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Chapter 15: Q8P (page 436)
What is the phase constant for the harmonic oscillator with the position functiongiven in Figure if the position function has the form? The vertical axis scale is set by.
Phase constant for motion is 1.91 rad
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Question: A physical pendulum consists of two-meter-long sticks joined together as shown in Figure. What is the pendulum’s period of oscillation about a pin inserted through point at the center of the horizontal stick?
A vertical spring stretches 9.6 cmwhen a 1.3 kgblock is hung from its end. (a) Calculate the spring constant. This block is then displaced an additional 5.0 cmdownward and released from rest. Find the (b) period, (c) frequency, (d) amplitude, and (e) maximum speed of the resulting SHM.
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.)
You are to build the oscillation transfer device shown in Fig.15-27. It consists of two spring–block systems hanging from a flexible rod. When the spring of system is stretched and then released, the resulting SHM of system at frequency oscillates the rod. The rod then exerts a driving force on system 2, at the same frequency . You can choose from four springs with spring constants k of 1600,1500,1400, and 1200 N/m, and four blocks with masses m of 800,500,400, and 200 kg. Mentally determine which spring should go with which block in each of the two systems to maximize the amplitude of oscillations in system 2.
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.
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