Oscillating loaded rules are a Paper 3 Question 1 regular. By hand, stick a 200 g mass near the free end of a metre rule clamped to the bench edge, loosen the G-clamp and slide the rule to set the overhang L, read L on the rule’s own mm scale through a magnifier, pull the end down, let go and time 10 oscillations with a real stopwatch. Tabulate T, T² and L³, plot T² against L³ and use the gradient to find the bending stiffness of the rule. Every attempt uses a different rule; the timing is real and the short periods make reaction time bite, so allow about 45 minutes.
Checked: Cambridge 9702 Paper 3, 2017 to 2019 and 2023 to 2025. Only the papers in our collection are listed, so the real number may be higher. Question papers are available from Cambridge.
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The scale reading at the centre of the mass and the first L, each to the nearest mm in metres and matching the bench; a stopwatch time for 10 oscillations taken at that L with the clamp tight, and T = t / 10.
Six sets of L and t that were really timed, L spread over the whole 0.300 m to 0.700 m range, five headings with units, every L to the nearest mm, every t to 0.01 s, and T² and L³ to the right significant figures row by row.
Axes and scales filling more than half the grid, plotting to half a small square, a balanced line of best fit, a gradient triangle with a hypotenuse longer than half the line, and the y-intercept read at L³ = 0 (not at a false origin).
P = gradient in s² m⁻³ and Q = y-intercept in s², to two or three significant figures, from your own line.
S = 4π²M / (3P) from your own P, its unit worked out as N m², and a value within 15% of the true stiffness of your rule.
The marking follows the conventions in published Cambridge mark schemes. The experiments, readings and wording on this page are our own.