### 16.1 Hooke’s Law: Stress and Strain Revisited

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- 2
*A*cm - 4
*A*cm

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?

In the formula $F\text{\hspace{0.17em}}=\text{\hspace{0.17em}}-kx$, 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

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

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

Use these figures to answer the following questions.

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

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

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

What is the displacement at time 8*π*?

- 1 m
- 0 m
- Not defined
- −1 m

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

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?

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

- $g\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{2\pi L}{{T}^{2}}$
- $g\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{4{\pi}^{2}L}{{T}^{2}}$
- $g\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{2\pi L}{T}$
- $g\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{2{\pi}^{2}L}{T}$

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

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

In the equation $x\text{\hspace{0.17em}}=\text{\hspace{0.17em}}A\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}w\mathrm{t,}$ what values can the position $x$ take?

- −1 to +1
- –
*A*to +*A* - 0
- –
*t*to*t*

### 16.7 Damped Harmonic Motion

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

- Mechanical energy
- Electrical energy
- Thermal energy
- None of the above

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

- 0
- Negative
- Positive
- Undefined

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
${\mu}_{k}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}0.06$. 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

How is constant amplitude sustained in forced oscillations?

### 16.9 Waves

Represent longitudinal and transverse waves in a graphical form.

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.

### 16.10 Superposition and Interference

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

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

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

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

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?

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?

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?

- 2
*A* - 3
*A* - 0
- 9
*A*

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?