Answer to Question #316234 in Physics for dlo

Question

what is the calculation and errors of simple pendulum expriment ?

Answer 1

The period of oscillation of a simple pendulum is given by

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

In experiment we use a simple pendulum to calculate the acceleration due gravity

$$g=\frac{4\pi^2l}{T^2}$$

The uncertainty of acceleration is given by

$$\frac{\Delta g}{g}=\sqrt{\left(\frac{\Delta l}{l}\right)^2+\left(\frac{2\Delta T}{T}\right)^2}$$