A student wishes to decide whether the following initial angular amplitudes are suitable for treating a simple pendulum as executing simple harmonic motion:
1∘,3∘,7∘,10∘,15∘.
(i) Arrange these amplitudes into two lists, “acceptable” and “not acceptable”, on the basis of the usual small-angle criterion.
(ii) For θ=7∘, calculate the percentage error introduced when sinθ is replaced by θ (with θ in radians). Show all working.
(iii) Comment, with numerical support, on whether 7∘ may still be considered acceptable in a school laboratory where timing errors of up to 2% in the measured period are tolerated.