Pendulum Period Calculator
Determine the period ($T$) of a simple pendulum.
Calculate Period
The period is calculated using the formula:
$$T = 2 \pi \sqrt{\frac{L}{g}}$$Where $g = 9.81 \, \text{m/s}^2$ (standard gravitational acceleration).
Understanding the Simple Pendulum
A simple pendulum is an idealized mechanical system used in physics to study oscillatory motion. It consists of a point mass (the bob) suspended from a fixed pivot by a massless, inextensible string. The time it takes for the pendulum to complete one full swing—from one side back to the starting point—is called its period ($T$).
The period of a simple pendulum is remarkably independent of the mass of the bob and the amplitude of the swing (provided the swing is small, less than about $10^{\circ}$). Crucially, the period depends only on the length ($L$) of the string and the gravitational acceleration ($g$) at that location. This relationship is defined by the equation:
This principle is vital for applications like building accurate clocks, determining local gravity, and understanding fundamental oscillatory dynamics in mechanics. This calculator makes it easy to explore this relationship instantly.
How to Use the Calculator
- Identify the Length ($L$): Measure the length of your pendulum string from the pivot point to the center of the bob. Ensure this measurement is in meters.
- Input the Value: Enter the measured length into the “Pendulum Length ($L$) in meters” input field.
- Calculate: Click the robust “Calculate Period” button.
- Review Results: The calculated period ($T$), presented in seconds with the correct LaTeX formatting, will appear in the green “Results” box below the input section. The result is based on the standard gravitational acceleration $g \approx 9.81 \, \text{m/s}^2$.
