Additional of parallel vibrations

Vector diagrams are very useful for addition of harmonic oscillations. Let us assume that frequencies of oscillations are equal to each other. However amplitudes and initial phases are different.

(8.62)

In complex form:

(8.63)

The resultant displacement equals to:

, (8.64)

where A – is unknown amplitude of a total oscillation; – is its phase.

Let’s consider (fig.8.3).

Figure 8.3

According to the theorem of cosines:

(8.65)

Questions

1. What is dynamics? What is the realm of classical mechanics?

2. The central problem of classical particle mechanics.

3. The program for solving the problem of mechanics.

4. First law of motion or law of inertia.

5. What is inertial frames?

6. Newton's second low.

7. Third law of motion.

8. What is a force of friction?

9. Forces of static friction and of kinetic friction.

10. The coefficient of static (kinetic) friction.

11. Centripetal force is not kind of force.

12. Kinetic Energy and the Work Energy Theorem.

13. Potential energy of elasticity.

14. Gook's law.

15. Gravitational potential energy.

16. Total mechanical energy.

17. What is closed system?

18. The law of conservation of mechanical energy.

19. The law of conservation of matter.

20. The principle of equivalence of mass and energy.

21. Law of conservation of momentum. Quantity of motion.

22. The centre of gravity of a body.

23. "Perfectly rigid" bodies.

24. The momentum of inertia of the body.

25. Steiner's theorem.

26. Moment of force (torque).

27. The work of rotating a body.

28. The fundamental equation of motion for a rotating body.

29. The law of conservation the total angular momentum.

Date: 2015-01-12; view: 977