Physics

Physics

Problem

During an experiment a student records that 30 complete oscillations of a pendulum take 39.6 s39.6\,\text{s}. Take g=9.8 m s−2g = 9.8\,\text{m}\,\text{s}^{-2}. a. (i) Find the time period of the pendulum. b. (ii) Calculate the length of the pendulum corresponding to this period. c. (iii) Express your answer from part (ii) in centimetres, correct to the nearest millimetre.
Intuitive explanation

The key is to find the period from the timing data, then use the pendulum period formula to extract the length. Since you know how long 30 swings take, dividing gives you the time for one complete oscillation. Then rearrange T=2πLgT = 2\pi\sqrt{\frac{L}{g}} to solve for LL—the length is what determines how fast a pendulum swings.

Intuitive explanation

The key is to find the period from the timing data, then use the pendulum period formula to extract the length. Since you know how long 30 swings take, dividing gives you the time for one complete oscillation. Then rearrange T=2πLgT = 2\pi\sqrt{\frac{L}{g}} to solve for LL—the length is what determines how fast a pendulum swings.

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