A physics team records the periods of a simple pendulum of fixed length 1.20m for several initial angular displacements. The table shows their measurements.
Amplitude θ0 (degrees): 3.0 7.0 12 18 25
Measured period T (s): 2.20 2.22 2.28 2.41 2.60
(a) Convert each amplitude to radians and record the values.
(b) For each trial, calculate the ratio 2πL/gT, where g=9.81ms−2. Tabulate your results.
(c) Sketch (on your own paper) a graph of the measured period T versus the initial angular displacement θ0 in radians. Describe the key trend shown by the data.
(d) Using your results from parts (b) and (c), evaluate the validity of the small-angle approximation at each amplitude and identify the approximate angular limit beyond which the SHM model ceases to provide an accurate prediction for the period.
(e) Provide a physical explanation for why the period increases as the amplitude becomes large, referring to changes in the restoring torque relative to displacement.