# Quiz 11: Harmonic Motion and Elasticity

Physics & Astronomy

Q 1Q 1

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 from equilibrium is a maximum (hence x = 8 cm when t = 0), what is the displacement of the mass when t = 3.7 s?
A) zero
B) 0.025 m
C) 0.049 m
D) 0.080 m

Free

Multiple Choice

B

Q 2Q 2

Consider the curve x = A sin(kt), with A > 0. At which point on the graph is it possible that t = 0?
A) Point t

_{1}B) Point t_{2}C) Point t_{3}D) Point t_{4}Free

Multiple Choice

C

Q 3Q 3

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos (t/8). What is its period of oscillation?
A) 100 s
B) 32 s
C) 16 s
D) 8.0 s

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Multiple Choice

C

Q 4Q 4

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos (t/16). What is its position at t = 6.0 s?
A) 0.160 m
B) 0.159 m
C) 0.061 m
D) 0.089 m

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Multiple Choice

Q 5Q 5

If a simple harmonic motion is described by , starting from , what is the first occurrence of a value of t for which ? Assume SI units.
A) t = 0 s
B) t =
C) t =
D) t = 0.5 s

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Q 6Q 6

If a simple harmonic motion is described by , what is the period of oscillation and what is the maximum speed during the oscillation? Assume SI units.
A)
B)
C)
D)

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Q 7Q 7

If a long spring with spring constant k is cut into 3 equal lengths, what is the spring constant of each of the 3 shorter springs?
A) It is still k.
B) It is 3k.
C) It is k/3.
D) It is k/9.

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Multiple Choice

Q 8Q 8

A pendulum on the Earth has a period T. The acceleration due to gravity on Mars is less than that on the Earth, and the acceleration due to gravity on the Moon is even less. Where would the period of an identical pendulum be the least?
A) on the Earth
B) on the Moon
C) on Mars
D) The period of a pendulum would be the same on the Earth, Moon, and Mars since the period depends on the pendulum's length which is the same for identical pendula.

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Multiple Choice

Q 9Q 9

Three identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion. What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?
A) k
B) k/3
C) 3k
D)

Free

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Q 10Q 10

The SI base units for the spring constant are which of the following?
A) kg·s

^{2}B) kg/m^{2}C) kg/s^{2}D) kg·m^{2}Free

Multiple Choice

Q 11Q 11

A large spring requires a force of 100 N to compress it only 0.010 m. What is the spring constant of the spring?
A) 1.0 N/m
B) 100 N/m
C) 10,000 N/m
D) 100,000 N/m

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Multiple Choice

Q 12Q 12

A 0.20-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal, frictionless surface. At the instant that it is displaced from equilibrium by 0.060 m, what is its acceleration?
A) 360 m/s

^{2}B) 30 m/s^{2}C) 3.0 m/s^{2}D) 0.18 m/s^{2}Free

Multiple Choice

Q 13Q 13

Doubling 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?
A) 4.0
B) 3.0
C) 2.0
D) 0.5

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Multiple Choice

Q 14Q 14

Doubling 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?
A) 4.0
B) 2.0
C) 1.0
D) 0.5

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Multiple Choice

Q 15Q 15

A tiny spring, with a spring constant of 1.20 N/m, will be stretched to what displacement by a 0.0060-N force?
A) 4.2 mm
B) 5.0 mm
C) 6.0 mm
D) 9.4 mm

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Multiple Choice

Q 16Q 16

A mass of 0.40 kg, attached to a spring with a spring constant of 80 N/m, is set into simple harmonic motion. What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.050 m from the equilibrium position?
A) zero
B) 5 m/s

^{2}C) 10 m/s^{2}D) 20 m/s^{2}Free

Multiple Choice

Q 17Q 17

A mass of 4.0 kg, resting on a horizontal, frictionless surface, is attached on the right to a horizontal spring with spring constant 30 N/m and on the left to a horizontal spring with spring constant 50 N/m. If this system is moved from equilibrium, what is the effective spring constant?
A) 16 N/m
B) 80 N/m
C) 20 N/m
D) 20 N/m

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Multiple Choice

Q 18Q 18

Suppose there is an object for which F = +kx. What will happen if the object is moved away from equilibrium (x = 0) and released?
A) It will return to the equilibrium position.
B) It will move further away with constant velocity.
C) It will move further away with constant acceleration.
D) It will move further away with increasing acceleration.

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Multiple Choice

Q 19Q 19

Which is not an example of approximate simple harmonic motion?
A) A ball bouncing on the floor.
B) A child swinging on a swing.
C) A piano string that has been struck.
D) A car's radio antenna as it waves back and forth.

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Multiple Choice

Q 20Q 20

If it takes 8.0 N to stretch a spring 6.0 cm, and if the spring is then cut in half, what force does it take to stretch one of the halves 3.0 cm?
A) 2.0 N
B) 4.0 N
C) 8.0 N
D) 16 N

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Multiple Choice

Q 21Q 21

Four identical springs each have the same spring constant k. If these four springs are attached end to end forming a spring four times the length of one of the original springs, what will be the spring constant of the combination?
A) k
B) k/4
C) 4k
D) 1.41k

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Multiple Choice

Q 22Q 22

An object is attached to a spring, and its frequency of oscillation is measured. Then another object is connected to the first object, and the resulting mass is nine times the original value. By what factor is the frequency of oscillation changed?
A) 9
B) 3
C) 1/3
D) 1/9

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Multiple Choice

Q 23Q 23

By what factor must one change the weight suspended vertically from a spring coil in order to double its period of simple harmonic motion?
A) 4
B) 2
C) 1/2
D) 1/4

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Multiple Choice

Q 24Q 24

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and amplitude of 8.0 cm. If the mass of the object is 0.25 kg, what is the spring constant?
A) 40 N/m
B) 87 N/m
C) 126 N/m
D) 158 N/m

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Multiple Choice

Q 25Q 25

For a mass suspended on a spring in the vertical direction, the time for one complete oscillation will depend on:
A) the value for g (the acceleration due to gravity).
B) the distance the mass was originally pulled down.
C) the maximum speed of the oscillating mass.
D) the time doesn't depend on any of the above.

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Multiple Choice

Q 26Q 26

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 5.0 cm. If a timer is started when its displacement is a maximum (hence x = 5 cm when t = 0), what is the acceleration magnitude when t = 3 s?
A) 31.6 m/s

^{2}B) 15.8 m/s^{2}C) 10.5 m/s^{2}D) zeroFree

Multiple Choice

Q 27Q 27

An object moving in simple harmonic motion has an amplitude of 0.020 m and a maximum acceleration of 20 m/s

^{2}. What is the frequency of the system? A) 0.40 Hz B) 5.0 Hz C) 10.1 Hz D) 32 HzFree

Multiple Choice

Q 28Q 28

The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a distance of 12.0 cm, what is its maximum speed when the engine is running at 3000 rpm?
A) 4.71 m/s
B) 9.42 m/s
C) 44.0m/s
D) 22.0 m/s

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Multiple Choice

Q 29Q 29

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.120 m) cos (t/16). What is the maximum net force on the mass as it oscillates?
A) 0.98 10

^{}^{3}N B) 7.4 10^{}^{3}N C) 3.0 10^{}^{3}N D) 4.7 NFree

Multiple Choice

Q 30Q 30

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 onesixth (1/6) that on the Earth, by what factor would the pendulum frequency be changed?
A) about 6.0
B) about 2.5
C) about 0.41
D) about 0.17

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Multiple Choice

Q 31Q 31

Halving the mass of the bob on a simple pendulum will cause a change in the frequency of the pendulum swing by what factor?
A) 4.0
B) 2.0
C) 1.0
D) 0.50

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Multiple Choice

Q 32Q 32

By what factor should the length of a simple pendulum be changed if the period of vibration were to be quadrupled?
A) 16
B) 4.0
C) 0.25
D) 1/16

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Multiple Choice

Q 33Q 33

A simple pendulum has a period of 1.0 s. What is the pendulum length? (g = 9.8 m/s

^{2}) A) 0.25 m B) 0.39 m C) 0.99 m D) 1.0 mFree

Multiple Choice

Free

Multiple Choice

Q 35Q 35

The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement from equilibrium is at what point in its swing?
A) zero displacement
B) 1/4 the amplitude
C) 1/2 the amplitude
D) equal the amplitude

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Multiple Choice

Q 36Q 36

A simple pendulum of length 2.00 m has a mass of 100 g attached. It is drawn back 30.0 and then released. What is the maximum speed of the mass?
A) 1.14 m/s
B) 4.58 m/s
C) 2.29 m/s
D) 1.62 m/s

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Multiple Choice

Q 37Q 37

A simple pendulum has a mass of 0.50 kg and a length of 1.0 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?
A) 2.0 J
B) 1.6 J
C) 0.66 J
D) 0.58 J

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Multiple Choice

Q 38Q 38

When an object is moving in simple harmonic motion, which of the following is at a minimum when the displacement from equilibrium is zero?
A) the magnitude of the velocity
B) the magnitude of the acceleration
C) the kinetic energy
D) the total mechanical energy

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Multiple Choice

Q 39Q 39

A 0.20-kg object is oscillating on a spring with a spring constant of k = 30 N/m. What is the potential energy of the system when the object's displacement is 0.040 m, exactly half the maximum amplitude?
A) 0.96 J
B) 0.024 J
C) 0.012 J
D) zero

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Multiple Choice

Q 40Q 40

A 0.40-kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal, frictionless surface in simple harmonic motion of amplitude of 0.080 m. What is its speed at the instant when its displacement is 0.040 m? (Hint: Use conservation of energy.)
A) 17 m/s
B) 35 cm/s
C) 3.5 cm/s
D) 6.9 cm/s

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Multiple Choice

Q 41Q 41

A mass of 0.40 kg, hanging from a spring with a spring constant of 160 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.10 m.
A) zero
B) 1.4 m/s
C) 2.0 m/s
D) 3.4 m/s

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Multiple Choice

Q 42Q 42

A mass of 0.40 kg, hanging from a spring with a spring constant of 160 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.
A) zero
B) 1.4 m/s
C) 1.7 m/s
D) 1.2 m/s

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Multiple Choice

Q 43Q 43

A runaway railroad car, with mass 30 10

^{4}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 4.0 10^{6}N/m, what is the maximum compression of the spring during the collision? (Assume the collision is elastic.) A) 0.77 m B) 0.55 m C) 0.34 m D) 1.07 mFree

Multiple Choice

Q 44Q 44

A 0.20-kg mass is oscillating on a spring over a horizontal, frictionless surface. When it is at a displacement of 2.6 cm from equilibrium, it has a kinetic energy of 2.7 J and a spring potential energy of 2.2 J. What is the maximum speed of the mass during its oscillation?
A) 3.7 m/s
B) 4.7 m/s
C) 6.0 m/s
D) 7.0 m/s

Free

Multiple Choice

Q 45Q 45

A 0.20-kg block rests on a frictionless, level surface and is attached to a horizontally aligned spring with a spring constant of 80 N/m. The block is initially displaced 4.0 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?
A) 2.1 m/s
B) 1.6 m/s
C) 0.80 m/s
D) 0.57 m/s

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Multiple Choice

Q 46Q 46

A 0.20-kg block rests on a frictionless, level surface and is attached to a horizontally aligned spring with a spring constant of 80 N/m. The block is initially displaced 4.0 cm from the equilibrium point and then released to set up a simple harmonic motion. 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?
A) 0.45 m/s
B) 0.63 m/s
C) 0.72 m/s
D) 1.2 m/s

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Multiple Choice

Q 47Q 47

The oxygen molecule (O

_{2}) 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 10^{}^{26}kg has a vibrational energy of 6.4 10^{}^{21}J and the effective spring constant is 50 N/m, then what is the amplitude of oscillation of each oxygen atom? A) 3.2 10^{}^{11}m B) 1.6 10^{}^{11}m C) 1.1 10^{}^{11}m D) 8.0 10^{}^{12}mFree

Multiple Choice

Q 48Q 48

Suppose a 0.30-kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.5 J. What is the spring constant?
A) 10 N/m
B) 20 N/m
C) 200 N/m
D) 300 N/m

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Q 49Q 49

Suppose a 0.30-kg mass on a spring that has been compressed 0.20 m has elastic potential energy of 1.0 J. How much further must the spring be compressed to triple the elastic potential energy?
A) 0.35 m
B) 0.15 m
C) 0.10 m
D) 0.05 m

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Multiple Choice

Q 50Q 50

Suppose a 0.30-kg mass on a spring-loaded gun that has been compressed 0.20 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?
A) 0.10 m
B) 0.34 m
C) 0.24 m
D) 0.14 m

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Q 51Q 51

An ore car of mass 2000 kg rolls downhill on tracks from a mine. At the end of the tracks, 10.0 m lower in elevation, is a spring with k = 400,000 N/m. How much is the spring compressed in stopping the ore car? Ignore friction.
A) 0.14 m
B) 0.99 m
C) 1.40 m
D) 1.96 m

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Q 52Q 52

Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?
A) speed
B) acceleration
C) kinetic energy
D) frequency

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Q 53Q 53

I attach a 2.0-kg block to a spring that obeys Hooke's Law and supply 4.0 J of energy to stretch the spring. I release the block; it oscillates with period 0.30 s. The amplitude is:
A) 38 cm.
B) 19 cm.
C) 9.5 cm.
D) 4.3 cm.

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Multiple Choice

Q 54Q 54

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 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 = 5 s?
A) zero
B) 0.0065 m/s
C) 0.016 m/s
D) 0.024 m/s

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Multiple Choice

Q 55Q 55

Suppose a simple harmonic oscillator has a frequency 20 Hz. What is frequency of occurrence of the maximum kinetic energy during its oscillations?
A) 20 Hz
B) Hz
C) 10 Hz
D) 40 Hz

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Q 56Q 56

To double the total energy of a simple harmonic oscillator, by what factor should the amplitude change?
A) 2
B)
C) 4
D)

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Q 57Q 57

A copper alloy wire of length 2.0 m, cross sectional area 7.1 10

^{}^{6}m^{2}, and Young's modulus 11 10^{10}N/m^{2}, has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s^{2}) A) 0.50 mm B) 1.0 mm C) 2.5 mm D) 5.0 mmFree

Multiple Choice

Q 58Q 58

In an elastic solid there is a direct proportionality between strain and:
A) elastic modulus.
B) temperature.
C) cross-sectional area.
D) stress.

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Q 59Q 59

The quantity "stress" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:
A) MLT

^{}^{1}. B) ML^{}^{1}T^{}^{2}. C) M^{2}L^{}^{1}T^{}^{3}. D) a dimensionless quantity.Free

Multiple Choice

Q 60Q 60

The quantity "strain" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:
A) MLT

^{}^{1}. B) ML^{}^{1}T^{}^{2}. C) M^{2}L^{}^{1}T^{}^{3}. D) a dimensionless quantity.Free

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Q 61Q 61

The bulk modulus of a material, as a meaningful physical property, is applicable to which of the following?
A) only solids
B) only liquids
C) only gases
D) solids, liquids and gases

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Q 62Q 62

A uniform pressure of 21 10

^{5}N/m^{2}is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 10^{10}N/m^{2}) A) 2.4 10^{}^{2 }% B) 1.5 10^{}^{3 }% C) 8.4 10^{}^{2 }% D) 0.5 10^{}^{3 }%Free

Multiple Choice

Q 63Q 63

Bar One has a Young's modulus that is bigger than that of Bar Two. This indicates Bar One:
A) is longer than Bar Two.
B) has a greater cross-sectional area than Bar Two.
C) has a greater elastic limit than Bar Two.
D) is made of material that is different from Bar Two.

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Q 64Q 64

A tire stops a car by use of friction. What modulus should we use to calculate the stress and strain on the tire?
A) Young's modulus
B) compression modulus
C) shear modulus
D) bulk modulus

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Multiple Choice

Q 65Q 65

How large a force is necessary to stretch a 2.0 mm radius steel wire (Y = 2.0 10

^{11}N/m^{2}) by 2.0%? A) 5.0 10^{4}N B) 2.5 10^{4}N C) 2.5 10^{3}N D) 1.3 10^{4}NFree

Multiple Choice

Q 66Q 66

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 10

^{9}Pa, and 1 atm = 1.0 10^{5}Pa.) A) 18 atm B) 270 atm C) 1080 atm D) 1800 atmFree

Multiple Choice

Q 67Q 67

A 2.0 cm 2.0 cm steel rod of length 80 cm has its left end clamped and a force of applied perpendicular to its length at its right end. By how much does the right end shift from its original position? For steel Young's modulus is , the bulk modulus is , and the shear modulus is .
A)
B)
C)
D) More information is needed.

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Multiple Choice

Q 68Q 68

A car with bad shocks bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1250 kg and is supported by four springs of force constant k. What is k for each spring?
A) 6580 N/m
B) 5480 N/m
C) 4440 N/m
D) 3630 N/m

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Q 69Q 69

When car shock absorbers wear out and lose their damping ability, what is the resulting oscillating behavior?
A) underdamped
B) critically damped
C) overdamped
D) hyperdamped

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Q 70Q 70

A child sits on a swing supported by ropes of length 4.0 m. With what frequency will she need to apply the driving force to maintain swinging?
A) 0.29 Hz
B) 0.48 Hz
C) 0.25 Hz
D) 0.38 Hz

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Multiple Choice

Q 71Q 71

If the torsion constant of the suspension fiber in the Cavendish experiment were doubled, what would happen to the frequency of oscillation? The last two answers have been rounded to 2 significant figures.
A) It would double.
B) It would halve.
C) It would increase by a factor of 1.4.
D) It would decrease by a factor of 0.71.

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Multiple Choice