What is meant by a free vibration?

A free vibration is an oscillation of a system that has been displaced and then left to oscillate on its own with no further external force, so it vibrates at its natural frequency.

What is meant by a forced vibration?

A forced vibration is an oscillation produced when a system is driven by a periodic external force, so it oscillates at the frequency of the driver rather than at its own natural frequency.

Resonance is the large-amplitude response that occurs when the frequency of a periodic driving force equals the natural frequency of the system being driven, so that energy is transferred to the system most efficiently.

What happens to the amplitude of a forced oscillation as the driving frequency is raised through the natural frequency?

The amplitude rises steeply to a sharp maximum as the driving frequency approaches the natural frequency, and then falls away again as the driving frequency continues to increase.

What is the phase relationship between the driver and the driven system at resonance?

At resonance the displacement of the driven system lags the driving force by a quarter of a cycle, π/2 radians, so the driving force is always in phase with the velocity and does the maximum work on the system.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Simple Harmonic Motion

Free vibrations, forced vibrations and resonance

3 things to know
Unit A2 1

Overview

Free vibration, natural frequency of a system and forced vibration.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Give an example of resonance that engineers must design against in a bridge.

Key term

What is meant by the natural frequency of a system?

Key term

Give a mechanical example of resonance involving a child on a swing.

Questions from this subtopic

Each one with the model answer underneath.

1
What is meant by a free vibration?
Model answer
A free vibration is an oscillation of a system that has been displaced and then left to oscillate on its own with no further external force, so it vibrates at its natural frequency.
2
What is meant by the natural frequency of a system?
Model answer
The natural frequency is the frequency at which a system oscillates freely when displaced and released, determined only by the properties of the system itself.
3
What is meant by a forced vibration?
Model answer
A forced vibration is an oscillation produced when a system is driven by a periodic external force, so it oscillates at the frequency of the driver rather than at its own natural frequency.
4
Define resonance.
Model answer
Resonance is the large-amplitude response that occurs when the frequency of a periodic driving force equals the natural frequency of the system being driven, so that energy is transferred to the system most efficiently.
5
What happens to the amplitude of a forced oscillation as the driving frequency is raised through the natural frequency?
Model answer
The amplitude rises steeply to a sharp maximum as the driving frequency approaches the natural frequency, and then falls away again as the driving frequency continues to increase.
6
What is the phase relationship between the driver and the driven system at resonance?
Model answer
At resonance the displacement of the driven system lags the driving force by a quarter of a cycle, π/2 radians, so the driving force is always in phase with the velocity and does the maximum work on the system.

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Free vibrations, forced vibrations and resonance

Overview

What you need to know

Give an example of resonance that engineers must design against in a bridge.

What is meant by the natural frequency of a system?

Give a mechanical example of resonance involving a child on a swing.

Questions from this subtopic

What is meant by a free vibration?

What is meant by the natural frequency of a system?

What is meant by a forced vibration?

Define resonance.

What happens to the amplitude of a forced oscillation as the driving frequency is raised through the natural frequency?

What is the phase relationship between the driver and the driven system at resonance?

Other ways to work this

What is inside Levo

The 3-step method, run for you

Cram a whole paper in one sitting

Blank Blitz makes facts automatic

Build It gets the exam shape right

Test It catches misconceptions

Brain Breaks between sessions

Every question in Simple Harmonic Motion, on a schedule.