Can a nonlinear vibration problem be identified by looking at its governing differential equation? 7. what is the difference between deterministic and random vibration? give two practical examples of each. 8. what methods are available for solving the governing equations of a vibration problem? 9. how do you connect several springs to increase the overall stiffness? 10. define spring stiffness and damping constant. 11. what are the common types of damping? 12. state three different ways of expressing a periodic function in terms of its harmonics. 13. define these terms: cycle, amplitude, phase angle, linear frequency, period, and natural frequency. 14. how are and f related to each other? 15. how can we obtain the frequency, phase, and amplitude of a harmonic motion from the corresponding rotating vector? 16. how do you add two harmonic motions having different frequencies? 17. what are beats? 18. define the terms decibel and octave. 19. explain gibbs phenomenon. 20. what are half-range expansions?

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russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

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