A student investigates the motion of a small pendulum and records both the period T…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A student investigates the motion of a small pendulum and records both the period T of one complete swing and the corresponding frequency f of the motion. The results are summarized in the data table below.
Trial | Period T (s) | Frequency f (Hz)
1 | 0.80 | 1.25
2 | 0.67 | 1.49
3 | 1.00 | 1.00
4 | 0.40 | 2.50
Assume measurements are free of significant experimental error.
(a) Using the data, describe the mathematical relationship between the period and the frequency of the pendulum’s motion. Support your answer with appropriate references to the numerical values in the table.
(b) For each trial, compute the product Tf. Interpret the physical significance of the numerical result you obtain.
(c) The student now adjusts the length of the pendulum so that its frequency becomes 1.8Hz. Predict the new period of the pendulum and explain your reasoning in words.