You have one spring and a set of masses. One way is to hang them and read the stretch with a ruler; the other is to set the spring oscillating and time the period with a stopwatch. Two fully independent routes, two completely different instruments. Their answers agree to better than half a percent — and both are two percent wrong.
What makes this one different
In the ten earlier experiments there was always a way to see the error: repeat it, plot it, take a slope, calibrate. Here, for the first time, the student’s data is structurally incapable of seeing it. The reason is one line of algebra. The static route gives k = m·g/x and the dynamic route gives k = 4π²(m + m_spring/3)/T². Both depend linearly on m. So if the masses are labelled 250 g and are really 244 g, both answers move together by the same factor and their difference does not move at all. Two methods agreeing about something they both took from the same place tells you nothing.
And the trap has three rungs, which is the worst part. Raw data: k is off by five percent and the two routes differ by seven — the student knows something is wrong. Apply the spring-mass correction: k is still two percent off, but the gap collapses to 0.2 percent. That is where they stop, because every internal check in the report has turned green. The only thing that moves them forward is walking to the balance and weighing the masses themselves — leaving the experiment’s own data behind. After that k lands within 0.1 percent and the gap stays at 0.2 percent, completely unmoved. The number they trusted was answering a different question all along.
In density by Archimedes we saw that removing one error makes the next visible, and in Young’s modulus that you must break the experiment to find its limit of validity. This one is harder than either: here the experiment stays healthy to the end and looks right. The test “two independent methods agreed” — in practice the single most persuasive argument in a student report — only means something when the two methods share no input. Here they shared one.
The Python section runs two students over identical data: one who trusts the agreement, one who checks the masses. Across eight sessions the first is off by 2.6 percent on average while confidently quoting a 0.5 percent agreement; the second is off by 0.2 percent. And the first student’s error is not scatter — it is signed, and it tracks the mass-set error exactly. Then it computes how wrong the masses would have to be before that 0.2 percent gap climbs out of the noise: 21 percent — by which point k is already off by twenty. So this test does not warn you late; it does not warn you at all.