Question

You are designing a pendulum clock to have a period of 4.7s. How long should the pendulum be?

Answer 1

The period of oscillation of a pendulum

$$T=2\pi\sqrt{\frac{l}{g}}.$$

The length of a pendulum

$$l=\frac{gT^2}{4\pi^2}=\frac{9.8\times 4.7^2}{4\pi^2}=5.48\:\rm m.$$