CIE AS/A Level Physics 17.3 Damped and forced oscillations, resonance Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 17.3 Damped and forced oscillations, resonance Study Notes – New Syllabus
CIE AS/A Level Physics 17.3 Damped and forced oscillations, resonance Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- understand that a resistive force acting on an oscillating system causes damping
- understand and use the terms light, critical and heavy damping and sketch displacement–time graphs illustrating these types of damping
- 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
Damping in Oscillatory Systems
An oscillating system (such as a mass–spring system or a pendulum) often experiences forces that oppose its motion. When a resistive force acts on the system, it removes energy from the oscillation, causing the motion to gradually die down. This process is called damping.
A resistive force (e.g., air resistance, friction, drag) removes energy from the system → amplitude decreases over time → the oscillation is said to be damped.
Characteristics of Damping:
- Damping always reduces the amplitude of oscillation.
- Energy is lost to the surroundings (usually as heat).
- The period may increase slightly depending on damping strength.
- In the extreme case, oscillations can stop completely (overdamping).
Sources of Resistive Forces:
- Air resistance
- Viscous drag in liquids
- Internal friction within materials
- Friction at pivot points or contact surfaces
Effect on the Oscillation:
Greater damping → faster reduction in amplitude Less damping → slow decay of oscillations
Example
A child’s swing slows down and eventually stops if no one keeps pushing it. Explain why.
▶️ Answer / Explanation
Air resistance and friction at the pivot act as resistive forces. These forces remove energy from the swing, reducing its amplitude over time. This loss of energy causes damping, so the swing eventually stops.
Example
A mass on a spring oscillates vertically in air. Its amplitude decreases slowly with time. What does this tell you about the damping force?
▶️ Answer / Explanation
The slow decrease in amplitude means that the resistive force (air resistance and internal friction) is relatively small. It removes energy gradually, resulting in light damping. The system still oscillates but with slowly decreasing amplitude.
Example
A mass–spring system oscillates inside a container of oil. Compared to oscillations in air, the amplitude decreases rapidly and the oscillations stop quickly. Explain this in terms of damping.
▶️ Answer / Explanation
Oil provides a much larger resistive force than air. The viscous drag removes energy from the system quickly. This is heavy damping:
- Large resistive force
- Rapid loss of energy
- Amplitude decreases sharply
- Oscillations stop early
In extreme cases, the system may return to equilibrium without oscillating at all (overdamped).
Types of Damping in Oscillatory Systems
When a resistive force acts on an oscillating system, the motion becomes damped. The nature of the damping depends on the strength of the resistive force. There are three main types of damping:
- Light damping
- Critical damping
- Heavy (over) damping
Light Damping
- Oscillations occur, but the amplitude decreases gradually with time.
- Energy is removed slowly.
- The system continues to oscillate but with smaller peaks each cycle.
Graph (qualitative):
A sinusoidal wave with exponentially decreasing amplitude.
Critical Damping
- The system returns to equilibrium in the shortest possible time without oscillating.
- Used in car shock absorbers, door closers, measuring instruments.
- Damping is exactly strong enough to prevent oscillations.
Graph (qualitative):
A smooth curve returning to equilibrium quickly and without crossing the axis.
Heavy (Over) Damping
- The system returns to equilibrium without oscillating, but more slowly than critical damping.
- Damping force is very large (e.g., motion in oil).
- System is sluggish and takes long to settle.
Graph (qualitative):
A slowly decaying, non-oscillatory curve that approaches equilibrium gently.
Qualitative Sketch Summary
- Light damping: oscillatory with decreasing amplitude
- Critical damping: fastest non-oscillatory return
- Heavy damping: slow non-oscillatory return
Example
A guitar string vibrates in air and its sound gradually fades. Which type of damping is this, and why?
▶️ Answer / Explanation
This is light damping. Air resistance slowly removes energy from the oscillating string, causing the amplitude to decrease gradually while the string continues to vibrate.
Example
A door fitted with a hydraulic closer returns to the closed position smoothly without oscillating. Which type of damping is being used?
▶️ Answer / Explanation
The door closer uses critical damping. The damping force is just enough to prevent oscillations and ensures the door returns to equilibrium (closed position) in the minimum time without swinging back and forth.
Example
Consider three oscillating systems placed in different media: (A) air, (B) water, (C) thick oil. Rank them in order of damping strength and describe the expected displacement–time graph for each.
▶️ Answer / Explanation
Damping strength (lowest → highest):
- System in air → light damping
- System in water → critical or near-critical damping (depends on shape)
- System in thick oil → heavy/over damping
Expected displacement–time graphs:
- Air: oscillations with gradually decreasing amplitude.
- Water: rapid decay without oscillation (almost critically damped).
- Oil: slow, non-oscillatory return to equilibrium (heavily damped).
Resonance in Oscillatory Systems
When an external periodic force acts on an oscillating system, it is said to be forced to oscillate. If the frequency of this driving force matches the system’s natural frequency, the system undergoes a dramatic increase in amplitude. This phenomenon is known as resonance.
Definition:
Resonance occurs when a system is forced to oscillate at a frequency equal to its natural frequency, resulting in a maximum amplitude of oscillation.
Conditions for Resonance:
- An external periodic force must act on the system.
- The driving frequency must equal the natural frequency:
\( \mathrm{f_{driving} = f_{natural}} \)
Effects of Resonance:
- Amplitude becomes very large (maximum possible).
- Energy transfer from driving force to system is most efficient.
- Damping affects the sharpness and height of the resonance peak.
Examples of Natural Frequency:
- A swing pushed at the right rhythm
- A guitar string vibrating at a certain pitch
- Air column in a pipe resonating with a tuning fork
Example
A child on a swing is pushed periodically by a parent. The swing reaches its maximum amplitude when the parent pushes at just the right timing. Explain this phenomenon.
▶️ Answer / Explanation
The swing has a natural frequency. When the pushing frequency matches this natural frequency, the swing absorbs the most energy each push. This produces maximum amplitude — this is resonance.
Example
A tuning fork vibrating at 256 Hz is placed near an open tube containing air. The sound from the tuning fork becomes very loud at a certain tube length. Explain why.
▶️ Answer / Explanation
The air column in the tube has a natural frequency determined by its length. When this natural frequency matches the frequency of the tuning fork (256 Hz), the air column resonates. This produces maximum amplitude of sound waves inside the tube, making the sound louder.
Example
A bridge has a natural frequency of \( \mathrm{0.5\ Hz} \). Wind gusts exert a periodic force on the bridge at a frequency of \( \mathrm{0.50\ Hz} \). Predict and explain the resulting motion, assuming very little damping is present.
▶️ Answer / Explanation
The driving frequency from the wind (0.50 Hz) matches the bridge’s natural frequency (0.5 Hz). This causes resonance.
Since damping is small:
- Energy builds up rapidly in the oscillation.
- Amplitude increases dramatically.
- The oscillations may become dangerously large.
This is why resonance can cause structural failure.