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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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In Figure, two identical springs of spring constantare attached to a block of mass. What is the frequency of oscillation on the frictionless floor?
The physical pendulum in Fig. 15-62 has two possible pivot points A and B. Point A has a fixed position but B is adjustable along the length of the pendulum as indicated by the scaling. When suspended from A, the pendulum has a period of. The pendulum is then suspended from B, which is moved until the pendulum again has that period. What is the distance L between A and B?
A 0.10 kgblock oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by. (a) What is the oscillation frequency? (b) What is the maximum speed acquired by the block? (c) At what value of x does this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what value of x does this occur? (f) What force, applied to the block by the spring, results in the given oscillation?
The center of oscillation of a physical pendulum has this interesting property: If an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations are felt at the point of support. Baseball players (and players of many other sports) know that unless the ball hits the bat at this point (called the 鈥渟weet spot鈥� by athletes), the oscillations due to the impact will sting their hands. To prove this property, let the stick in Fig. simulate a baseball bat. Suppose that a horizontal force (due to impact with the ball) acts toward the right at P, the center of oscillation. The batter is assumed to hold the bat at O, the pivot point of the stick. (a) What acceleration does the point O undergo as a result of? (b) What angular acceleration is produced by about the center of mass of the stick? (c) As a result of the angular acceleration in (b), what linear acceleration does point O undergo? (d) Considering the magnitudes and directions of the accelerations in (a) and (c), convince yourself that P is indeed the 鈥渟weet spot.
A simple harmonic oscillator consists of a block attached to a spring with k=200 N/m. The block slides on a frictionless surface, with an equilibrium point x=0and amplitude 0.20 m. A graph of the block鈥檚 velocity v as a function of time t is shown in Fig. 15-60. The horizontal scale is set by. What are (a) the period of the SHM, (b) the block鈥檚 mass, (c) its displacement at, (d) its acceleration at, and (e) its maximum kinetic energy.
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