Oscillations Chapter 15 Test Bank Answers - Physics Extended 11e | Test Bank by Halliday by David Halliday. DOCX document preview.
Chapter: Chapter 15
Learning Objectives
LO 15.1.0 Solve problems related to simple harmonic motion.
LO 15.1.1 Distinguish simple harmonic motion from other types of periodic motion.
LO 15.1.2 For a simple harmonic oscillator, apply the relationship between position x and time t to calculate either if given a value for the other.
LO 15.1.3 Relate period T, frequency f, and angular frequency ω.
LO 15.1.4 Identify (displacement) amplitude xm, phase constant (or phase angle) φ, and phase ωt + φ.
LO 15.1.5 Sketch a graph of the oscillator’s position x versus time t, identifying amplitude xm and period T.
LO 15.1.6 From a graph of position versus time, velocity versus time, or acceleration versus time, determine the amplitude of the plot and the value of the phase constant φ.
LO 15.1.7 On a graph of position x versus time t, describe the effects of changing period T, frequency f, amplitude xm, or phase constant φ.
LO 15.1.8 Identify the phase constant φ that corresponds to the starting time (t = 0) being set when a particle in SHM is at an extreme point or passing through the center point.
LO 15.1.9 Given an oscillator’s position x(t) as a function of time, find its velocity v(t) as a function of time, identify the velocity amplitude vm in the result, and calculate the velocity at any given time.
LO 15.1.10 Sketch a graph of an oscillator’s velocity v versus time t, identifying the velocity amplitude vm.
LO 15.1.11 Apply the relationship between velocity amplitude vm, angular frequency ω, and (displacement) amplitude xm.
LO 15.1.12 Given an oscillator’s velocity v(t) as a function of time, calculate its acceleration a(t) as a function of time, identify the acceleration amplitude am in the result, and calculate the acceleration at any given time.
LO 15.1.13 Sketch a graph of an oscillator’s acceleration a versus time t, identifying the acceleration amplitude am.
LO 15.1.14 Identify that for a simple harmonic oscillator the acceleration a at any instant is always given by the product of a negative constant and the displacement x just then.
LO 15.1.15 For any given instant in an oscillation, apply the relationship between acceleration a, angular frequency ω, and displacement x.
LO 15.1.16 Given data about the position x and velocity v at one instant, determine the phase ωt + φ and phase constant φ.
LO 15.1.17 For a spring-block oscillator, apply the relationships between spring constant k and mass m and either period T or angular frequency ω.
LO 15.1.18 Apply Hooke’s law to relate the force F on a simple harmonic oscillator at any instant to the displacement x of the oscillator at that instant.
LO 15.2.0 Solve problems related to energy in simple harmonic motion.
LO 15.2.1 For a spring-block oscillator, calculate the kinetic energy and elastic potential energy at any given time.
LO 15.2.2 Apply the conservation of energy to relate the total energy of a spring-block oscillator at one instant to the total energy at another instant.
LO 15.2.3 Sketch a graph of the kinetic energy, potential energy, and total energy of a spring-block oscillator, first as a function of time and then as a function of the oscillator’s position.
LO 15.2.4 For a spring-block oscillator, determine the block’s position when the total energy is entirely kinetic energy and when it is entirely potential energy.
LO 15.3.0 Solve problems related to an angular simple harmonic oscillator.
LO 15.3.1 Describe the motion of an angular simple harmonic oscillator.
LO 15.3.2 For an angular simple harmonic oscillator, apply the relationship between the torque τ and the angular displacement θ (from equilibrium).
LO 15.3.3 For an angular simple harmonic oscillator, apply the relationship between the period T (or frequency f), the rotational inertia I, and the torsion constant κ.
LO 15.3.4 For an angular simple harmonic oscillator at any instant, apply the relationship between the angular acceleration α, the angular frequency ω, and the angular displacement θ.
LO 15.4.0 Solve problems related to pendulums, circular motion.
LO 15.4.1 Describe the motion of an oscillating simple pendulum.
LO 15.4.2 Draw a free-body diagram of the pendulum bob with the pendulum at angle θ to the vertical.
LO 15.4.3 For small-angle oscillations of a simple pendulum, relate the period T (or frequency f) to the pendulum’s length L.
LO 15.4.4 Distinguish between a simple pendulum and a physical pendulum.
LO 15.4.5 For small-angle oscillations of a physical pendulum, relate the period T (or frequency f) to the distance h between the pivot and the center of mass.
LO 15.4.6 For an oscillating system, determine the angular frequency ω from either an equation relating torque τ and angular displacement θ or an equation relating angular acceleration α and angular displacement θ.
LO 15.4.7 Distinguish between a pendulum’s angular frequency ω (having to do with the rate at which cycles are completed) and its dθ/dt (the rate at which its angle with the vertical changes).
LO 15.4.8 Given data about the angular position θ and rate of change dθ/dt at one instant, determine the phase constant and amplitude θm.
LO 15.4.9 Describe how the free-fall acceleration can be measured with a simple pendulum.
LO 15.4.10 For a given physical pendulum, determine the location of the center of oscillation.
LO 15.4.11 Describe how simple harmonic motion is related to uniform circular motion.
LO 15.5.0 Solve problems related to damped simple harmonic motion.
LO 15.5.1 Describe the motion of a damped simple harmonic oscillator and sketch a graph of the oscillator’s position as a function of time.
LO 15.5.2 For any particular time, calculate the position of a damped simple harmonic oscillator.
LO 15.5.3 Determine the amplitude at any given time.
LO 15.5.4 Calculate the angular frequency of a damped simple harmonic oscillator in terms of the spring constant, the damping constant, and the mass.
LO 15.5.5 Apply the equation giving the (approximate) total energy of a damped simple harmonic oscillator as a function of time.
LO 15.6.0 Solve problems related to forced oscillations and resonance.
LO 15.6.1 Distinguish between natural angular frequency ω and driving angular frequency ωd.
LO 15.6.2 For a forced oscillator, sketch a graph of the oscillation amplitude versus the ratio ωd/ω of driving angular frequency to natural angular frequency, identify the approximate location of resonance, and indicate the effect of increasing the damping constant.
LO 15.6.3 For a given natural angular frequency ω, identify the approximate driving angular frequency ωd that gives resonance.
Multiple Choice
1. A particle oscillating in simple harmonic motion is:
A) never in equilibrium because it is in motion
B) never in equilibrium because there is a force
C) in equilibrium at the ends of its path because its velocity is zero there
D) in equilibrium at the center of its path because the acceleration is zero there
E) in equilibrium at the ends of its path because the acceleration is zero there
Difficulty: E
Section: 15-1
Learning Objective 15.1.0
2. An object is undergoing simple harmonic motion. Throughout a complete cycle it:
A) has constant speed
B) has varying amplitude
C) has varying period
D) has varying acceleration
E) has varying mass
Difficulty: E
Section: 15-1
Learning Objective 15.1.0
3. When a body executes simple harmonic motion, its acceleration at the ends of its path must be:
A) zero
B) less than g
C) more than g
D) suddenly changing in sign
E) none of these
Difficulty: E
Section: 15-1
Learning Objective 15.1.0
4. A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:
A) T
B) 1.5 T
C) 2T
D) T/2
E) 4T
Difficulty: E
Section: 15-1
Learning Objective 15.1.0
5. It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:
A) masses
B) periods
C) amplitudes
D) spring constants
E) kinetic energies
Difficulty: E
Section: 15-1
Learning Objective 15.1.0
6. An oscillatory motion must be simple harmonic if:
A) the amplitude is small
B) the potential energy is equal to the kinetic energy
C) the motion is along the arc of a circle
D) the acceleration varies sinusoidally with time
E) the derivative, dU/dx, of the potential energy is negative
Difficulty: E
Section: 15-1
Learning Objective 15.1.1
7. A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At the times listed below it is at various points in its cycle. Which of them is farthest away from the equilibrium point?
A) 0.5T
B) 0.7T
C) T
D) 1.4T
E) 1.5T
Difficulty: E
Section: 15-1
Learning Objective 15.1.2
8. A particle moves back and forth along the x axis from x = –xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:
A) it is at x = 0 and is traveling toward x = +xm
B) it is at x = 0 and is traveling toward x = –xm
C) it is at x = +xm and is at rest
D) it is between x = 0 and x = +xm and is traveling toward x = –xm
E) it is between x = 0 and x = –xm and is traveling toward x = –xm
Difficulty: E
Section: 15-1
Learning Objective 15.1.2
9. A particle is in simple harmonic motion with period T. At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point. The next time it is at the same place is:
A) t = T
B) t = T/2
C) t = T/3
D) t = T/4
E) none of the above
Difficulty: M
Section: 15-1
Learning Objective 15.1.2
10. An object attached to one end of a spring makes 20 complete vibrations in 10s. Its period is:
A) 2 Hz
B) 10 s
C) 0.5 Hz
D) 2 s
E) 0.50 s
Difficulty: E
Section: 15-1
Learning Objective 15.1.3
11. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is:
A) 2 Hz
B) 10 s
C) 0.05 Hz
D) 2 s
E) 0.50 s
Difficulty: E
Section: 15-1
Learning Objective 15.1.3
12. An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its angular frequency is:
A) 0.79 rad/s
B) 1.57 rad/s
C) 2.0 rad/s
D) 6.3 rad/s
E) 12.6 rad/s
Difficulty: E
Section: 15-1
Learning Objective 15.1.3
13. Frequency f and angular frequency are related by
A) f =
B) f = 2
C) f = /
D) f = /2
E) f = 2/
Difficulty: E
Section: 15-1
Learning Objective 15.1.3
14. A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:
A) 40 cm, 2 Hz
B) 20 cm, 4 Hz
C) 40 cm, 4 Hz
D) 25 cm, 4 Hz
E) 20 cm, 2 Hz
Difficulty: E
Section: 15-1
Learning Objective 15.1.4
15. This plot shows a mass oscillating as x = xm cos (ωt + φ). What are xm and φ?
A) 1 m, 0°
B) 2 m, 0°
C) 2 m, 90°
D) 4 m, 0°
E) 4 m, 90°
Difficulty: E
Section: 15-1
Learning Objective 15.1.6
16. The amplitude and phase constant of an oscillator are determined by:
A) the frequency
B) the angular frequency
C) the initial displacement alone
D) the initial velocity alone
E) both the initial displacement and velocity
Difficulty: E
Section: 15-1
Learning Objective 15.1.8
17. In simple harmonic motion, the displacement is maximum when the:
A) acceleration is zero
B) velocity is maximum
C) velocity is zero
D) kinetic energy is maximum
E) momentum is maximum
Difficulty: E
Section: 15-1
Learning Objective 15.1.9
18. Two identical undamped oscillators have the same amplitude of oscillation only if:
A) they are started with the same displacement x0
B) they are started with the same velocity v0
C) they are started with the same phase
D) they are started so the combination is the same
E) they are started so the combination is the same
Difficulty: M
Section: 15-1
Learning Objective 15.1.11
19. The amplitude of any oscillator will be doubled by:
A) doubling only the initial displacement
B) doubling only the initial speed
C) doubling the initial displacement and halving the initial speed
D) doubling the initial speed and halving the initial displacement
E) doubling both the initial displacement and the initial speed
Difficulty: M
Section: 15-1
Learning Objective 15.1.11
20. A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds. Its maximum velocity is:
A) 100 sin(50t) m/s
B) 100 cos(50t) m/s
C) 100 m/s
D) 200 m/s
E) none of these
Difficulty: M
Section: 15-1
Learning Objective 15.1.11
21. An object of mass m, oscillating on the end of a spring with spring constant k has amplitude A. Its maximum speed is:
A)
B) A2k/m
C)
D) Am/k
E) A2m/k
Difficulty: M
Section: 15-1
Learning Objective 15.1.11
22. A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:
A) 0.0020 m
B) 0.10 m
C) 0.20 m
D) 25 m
E) 250 m
Difficulty: M
Section: 15-1
Learning Objective 15.1.11
23. The acceleration of a body executing simple harmonic motion leads the velocity by what phase?
A) 0 rad
B) /8 rad
C) /4 rad
D) /2 rad
E) rad
Difficulty: E
Section: 15-1
Learning Objective 15.1.12
24. In simple harmonic motion, the magnitude of the acceleration is greatest when:
A) the displacement is zero
B) the displacement is maximum
C) the speed is maximum
D) the force is zero
E) the speed is between zero and its maximum
Difficulty: E
Section: 15-1
Learning Objective 15.1.14
25. In simple harmonic motion:
A) the acceleration is greatest at the maximum displacement
B) the velocity is greatest at the maximum displacement
C) the period depends on the amplitude
D) the acceleration is constant
E) the acceleration is greatest at zero displacement
Difficulty: E
Section: 15-1
Learning Objective 15.1.14
26. In simple harmonic motion, the magnitude of the acceleration is:
A) constant
B) proportional to the displacement
C) inversely proportional to the displacement
D) greatest when the velocity is greatest
E) never greater than g
Difficulty: E
Section: 15-1
Learning Objective 15.1.14
27. A 1.2-kg mass is oscillating without friction on a spring whose spring constant is 3400 N/m. When the mass’s displacement is 7.2 cm, what is its acceleration?
A) −3.8 m/s2
B) −200 m/s2
C) −240 m/s2
D) −2.0 x 104 m/s2
E) cannot be calculated without more information
Difficulty: M
Section: 15-1
Learning Objective 15.1.16
29. The displacement of an object oscillating on a spring is given by x(t) = xmcos(t + ). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant is between:
A) 0 and /2 radians
B) /2 and radians
C) and 3/2 radians
D) 3/2 and 2 radians
E) none of the above ( is exactly 0, /2, , or 3/2 radians)
Difficulty: M
Section: 15-1
Learning Objective 15.1.16
30. A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The angular frequency of this mass-spring system:
A) is 0.088 rad/s
B) is 33 rad/s
C) is 200 rad/s
D) is 1140 rad/s
E) cannot be computed unless the value of M is given
Difficulty: M
Section: 15-1
Learning Objective 15.1.17
31. A 3-kg block, attached to a spring, executes simple harmonic motion according to
x = 2cos(50t) where x is in meters and t is in seconds. The spring constant of the spring is:
A) 1 N/m
B) 100 N/m
C) 150 N/m
D) 7500 N/m
E) none of these
Difficulty: M
Section: 15-1
Learning Objective 15.1.17
32. A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. The particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be:
A) 2T
B)
C)
D) T
E) T/2
Difficulty: M
Section: 15-1
Learning Objective 15.1.17
33. In simple harmonic motion, the restoring force must be proportional to the:
A) amplitude
B) frequency
C) velocity
D) displacement
E) displacement squared
Difficulty: E
Section: 15-1
Learning Objective 15.1.18
34. Let U be the potential energy (with the zero at zero displacement) and K be the kinetic energy of a simple harmonic oscillator. Uavg and Kavg are the average values over a cycle. Then:
A) Kavg > Uavg
B) Kavg < Uavg
C) Kavg = Uavg
D) K = 0 when U = 0
E) K + U = 0
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
35. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = xm, the kinetic and potential energies are:
A) K = 5 J and U = 3 J
B) K = 5 J and U = –3 J
C) K = 8 J and U = 0 J
D) K = 0 J and U = 8 J
E) K = 0 J and U = –8 J
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
36. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = –1/2 xm, the kinetic and potential energies are:
A) K = 6 J and U = 2 J
B) K = 6 J and U = –2 J
C) K = 8 J and U = 0 J
D) K = 0 J and U = 8 J
E) K = 0 J and U = –8 J
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
37. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the amplitude of the oscillation is:
A) 0.06 m
B) 0.17 m
C) 0.24 m
D) 4.9 m
E) 6.9 m
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
38. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the maximum speed of the block is:
A) 0.06 m/s
B) 0.17 m/s
C) 0.24 m/s
D) 4.9 m/s
E) 6.9 m/s
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
39. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is:
A) 0.13 m/s
B) 0.18 m/s
C) 3.7 m/s
D) 5.2 m/s
E) 13 m/s
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
40. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:
A) 0.13 m
B) 0.18 m
C) 3.7 m
D) 5.2 m
E) 13 m
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
41. An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:
A) the amplitude is half as great and the maximum acceleration is twice as great
B) the amplitude is twice as great and the maximum acceleration is half as great
C) both the amplitude and the maximum acceleration are twice as great
D) both the amplitude and the maximum acceleration are four times as great
E) the amplitude is four times as great and the maximum acceleration is twice as great
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
42. 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:
A) 0 J
B) 12.5 J
C) 25 J
D) 37.5 J
E) 50 J
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
43. A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is
A) 0
B) A/4
C)
D) A/2
E) anywhere between –A and +A
Difficulty: M
Section: 15-2
Learning Objective 15.2.1
44. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = –1/2 xm, its total energy is:
A) 0 J
B) 3 J
C) 4 J
D) 5 J
E) 8 J
Difficulty: E
Section: 15-2
Learning Objective 15.2.2
45. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When its kinetic energy is 8 J, it is at:
A) x = 0
B) x = x1
C) x = xm/2
D) x = xm/
E) x = xm
Difficulty: E
Section: 15-2
Learning Objective 15.2.4
46. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When its potential energy is 8 J, it is at:
A) x = 0
B) x = x1
C) x = xm/2
D) x = xm/
E) x = xm
Difficulty: E
Section: 15-2
Learning Objective 15.2.4
47. An angular simple harmonic oscillator:
A) oscillates at an angle to the x axis
B) oscillates along the y axis
C) involves an angular displacement and a restoring torque
D) involves an angular displacement and a restoring force
E) involves a linear displacement and a restoring torque
Difficulty: E
Section: 15-3
Learning Objective 15.3.1
48. An angular simple harmonic oscillator is displaced 5.2 x 10-2 rad from its equilibrium position. If the torsion constant is 1200 N∙m/rad, what is the torque?
A) 12 N∙m
B) 23 N∙m
C) 43 N∙m
D) 52 N∙m
E) 62 N∙m
Difficulty: E
Section: 15-3
Learning Objective 15.3.2
49. A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad. What is the angular frequency of its torsional oscillations?
A) 0.20 rad/s
B) 0.44 rad/s
C) 1.0 rad/s
D) 2.3 rad/s
E) 5.1 rad/s
Difficulty: E
Section: 15-3
Learning Objective 15.3.3
50. A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad. When its angular displacement is −0.23 rad, what is its angular acceleration?
A) 1.0 x 10-2 rad/s2
B) 4.5 x 10-2 rad/s2
C) 0.23 rad/s2
D) 0.52 rad/s2
E) 1.2 rad/s2
Difficulty: M
Section: 15-3
Learning Objective 15.3.4
51. The amplitude of oscillation of a simple pendulum is increased from 1 to 4. Its maximum acceleration changes by a factor of:
A) 1/4
B) 1/2
C) 2
D) 4
E) 16
Difficulty: M
Section: 15-4
Learning Objective 15.4.0
52. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g and a is:
A)
B)
C)
D)
E)
Difficulty: M
Section: 15-4
Learning Objective 15.4.0
53. A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension in the string is:
A) constant
B) a sinusoidal function of time
C) the square of a sinusoidal function of time
D) the reciprocal of a sinusoidal function of time
E) none of the above
Difficulty: E
Section: 15-4
Learning Objective 15.4.0
54. Three physical pendulums, with masses m1, m2 = 2m1, and m3 = 3m1, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest.
A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 2, 1, 3
E) All three are the same
Difficulty: E
Section: 15-4
Learning Objective 15.4.0
55. Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are
hoop 1: M = 150g and R = 50 cm | |
hoop 2: M = 200g and R = 40 cm | |
hoop 3: M = 250g and R = 30 cm | |
hoop 4: M = 300g and R = 20 cm | |
hoop 5: M = 350g and R = 10 cm |
Order the hoops according to the periods of their motions, smallest to largest.
A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 1, 2, 3, 5, 4
D) 1, 2, 5, 4, 3
E) 5, 4, 1, 2, 3
Difficulty: M
Section: 15-4
Learning Objective 15.4.0
56. Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?
A) a point mass
B) a massless string
C) a small amplitude
D) gravitational force
E) a large spring constant
Difficulty: E
Section: 15-4
Learning Objective 15.4.1
57. If the length of a simple pendulum is doubled, its period will:
A) halve
B) increase by a factor of
C) decrease by a factor of
D) double
E) remain the same
Difficulty: E
Section: 15-4
Learning Objective 15.4.3
58. A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f:
A) increase its length to 4L
B) increase its length to 2L
C) decrease its length to L/2
D) decrease its length to L/4
E) decrease its mass to < M/4
Difficulty: M
Section: 15-4
Learning Objective 15.4.3
59. A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:
A) 2T
B) T
C) T/2
D) T/4
E) none of the above
Difficulty: M
Section: 15-4
Learning Objective 15.4.3
60. Which of the following is the difference between a simple pendulum and a physical pendulum?
A) The physical pendulum does not rotate around its center of mass.
B) The physical pendulum does not depend on the acceleration of gravity.
C) The physical pendulum has an extended mass.
D) The simple pendulum has a small amplitude.
E) The physical pendulum rotates around its center of mass.
Difficulty: E
Section: 15-4
Learning Objective 15.4.4
61. A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?
A) a = 0.1 m
B) a = 0.2 m
C) a = 0.3 m
D) a = 0.4 m
E) a = 0.5 m
Difficulty: M
Section: 15-4
Learning Objective 15.4.5
62. Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces. The one with the longer period of oscillation is the one with:
A) the larger mass
B) the smaller mass
C) the larger rotational inertia
D) the smaller rotational inertia
E) the larger radius
Difficulty: M
Section: 15-4
Learning Objective 15.4.5
63. At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s2. What is its angular frequency of oscillation?
A) 6.6 rad/s
B) 14 rad/s
C) 20 rad/s
D) 44 rad/s
E) 200 rad/s
Difficulty: M
Section: 15-4
Learning Objective 15.4.6
64. The angular frequency of a simple pendulum depends on its length and on the local acceleration due to gravity. The rate at which the angular displacement of the pendulum changes, dθ/dt, is:
A)
B)
C) 2π
D)
E) none of the above
Difficulty: M
Section: 15-4
Learning Objective 15.4.7
65. The angular displacement of a simple pendulum is given by θ(t) = θm cos (ωt + φ). If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θm?
A) 4.6 rad
B) 3.4 rad
C) 1.4 rad
D) 0.73 rad
E) 0.45 rad
Difficulty: M
Section: 15-4
Learning Objective 15.4.8
66. 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:
A) 1 s
B) s
C) 1/10 s
D) s
E) 10 s
Difficulty: E
Section: 15-4
Learning Objective 15.4.9
67. The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:
A) 33 cm
B) 50 cm
C) 67 cm
D) 100 cm
E) 150 cm
Difficulty: M
Section: 15-4
Learning Objective 15.4.10
68. Both the x and y coordinates of a point execute simple harmonic motion. The result might be a circular orbit if:
A) the amplitudes are the same but the frequencies are different
B) the amplitudes and frequencies are both the same
C) the amplitudes and frequencies are both different
D) the phase constants are the same but the amplitudes are different
E) the amplitudes and the phase constants are both different
Difficulty: E
Section: 15-4
Learning Objective 15.4.11
69. Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be:
A) an ellipse
B) a circle
C) a parabola
D) a hyperbola
E) a square
Difficulty: E
Section: 15-4
Learning Objective 15.4.11
70. For an oscillator subjected to a damping force proportional to its velocity:
A) the displacement is a sinusoidal function of time
B) the velocity is a sinusoidal function of time
C) the frequency is a decreasing function of time
D) the mechanical energy is constant
E) none of the above is true
Difficulty: E
Section: 15-5
Learning Objective 15.5.1
71. A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle’s position at t = 5.0 s?
A) -1.5 m
B) -0.73 m
C) 0 m
D) 0.73 m
E) 1.5 m
Difficulty: H
Section: 15-5
Learning Objective 15.5.2
72. A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?
A) 1.5 m
B) 1.3 m
C) 1.0 m
D) 0.67 m
E) 0.24 m
Difficulty: M
Section: 15-5
Learning Objective 15.5.3
73. A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations?
A) 4.0 rad/s
B) 8.0 rad/s
C) 12 rad/s
D) 23 rad/s
E) 45 rad/s
Difficulty: M
Section: 15-5
Learning Objective 15.5.4
74. Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?
A) k = 100 N/m, m = 50 g, b = 8 g∙m/s
B) k = 150 N/m, m = 50 g, b = 5 g∙m/s
C) k = 150 N/m, m = 10 g, b = 8 g∙m/s
D) k = 200 N/m, m = 8 g, b = 6 g∙m/s
E) k = 100 N/m, m = 2 g, b = 4 g∙m/s
Difficulty: M
Section: 15-5
Learning Objective 15.5.5
75. Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?
k | b | m | ||
A) | k0 | b0 | m0 | |
B) | 3k0 | 2b0 | m0 | |
C) | k0/2 | 6b0 | 2m0 | |
D) | 4k0 | b0 | 2m0 | |
E) | k0 | b0 | 10m0 | |
Difficulty: M
Section: 15-5
Learning Objective 15.5.5
76. 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:
A) its amplitude is an increasing function of time
B) its amplitude is a decreasing function of time
C) its amplitude is constant
D) its amplitude is a decreasing function of time only if the damping constant is large
E) its amplitude increases over some portions of a cycle and decreases over other portions
Difficulty: E
Section: 15-6
Learning Objective 15.6.0
77. A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity. The energy dissipated by damping is supplied by:
A) the potential energy of the spring
B) the kinetic energy of the mass
C) gravity
D) friction
E) the applied force
Difficulty: E
Section: 15-6
Learning Objective 15.6.0
78. An oscillator is driven by a sinusoidal force. The frequency of the applied force:
A) must be equal to the natural frequency of the oscillator
B) becomes the natural frequency of the oscillator
C) must be less than the natural frequency of the oscillator
D) must be greater than the natural frequency of the oscillator
E) is independent of the natural frequency of the oscillator
Difficulty: E
Section: 15-6
Learning Objective 15.6.1
79. A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:
A) the damping force
B) the initial amplitude
C) the initial velocity
D) the force of gravity
E) none of the above
Difficulty: E
Section: 15-6
Learning Objective 15.6.2
80. A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:
A) half the natural frequency of the oscillator
B) the same as the natural frequency of the oscillator
C) twice the natural frequency of the oscillator
D) unrelated to the natural frequency of the oscillator
E) determined from the maximum speed desired
Difficulty: E
Section: 15-6
Learning Objective 15.6.3