The time t1, t2 and t3 for 20 complete oscillations of a simple pendulum experiment are 32.0s, 34.6s and 35.5s…

Analyze the question: Three timings were taken, each for 20 complete oscillations. We need the mean period, which is the time for one oscillation.

Concept:

• Period T = time taken ÷ number of oscillations
• Mean time = (t₁ + t₂ + t₃) ÷ 3

Solution:

Step 1: Find the mean time for 20 oscillations.

Mean t = (32.0 + 34.6 + 35.5) ÷ 3 = 102.1 ÷ 3 = 34.03 s

Step 2: Divide by the number of oscillations.

T = 34.03 ÷ 20 = 1.70 s (to 3 s.f., 1.7015)

Check against the options: 1.70 s is option B.

(Option C, 1.73 s, would come from 34.6 ÷ 20, which uses only one reading instead of the mean. Option E, 5.11 s, comes from dividing the total 102.1 by 20, which forgets that there are 3 readings, so it is not the mean.)

Tip: For "mean period" questions, average the times first, then divide by the number of oscillations. Always check that the number of oscillations (here 20) is used, because the question asks for the time of one oscillation, not of all 20.