In simple terms
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Damped and forced oscillations, resonance
Cambridge 9702 Paper 4 — Damped and forced oscillations, resonance (17.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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17.3 Damped and forced oscillations, resonance.
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All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
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These resistive forces act on an oscillating system causing damping .
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Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 17.3.1
Understand that a resistive force acting on an oscillating system causes damping
- 17.3.2
Understand and use the terms light, critical and heavy damping and sketch displacement-time graphs illustrating these types of damping
- 17.3.3
Understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency
Explore the concept
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Full topic notes
Formal explanation with the rigour you need for the exam.
Damping: The Loss of Energy
Damping is essentially the process where energy is taken away from an oscillating system. This energy dissipation reduces the total mechanical energy, causing a gradual decrease in the maximum displacement, or amplitude, of the oscillations until the system eventually comes to rest. Damping forces always oppose the direction of motion, like air resistance or friction.
17.3 Damped and forced oscillations, resonance.
All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
These resistive forces act on an oscillating system causing damping .
Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
Damping continues until the oscillator comes to rest at the equilibrium position.
Frequency does not change during damping only the amplitude of the oscillation decreases.
Free vs. Forced Oscillations
A system performing free oscillations moves only under the influence of its internal restorative forces, like a spring-mass system in a vacuum. It oscillates at its own unique natural frequency (f₀), which depends on its physical properties, such as mass and stiffness, without any external interference.
Forced oscillations, on the other hand, occur when an external, periodic driving force is continuously applied to a system. This force makes the system oscillate at the driving frequency (f_d) of the external force. Think of pushing a child on a swing – you are applying a periodic driving force.
Resonance: The Perfect Frequency Match
Resonance is a special case of forced oscillation that happens when the driving frequency of the external force exactly matches the natural frequency of the oscillating system (f_d = f₀). When this condition is met, there's incredibly efficient transfer of energy from the driving force to the system.
This efficient energy transfer causes a dramatic and significant increase in the amplitude of the oscillations. Even a small driving force can produce very large amplitudes if applied at the resonant frequency.
Useful Applications: Resonance is vital for tuning radio receivers, generating sound in musical instruments, and in MRI scanners.
Undesirable Effects: Can be destructive, such as bridges collapsing under resonant wind forces or excessive vibrations damaging machinery components.
The Damping-Resonance Relationship
Damping has a crucial role in controlling the effects of resonance. Without damping, theoretical resonance could lead to infinite amplitude, which isn't physically possible. In reality, damping limits the maximum amplitude achieved at resonance.
Peak Amplitude: Increasing damping significantly reduces the maximum amplitude reached at the resonant frequency.
Sharpness of Resonance: Higher damping makes the resonance curve broader and less 'sharp', meaning the amplitude doesn't drop off as quickly away from f₀.
Resonant Frequency Shift: Heavy damping can also cause a slight shift in the frequency at which the peak amplitude (resonance) occurs, typically to a slightly lower frequency.
Worked examples
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An oscillating system experiences resonance. Describe how its amplitude-driving frequency graph would change if the damping in the system was increased significantly.
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Reduced Peak Amplitude: The most noticeable change would be a substantial decrease in the maximum amplitude achieved at the resonant frequency. The peak of the curve would be much lower.
A mechanical oscillator of mass 0.50 kg is attached to a spring, giving it a natural frequency of 2.0 Hz. The system is lightly damped and is driven by a periodic force at its resonant frequency. The system reaches a steady-state amplitude of 5.0 cm. The damping force is given by F_d = -0.8v, where v is the velocity in m/s. Calculate the average power that must be supplied by the driving force to maintain this constant amplitude.
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Identify knowns and the goal:
How it all connects
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Glossary
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Quick check
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Revision flashcards
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What is the fundamental definition of damping in an oscillating system?
Damping is the process where energy is gradually lost from an oscillating system, causing the amplitude of its oscillations to decrease over time.
Key takeaways
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17.3 Damped and forced oscillations, resonance.
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All oscillations eventually come to a stop due to resistive forces, such as friction or air resistance (drag).
- ✓
These resistive forces act on an oscillating system causing damping .
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Damping is defined as the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system .
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Damping continues until the oscillator comes to rest at the equilibrium position.
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Frequency does not change during damping only the amplitude of the oscillation decreases.
Practice — then mark it
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