements were repeated n times (n is given by the teacher).

2. According to the formula

(1.1.13)

calculate the period of oscillation.

3. Definitions sredngo arithmetic mean value of the oscillation period

4. According to the formula (1.1.9) to find the standard deviation of T.

5. From the table to find the value of the Student's coefficient corresponding to reliability, said the teacher (Student coefficient table is available in the laboratory).

6. When the values found and the formula (1.1.10) to calculate the absolute error.

7. Calculate the relative error by the formula (1.1.12).

8. The results of measurement and computation recorded in the table

Table (1.1.2)

N	п	ti с	Тi с	Тi с

Control questions

1. What kinds of measurements are divided and associated errors.

2. How is the absolute error.

3. What is the Student factor is introduced.

4. What do the confidence interval and confidence level.

5. Why is it necessary to calculate the relative error.

6. What is called a mathematical pendulum.

7. What is called the period of oscillation.

Literature

1. Kassandrova ON, VV Lebedev Processing of observations. M .: Nauka, 1970.

2. Agekyan TA Fundamentals of the theory of errors for astronomers and physicists. M .: Nauka, 1972.

1.2.Obrabotka indirect measurements

Accessories. ruler, calipers, micrometers, scales with the posting, a set of bodies of regular geometric shape.

Objective. familiarization with the method of calculating the error of indirect measurement of physical quantities.

Evaluation of the accuracy of the result of direct measurement. If in the course of multiple measurements the instrument gives one and the same reading, the measurement repetition is meaningless - to spend it only once. This is obtained, obviously, in the case where the absolute error of the measuring device is working more than the residual error of the individual measurements. Maximum absolute error or is listed in the data sheet measuring device, or the price determined by the half of the smallest division of its scale.

Example. When measuring the value mm was obtained caliper side of the cube. Graduation mm caliper. Consequently, the limiting absolute error of measurement equal to the caliper relative error:

                  (1.2.1.)

The result of measurement should be written as follows:

мм (1.2.2.)

Often in the works give the value of the different variables measured in advance: the number of physical constants, tabular data. In such cases, the absolute error is taken equal to its limit value, ie, equal to half the smallest unit of the discharge represented in the figure. For example, if a given body weight, r, g, therefore г, etc.