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Chapter 15: Q4Q (page 435)
Which of the following relationships between the acceleration a and the displacement x of a particle involve SHM: (a) a=0.5x, (b) a=400, (c) a=20x, (d)a=-3?
The relationship between acceleration and displacement is a=-20x .
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Figure 15-25shows plots of the kinetic energy K versus position x for three harmonic oscillators that have the same mass. Rank the plots according to (a) the corresponding spring constant and (b) the corresponding period of the oscillator, greatest first.
A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. 15-58a Figuregives the magnitude of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle . The vertical axis scale is set by =.The disk is rotated to rad and then released. Figure 15-58bshows the resulting oscillation in terms of angular position versus time t. The horizontal axis scale is set by . (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speedof the disk? (Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol. Hint: The potential energy U of a torsion pendulum is equal to , analogous to for a spring.)
The amplitude of a lightly damped oscillator decreases by 3.0 %during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
A uniform spring with k = 8600 N.mis cut into pieces 1and 2of unstretched lengths and. What are (a)and (b)? A block attached to the original spring as in Fig.15-7oscillates at 200 Hz. What is the oscillation frequency of the block attached to (c) piece 1and (d) piece 2?
A block weighing 10.0 Nis attached to the lower end of a vertical spring (), the other end of which is attached to a ceiling. The block oscillates vertically and has a kinetic energy of 2.00 Jas it passes through the point at which the spring is unstretched. (a) What is the period of the oscillation? (b) Use the law of conservation of energy to determine the maximum distance the block moves both above and below the point at which the spring is unstretched. (These are not necessarily the same.) (c) What is the amplitude of the oscillation? (d) What is the maximum kinetic energy of the block as it oscillates?
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