Example

Question:

What is the length of a simple pendulum, which ticks seconds?

Solution:

The time period of a simple pendulum is given by \[ T = 2\pi \sqrt{\frac{L}{g}} \] Rearranging, \[ L = \frac{gT^2}{4\pi^2} \] For a seconds pendulum, \(T = 2\,\mathrm{s}\), \(g = 9.8\,\mathrm{m\,s^{-2}}\): \[ L = \frac{9.8 \times 4}{4\pi^2} = 1\,\mathrm{m} \]