11 mark
Which graph shows light, critical, or heavy damping?
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6.3 Forced Vibrations & Resonance
21 mark
When the frequency of an external force acting on an oscillating system is equal to the natural frequency of the system, the amplitude of the resulting oscillations is observed to increase significantly.
What is this phenomenon known as?
simple harmonic motion
resonance
critical damping
free oscillation
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31 mark
Which of the following correctly describes a free oscillation and a forced oscillation?
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41 mark
The following scenarios demonstrate free and forced oscillations
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1 |
When a large number of people walk across a suspension bridge simultaneously and set it into oscillation |
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2 |
Pushing a child on a swing each time it reaches its highest point |
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3 |
Setting a pendulum into motion by pulling it to one side and releasing it |
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4 |
Plucking a string on a guitar |
Which row correctly shows the scenarios that are free or forced oscillations?
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51 mark
An oscillatory system, subject to damping, is set into vibration by a periodic driving force of frequency f.
The graphs, A to D, which are to the same scale, show how the amplitude of vibration A of the system might vary with f, for various degrees of damping.
Which graph best shows the heaviest damping ?
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11 mark
In microwave ovens, water molecules in food are set into resonance when microwaves of fixed frequency are incident upon them. This causes the molecules to receive energy and hence this warms up the food.
Which of the following would result in the food being warmed up faster?
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21 mark
The diagram shows a string XY supporting a heavy pendulum P and four pendulums A, B, C and D of smaller mass.
Pendulum P is set in oscillation perpendicular to the plane of the diagram.
Which row shows the correct amplitude and phase of A, B, C or D in relation to P?
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31 mark
Identical masses oscillate vertically in a liquid attached to springs P and Q. The support vibrates with a driving frequency which can be varied.
In the first setup, spring P is suspended in a beaker of water, whilst in a second similar setup, spring Q, a stiffer spring, is suspended in a beaker of honey, as shown in the diagram below.
Which graph best represents the way in which the amplitudes of springs P and Q vary with the driving frequency, f ?
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41 mark
A pendulum is constructed from a fixed length of light thread and a light spherical bob.
It is forced to oscillate at different frequencies in a vacuum. The following graph of amplitude against frequency is obtained:
Which one of the following graphs best represents the results if the experiment were to be repeated in air?
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51 mark
Two objects X and Y are given the same initial displacement and are then released. The following graphs show the variation of their displacement, x, with the time, t.
X and Y are then subjected to driving forces of the same constant amplitude and of variable frequency, f.
Which graph represents the variation of f with the amplitudes A of X and Y?
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11 mark
Which one of the following statements always applies to a damping force acting on a vibrating system?
It is in the same direction as the acceleration
It is in the same direction as the displacement
It is in the opposite direction to the velocity
It is proportional to the displacement
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21 mark
When a car driver is driving, they notice a periodic force is applied to their lightly damped rear-view mirror causing it to oscillate.
The graph shows how the amplitude, A, of the oscillations varies with the frequency, f, of the periodic force.
Which one of the following statements best describes how the shape of the curve would differ if the damping on the rear-view mirror was greater?
The curve would be lower at all frequencies
The curve would be higher at all frequencies
The curve would be unchanged except at frequencies above the resonant frequency where it would be lower
The curve would be unchanged except at frequencies above the resonant frequency where it would be higher
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31 mark
Which of the following graphs shows the correct variation of displacement, y, of an object undergoing lightly damped oscillations against time, t ?
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41 mark
Which one of the following statements concerning forced vibrations and resonance is correct?
An oscillating body that is not resonating will return to its natural frequency when the forcing vibration is removed
At resonance, the displacement of the oscillating body is 180° out of phase with the forcing vibration
A pendulum with a dense bob is more heavily damped than one with a less dense bob of the same size
Resonance can only occur in mechanical systems
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51 mark
Which one of the following statements about an oscillating mechanical system at resonance, when it oscillates with a constant amplitude, is not correct?
The amplitude of oscillations depends on the amount of damping
The frequency of the applied force is the same as the natural frequency of oscillation of the system
The total energy of the system is constant
The applied force prevents the amplitude from becoming too large
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61 mark
Which of the following does not demonstrate resonance?
A tuning fork vibrating when a certain note is played on the piano
A stationary wave forming inside a musical instrument
A pendulum swinging at its natural frequency
A window in a vehicle vibrating violently at a certain speed
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71 mark
A mechanical oscillator is set into motion by a periodic driving force whose frequency is steadily increased from a low value.
Which of the following is correct for this system?
The oscillator is subject to damping only at the resonant frequency
Forced vibrations occur only at particular frequencies
The oscillator will not continue to resonate when the periodic driving force is removed
When resonance occurs the damping force is a minimum
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