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B.4 – Forced vibrations and resonance (HL only)
Description
Nature of science:
Risk assessment: The ideas of resonance and forced oscillation have application in many areas of engineering ranging from electrical oscillation to the safe design of civil structures. In large-scale civil structures, modelling all possible effects is essential before construction. (4.8)
Understandings:
- Natural frequency of vibration
- Q-factor and damping
- Periodic stimulus and the driving frequency
- Resonance
Applications and skills:
- Qualitatively and quantitatively describing examples of under-, over- and critically-damped oscillations
- Graphically describing the variation of the amplitude of vibration with driving frequency of an object close to its natural frequency of vibration
- Describing the phase relationship between driving frequency and forced oscillations
- Solving problems involving Q factor
- Describing the useful and destructive effects of resonance
Guidance:
- Only amplitude resonance is required
Data booklet reference:
International-mindedness:
- Communication through radio and television signals is based on resonance of the broadcast signals
Utilization:
- Science and technology meet head-on when the real behaviour of damped oscillating systems is modelled
Aims:
- Aim 6: experiments could include (but are not limited to): observation of sand on a vibrating surface of varying frequencies; investigation of the effect of increasing damping on an oscillating system, such as a tuning fork; observing the use of a driving frequency on forced oscillations
- Aim 7: to investigate the use of resonance in electrical circuits, atoms/molecules, or with radio/television communications is best achieved through software modelling examples
Directly related questions
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18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
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18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
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18M.3.HL.TZ1.b.ii:
calculate the Q at the start of the motion.
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18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
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18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
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18M.3.HL.TZ2.a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
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18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
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18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
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18N.3.HL.TZ0.b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
- 19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
- 19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
- 19M.3.HL.TZ2.c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
- 19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
- 19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
- 19M.3.HL.TZ2.b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
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19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
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19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
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19M.3.HL.TZ1.b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
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19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
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19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
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19M.3.HL.TZ1.a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
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19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.
When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
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19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.
When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
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19N.3.HL.TZ0.c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.
When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
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19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
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19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
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19N.3.HL.TZ0.b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
- 19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
- 19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
- 19N.3.HL.TZ0.a: Describe what is meant by damped motion.
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17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s–1.
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17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s–1.
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17N.3.HL.TZ0.a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s–1.
- 17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
- 17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
- 17N.3.HL.TZ0.b: Outline what change would be required to the value of Q for the mass–spring system in order for...
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18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
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18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
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18M.3.HL.TZ1.a:
Describe the motion of the spring-mass system.
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18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
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18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
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18M.3.HL.TZ2.b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
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18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
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18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
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18N.3.HL.TZ0.a:
State and explain the direction of motion of the mass at this instant.
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19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
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19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
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19M.3.HL.TZ2.a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
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20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by . Calculate the factor for this system.
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20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by . Calculate the factor for this system.
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20N.3.HL.TZ0.c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by . Calculate the factor for this system.
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23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.
n is a positive integer.
What expression is correct about the frequencies of the harmonics in the pipe?
A.B.
C.
D.
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23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.
n is a positive integer.
What expression is correct about the frequencies of the harmonics in the pipe?
A.B.
C.
D.
- 23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
- 23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
- 23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
- 23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
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23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency .
A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s−1.
What is ?
A. 400 HzB. 200 Hz
C. 100 Hz
D. 50 Hz
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23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency .
A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s−1.
What is ?
A. 400 HzB. 200 Hz
C. 100 Hz
D. 50 Hz