Exercise 3: sample answer

Expected result: with a string of 25 cm, 20 swings take about 20 seconds (a full back-and-forth is about 1 second); with a string of 50 cm, 20 swings take about 28 seconds. Doubling the length does not double the time: it multiplies it by about 1.4, the square root of 2 (check by repeating the experiment a few times).

Example write-up: "The short pendulum took about 20 seconds for 20 swings and the long one about 28. Doubling the length made each swing roughly 40 percent longer, not twice as long, which fits the rule that time grows with the square root of the length."

Tips: time many swings and divide, to reduce the error from your reaction time; keep the swings small (under about 15 degrees); and measure the length from the pivot to the centre of the weight.