Compare damping in oscillating systems
Explain how a resistive force damps oscillations and distinguish light, critical and heavy damping from displacement–time graphs.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 17. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use displacement, velocity, acceleration, force, energy and trigonometric functions with SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What causes damping in an oscillating system?
What you will learn
- Explain damping as the effect of a resistive force
- Distinguish light, critical and heavy damping
- Describe displacement–time graphs for each damping type
A resistive force reduces oscillation amplitude
Damping occurs when a resistive force acts on an oscillating system. The force transfers mechanical energy to the surroundings, for example as thermal energy, so successive oscillations have smaller amplitude.
Light damping allows repeated oscillations while amplitude gradually decreases. Its displacement–time graph shows several cycles within a shrinking envelope.
Critical and heavy damping return without oscillation
Critical damping is the boundary case that returns the system to equilibrium in the shortest time without overshooting and oscillating. Heavy damping also prevents oscillation, but the return to equilibrium is slower than in the critically damped case.
Sketch each displacement–time trace from the same initial displacement: light damping crosses equilibrium repeatedly with decaying peaks; critical damping returns fastest without crossing; heavy damping approaches more slowly without oscillating. A resistive force's direction opposes motion.
Pause and explain
Which damping returns a system to equilibrium fastest without oscillation?
Worked example
A displacement–time trace crosses equilibrium many times with successively smaller peaks. Identify the damping type and explain the trend.
Show the worked solution
- Repeated crossings show continued oscillation.
- Successive peak sizes show that amplitude decreases.
- Match an oscillating, shrinking trace to light damping.
Answer This is light damping: the system continues to oscillate while its amplitude gradually decreases because resistive forces remove energy.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Describe the displacement–time trace for a lightly damped oscillator.
Give me a hint
Consider whether it crosses equilibrium and how the peaks change.
Compare my reasoning
- The system continues to pass through equilibrium repeatedly.
- Successive positive and negative extrema have smaller magnitude.
- The trace is an oscillation within a gradually shrinking amplitude envelope.
A light-damping graph oscillates about equilibrium with peak magnitudes that decrease over time.
Look for these in your work
- Repeated oscillations stated
- Peak reduction stated
- Graph envelope described
A door closer returns a door to its rest position without repeated swinging, but it moves slowly. Compare this response with critical damping.
Give me a hint
Both responses avoid oscillation; compare return time.
Compare my reasoning
- No repeated crossing or oscillation indicates strong damping.
- Heavy damping returns without oscillating but does so more slowly than critical damping.
- Critical damping would reach rest in the shortest time without oscillation.
The slow non-oscillatory return is consistent with heavy damping; critical damping is the faster non-oscillatory boundary case.
Look for these in your work
- No oscillation identified
- Heavy damping described
- Critical comparison correct
A student draws a critically damped displacement graph that crosses equilibrium twice. Explain the correction.
Give me a hint
Critical damping returns without overshooting or oscillation.
Compare my reasoning
- Crossing equilibrium implies the system has overshot.
- Critical damping returns to equilibrium without oscillating.
- Redraw a smooth, fastest non-oscillatory approach from the initial displacement.
The trace should approach equilibrium without crossing it or oscillating; the crossing belongs to an underdamped response, not critical damping.
Look for these in your work
- Crossing interpreted
- Critical behavior stated
- Graph correction described
Common mistakes
- Calling a resistive force a restoring force
- Saying critical damping oscillates once or overshoots
- Describing heavy damping as faster than critical damping
- Showing constant-amplitude peaks for a damped oscillator
What can you explain now?
What causes damping in an oscillating system?
Compare with the explanation
A resistive force acting on the system
The force removes mechanical energy from the oscillation.
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Make it stick
How do the light, critical and heavy damping graphs differ in oscillation and return time?
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