A pendulum completes 20 oscillations in 32 s. (a) Calculate the period of the pendulum. [2] (b) Calculate the frequency of the pendulum. [2] (c) State why t...
Question 1 Report
A pendulum completes 20 oscillations in 32 s.
(a) Calculate the period of the pendulum. [2]
(b) Calculate the frequency of the pendulum. [2]
(c) State why the student timed 20 oscillations rather than just one. [1]
Answer Details
(a) Period of the pendulum
The period is the time for one complete oscillation. The student timed 20 oscillations in 32 s:
\( T = \frac{\text{total time}}{\text{number of oscillations}} = \frac{32}{20} \) [1]
\( T = 1.6 \text{ s} \) [1]
(b) Frequency of the pendulum
Frequency is the number of oscillations per second, and is the reciprocal of the period:
\( f = \frac{1}{T} = \frac{1}{1.6} \) [1]
\( f = 0.625 \text{ Hz} \) [1]
This means the pendulum completes 0.625 full swings every second.
(c) Why 20 oscillations were timed rather than one
Timing a single oscillation (1.6 s) would introduce a large percentage error because human reaction time (typically 0.2-0.3 s) is a significant fraction of 1.6 s. By timing 20 oscillations (32 s total), the reaction time error becomes a much smaller fraction of the measured time, greatly reducing the percentage error [1]. For example, a 0.2 s reaction time error on a 32 s measurement gives only about 0.6% error, compared to about 13% on a 1.6 s measurement.
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