8.1 A material point that performs harmonic oscillations with a frequency v =2 Hz passes through the position determined by the coordinate x 0 =6 cm at the time t =0, with a velocity v 0 = 14 cm/s. Determine the amplitude of the oscillation.
8.2. The total energy of the harmonically vibrating point is 30 μJ, and the maximum force acting on the point is 1.5 mN. Write the equation of motion of this point if the oscillation period is 2 s, and the initial phase π/3.
8.3. At suspension of bodies by masses m 1 =500 g and m 2 =400 g to free springs the latter elongated equally (D l =15 cm). Neglecting the mass of springs, determine: 1) periods of oscillations of bodies; 2) which of bodies at identical amplitudes possesses greater energy and how many times.
8.4. A physical pendulum is a thin, uniform rod with a length of 25 cm. Determine at what distance from the center of mass there should be a point of suspension so that the oscillation frequency is maximum.
8.5. Two mathematical pendulums, lengths of which differ by D l = 16 cm, are matched at the same time: one n 1 =10 oscillations, another n 2 -6 oscillations. Determine the lengths of the pendulums l 1 and l 2
8.7. The phase difference between two equally directed harmonic oscillations of the same period of 8 s and the same amplitude of 2 cm is π/4. Write the equation of motion resulting from the addition of these oscillations, if the initial phase of one of them is zero.
8.8. The point participates simultaneously in two harmonic oscillations, occurring in mutually perpendicular directions and described by the equations x = cospt и y = cosπt/2. Determine the equation of the trajectory of a point and draw it with scale.
8.9. During the time for which the system makes 100 full oscillations, the amplitude decreases threefold. Determine the quality factor of the system.
8.10. When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz. One of the resonant frequencies (below 200 Hz) is missing. What is it?
8.11. A stretched string, clamped at its ends, vibrates in its fundamental frequency. To double the fundamental frequency, one can change the string tension by a factor of:
8.12. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. The wavelength of the constituent traveling waves is:
8.13. An object attached to one end of a spring makes 20 complete oscillations in 10 s. Its period is:
8.14. An object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is:
8.15. An object attached to one end of a spring makes 20 vibrations in 10 s. Its angular frequency is:
8.16. An object of mass m, oscillating on the end of a spring with spring constant k, has amplitude A. Its maximum speed is:
8.17. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200N/m. If the system has an energy of 6.0 J, then the maximum speed of the block is:
8.18. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200N/m. If the oscillation is started by elongating the spring 0.15m and giving the block a speed of 3.0m/s, then the amplitude of the oscillation is:
8.19. A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic energy is:
8.20. The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes
8.21. Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:
8.22. Take the speed of sound to be 340m/s. A thunder clap is heard about 3 s after the lightning is seen. The source of both light and sound is:
8.23. A sound wave has a wavelength of 3.0m. The distance from a compression center to the adjacent rarefaction center is:
8.24. A fire whistle emits a tone of 170 Hz. Take the speed of sound in air to be 340m/s. The wavelength of this sound is about:
8.25. Two stationary tuning forks (350 and 352 Hz) are struck simultaneously. The resulting sound is observed to:
8.26. When listening to tuning forks of frequency 256 Hz and 260 Hz, one hears the following number of beats per second:
8.27. Two identical tuning forks vibrate at 256 Hz. One of them is then loaded with a drop of wax, after which 6 beats/s are heard. The period of the loaded tuning fork is:
8.28. The sound intensity 5.0m from a point source is 0.50W/m2. The power output of the source is:
8.29. The intensity of a certain sound wave is 6 μW/cm2. If its intensity is raised by 10 db, the new intensity (in μW/cm2) is:
8.30. The sound level at a point P is 14 db below the sound level at a point 1.0m from a point source. The distance from the source to point P is:
8.31. A piano wire has a length of 81 cm and a mass of 2.0 g. If its fundamental frequency is to be 394 Hz, its tension must be:
8.32. A column of argon is open at one end and closed at the other. The shortest length of such a column that will resonate with a 200 Hz tuning fork is 42.5 cm. The speed of sound in argon must be:
8.33. A 1024 Hz tuning fork is used to obtain a series of resonance levels in a gas column of variable length, with one end closed and the other open. The length of the column changes by 20 cm from resonance to resonance. From this data, the speed of sound in this gas is: