Chapter 11 Questions
A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring? A) 24.1 N/m B) 0.610 N/m C) 0.102 N/m D) 2.45 N/m E) 12.1 N/m
A) 24.1 N/m
An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earthʹs gravitational field. The spring stretches 2.2 cm before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency? A) 3.4 Hz B) 0.52 Hz C) 1.6 Hz D) 0.28 x 10^-3 Hz
A) 3.4 Hz
An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object? A) T B) 4T C) T/2 D) T/4 E) 2T
A) T
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity? A) The period does not change. B) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. C) The period decreases. D) The period becomes zero. E) The period increases.
A) The period does not change
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum? A) one-third of the way between A and B B) midway between A and B C) one-fourth of the way between A and B D) at either A or B E) at none of the above points
B) midway between A and B
In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.) A) when the magnitude of the acceleration is a maximum B) when the potential energy is a zero C) when the magnitude of the acceleration is a minimum D) when the potential energy is a maximum E) when the displacement is a maximum
B) when the potential energy is a zero C) when the magnitude of the acceleration is a minimum
A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute? A) 8.53 B) 512 C) 30,700 D) 1610 E) 26.8
C) 30,700
A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is4.9 m, how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables. A) 5.3 s B) 5.7 s C) 4.4 s D) 4.8 s
C) 4.4 s
If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct choice.) A) 600 Hz B) 300 Hz C) 500 Hz D) 75 Hz E) 450 Hz
C) 500 Hz D) 75 Hz
A simple pendulum takes 2.00 s to make one complete swing. If we now triple the length, how long will it take for one complete swing? A) 1.15 s B) 0.667 s C) 6.00 s D) 3.46 s E) 2.00 s
D) 3.46 s
A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 570 N/m. The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is x = 0.057 m, its kinetic energy is closest to A) 0.84 J. B) 0.90 J. C) 1.1 J. D) 1.0 J. E) 0.95 J.
B) 0.90
If a wave has a speed of 362 m/s and a period of 4.17 ms, what is its wavelength? A) 86.8 m B) 1.51 m C) 86,800 m D) 0.0115 m E) 1510 m
B) 1.51 s
A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0.00 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2. The force constant (spring constant) of the spring is closest to A) 11 N/m. B) 15 N/m. C) 12 N/m. D) 13 N/m. E) 14 N/m.
B) 15 N/mA
If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration? A) 250 Hz B) 1500 Hz C) 1750 Hz D) 750 Hz
B) 1500 Hz
A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant (force constant) of the bungee cord? A) 19.6 N/m B) 16.3 N/m C) 26.1 N/m
B) 16.3
If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4
B) 4
What is the frequency of a pressure wave of wavelength 2.5 m that is traveling at 1400 m/s? A) 5.6 kHz B) 560 Hz C) 1.78 kHz D) 178 Hz
B) 560 Hz
A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal segments? A) 120 Hz B) 600 Hz C) 240 Hz D) 360 Hz
B) 600 Hz
Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string? A) A B) B C) C D) D E) E
B) B
If both the mass of a simple pendulum and its length are doubled, the period will A) increase by a factor of 2. B) increase by a factor of sqrt(2). C) increase by a factor of 1/sqrt(2). D) be unchanged. E) increase by a factor of 4.
B) Increase by a factor of sqrt(2)
Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Decrease the amplitude of swing by a small amount. B) Lower the weight. C) Remove some mass from the weight. D) Raise the weight. E) Add more mass to the weight.
B) Lower the weight
Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B? A) 2T B) T C) T 2 D) T/ 2 E) T/2
B) T
A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period? A) T/ sqrt(2) B) T sqrt(2) C) T/2 D) 2T E) T
B) T sqrt(2)
A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be? A) T/3 B) T/sqrt(3 ) C) 3T D) T E) sqrt(3T)
B) T/sqrt(3)
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum? A) midway between A and B B) at either A or B C) one-fourth of the way between A and B D) one-third of the way between A and B E) at none of the above points
B) at either A or B
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum? A) one-third of the way between A and B B) midway between A and B C) one-fourth of the way between A and B D) at either A or B E) at none of the above points
B) at either A or B
A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its elastic potential energy is zero. B) Its speed is zero. C) Its acceleration is zero. D) Its kinetic energy is a maximum. E) Its total mechanical energy is zero.
B)Its speed is zero
A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also increase? (There could be more than one correct choice.) A) the wavelength of the traveling waves on the string B) the period of the traveling waves on the string C) the speed of the traveling waves on the string D) the amplitude of the traveling waves on the string E) none of the above
E) none of the above
When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string? A) v/2 B) 4v C) v/sqrt(2) D) 2v E) vsqrt(2)
E) vsqrt(2)
A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total mechanical energy of the system? A) 0.0101 J B) 0.269 J C) 0.0201 J D) 0.134 J E) 0 J
A) 0.0101 JD
Transverse waves travel at 43.2 m/s in a string that is subjected to a tension of 60.5 N. If the string is 15.9 m long, what is its mass? A) 0.515 kg B) 0.597 kg C) 0.216 kg D) 0.366 kg
A) 0.515 kg
What is the length of a simple pendulum with a period of 2.0 s? A) 0.99 m B) 1.6 m C) 20 m D) 1.2 m E) 0.87 m
A) 0.99 m
How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz? A) 1.00 kg B) 6.29 kg C) 1.56 kg D) 39.5 kg E) 2.00 kg
A) 1.00 kg
If your heart is beating at 76.0 beats per minute, what is the frequency of your heartʹs oscillations in hertz? A) 1.27 Hz B) 2.54 Hz C) 1450 Hz D) 4560 Hz E) 3.98 Hz
A) 1.27 Hz
A leaky faucet drips 40 times in 30.0 s. What is the frequency of the dripping? A) 1.3 Hz B) 1.6 Hz C) 0.75 Hz D) 0.63 Hz
A) 1.3 Hz
A fisherman fishing from a pier observes that the float on his line bobs up and down, taking 2.4 s to move from its highest point to its lowest point. He also estimates that the distance between adjacent wave crests is 48 m. What is the speed of the waves going past the pier? A) 10 m/s B) 5.0 m/s C) 1.0 m/s D) 20 m/s E) 120 m/s
A) 10 m/s
An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s? A) 14.9 cm/s^2 B) 1.33 cm/s^2 C) 11.5 cm/s^2 D) 0.00 cm/s^2 E) 0.784 cm/s^2
A) 14.9 cm/s^2
If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4
A) 2
If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4
A) 2
The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation? A) 30.5 μs B) 0.191 ms C) 9.71 μs D) 15.3 μs E) 95.8 μs
A) 30.5 μs
If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change? A) 4 B) 2/π C) 2 D) sqrt(2)
A) 4
A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency? A) 4.6 Hz B) 3.2 Hz C) 2.3 Hz D) 1.4 Hz
A) 4.6 Hz
In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale? A) 650 N/m B) 820 N/m C) 410 N/m D) 600 N/m E) 330 N/m
A) 650 N/m
The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency 660 Hz in steel? A) 7.58 m B) 1.21 m C) 0.132 m D) 2.41 m E) 0.829 m
A) 7.58 m
A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 360 N/m. The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position is x = -0.037 m, what is the acceleration of the block? A) 83 m/s^2 B) 43 m/s^2 C) 64 m/s^2 D) 370 m/s^2 E) 270 m/s^2
A) 83 m/s^2
Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same period? A) I and III, and also II and IV B) I and II, and also III and IV C) I and IV, and also II and III D) All of them have the same period. E) They all have different periods.
A) I and III, and also II and IV
A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its elastic potential energy is zero. B) Its acceleration is zero. C) Its speed is zero. D) Its total mechanical energy is zero. E) Its kinetic energy is a maximum.
A) Its elastic potential energy is zero B) Its acceleration is zero E) Its kinetic energy is a maximum
Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Raise the weight. B) Remove some mass from the weight. C) Add more mass to the weight. D) Lower the weight. E) Increase the amplitude of swing by a small amount.
A) Raise the weight
If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.) A) The period is reduced to one-half of what it was. B) The angular frequency is doubled. C) The amplitude is doubled. D) The angular frequency is reduced to one-half of what it was. E) The period is doubled.
A) The period is reduced to one half of what it was B)The angular frequency is doubled
The total mechanical energy of a simple harmonic oscillating system is A) a non-zero constant. B) a maximum when it passes through the equilibrium point. C) zero as it passes the equilibrium point. D) zero when it reaches the maximum displacement. E) a minimum when it passes through the equilibrium point.
A) a non-zero constant
The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I? A) d/sqrt(2) B) d/4 C) d/8 D) d/2
A) d/sqrt(2)
A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency? A) f B) f/2 C) f/4 D) 2f E) 4f
A) f
An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a maximum? A) midway between A and B B) at either A or B C) one-fourth of the way between A and B D) one-third of the way between A and B E) at none of the above points
A) midway between A and B
When a guitar is tuned to adjust it pitch, what is it that is changed? A) The frequency of the fundamental. B) The wavelength of the fundamental. C) The amplitude of the fundamental.
A) the frequency of the fundamental
A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami? A) 1.1 Hz B) 0.00026 Hz C) 0.93 Hz D) 6.8 Hz E) 0.15 Hz
B) 0.00026 Hz
When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations? A) 0.0769 s B) 0.695 s C) 1.44 s D) 0.483 s E) 0.286 s
B) 0.695 s
A package is oscillating on a spring scale with a period of 4.60 s. At time t = 0.00 s the package has zero speed and is at x = 8.30 cm. At what time after t = 0.00 s will the package first be at x = 4.15 cm? A) 1.15 s B) 0.575 s C) 0.767 s D) 1.53 s E) 1.30 s
C) 0.767
A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations? A) 2.57 s B) 0.263 s C) 1.29 s D) 1.14 s E) 0.527 s
C) 1.29 s
A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 450 N/m. The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. The maximum elastic potential energy of the system is closest to A) 1.8 J. B) 1.7 J. C) 1.4 J. D) 1.3 J. E) 1.6 J.
C) 1.4 J
A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point? A) 2.58 s B) 21.5 s C) 4.11 s D) 32.2 s E) 42.9 s
C) 4.11 sA
An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the objectʹs angular frequency? A) 4.0 rad/s B) 4.8 rad/s C) 4.3 rad/s D) 3.5 rad/s
C) 4.3 rad/s
A piano wire of linear mass density 0.0050 kg/m is under a tension of 1350 N. What is the wave speed in this wire? A) 260 m/s B) 130 m/s C) 520 m/s D) 1040 m/s
C) 520 m/s
Crests of an ocean wave pass a pier every 10.0 s. If the waves are moving at 5.6 m/s, what is the wavelength of the ocean waves? A) 64 m B) 48 m C) 56 m D) 28 m
C) 56 m
The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source? A) 2I B) I/sqrt(2) C) I/4 D) I/2 E) 4I
C) I/4
Why does the intensity of waves from a small source decrease with the square of the distance from the source? A) The frequency of the waves decreases as they get farther from the source. B) The waves slow down as they travel away from the source. C) The waves spread out as they travel. D) The medium through which the waves travel absorbs the energy of the waves. E) The waves run out of energy as they travel.
C) The waves spread out as they travel
On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? A) T/ sqrt(6) B) 6T C) Tsqrt(6) D) T/3 E) T/6
C) Tsqrt(6)
In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.) A) when the displacement is a zero B) when the speed is a maximum C) when the magnitude of the displacement is a maximum D) when the potential energy is a maximum E) when the kinetic energy is a minimum
C) When the magnitude of the displacement is a maximum D) When the potential Energy is a maximum E) When the kinetic energy is a minimum
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration? A) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. B) The period increases. C) The period decreases. D) The period does not change. E) The period becomes zero.
C) the period decreases
A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems? A) Both periods would decrease. B) Both periods would increase. C) The period of the pendulum would increase but the period of the spring would stay the same. D) The period of the pendulum would decrease but the period of the spring would stay the same. E) Both periods would remain the same.
C) the period of the pendulum would increase but the period of the spring would stay the same
A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period? A) T sqrt(2) B) T/2 C) T D) 2T E) T/ sqrt(2)
C)T
A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same? A) 0.029 m B) 0.017 m C) 0.12 m D) 0.17 m
D) 0.17 m
An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. The object has a maximum displacement at t = 0.00 s of 0.232 m. If the force constant (spring constant) is 29.8 N/m, what is the potential energy stored in the mass-spring system when t = 1.42 s? A) 0.399 J B) 0.256 J C) 0.329 J D) 0.350 J
D) 0.350 JD
What is the frequency of the wave shown in the figure? A) 1 Hz. B) 4 Hz. C) 2 Hz. D) 0.5 Hz. E) It cannot be determined from the given information.
D) 0.5 Hz
A 1.53-kg piece of iron is hung by a vertical ideal spring. When perturbed slightly, the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. If we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging iron, what is the total mechanical energy of the system? A) 0.955 J B) 0.633 J C) 0.000 J D) 0.646 J E) 0.844 J
D) 0.646 J
The period of a simple pendulum that is 1.00 m long on another planet is 1.66 s. What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg? A) 17.2 m/s^2 B) 15.7 m/s^2 C) 13.3 m/s^2 D) 14.3 m/s^2
D) 14.3 m/s^2
A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) k1 and k2. What is the oscillation angular frequency of the block if k1= 7.6 N/m and k2 = 5.0 N/m? A) 0.56 rad/s B) 0.40 rad/s C) 3.5 rad/s D) 2.5 rad/s
D) 2.5 rad/s
A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s^2. If the force constant (spring constant) of the spring is 12 N/m, find the period of oscillation of this set upon a planet where g = 1.60 m/s^2. A) 5.70 s B) 4.36 s C) 2.51 s D) 3.35 s
D) 3.35 s
An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N-40? A) 9.81 m/s^2 B) 4.85 m/s^2 C) 2.39 m/s^2 D) 3.74 m/s^2 E) 1.66 m/s^2
D) 3.74 m/s^2
A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 . The mass of the block is closest to A) 2.3 kg B) 2.6 kg C) 9.4 kg D) 4.7 kg
D) 4.7 kg
An object undergoing simple harmonic motion has a maximum displacement of 6.2 m at t = 0.00 s. If the angular frequency of oscillation is 1.6 rad/s, what is the objectʹs displacement when t = 3.5 s? A) 3.7 m B) 3.1 m C) 5.6 m D) 4.8 m
D) 4.8 m
The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s^-1)t]. What is the angular frequency for this motion? A) 0.183 rad/s B) 0.869 rad/s C) 17.4 rad/s D) 5.46 rad/s E) 2.34 rad/s
D) 5.46 rad/s
A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems? A) Both periods would increase. B) Both periods would decrease. C) The period of the pendulum would decrease but the period of the spring would stay the same. D) Both periods would remain the same. E) The period of the pendulum would increase but the period of the spring would stay the same.
D) Both periods would remain the same
Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.) A) On the Moon, ball B will execute more vibrations each minute than ball A. B) Both systems will have the same period on the Moon as on Earth. C) On the Moon, ball A will take longer to complete one cycle than ball B. D) On the Moon, ball A will execute more vibrations each minute than ball B. E) On the Moon, ball B will take longer to complete one cycle than ball A.
D) On the Moon, ball A will execute more vibrations E) On the Moon, ball B will take longer to complete one cycle than ball A
An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could A) double both the amplitude and force constant (spring constant). B) double both the mass and amplitude of vibration. C) double the mass. D) double the force constant (spring constant) of the spring. E) double the amplitude of vibration.
D) double the force constant (spring constant) of the spring
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall? A) The period decreases slightly. B) The period does not change. C) The period increases slightly. D) The period becomes infinite because the pendulum would not swing. E) The period becomes zero.
D) the period becomes infinite because the pendulum would not swing
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration? A) The period does not change. B) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. C) The period decreases. D) The period increases. E) The period becomes zero.
D) the period increases
A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension? A) 2v B) 4v C) v/2 D) vsqrt(2) E) v/sqrt(2)
D) vsqrt(2)
A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension? A) v/2 B) v/sqrt(2) C) 2v D) vsqrt(2) E) 4v
D) vsqrt(2)
An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. At time t = 0.00 s the cart is released at the position x = +0.250 m. What is the position of the cart when t = 29.6 s? A) x = 0.342 m B) x = 0.218 m C) x = 0.210 m D) x = 0.0461 m E) x = -0.218 m
D) x = 0.0461 m
A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position? A) 0.45 J B) 1.4 J C) 0.90 J D) 0.22 J E) 0.00 J
E) 0.00 J
The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s^-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm? A) 7.39 s B) 7.75 s C) 0.108 s D) 4.34 s E) 0.129 s
E) 0.129 s
An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid? A) 0.0544 m/s^2 B) 5.51 m/s^2 C) 1.74 m/s^2 D) 1.66 m/s^2 E) 0.307 m/s^2
E) 0.307 m/s^2
In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. How long would it have taken for Foucaultʹs pendulum to make one complete swing back to its starting point if g = 9.81 m/s2 at the observatory? A) 2.12 s B) 1.79 s C) 5.63 s D) 2.58 s E) 6.65 s
E) 6.65 s
A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car? A) 1900 kg B) 760 kg C) 920 kg D) 990 kg E) 890 kg
E) 890 kgD
A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the greatest? A) B B) A and B C) C D) A and C E) A and D
E) A and D
Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same speed? A) III and IV B) I and III C) II and IV D) II and III E) I and II
E) I and II
What is the wavelength of the wave shown in the figure? A) 2 m. B) 4 m. C) 1 m. D) 8 m. E) It cannot be determined from the given information.
E) it cannot be determined from the given information
The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?
Graph A
The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a function of time?
Graph B
The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?
Graph B
