Pendulum and Timing Experiments
For small angular amplitude and negligible damping, a simple pendulum obeys T = 2 pi sqrt(L/g); measuring total time t_N for N cycles gives T=t_N/N, and g can be inferred from 4 pi^2 L/T^2.
Why this shows up in the exam
School gravity experiments · Clock calibration · Demonstrating error reduction by repeated cycles
Learn the idea
Repeated timing of many oscillations reduces reaction-time fraction when determining a pendulum period or gravitational acceleration. Timing twenty swings spreads nearly the same stopwatch reaction uncertainty over a larger total interval than timing one swing.
🧠 Memory hook: Time many cycles, divide once.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- T = t_N/N — period from timing N oscillations
- T = 2 pi sqrt(L/g) — small-amplitude simple pendulum
- g = 4 pi² L/T² — derived gravitational acceleration
How to approach it
- 1Measure suspension point to bob centre
- 2Time many complete oscillations repeatedly
- 3Average T and propagate L and T uncertainty
Common slip-ups that cost marks
- •Using the bob radius incorrectly in effective length
- •Timing half oscillations as full cycles
- •Ignoring the squared period in error propagation
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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