Damping | CAIE 9702 Paper 4 Notes · Conquer Your A Levels

Paper 4

Physics9702

Damping

A real oscillator meets air resistance, friction or drag. These resistive forces transfer energy out of the oscillation.

Why the amplitude becomes smaller

Definition

2 marks

What is meant by damping?

Model answer: The loss of energy of an oscillation due to resistive forces.

Recent mark schemes award one mark for energy loss and one for the resistive force (9702/42/O/N/25 Q5(b)(i)) (9702/41/M/J/24 Q4(b)(ii)).

Swipe left or right to see the whole diagram →

Light damping: the amplitude decays inside an exponential envelope. The peak spacing in one trace stays approximately constant; the damped period can differ slightly from the undamped period.

With light damping, the object still crosses equilibrium many times. Its amplitude becomes smaller on each cycle.
The dashed envelope joins the positive and negative amplitude values. It is not the path of the object.
In the idealised trace, the period remains approximately constant while the amplitude decreases.

Light, critical and heavy damping

Definition

2 marks

What is meant by critical damping?

Model answer: The minimum damping that returns a displaced system to equilibrium without oscillating.

Swipe left or right to see the whole diagram →

Released from x₀ into three environments. Critical damping: the quickest smooth return to zero with no crossing of the axis. Heavy damping: still no crossing, but the return is slow. Light damping (faint) keeps oscillating.

Light damping

Crosses equilibrium many times.

Returns gradually while oscillating.

Critical damping

Does not cross equilibrium.

Fastest return without oscillation.

Heavy damping

Does not cross equilibrium.

Returns more slowly than critical damping.

A car suspension is designed to be close to critical damping. It should settle quickly after a bump without repeated bouncing.
Heavy damping is not the fastest return. A large resistive force also opposes the movement back to equilibrium.

How damping sketches are marked

Start from the displacement stated in the question.
A light-damping curve must cross the axis repeatedly with a shrinking amplitude.
A critical-damping curve must approach zero without crossing it.
A heavy-damping curve also stays on one side, but approaches zero more slowly.
Draw smooth curves. Do not add sudden corners or straight sections.

The latest heavy-damping question awarded separate marks for the starting point, staying on one side and a continuously decreasing displacement and gradient (9702/42/O/N/25 Q5(b)(ii)).