Question 1

If a simple harmonic motion is described by x = 3 cos(πt),starting from t = 0 s,what is the first occurrence of a value of t for which x = 0? Assume SI units.

Accepted Answer

A) t = 0 s 
B) t =   s 
C) t =   s 
D) t =   s 
A) t = 0 s 
B) t =   s 
C) t =   s 
D) t =   s

Question 2

By what factor must one change the weight suspended vertically from a spring coil in order to increase its period of simple harmonic motion by five?

Accepted Answer

A) 1/25 
B) 1/5 
C) 5 
D) 25 
E) 1 
A) 1/25 
B) 1/5 
C) 5 
D) 25 
E) 1

Question 3

The position of a 0.700-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its position at t = 5.80 s?

Accepted Answer

A) -0.0670 m 
B) 0.0622 m 
C) 6.25 m 
D) 0.0670 m 
E) 0.610 m 
A) -0.0670 m 
B) 0.0622 m 
C) 6.25 m 
D) 0.0670 m 
E) 0.610 m

Question 4

When an object is moving in simple harmonic motion,which of the following is at a minimum when the displacement from equilibrium is zero?

Accepted Answer

A) the magnitude of the velocity 
B) the magnitude of the acceleration 
C) the kinetic energy 
D) the total mechanical energy 
A) the magnitude of the velocity 
B) the magnitude of the acceleration 
C) the kinetic energy 
D) the total mechanical energy

Question 5

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?

Accepted Answer

A) 0.33 
B) 1.0 
C) 3.0 
D) 9.0 
E) 0.11 
A) 0.33 
B) 1.0 
C) 3.0 
D) 9.0 
E) 0.11

Question 6

Two water waves meet at the same point,one having a displacement above equilibrium of 50 cm and the other having a displacement above equilibrium of 90 cm.At this moment,what is the resulting displacement above equilibrium?

Accepted Answer

A) 140 cm 
B) 95 cm 
C) 40 cm 
D) Information about the amplitudes needs to be given to find an answer. 
E) 65 cm 
A) 140 cm 
B) 95 cm 
C) 40 cm 
D) Information about the amplitudes needs to be given to find an answer. 
E) 65 cm

Question 7

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 1.6 × 10−21 J and the effective spring constant is 86 N/m,then what is the amplitude of oscillation of each oxygen atom?

Accepted Answer

A) 3.2E-11 m 
B) 1.6E-11 m 
C) 1.1E-11 m 
D) 6.1E-12 m 
E) 4.3E-12 m 
A) 3.2E-11 m 
B) 1.6E-11 m 
C) 1.1E-11 m 
D) 6.1E-12 m 
E) 4.3E-12 m

Question 8

A simple pendulum of length 1.87 m has a mass of 120 g attached.It is drawn back 38.0° and then released.What is the maximum speed of the mass?

Accepted Answer

A) 1.44 m/s 
B) 3.93 m/s 
C) 2.74 m/s 
D) 2.79 m/s 
E) 0.249 m/s 
A) 1.44 m/s 
B) 3.93 m/s 
C) 2.74 m/s 
D) 2.79 m/s 
E) 0.249 m/s

Question 9

A 0.30-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 52.0 N/m.The block is initially displaced 3.20 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?

Accepted Answer

A) 2.36 m/s 
B) 0.596 m/s 
C) 1.67 m/s 
D) 0.421 m/s 
E) 2.28 m/s 
A) 2.36 m/s 
B) 0.596 m/s 
C) 1.67 m/s 
D) 0.421 m/s 
E) 2.28 m/s

Question 10

Waves propagate at 7.40 m/s along a stretched string.The end of the string is vibrated up and down once every 2.25 s.What is the wavelength of the waves that travel along the string?

Accepted Answer

A) 4.50 m 
B) 16.7 m 
C) 3.29 m 
D) 37.5 m 
E) 8.09 m 
A) 4.50 m 
B) 16.7 m 
C) 3.29 m 
D) 37.5 m 
E) 8.09 m

Question 11

An object moving in simple harmonic motion has an amplitude of 0.0450 m and a maximum acceleration of 40.0 m/s2.What is the frequency of the system?

Accepted Answer

A) 14.9 Hz 
B) 187 Hz 
C) 4.75 Hz 
D) 11.9 Hz 
E) 1.80 Hz 
A) 14.9 Hz 
B) 187 Hz 
C) 4.75 Hz 
D) 11.9 Hz 
E) 1.80 Hz

Question 12

Wave #1 has frequency f1 and wavelength λ1.Wave #2 has frequency f2 = 6 f1 and wavelength λ2 = 2λ1.How does the speed v2 of wave #2 compare with the speed v1 of wave #1?

Accepted Answer

A) v2 = 12v1 
B) v2 = 6v1 
C) v2 = 1.5v1 
D) v2 = v1/6 
A) v2 = 12v1 
B) v2 = 6v1 
C) v2 = 1.5v1 
D) v2 = v1/6

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?

Accepted Answer

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. 
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

A 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

Accepted Answer

A) 2 200 m/s2 
B) −220 m/s2 
C) 0.220 m/s2 
D) 1.38 m/s2 
E) 0.550 m/s2 
A) 2 200 m/s2 
B) −220 m/s2 
C) 0.220 m/s2 
D) 1.38 m/s2 
E) 0.550 m/s2

Question 15

Two 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?

Accepted Answer

A) k 
B) 2k 
C) k/2 
D)    
A) k 
B) 2k 
C) k/2 
D)

Question 16

Which is not an example of approximate simple harmonic motion?

Accepted Answer

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. 
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.

Question 17

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its period of oscillation?

Accepted Answer

A) 100 s 
B) 32 s 
C) 16 s 
D) 8.0 s 
E) 4.0 s 
A) 100 s 
B) 32 s 
C) 16 s 
D) 8.0 s 
E) 4.0 s

Question 18

A water bug on the surface of a pond bobs up and down three times per second on ripples with wavelength 10.5 cm.A fish resting at the surface of the pond is 8.50 m from the water bug.How long does it take a ripple passing the water bug to reach the fish?

Accepted Answer

A) 27.0 s 
B) 243 s 
C) 81.0 s 
D) 0.893 s 
A) 27.0 s 
B) 243 s 
C) 81.0 s 
D) 0.893 s

Question 19

For a wave on the ocean,the amplitude is:

Accepted Answer

A) the distance between crests. 
B) the height difference between a crest and a trough. 
C) one half the height difference between a crest and a trough. 
D) how far the wave goes up on the beach. 
A) the distance between crests. 
B) the height difference between a crest and a trough. 
C) one half the height difference between a crest and a trough. 
D) how far the wave goes up on the beach.

Question 20

A mass on a spring vibrates in simple harmonic motion at a frequency of 3.2 Hz and an amplitude of 6.4 cm.If a timer is started when its displacement is a maximum (hence x = 6.4 cm when t = 0),what is the displacement of the mass when t = 3.3 s?

Accepted Answer

A) zero 
B) -5.95 cm 
C) -2.36 cm 
D) 2.53 cm 
A) zero 
B) -5.95 cm 
C) -2.36 cm 
D) 2.53 cm

Exam 13: Vibrations and Waves

If a simple harmonic motion is described by x = 3 cos(πt),starting from t = 0 s,what is the first occurrence of a value of t for which x = 0? Assume SI units.

By what factor must one change the weight suspended vertically from a spring coil in order to increase its period of simple harmonic motion by five?

The position of a 0.700-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its position at t = 5.80 s?

When an object is moving in simple harmonic motion,which of the following is at a minimum when the displacement from equilibrium is zero?

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?

Two water waves meet at the same point,one having a displacement above equilibrium of 50 cm and the other having a displacement above equilibrium of 90 cm.At this moment,what is the resulting displacement above equilibrium?

A simple pendulum of length 1.87 m has a mass of 120 g attached.It is drawn back 38.0° and then released.What is the maximum speed of the mass?

Waves propagate at 7.40 m/s along a stretched string.The end of the string is vibrated up and down once every 2.25 s.What is the wavelength of the waves that travel along the string?

An object moving in simple harmonic motion has an amplitude of 0.0450 m and a maximum acceleration of 40.0 m/s2.What is the frequency of the system?

Wave #1 has frequency f1 and wavelength λ1.Wave #2 has frequency f2 = 6 f1 and wavelength λ2 = 2λ1.How does the speed v2 of wave #2 compare with the speed v1 of wave #1?

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 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

Two 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?

Which is not an example of approximate simple harmonic motion?

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m)cos (πt/16).What is its period of oscillation?

A water bug on the surface of a pond bobs up and down three times per second on ripples with wavelength 10.5 cm.A fish resting at the surface of the pond is 8.50 m from the water bug.How long does it take a ripple passing the water bug to reach the fish?

For a wave on the ocean,the amplitude is:

A mass on a spring vibrates in simple harmonic motion at a frequency of 3.2 Hz and an amplitude of 6.4 cm.If a timer is started when its displacement is a maximum (hence x = 6.4 cm when t = 0),what is the displacement of the mass when t = 3.3 s?

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An object moving in simple harmonic motion has an amplitude of 0.0450 m and a maximum acceleration of 40.0 m/s².What is the frequency of the system?

Wave #1 has frequency f₁ and wavelength λ₁.Wave #2 has frequency f₂ = 6 f₁ and wavelength λ₂ = 2λ₁.How does the speed v₂ of wave #2 compare with the speed v₁ of wave #1?