A simple pendulum of length 1.0000 m is timed and found to have a period of 2.0100 s. What is the acceleration due to gravity at that place?

1. Square the pendulum period formula T = 2 pi sqrt(L/g) to get T squared = 4 pi squared L / g. 2. Rearrange for gravity: g = 4 pi squared L / T squared. 3. Square the period: (2.0100 s) squared = 4.0401 s squared. 4. The numerator is 4 pi squared x 1.0000 m = 39.478 m. 5. g = 39.478 m / 4.0401 s squared = 9.772 m/s squared. 6. Because g depends on the square of the period, five-digit timing is needed for four-digit accuracy in g. 7. Dropping the square on the period gives 19.64 m/s squared, roughly double the real value. 8. Leaving the length in centimetres gives 977.2 m/s squared, a hundred times too large. 9. Dividing by 4 pi squared instead of multiplying gives 1.564 m/s squared, closer to a moon than a planet. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section 16.4 The Simple Pendulum_