Pendulum Period/Frequency
Table of Contents
The formula for the period of a simple pendulum is:
$$ T_p = 2 \pi \sqrt{\frac{\ell}{g}} $$
Where
- \(\small T_p\) is the period of oscillation,
- \(\small \ell\) is the length of the pendulum, and
- \(\small g\) is the acceleration due to gravity.
The frequency of oscillation is the reciprocal of the period:
$$ f_p = \frac{1}{2 \pi} \sqrt{\frac{g}{\ell}} $$
Where
- \(\small f_p\) is the frequency of oscillation.
Note: These formulas use an approximation that assume small oscillations (small angles) and neglects air resistance, damping, and the mass of the string.