Answer key: Pendulum Period Worksheet

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Goal: Discover which factors change a pendulum’s period (length, gravity or starting angle) and test the formula T = 2π√(L/g).

Completed results table

Values are the simulation’s own readouts for each setting.

Answers

1. Did changing the starting angle from 10° to 3° change the period? What does that tell you?

   No, both swings take 2.006 s. For small angles the period does not depend on the amplitude: a bigger swing travels farther but also moves faster. This small-angle rule is why the lab limits the angle to 15°.

2. Compare the 0.25 m, 1 m and 4 m pendulums. What happens to the period each time the length is multiplied by 4?

   The period doubles each time: 1.003 s, 2.006 s, then 4.012 s. The period is proportional to √L, and √4 = 2.

3. Use T = 2π√(L/g) to calculate the period of the 3 m pendulum. Does it match the lab?

   T = 2π√(3 ÷ 9.81) = 2π × 0.553 = 3.475 s, which matches the lab.

4. Why does the same pendulum swing more slowly on the Moon? By what factor is its period longer?

   Weaker gravity pulls it back toward the middle more gently, so each swing takes longer: 4.937 s instead of 2.006 s, about 2.46 times longer. The factor is √(9.81 ÷ 1.62).

5. Frequency is 1 ÷ period. What happens to the frequency when the period doubles? Use your table.

   It halves: the 1 m pendulum swings at 0.498 Hz and the 4 m pendulum at 0.249 Hz.

6. Challenge: a clockmaker wants a period of exactly 1 s. Using your table, about how long should the pendulum be? Then solve T = 2π√(L/g) for L.

   Just under 0.25 m: the 0.25 m pendulum takes 1.003 s, slightly too long. Solving gives L = gT² ÷ (4π²) = 0.2485 m for T = 1 s.