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A 2.0 kg block is attached to a spring that obeys Hooke's Law. An amount of energy, 16 J, is done to stretch the spring. The block is then released and oscillates with a period of 0.30 s. What is the amplitude of the motion?
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1. 38.0 cm
2. 19.0 cm
3. 9.5 cm
4. 4.3 cm
A 0.20 kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m. The block is initially displaced 4 cm from the equilibrium point and then released to set up a simple harmonic motion. What is the speed of the block when it passes through the equilibrium point?
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1. 2.13 m/s
2. 1.62 m/s
3. 1.10 m/s
4. 0.57 m/s
A runaway railroad car, with mass 30 x 104 kg, coasts across a level track at 2.0 m/s when it collides with a spring loaded bumper at the end of the track. If the spring constant of the bumper is 2 x 106 N/m, what is the maximum compression of the spring during the collision? (Assume collision is elastic.)
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1. 0.77 m
2. 0.58 m
3. 0.34 m
4. 1.07 m
A mass of 0.4 kg, hanging from a spring with a spring constant of 720 N/m, is set into an up-and-down simple harmonic motion. What is the potential energy stored in the spring alone when the mass is displaced 0.1 m?
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1. zero
2. 1.8 J
3. 3.6 J
4. 7.2 J
A mass of 0.4 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the 0.2 kg mass when moving through the equilibrium point? The starting displacement is 0.1 m.
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1. zero
2. 1.4 m/s
3. 2.0 m/s
4. 3.4 m/s
A mass of 0.4 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the 0.2 kg mass when moving through a point at 0.05 m displacement? The starting displacement is 0.1 m.
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1. zero
2. 1.4 m/s
3. 1.7 m/s
4. 1.2 m/s
A mass of 0.4 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the acceleration of the mass when at its maximum displacement of 0.1 m?
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1. zero
2. 5 m/s2
3. 10 m/s2
4. 20 m/s2
. A car with bad shocks bounces up and down with a period of 1.5 seconds after hitting a bump. The car has a mass of 1500 kg and is supported by four springs of force constant k. What is k for each spring?
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1. 6580 N/m
2. 5850 N/m
3. 4440 N/m
4. 3630 N/m
A simple pendulum has a mass of 0.25 kg and a length of 1 m. It is displaced through an angle of 30° and then released. After a time, the maximum angle of swing is only 10°. How much energy has been lost to friction?
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1. 0.29 J
2. 0.65 J
3. 0.8 J
4. 1.0 J
A 2-m long piano string of mass 10 grams is under a tension of 338 N. Find the velocity with which a wave travels on this string.
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1. 130 m/s
2. 260 m/s
3. 520 m/s
4. 1040 m/s
Transverse waves travel with a speed of 200 m/s along a taut copper wire that has a diameter of 1.5 mm. What is the tension in the wire? (The density of copper is 8.93 grams/cm3 .)
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1. 1893 N
2. 1262 N
3. 631 N
4. 315 N
An earthquake emits both P-waves and S-waves which travel at different speeds through the Earth. A P-wave travels at 9000 m/s and an S-wave at 5000 m/s. If P-waves are received at a seismic station 1 minute before an S-wave arrives, how far to the earthquake center?
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1. 2420 km
2. 1210 km
3. 680 km
4. 240 km
The motion of a piston in an automobile engine is nearly simply harmonic. If the 1 kg piston travels back and forth over a total distance of 10 cm, what is its maximum velocity when the engine is running at 3000 rpm?
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1. 31.4 m/s
2. 15.7 m/s
3. 7.8 m/s
4. 3.9 m/s
Waves propagate along a stretched string with a speed of 8 m/s. The end of the string is vibrated up and down once every 1.5 s. What is the wavelength of the waves that travel along the string?
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1. 3.0 m
2. 12.0 m
3. 6.0 m
4. 5.33 m
Consider two identical wave pulses on a string. Suppose the first pulse reaches the fixed end of the string and is reflected back and then meets the second pulse. When the two pulses overlap exactly, the superposition principle predicts that the amplitude of the resultant pulses, at that moment, will be what factor times the amplitude of one of the original pulses?
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1. 0
2. 1
3. 2
4. 4
An ore car of mass 4000 kg rolls downhill on tracks from a mine. At the end of the tracks, at 10 m elevation lower is a spring with k = 400,000 N/m. How much is the spring compressed in stopping the ore car? Ignore friction.
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1. 0.14 m
2. 0.56 m
3. 1.40 m
4. 1.96 m
Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?
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1. 1.5 mm
2. 3.5 mm
3. 5.5 mm
4. 7.5 mm
Consider the curve f = 3 cos(2px/I). The wavelength of the wave will be
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1. the distance O to A.
2. twice the distance O to A.
3. the distance x2 to x3.
4. twice the distance x2 to x3.
Tripling the mass of the bob on a simple pendulum will cause a change in the frequency of the pendulum swing by what factor?
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1. 0.33
2. 1.0
3. 3.0
4. 9.0
By what factor must one change the weight suspended vertically from a spring coil in order to triple its period of simple harmonic motion?
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1. 1/9
2. 0.33
3. 3.0
4. 9.0
Tripling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?
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1. 0.33
2. 1.0
3. 3.0
4. 9.0
By what factor should the length of a simple pendulum be changed if the period of vibration were to be tripled?
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1. 1/9
2. 0.33
3. 3.0
4. 9.0
Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?
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1. velocity
2. acceleration
3. kinetic energy
4. frequency
The wavelength of a traveling wave is a function of which of the following?
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1. frequency
2. velocity
3. both frequency and velocity are valid
4. amplitude
A coil spring, with a spring constant of 120 N/m, will be stretched to what displacement by a 60 N force?
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1. 0.5 m
2. 2.0 m
3. 4.0 m
4. 7200 m
If one could transport a simple pendulum of constant length from the Earth's surface to the moon's, where the acceleration due to gravity is one-sixth (1/6th) that on the Earth, by what factor would the pendulum frequency be changed?
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1. almost 6.0
2. almost 2.5
3. almost 0.4
4. almost 0.17
The tension in a guitar string is increased by a factor of two. By what factor does the wave velocity change?
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1. 2.0
2. 1.4
3. 0.7
4. 0.5
If the frequency of a traveling wave train is increased by a factor of three in a medium where the velocity is constant, which of the following is the result?
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1. amplitude is one-third as big
2. amplitude is tripled
3. wavelength is one-third as big
4. wavelength is tripled
What is the phase difference when two waves, traveling in the same medium, undergo constructive interference?
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1. 270°
2. 180°
3. 90°
4. 0°
The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement is at what point in its swing?
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1. zero displacement
2. 1/4 the amplitude
3. 1/2 the amplitude
4. equals the amplitude
Tripling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?
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1. 0.33
2. 1.0
3. 3.0
4. 9.0
A 0.2 kg object is suspended from a spring with spring constant, k = 10 N/m, and moves with simple harmonic motion. At the instant that it is displaced from equilibrium by -0.05 m, what is its acceleration?
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1. 1000 m/s2
2. 40 m/s2
3. 0.1 m/s2
4. 2.5 m/s2
A 0.2 kg object is suspended from a spring with a spring constant of k = 10 N/m. The object moves with simple harmonic motion and has an amplitude of 0.08 m. What is the potential energy of the system when the object displacement is 0.08 m?
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1. 0.40 J
2. zero
3. 3.2 x 10-2 J
4. 62.5 J
A 0.2 kg object, suspended from a spring with a spring constant of k = 10 N/m, is moving in simple harmonic motion and has an amplitude of 0.08 m. What is its velocity at the instant when its displacement is 0.04 m? (Hint: Use conservation of energy.)
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1. 9.8 m/s
2. 4.9 m/s
3. 49.0 cm/s
4. 24.5 cm/s
If a force of 50 N stretches a spring 0.10 m, what is the spring constant of the spring?
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1. 5.0 N/m
2. 500 N/m
3. 0.002 N/m
4. 0.25 N/m
Replacing an object on a spring with one of nine times the mass will have the result of changing the frequency of the vibrating spring by what factor?
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1. 1/9
2. 0.33
3. 3.0
4. 9.0
A simple pendulum of length 1 m has a mass of 100 grams attached, is drawn back 30° and then released. What is the maximum velocity of the mass?
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1. 1.14 m/s
2. 3.13 m/s
3. 2.21 m/s
4. 1.62 m/s
Consider the curve x = A sin(kt), with A > 0. At which point on the graph below is it possible that t = 0?
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1. Point A
2. Point B
3. Point C
4. Point D
Suppose a 0.30 kg mass on a spring-loaded gun that has been compressed 0.10 m has elastic potential energy of 1.0 J. How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?
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1. 0.10 m
2. 3.3 m
3. 0.34 m
4. 10 m
As a gust of wind blows across a field of grain, a wave can be seen to move across the field as the tops of the plants sway back and forth. This wave is a
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1. transverse wave
2. longitudinal wave
3. polarized wave
4. interference of waves
For a wave on the ocean, the amplitude is
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1. the distance between crests.
2. the height difference between a crest and a trough.
3. one-half the height difference between a crest and a trough.
4. how far the wave goes up on the beach.
For a mass suspended on a spring in the vertical direction, the time for one complete oscillation will depend on
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1. the value for g (the acceleration of gravity).
2. the distance the mass was originally pulled down.
3. the maximum speed of the oscillating mass.
4. none of these.
Suppose a 0.3 kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1 J. What is the spring constant?
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1. 10 N/m
2. 20 N/m
3. 200 N/m
4. 300 N/m
Suppose a 0.3 kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.0 J. How much further must the spring be compressed to triple the elastic potential energy?
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1. 0.30 m
2. 0.20 m
3. 0.17 m
4. 0.07 m
Which is not an example of approximate simple harmonic motion?
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1. A ball bouncing on the floor.
2. A child swinging on a swing.
3. A piano string that has been struck.
4. A car's radio antenna as it waves back and forth.
Tripling the tension in a guitar string will result in changing the wave velocity in the string by what factor?
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1. 0.58
2. 1.00
3. 1.73
4. 3.00
Tripling the density, in mass per unit length, of a guitar string will result in changing the wave velocity in the string by what factor?
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1. 0.58
2. 1.00
3. 1.73
4. 3.00
If a wave pulse is reflected from a free boundary, which of the following choices best describes what happens to the reflected pulse?
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1. becomes inverted
2. remains upright
3. halved in amplitude
4. doubled in amplitude
A radio wave has a speed of 3 x 108 m/s and a frequency of 107.7 MHz. What is its wavelength?
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1. 3.21 m
2. 45.0 m
3. 0.10 m
4. 2.78 m
An object moving in simple harmonic motion has an amplitude of 0.02 m and a maximum acceleration of 40 m/s2 . What is the frequency of the system?
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1. 0.60 Hz
2. 51.0 Hz
3. 7.1 Hz
4. 16.0 Hz
Suppose there is an object for which F = +kx. What will happen if the object is moved away from equilibrium (x = 0) and released?
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1. It will return to the equilibrium position.
2. It will move further away with constant velocity.
3. It will move further away with constant acceleration.
4. It will move further away with increasing acceleration.
A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the displacement of the mass when t = 3.7 s?
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1. zero
2. 0.025 m
3. 0.036 m
4. 0.080 m
A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If the mass of the object is 0.20 kg, what is the spring constant?
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1. 40 N/m
2. 87 N/m
3. 126 N/m
4. 160 N/m
A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the acceleration magnitude when t = 3 s?
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1. zero
2. 0.13 m/s2
3. 0.33 m/s2
4. 0.51 m/s2
If a simple pendulum has a period of 2.0 s, what is the pendulum length? (g = 9.8 m/s2 )
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1. 0.36 m
2. 0.78 m
3. 0.99 m
4. 2.45 m
A traveling wave train has a wavelength of 0.50 m and a speed of 20 m/s. What is the wave frequency?
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1. 0.025 Hz
2. 20 Hz
3. 40 Hz
4. 10 Hz
A musical tone, sounded on a piano, has a frequency of 410 Hz and a wavelength in air of 0.80 m. What is the wavespeed?
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1. 170 m/s
2. 235 m/s
3. 328 m/s
4. 587 m/s
The oxygen molecule (O2 ) may be regarded as two masses
connected by a spring. In vibrational motion, each oxygen atom alternately approaches, then moves away from the center of mass of the system. If each oxygen atom of mass (m = 2.67 x 10-26 kg) has a vibrational energy of 1.6 x 10-21 J, and the effective spring constant is 50 N/m, then what is the amplitude of oscillation of each oxygen atom?
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1. 3.2 x 10-11 m
2. 1.6 x 10-11 m
3. 1.1 x 10-11 m
4. 8.0 x 10-12 m
A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the speed of the mass when t = 3 s?
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1. zero
2. 0.0065 m/s
3. 0.015 m/s
4. 0.024 m/s
A 0.20 kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m. The block is initially displaced 4 cm from the equilibrium point and then released to set up a simple harmonic motion. Suppose that a frictional force of 0.3 N exists between the block and surface. What is the speed of the block when it passes through the equilibrium point after being released from the 4.0 cm displacement point?
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1. 0.45 m/s
2. 0.63 m/s
3. 0.80 m/s
4. 1.16 m/s
