- 1). Divide the angle between the string and the vertical by 180. If the string starts, for instance, at 40 degrees from the vertical: 40 / 180 = 0.222. This is the fraction of a full circle through which the bob travels.
- 2). Multiply 6.283, which is twice the constant pi, by the string's length. With a length, for instance, of 0.3 meters: 6.283 x 0.3 = 1.885. This is the circumference of a full circle with the string as its radius.
- 3). Multiply the previous two answers together: 0.222 x 1.885 = 0.418m. This is the length of one of the pendulum's swing.
- 4). Multiply the length by 2: 0.418 x 2 = 0.836. The bob travels 0.836m during a full period.
- 5). Divide the length of the string by 9.81, which is the acceleration due to gravity: 0.3 / 9.81 = 0.0306.
- 6). Find the square root of this answer: 0.0306 ^ 0.5 = 0.175.
- 7). Multiply the answer by 6.283: 0.175 x 6.283 = 1.099. This is the length, in time, of a single period.
- 8). Multiply one period's distance by its duration: 0.836 / 1.099 = 0.76 meters per second. This is the pendulum's average speed as it swings.
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