Physics 9702 · Paper 4

Damping

Real oscillations die away. How fast, and whether they oscillate at all on the way down, is a three-way classification that P4 tests with tightly-marked sketches.

What damping is (two marks)

is the loss of energy of the oscillations due to resistive forces (air resistance, friction, drag in a liquid). Each half is a mark (9702/42/O/N/25 Q5(b)(i)); asked only for the cause, “resistive forces” is the accepted phrase (9702/42/F/M/23 Q3(c)(i)).

Light damping: the amplitude decays exponentially (dashed envelope), but the period does not change — successive peaks arrive at the same spacing, just lower.

Light damping: the system still oscillates, with amplitude decaying exponentially inside the dashed envelope — and the period stays the same as the peaks shrink. Reading $T$ off a decaying graph is safe; reading the amplitude requires the envelope (9702/41/M/J/24 Q4(b)).
Exponential decay means a fixed fraction lost per cycle. A 2023 part gave 8.0% energy loss per oscillation: after 6 cycles the energy is $6.4 \times 0.92^{6}$ mJ, so 2.5 mJ has gone (9702/42/F/M/23 Q3(c)(ii)) — multiply the factors, never subtract 8% six times.

Critical and heavy damping

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.

Damping	Does it cross equilibrium?	Return to rest
light	yes — many times, inside a shrinking envelope	slowly, oscillating all the way
critical	no — one smooth run to zero	the fastest possible without oscillating
heavy (over-damped)	no	slow — the resistive force also fights the return

The sketches are marked feature by feature. Critical (sphere released in water): start at $(0, x_0)$ , never touch $\pm x_0$ again, no sudden gradient changes, and reach zero — with zero gradient — within a couple of periods (9702/41/O/N/23 Q4(c)). Heavy (thick oil): the curve stays entirely on one side of the axis, with both the displacement and the gradient continuously decreasing, and does not reach zero within the plotted $2T$ (9702/42/O/N/25 Q5(b)(ii)).
Critical damping is engineered on purpose: car suspensions and swing doors should return to equilibrium fast and stay there, not bounce.

Damping = energy loss to resistive forces. Light: oscillates in an exponential envelope, period unchanged. Critical: fastest no-oscillation return. Heavy: no oscillation, slow return.

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Damping

Real oscillations die away. How fast, and whether they oscillate at all on the way down, is a three-way classification that P4 tests with tightly-marked sketches.

What damping is (two marks)

is the loss of energy of the oscillations due to resistive forces (air resistance, friction, drag in a liquid). Each half is a mark (9702/42/O/N/25 Q5(b)(i)); asked only for the cause, “resistive forces” is the accepted phrase (9702/42/F/M/23 Q3(c)(i)).

Light damping: the amplitude decays exponentially (dashed envelope), but the period does not change — successive peaks arrive at the same spacing, just lower.

Light damping: the system still oscillates, with amplitude decaying exponentially inside the dashed envelope — and the period stays the same as the peaks shrink. Reading $T$ off a decaying graph is safe; reading the amplitude requires the envelope (9702/41/M/J/24 Q4(b)).
Exponential decay means a fixed fraction lost per cycle. A 2023 part gave 8.0% energy loss per oscillation: after 6 cycles the energy is $6.4 \times 0.92^{6}$ mJ, so 2.5 mJ has gone (9702/42/F/M/23 Q3(c)(ii)) — multiply the factors, never subtract 8% six times.

Critical and heavy damping

Damping	Does it cross equilibrium?	Return to rest
light	yes — many times, inside a shrinking envelope	slowly, oscillating all the way
critical	no — one smooth run to zero	the fastest possible without oscillating
heavy (over-damped)	no	slow — the resistive force also fights the return

The sketches are marked feature by feature. Critical (sphere released in water): start at $(0, x_0)$ , never touch $\pm x_0$ again, no sudden gradient changes, and reach zero — with zero gradient — within a couple of periods (9702/41/O/N/23 Q4(c)). Heavy (thick oil): the curve stays entirely on one side of the axis, with both the displacement and the gradient continuously decreasing, and does not reach zero within the plotted $2T$ (9702/42/O/N/25 Q5(b)(ii)).
Critical damping is engineered on purpose: car suspensions and swing doors should return to equilibrium fast and stay there, not bounce.

Damping = energy loss to resistive forces. Light: oscillates in an exponential envelope, period unchanged. Critical: fastest no-oscillation return. Heavy: no oscillation, slow return.