MIPT crossword

31

Deal with $x_2$. The oscillations of weights corresponding to these formulas are presented graphically at figure 12, $a$, $b$. Movements of this kind are called beats (or modified oscillations). It is easy to find the period of beats. It is equal to the half-period of the sine (dotted curve) and is determined by the formula

$$\frac{\omega_1 - \omega_2}{2} T_0 = \pi$$ or $$\frac{1}{T_0} = \frac{1}{T_2} - \frac{1}{T_1},$$

where $T_1$ and $T_2$ are periods of normal oscillations. The frequency of the beat is equal to the frequency of normal oscillations. The beat period is greater, the closer $T_1$ and $T_2$ are to each other.

Of course, with a very large beat period, the motion picture will be confused due to the damping of the oscillations.

3. When the double matrix moves, beats are observed. The light matnik either oscillates with great swing, then almost stops. The movement of a heavy matrix can be almost imperceptible. Such beats are explained by the addition of two normal vibrations, shown in figure 13. Do the explanation yourself.

Exercises

1. Derive a formula for the period of oscillation of a mathematical matrix, considering its movements as rotation around each axis.
2. Select the length of the expanded suspension of the matrix so that the weight can be described with eight hands.
3. Select the lengths of two independent matrices so that with their help you can determine time intervals of 10 seconds, 20 seconds, not counting the oscillation “piece by piece”. Such matrices can be used to measure heart rate after charging. (Galileo randomly measured the periods of vibration of lamps in a church, using the pulse beat of a clock).

MIPT crossword

There are many types of student folkcore: songs, jokes, fairy tales. Students of the Moscow Institute of Physics, in addition to those listed, have one more thing - crosswords.

In order to solve such a crossword puzzle, you must first of all have a sense of numbers and imagination. Encyclopedias and reference books will not help here. Among MIPT teachers, individual halves of the crossword words are considered excellent access; among students, the figures are slightly higher. If the crossword puzzle below does not work for you, then look at page 38, where it unscrambles the words horizontally, and write them down, then try to debug the words vertically on your own. The answers to these are given on page 65.

Horizontally: 1. Computer center of a research institute for the organization of individual workers of a production and training plant. 6. The devil is in the nose. 7. Far away. 8. Natural compound. 11. A character from Russian folk tales who appears primarily from behind the mountains. 13. Musical instrument without sound. 14. Srednezamatsky catrist, philosopher, composer, and therefore singer. 17. Patient Cossack. 20. Son of the East. 21. A device for stopping a train by pressing a button. 22. Trick with light.

Vertically: 1. A bad person and also a drinker. 2. Subtlety. 3. Work by P. I. Tchaikovsky. 4. Type of coal. 5. Spectacled kite. 9. Lonely inhabitant of the wild world. 10. The force of attraction to the Earth. 12. Very large wardrobe. 15. Man with a shovel. 16. Legendary downsizing. 18. No goals. 19. Several identical letters.