A pendulum is to be built with a period of 2.00 s at a place where g is 9.80 m/s squared. What length of string is needed?

1. Start from T = 2 pi sqrt(L/g) and square both sides: T squared = 4 pi squared L / g. 2. Rearrange for length: L = g T squared / (4 pi squared). 3. Substitute: L = (9.80 m/s squared)(2.00 s) squared / (4 pi squared) = 39.2 / 39.478. 4. L = 0.993 m, so a pendulum a little under a metre long ticks out two-second swings. 5. Forgetting the 4 pi squared divisor gives 3.92 m, which is four times too long. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section 16.4 The Simple Pendulum_