Gregg Wolfe; Erika Gasper; John Stoke; Julie Kretchman; David Anderson; Nathan Czuba; Sudhi Oberoi; Liza Pujji; Irina Lyublinskaya; Douglas Ingram

16.1 Hooke’s Law: Stress and Strain Revisited

1.

Which of the following represents the distance (how much ground the particle covers) moved by a particle in a simple harmonic motion in one time period? (Here, A represents the amplitude of the oscillation.)

0 cm
A cm
2A cm
4A cm

2.

A spring has a spring constant of 80 N∙m⁻¹. What is the force required to (a) compress the spring by 5 cm and (b) expand the spring by 15 cm?

3.

In the formula $F = - k x$ , what does the minus sign indicate?

It indicates that the restoring force is in the direction of the displacement.
It indicates that the restoring force is in the direction opposite the displacement.
It indicates that mechanical energy in the system decreases when a system undergoes oscillation.
None of the above

4.

The splashing of a liquid resembles an oscillation. The restoring force in this scenario will be due to which of the following?

Potential energy
Kinetic energy
Gravity
Mechanical energy

16.2 Period and Frequency in Oscillations

5.

A mass attached to a spring oscillates and completes 50 full cycles in 30 s. What is the time period and frequency of this system?

16.3 Simple Harmonic Motion: A Special Periodic Motion

6.

Use these figures to answer the following questions.

The image shows two graphs with oscillating lines. The top graph has amplitude from negative A to positive A on the y axis, and time 0 to 8 pi on the x axis. The line starts at 0, A, curves down to cross amplitude 0, and then meet pi, negative A. It curves up, and passes through amplitude 0 again, and then meets 2 pi, A. It curves down, passing through amplitude 0 again, and then meets 3 pi, negative A. It continues this way, finally passing through 8 pi, A. The bottom graph has displacement from negative 3 A over 2 to positive 3 A over 2 on the y-axis, and time 0 to 24 pi on the x-axis. The line starts at 0, 3 A over two curves down through amplitude 0, and meets negative 3 A over 2 at an unmarked x-value. It curves up, passes through amplitude 0 again, and meets 3 pi, 3 A over 2. It goes on in this way, finally meeting 24 pi, 3 A over 2.

Figure 16.49

Which of the two pendulums oscillates with larger amplitude?
Which of the two pendulums oscillates at a higher frequency?

7.

A particle of mass 100 g undergoes a simple harmonic motion. The restoring force is provided by a spring with a spring constant of 40 N∙m⁻¹. What is the period of oscillation?

10π
0.5π
0.1π
1π

8.

The graph shows the simple harmonic motion of a mass m attached to a spring with spring constant k.

The image shows a graph of an oscillating line. The y-axis has amplitude from negative 1 meter to positive 1 meter. The x-axis has time from 0 seconds to 8 pi seconds. The line starts at 0, positive 1, curves down to pass through amplitude 0, and meets pi, negative one. The line curves up and passes through amplitude equals 0 again, and then meets 2 pi, positive 1. It continues this way, finally meeting 8 pi, positive 1.

Figure 16.50

What is the displacement at time 8π?

1 m
0 m
Not defined
−1 m

9.

A pendulum of mass 200 g undergoes simple harmonic motion when acted upon by a force of 15 N. The pendulum crosses the point of equilibrium at a speed of 5 m∙s⁻¹. What is the energy of the pendulum at the center of the oscillation?

16.4 The Simple Pendulum

10.

A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a location that is away from the Earth’s surface by twice the radius of the Earth. What is the acceleration due to gravity at that height and what is the period of the oscillations?

11.

Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?

$g = \frac{2 π L}{T^{2}}$
$g = \frac{4 π^{2} L}{T^{2}}$
$g = \frac{2 π L}{T}$
$g = \frac{2 π^{2} L}{T}$

12.

Tom has two pendulums with him. Pendulum 1 has a ball of mass 0.1 kg attached to it and has a length of 5 m. Pendulum 2 has a ball of mass 0.5 kg attached to a string of length 1 m. How does mass of the ball affect the frequency of the pendulum? Which pendulum will have a higher frequency and why?

16.5 Energy and the Simple Harmonic Oscillator

13.

A mass of 1 kg undergoes simple harmonic motion with amplitude of 1 m. If the period of the oscillation is 1 s, calculate the internal energy of the system.

16.6 Uniform Circular Motion and Simple Harmonic Motion

14.

In the equation $x = A \sin w t,$ what values can the position $x$ take?

−1 to +1
–A to +A
0
–t to t

16.7 Damped Harmonic Motion

15.

The non-conservative damping force removes energy from a system in which form?

Mechanical energy
Electrical energy
Thermal energy
None of the above

16.

The time rate of change of mechanical energy for a damped oscillator is always:

0
Negative
Positive
Undefined

17.

A 0.5-kg object is connected to a spring that undergoes oscillatory motion. There is friction between the object and the surface it is kept on given by coefficient of friction $μ_{k} = 0.06$ . If the object is released 0.2 m from equilibrium, what is the distance that the object travels? Given that the force constant of the spring is 50 N m^-1 and the frictional force between the objects is 0.294 N.

16.8 Forced Oscillations and Resonance

18.

How is constant amplitude sustained in forced oscillations?

16.9 Waves

19.

What is the difference between the waves coming from a tuning fork and electromagnetic waves?

20.

Represent longitudinal and transverse waves in a graphical form.

21.

Why is the sound produced by a tambourine different from that produced by drums?

22.

A transverse wave is traveling left to right. Which of the following is correct about the motion of particles in the wave?

The particles move up and down when the wave travels in a vacuum.
The particles move left and right when the wave travels in a medium.
The particles move up and down when the wave travels in a medium.
The particles move right and left when the wave travels in a vacuum.

23.

The image shows a graph of an oscillating line. The y-axis has displacement from negative 1 meter to positive 1 meter. The x-axis has time from 0 seconds to 8 pi seconds. The line starts at 0, positive 1, curves down to pass through displacement 0, and meets pi, negative one. The line curves up and passes through displacement equals 0 again, and then meets 2 pi, positive 1. It continues this way, finally meeting 8 pi, positive 1.

Figure 16.51

The graph shows propagation of a mechanical wave. What is the wavelength of this wave?

16.10 Superposition and Interference

24.

A guitar string has a number of frequencies at which it vibrates naturally. Which of the following is true in this context?

The resonant frequencies of the string are integer multiples of fundamental frequencies.
The resonant frequencies of the string are not integer multiples of fundamental frequencies.
They have harmonic overtones.
None of the above

25.

Explain the principle of superposition with figures that show the changes in the wave amplitude.

26.

In this figure which points represent the points of constructive interference?

Two wave generators are shown with their resulting rarefaction and compression marked. Points A, C, D, and E are at the intersection of two compression lines. Point B is at the intersection of two rarefaction lines. Point F is at the intersection of a compression line and a rarefaction line.

Figure 16.52

A, B, F
A, B, C, D, E, F
A, C, D, E
A, B, D

27.

A string is fixed on both sides. It is snapped from both ends at the same time by applying an equal force. What happens to the shape of the waves generated in the string? Also, will you observe an overlap of waves?

28.

In the preceding question, what would happen to the amplitude of the waves generated in this way? Also, consider another scenario where the string is snapped up from one end and down from the other end. What will happen in this situation?

29.

Two sine waves travel in the same direction in a medium. The amplitude of each wave is A, and the phase difference between the two is 180°. What is the resultant amplitude?

2A
3A
0
9A

30.

Standing wave patterns consist of nodes and antinodes formed by repeated interference between two waves of the same frequency traveling in opposite directions. What are nodes and antinodes and how are they produced?

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