Oscillations, and SHM

The speed of the block reaches its maximum value when the block is

in the equilibrium position.

https://session.masteringphysics.com/problemAsset/1013232/11/1013232.jpg Beginning the instant the object is released, select the graph that best matches the acceleration vs. time graph for the object.

F

https://session.masteringphysics.com/problemAsset/1013232/11/1013232.jpg Beginning the instant the object is released, select the graph that best matches the position vs. time graph for the object.

H

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.) Check all that apply. The period is doubled. The amplitude is doubled. The angular frequency is doubled. The period is reduced to one-half of what it was. The angular frequency is reduced to one-half of what it was.

The angular frequency is doubled. The period is reduced to one-half of what it was.

https://session.masteringphysics.com/problemAsset/1003614/24/168450B.jpg Which points on the x axis are located a distance AAA from the equilibrium position? R only Q only both R and Q

both R and Q

An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could double both the amplitude and force constant (spring constant). double the amplitude of vibration. double the mass. double the force constant (spring constant) of the spring. double both the mass and amplitude of vibration.

double the force constant (spring constant) of the spring.

https://session.masteringphysics.com/problemAsset/1010949/20/MFS_spC.jpg Consider graph B. (Figure 3) What might this graph represent?

force vs. position

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? https://session.masteringphysics.com/problemAsset/1902323/2/8514111005.jpg https://session.masteringphysics.com/problemAsset/1902323/2/8514111006.jpg

graph a

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? https://session.masteringphysics.com/problemAsset/1902322/2/8514111003.jpg https://session.masteringphysics.com/problemAsset/1902322/2/8514111004.jpg

graph b

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted TTT and is measured in seconds. The frequency, denoted fff, is the number of cycles that are completed per unit of time: f=1/Tf=1/T. In SI units, fff is measured in inverse seconds, or hertz (HzHz). If the period is doubled, the frequency is unchanged. doubled. halved.

halved

An air-track glider attached to a spring oscillates between the 13.0 cmcm mark and the 64.0 cmcm mark on the track. The glider completes 15.0 oscillations in 36.0 ss . What is the period of the oscillations? Express your answer using two significant figures.

2.4 s

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the amplitude. Express your answer using two significant figures.

2.5 cm

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg Which moment corresponds to the maximum potential energy of the system? A B C D

A

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg Which moment corresponds to the minimum kinetic energy of the system? A B C D

A

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? https://session.masteringphysics.com/problemAsset/1902336/2/8514111007.jpg A and B C B A and C A and D

A and D

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? Both periods would remain the same. The period of the pendulum would decrease but the period of the spring would stay the same. Both periods would decrease. Both periods would increase. The period of the pendulum would increase but the period of the spring would stay the same.

Both periods would remain the same.

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg Which moment corresponds to the maximum kinetic energy of the system? A B C D

C

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg Which moment corresponds to the minimum potential energy of the system? A B C D

C

An object of mass mmm attached to a spring of force constant kkk oscillates with simple harmonic motion. The maximum displacement from equilibrium is AAA and the total mechanical energy of the system is EEE. What is the system's potential energy when its kinetic energy is equal to 3/4E? kA2 kA2/2k kA2/4 kA2/8

kA2/8

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? one-third of the way between A and B midway between A and B one-fourth of the way between A and B at either A or B at none of the above points

midway between A and 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 maximum? at either A or B one-fourth of the way between A and B one-third of the way between A and B midway between A and B at none of the above points

midway between A and B

https://session.masteringphysics.com/problemAsset/1003614/24/168450A.jpg After the block is released from x=A, it will remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches x=−Ax=−A and stop there. move to the left until it reaches x=−Ax=−A and then begin to move to the right.

move to the left until it reaches x=−Ax=−A and then begin to move to the right.

Consider the block in the process of oscillating. If the kinetic energy of the block is increasing, the block must be at the equilibrium position. at the amplitude displacement. moving to the right. moving to the left. moving away from equilibrium. moving toward equilibrium.

moving toward equilibrium.

An object of mass mmm attached to a spring of force constant kkk oscillates with simple harmonic motion. The maximum displacement from equilibrium is AAA and the total mechanical energy of the system is EEE. What is the object's velocity when its potential energy is 2/3E?

±km−−√A3-√

A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T. If the pendulum is brought on the moon where the gravitational acceleration is about g/6, approximately what will its period now be? T/6 T/√6 √6T 6T

√6T

If the frequency is 40 HzHz, what is the period TTT ? Express your answer in seconds.

T =0.025s

The magnitude of the block's acceleration reaches its maximum value when the block is

at either its rightmost or leftmost position.

The speed of the block is zero when it is

at either its rightmost or leftmost position.

When a guitar string plays the note "A," the string vibrates at 440 HzHz . What is the period of the vibration? Express your answer using two significant figures.

2.3×10^−3s

As shown in the figure(Figure 2), a coordinate system with the origin at the equilibrium position is chosen so that the x coordinate represents the displacement from the equilibrium position. (The positive direction is to the right.) What is the initial acceleration of the block, a0a0a_0, when the block is released at a distance AAA to the right from its equilibrium position? Express your answer in terms of some or all of the variables AAA, mmm, and kkk. https://session.masteringphysics.com/problemAsset/1013381/14/1013381B.JPG

(−k/m)A

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the period. Express your answer using two significant figures.

.57 s

At what displacement, as a fraction of A, is the mechanical energy half kinetic and half potential? Express your answer using two significant figures.

.71

When the displacement of a mass on a spring is 1/2A the half of the amplitude, what fraction of the mechanical energy is kinetic energy? Express your answer using two significant figures.

.75

What is the acceleration a1a1a_1 of the block when it passes through its equilibrium position? Express your answer in terms of some or all of the variables AAA, mmm, and kkk.

0

How much time ttt does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds.

0.01 s

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 mm and the t coordinate of point K is 0.0050 ss. What is the period TTT ? Express your answer in seconds.

0.02 s

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the velocity at ttt1 = 0.43 ss . Express your answer using two significant figures.

0.275 m/s

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the maximum speed. Express your answer using two significant figures.

0.28 m/s

The free-fall acceleration on the moon is 1.62 m/s2m/s2 . What is the length of a pendulum whose period on the moon matches the period of a 1.80-m-long pendulum on the earth? Express your answer using three significant figures.

0.298 m

What distance ddd does the object cover between the moments labeled K and N on the graph? Express your answer in meters.

0.36 m

An air-track glider attached to a spring oscillates between the 13.0 cmcm mark and the 64.0 cmcm mark on the track. The glider completes 15.0 oscillations in 36.0 ss . What is the frequency of the oscillations? Express your answer using two significant figures.

0.42 Hz

What distance ddd does the object cover during one period of oscillation? Express your answer in meters.

0.48 m

What is the frequency of the oscillation shown in the figure? Express your answer using two significant figures. https://session.masteringphysics.com/problemAsset/1810995/3/jfk.Figure.P14.08.jpg

0.50 Hz

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the total energy. Express your answer using two significant figures

1.9×10−3 J

An oscillating object takes 0.10 ss to complete one cycle; that is, its period is 0.10 ss. What is its frequency fff? Express your answer in hertz.

10 Hz

What is the amplitude of the oscillation shown in (Figure 1)? Express your answer using two significant figures. https://session.masteringphysics.com/problemAsset/1810995/3/jfk.Figure.P14.08.jpg

10 cm

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 53.0 cm . The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 132 s . What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second.

11.5 m/s2

An air-track glider attached to a spring oscillates between the 13.0 cmcm mark and the 64.0 cmcm mark on the track. The glider completes 15.0 oscillations in 36.0 ss . What is the amplitude of the oscillations? Express your answer using two significant figures.

26 cm

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg Find the kinetic energy KKK of the block at the moment labeled B. Express your answer in terms of kkk and AAA.

3/8kA^2

A vertical scale on a spring balance reads from 0 to 180 NN . The scale has a length of 13.5 cmcm from the 0 to 180 NN reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.40 HzHz . Ignoring the mass of the spring, what is the mass mmm of the fish? Express your answer in kilograms.

5.86 kg

The position of a 51 gg oscillating mass is given by x(t)=(2.5cm)cos11tx(t)=(2.5cm)cos⁡11t, where tt is in seconds. Determine the spring constant. Express your answer using two significant figures.

6.2 N/m

A spring scale hung from the ceiling stretches by 5.9 cmcm when a 1.2 kgkg mass is hung from it. The 1.2 kgkg mass is removed and replaced with a 1.4 kgkg mass What is the stretch of the spring? Express your answer with the appropriate units.

6.9 cm

A heavy steel ball is hung from a cord to make a pendulum. The ball is pulled to the side so that the cord makes a 4 ∘∘ angle with the vertical. Holding the ball in place takes a force of 40 NN . If the ball is pulled farther to the side so that the cord makes a 6 ∘∘ angle, what force is required to hold the ball? Express your answer to two significant figures and include the appropriate units.

60 N

An air-track glider attached to a spring oscillates between the 13.0 cmcm mark and the 64.0 cmcm mark on the track. The glider completes 15.0 oscillations in 36.0 ss . What is the maximum speed of the glider? Express your answer using two significant figures.

67 cm/s

A 150 gg ball is tied to a string. It is pulled to an angle of 6.80 ∘∘ and released to swing as a pendulum. A student with a stopwatch finds that 10 oscillations take 16.5 ss . How long is the string? Express your answer using three significant figures.

67.6 cm

https://session.masteringphysics.com/problemAsset/1003620/25/1003620.jpg At which moment is K=U? A B C D

D

https://session.masteringphysics.com/problemAsset/1013232/11/1013232.jpg Beginning the instant the object is released, select the graph that best matches the velocity vs. time graph for the object.

E

A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T. If the pendulum is taken into the orbiting space station what will happen to the bob? -It will continue to oscillate in a vertical plane with the same period. -It will no longer oscillate because there is no gravity in space. -It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. -It will oscillate much faster with a period that approaches zero.

It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall.

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.) Check all that apply. Its kinetic energy is a maximum. Its speed is zero. Its acceleration is zero. Its elastic potential energy is zero. Its total mechanical energy is zero.

Its kinetic energy is a maximum. Its acceleration is zero. Its elastic potential energy is zero.

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.) Check all that apply. Its acceleration is zero. Its elastic potential energy is zero. Its speed is zero. Its kinetic energy is a maximum. Its total mechanical energy is zero.

Its speed is zero.

https://session.masteringphysics.com/problemAsset/1003614/24/168450B.jpg Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? K and L K and M K and P L and N M and P

K and P

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? 4T T T/4 T/2 2T

T

Two simple pendulums, A and B, are each 3.0 mm long, and the period of pendulum A is TT. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B? 2T T√2 T T/2 T/√2

T

A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T. If the bob's mass is doubled, approximately what will the pendulum's new period be? T/2 T √T2 2T

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 would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall? The period does not change. The period becomes infinite because the pendulum would not swing. The period decreases slightly. The period becomes zero. The period increases slightly.

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 upward with constant acceleration? The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. The period decreases. The period does not change. The period increases. The period becomes zero.

The period decreases.

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? The period becomes zero. The period decreases. The period increases. The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. The period does not change.

The period does not change.

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? The period decreases. The period does not change. The period increases. The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. The period becomes zero.

The period increases.

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? Both periods would decrease. Both periods would remain the same. The period of the pendulum would decrease but the period of the spring would stay the same. The period of the pendulum would increase but the period of the spring would stay the same. Both periods would increase.

The period of the pendulum would increase but the period of the spring would stay the same.

Which of the following statements best describes the characteristic of the restoring force in the spring-mass system described in the introduction? The restoring force is constant. The restoring force is directly proportional to the displacement of the block. The restoring force is proportional to the mass of the block. The restoring force is maximum when the block is in the equilibrium position.

The restoring force is directly proportional to the displacement of the block.

The total mechanical energy of a simple harmonic oscillating system is a maximum when it passes through the equilibrium point. zero when it reaches the maximum displacement. a minimum when it passes through the equilibrium point. a non-zero constant. zero as it passes the equilibrium point.

a non-zero constant.

Select the correct expression that gives the block's acceleration at a displacement xxx from the equilibrium position. Note that xxx can be either positive or negative; that is, the block can be either to the right or left of its equilibrium position. a=−kx a=kx a=(k/m)x a=(−k/m)x

a=(−k/m)x

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? one-fourth of the way between A and B midway between A and B at either A or B one-third of the way between A and B at none of the above points

at either A or B

https://session.masteringphysics.com/problemAsset/1010949/20/MFS_spB.jpg Consider graph A. (Figure 2) What might this graph represent?

position vs. time

https://session.masteringphysics.com/problemAsset/1010949/20/MFS_spD.jpg Consider graph C. (Figure 4) What might this graph represent?

velocity vs. time

Because of the periodic properties of SHM, the mathematical equations that describe this motion involve sine and cosine functions. For example, if the block is released at a distance AAA from its equilibrium position, its displacement xxx varies with time ttt according to the equation x=Acosωtx=Acos⁡ωt, where ωωomega is a constant characteristic of the system. If time is measured is seconds, ωωomega must be expressed in radians per second so that the quantity ωtωt is expressed in radians. Use this equation and the information you now have on the acceleration and speed of the block as it moves back and forth from one side of its equilibrium position to the other to determine the correct set of equations for the block's x components of velocity and acceleration, vxvxv_x and axaxa_x, respectively. In the expressions below, BBB and CCC are nonzero positive constants. vx=−Bsinωt, ax=Ccos⁡ωt vx=Bcosωt, ax=Csin⁡ωt vx=−Bcosωt, ax=−Ccos⁡ωt vx=−Bsinωt, ax=−Ccos⁡ωt

vx=−Bsinωt, ax=−Ccos⁡ωt

In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.) Check all that apply. when the displacement is a zero when the speed is a maximum when the kinetic energy is a minimum when the potential energy is a maximum when the magnitude of the displacement is a maximum

when the kinetic energy is a minimum when the potential energy is a maximum when the magnitude of the displacement is a maximum

In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.) Check all that apply. when the displacement is a maximum when the potential energy is a zero when the potential energy is a maximum when the magnitude of the acceleration is a minimum when the magnitude of the acceleration is a maximum

when the potential energy is a zero when the magnitude of the acceleration is a minimum