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1 第 1 頁, 共 6 頁 Chap15 1. Test Bank, Question 23 The displacement of an object oscillating on a spring is given by x(t) = x m cos( t + ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant is: 0 /2 radians radians 3 /2 radians 2 radians 2. *Chapter 15, Problem 21 In Fig , two springs are attached to a block that can oscillate over a frictionless floor. If the left spring is removed, the block oscillates at a frequency of 33 Hz. If, instead, the spring on the right is removed, the block oscillates at a frequency of 45 Hz. At what frequency (in Hz) does the block oscillate with both springs attached? Number Units Hz 3. *Chapter 15, Problem 25 In Fig , a block weighing 14.1 N, which can slide without friction on an incline at angle θ = , is connected to the top of the incline by a massless spring of spring constant 150 N/m. The block is initially at its equilibrium position. Then it is pulled down the incline by a short distance x and released. With what period does it oscillate? Fig Number Units s

2 第 2 頁, 共 6 頁 4. *Chapter 15, Problem 17 An oscillator consists of a block attached to a spring (k = 334 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = m, v = m/s, and a = -107 m/s 2. Calculate (a) the frequency (in Hz) of oscillation, (b) the mass of the block, and (c) the amplitude of the motion. (a) Number Units Hz (b) Number Units kg (c) Number Units m 5. *Chapter 15, Problem 22 Figure shows block 1 of mass kg sliding to the right over a frictionless elevated surface at a speed of 9.45 m/s. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant 1181 N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of s, and block 1 slides off the opposite end of the elevated surface, landing a distance d from the base of that surface after falling height h = 5.70 m. What is the value of d? Number Unit m 6. Test Bank, Question 40 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: zero 12.5 J 25 J 37.5 J 50 J

3 第 3 頁, 共 6 頁 7. *Chapter 15, Problem 36 If the phase angle for a block-spring system in SHM is π/9 rad and the block's position is given by x = x m cos(ωt + φ), what is the ratio of the kinetic energy to the potential energy at time t = 0? Number Units This answer has no units 8. *Chapter 15, Problem 37 A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position y i such that the spring is at its rest length. The object is then released from y i and oscillates up and down, with its lowest position being 14 cm below y i. (a) What is the frequency (in Hz) of the oscillation? (b) What is the speed of the object when it is 11 cm below the initial position? (c) An object of mass 170 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass (in kg) of the first object? (d) How far below y i is the new equilibrium (rest) position with both objects attached to the sping? (a) Number Units Hz (b) Number Units m/s (c) Number Units kg (d) Number 0.28 Units m 9. *Chapter 15, Problem 100 In Figure 15-57, a solid cylinder attached to a horizontal spring (k = 3.40 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 4.30 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) (a) Number Units J (b) Number Units J (c) Number Units s 10. *Chapter 15, Problem 49 The angle (with respect to the vertical) of a simple pendulum is given by θ = θ m cos[(5.54 rad/s)t + φ]. If at t = 0, θ = rad and dθ/dt = rad/s, what are (a) the phase constant φ and (b) the maximum angle θ m? (Hint: Don't confuse the rate dθ/dt at which θ changes with the ω of the SHM.)

4 第 4 頁, 共 6 頁 (a) Number Unit rad (b) Number Unit rad 11. *Chapter 15, Problem 70 A wheel is free to rotate about its fixed axle. A spring with constant k = 160 N/m is attached to one of its spokes a distance r = 23 cm from the axle, as shown in Fig (a) Assuming that the wheel is a hoop of mass m = 240 g and radius R = 1.4 m, what is the angular frequency ω of small oscillations of this system? What is ω if (b)r = R and (c)r = 0? (a) Number Units rad/s (b) Number Units rad/s (c) Number 0 Units rad/s 12. *Chapter 15, Problem 51 In Fig , a stick of length L = 1.3 m oscillates as a physical pendulum. (a) What value of distance x between the stick's center of mass and its pivot point O gives the least period? (b) What is that least period?

5 第 5 頁, 共 6 頁 (a) Number Units m (b) Number Units s 13. *Chapter 15, Problem 82 A simple pendulum of length 13 cm and mass 100 g is suspended in a race car traveling with constant speed 59 m/s around a circle of radius 19 m. If the pendulum undergoes small oscillations in a radial direction about its equilibrium position, what is the frequency (in Hz) of oscillation? Number Units Hz 14. *Chapter 15, Problem 92 A grandfather clock has a pendulum that consists of a thin brass disk of radius r = cm and mass kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in Fig If the pendulum is to have a period of s for small oscillations at a place where g = m/s 2, what must be the rod length L (in m)? Number Units m

6 第 6 頁, 共 6 頁 15. Test Bank, Question 59 A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by: the damping force the initial amplitude the initial velocity the force of gravity none of the above 16. Test Bank, Question 60 An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time: its amplitude is a decreasing function of time its amplitude is a decreasing function of time only if the damping constant is large its amplitude is constant its amplitude increases over some portions of a cycle and decreases over other portions its amplitude is an increasing function of time