Question

A simple pendulum can be used to measure gravitational acceleration. A geophysicist measures the frequency of a 0.22 m long simple pendulum to be 0.57 Hz at a particular location on Earth. What is the gravitational acceleration at that location?

Answer 1

The frequency of a simple pendulum is given as follows:

$$f = \dfrac{1}{2\pi}\sqrt{\dfrac{g}{L}}$$

where $L = 0.22m$ and $g$ is the gravitational acceleration. Thus, obtain:

$$g = 4\pi^2 f^2 L = 4\pi^2\cdot 0.57^2\cdot 0.22 \approx 2.8m/s^2$$

Answer. 2.8 m/s^2.