### Lecture 7: Damped Oscillations, Forced Oscillations, Resonance, and Waves
#### Multiple Choice Questions
1. What characterizes damped oscillations?
- A) Increasing amplitude
- B) Constant amplitude
- C) Decreasing amplitude
- D) No change in amplitude
2. Which force is associated with damping in oscillatory motion?
- A) Elastic force
- B) Gravitational force
- C) Frictional force
- D) Electromagnetic force
3. What is the damping coe cient denoted by?
- A) \( \omega \)
- B) \( \beta \)
- C) \( \phi \)
- D) \( A \)
4. Which of the following best describes forced oscillations?
- A) Oscillations that occur naturally without external in uence
- B) Oscillations under the in uence of an external periodic force
- C) Oscillations with no external forces
- D) Oscillations that stop immediately
5. At resonance, what is the relationship between the driving frequency and the natural frequency?
- A) They are equal
- B) Driving frequency is half of the natural frequency
- C) Driving frequency is double the natural frequency
- D) There is no relationship
6. What phenomenon occurs when the amplitude of forced oscillations is maximal?
- A) Damping
- B) Resonance
- C) Interference
- D) Di raction
7. Which type of wave has particles oscillating perpendicular to the direction of wave propagation?
- A) Longitudinal wave
- B) Transverse wave
- C) Surface wave
- D) Electromagnetic wave
8. In a running wave, what happens to energy?
- A) It remains stationary
- B) It propagates through space
- C) It decreases over time
- D) It increases over time
9. What is the result of the superposition of two oncoming traveling waves?
- A) Standing wave
- B) Running wave
- C) No wave
- D) Sound wave
10. What is the e ect of resonance on the human body?
- A) Enhances bodily functions
- B) Can cause damage or discomfort
- C) Has no e ect
- D) Improves visual perception
11. What describes the frequency of a wave?
- A) The distance between two consecutive crests
- B) The number of oscillations per unit time
- C) The height of the wave
- D) The speed of the wave
12. In a damped harmonic oscillator, what role does the damping coe cient play?
- A) It increases the frequency
- B) It decreases the amplitude over time
- C) It keeps the amplitude constant
- D) It has no e ect on the motion
13. Which of the following is true for a critically damped system?
- A) It oscillates with increasing amplitude
- B) It returns to equilibrium without oscillating
- C) It oscillates inde nitely
- D) It takes the longest time to return to equilibrium
14. The phase di erence between the driving force and the displacement in a damped driven oscillator is:
- A) Zero at resonance
- B) \( \pi/4 \) at resonance
- C) \( \pi/2 \) at resonance
- D) \( \pi \) at resonance
15. Which wave phenomenon occurs when two waves meet and combine?
- A) Re ection
- B) Refraction
- C) Di raction
- D) Interference
16. In the context of waves, what is the principle of superposition?
- A) The wave speed is the product of frequency and wavelength
- B) The total displacement is the sum of individual displacements
- C) The wave energy is constant
- D) The wave amplitude is always positive
17. The speed of a wave on a string is determined by:
- A) The frequency of the wave
- B) The amplitude of the wave
- C) The tension in the string and the mass per unit length
- D) The length of the string
18. What is the primary factor that a ects the speed of sound in air?
- A) Amplitude of the sound wave
- B) Frequency of the sound wave
- C) Temperature of the air
- D) Pressure of the air
19. What is the formula for the speed of a wave?
- A) \( v = f \lambda \)
- B) \( v = \lambda / f \)
- C) \( v = f^2 \lambda \)
- D) \( v = \lambda^2 / f \)
20. Which type of wave requires a medium for propagation?
- A) Electromagnetic wave
- B) Mechanical wave
- C) Gravitational wave
- D) Matter wave
21. When two waves are in phase, their superposition results in:
- A) Destructive interference
- B) Constructive interference
- C) Standing waves
- D) Re ected waves
22. What is a node in a standing wave?
- A) A point of maximum displacement
- B) A point of zero displacement
- C) A point where two waves cancel each other
- D) A point where waves re ect
23. Which term describes the energy carried by a wave per unit area per unit time?
- A) Amplitude
- B) Intensity
- C) Wavelength
- D) Frequency
24. What happens to the wavelength of a wave if its frequency is doubled, while the speed remains constant?
- A) It doubles
- B) It halves
- C) It remains the same
- D) It becomes zero
25. In wave motion, what does the term "period" refer to?
- A) The number of waves passing a point per second
- B) The time it takes for one complete wave to pass a point
- C) The distance between successive wave crests
- D) The height of the wave crest
26. What is resonance in the context of waves?
- A) The re ection of a wave from a surface
- B) The absorption of a wave by a medium
- C) The ampli cation of a wave when its frequency matches the natural frequency of a system
- D) The scattering of a wave by particles
27. How does damping a ect the amplitude of a wave over time?
- A) Increases it
- B) Decreases it
- C) Keeps it constant
- D) Has no e ect
28. What is the condition for constructive interference between two waves?
- A) They must have the same amplitude
- B) They must be in phase
- C) They must have the same frequency
- D) They must travel in opposite directions
29. Which type of wave can travel through a vacuum?
- A) Sound wave
- B) Seismic wave
- C) Water wave
- D) Light wave
30. What happens to the frequency of a wave if its wavelength is increased, while the speed remains constant?
- A) It increases
- B) It decreases
- C) It remains the same
- D) It becomes zero
#### Answers
1. C
2. C
3. B
4. B
5. A
6. B
7. B
8. B
9. A
10. B
11. B
12. B
13. B
14. C
15. D
16. B
17. C
18. C
19. A
20. B
21. B
22. B
23. B
24. B
25. B
26. C
27. B
28. B
29. D
30. B
