A group of students records the time for 50 complete oscillations of a simple…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A group of students records the time for 50 complete oscillations of a simple pendulum of length

0.80\,\text{m}

released from an initial angle of

12^{\circ}

. Their measured average time for 50 oscillations is

113.2\,\text{s}

. (a) Calculate the experimental value of the period

T_{\text{exp}}

. (b) Using the small-angle formula, compute the theoretical period

T_{0}

for the same length, taking

g=9.8\,\text{m} \,\text{s}^{-2}

. (c) Determine the percentage difference between

T_{\text{exp}}

and

T_{0}

. (d) Assuming that the entire discrepancy arises because the initial angle is outside the strict small-angle limit, state whether the measured data support this assumption. Give a brief justification based on your result in part (c).

Related theory

Measurement Errors
Simple Pendulum
Pendulums
Pendulum and spring systems
Simple harmonic motion
Oscillations

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