For a time-keeping demonstration, a teacher requires that the period of a simple pendulum should not differ from the value predicted by T=2πL/g by more than 1%.
(a) Derive an expression for the percentage error committed in using the approximation sinθ≈θ at an initial angular amplitude θ0.
(b) Using the result of part (a), determine the largest initial angular displacement θ0max (in degrees, correct to one decimal place) that satisfies the teacher’s requirement.
(c) Suggest one experimental method for ensuring that the release angle does not exceed the value obtained in part (b).