Deck 11: Harmonic Motion and Elasticity

Question 1

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.

Answer 1

A ball bouncing on the floor.

Question 2

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

Answer 2

2.0

Question 3

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

Answer 3

5.0 mm

Question 4

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

A) Point t₁
B) Point t₂
C) Point t₃
D) Point t₄

Question 5

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

Question 6

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.

Question 7

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

Question 8

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( $\pi$ t/8). What is its period of oscillation?

A) 100 s
B) 32 s
C) 16 s
D) 8.0 s

Question 9

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

Question 10

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/s²
C) 10 m/s²
D) 20 m/s²

Question 11

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/s²"
B) "-30 m/s²"
C) "3.0 m/s²"
D) "0.18 m/s²"

Question 12

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)

Question 13

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.

Question 14

The SI base units for the spring constant are which of the following?

A) kg·s²
B) kg/m²
C) kg/s²
D) kg·m²

Question 15

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"

Question 16

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

Question 17

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( $\pi$ 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

Question 18

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)

Question 19

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

Question 20

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.

Question 21

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

Question 22

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

Question 23

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

Question 24

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 (1/6) 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

Question 25

A simple pendulum has a period of 1.0 s. What is the pendulum length? (g = 9.8 m/s²)

A) 0.25 m
B) 0.39 m
C) 0.99 m
D) 1.0 m

Question 26

What are the base SI units for the torsion constant ?

A)
B)
C)
D)

Question 27

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/s²
B) 15.8 m/s²
C) 10.5 m/s²
D) zero

Question 28

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.120 m) cos ( $\pi$ 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 N

Question 29

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

Question 30

A simple pendulum of length 2.00 m has a mass of 100 g attached. It is drawn back 30.0 $\degree$ 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

Question 31

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

Question 32

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

Question 33

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.

Question 34

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

Question 35

An object moving in simple harmonic motion has an amplitude of 0.020 m and a maximum acceleration of 20 m/s². What is the frequency of the system?

A) 0.40 Hz
B) 5.0 Hz
C) 10.1 Hz
D) 32 Hz

Question 36

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 $\degree$ and then released. After a time, the maximum angle of swing is only 10 $\degree$ . How much energy has been lost to friction?

A) 2.0 J
B) 1.6 J
C) 0.66 J
D) 0.58 J

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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.

Question 43

A runaway railroad car, with mass 30 *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 4.0 *10⁶ 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 m

Question 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

Question 45

In an elastic solid there is a direct proportionality between strain and:

A) elastic modulus.
B) temperature.
C) cross-sectional area.
D) stress.

Question 46

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

Question 47

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) M²L ^{- 1}T ^{- 3}.
D) a dimensionless quantity.

Question 48

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

Question 49

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 *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 m

Question 50

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

Question 51

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

Question 52

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

Question 53

To double the total energy of a simple harmonic oscillator, by what factor should the amplitude change?

A) 2
B)
C) 4
D)

Question 54

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

Question 55

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

Question 56

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

Question 57

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) M²L ^{- 1}T ^{- 3}.
D) a dimensionless quantity.

Question 58

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

Question 59

A copper alloy wire of length 2.0 m, cross sectional area 7.1 *10^-6 m², and Young's modulus 11 *10¹⁰ N/m², has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s²)

A) 0.50 mm
B) 1.0 mm
C) 2.5 mm
D) 5.0 mm

Question 60

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

Question 61

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.

Question 62

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

Question 63

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.

Question 64

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.

Question 65

How large a force is necessary to stretch a 2.0 mm radius steel wire (Y = 2.0 *10¹¹ N/m²) by 2.0%?

A) 5.0 * 10⁴ N
B) 2.5 * 10⁴ N
C) 2.5 *10³ N
D) 1.3 * 10⁴ N

Question 66

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

Question 67

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

Question 68

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 *10⁹ Pa, and 1 atm = 1.0 *10⁵ Pa.)

A) 18 atm
B) 270 atm
C) 1080 atm
D) 1800 atm

Question 69

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

Question 70

A uniform pressure of 21 * 10⁵ N/m² is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 * 10¹⁰ N/m²)

A) 2.4 *10^-2 %
B) 1.5 * 10^-3 %
C) 8.4 *10^-2 %
D) 0.5 *10^-3 %

Question 71

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