A simple pendulum is a mass hanging from a massless string of length L swinging from a central pivot point. As the mass is pulled out at a small angle theta and released, the mass will swing back and forth in periodic motion. This example problem will show how to calculate the period of a simple pendulum.

The period of a simple pendulum refers to the time it takes for the mass to complete one complete cycle of its swinging motion. This time can be calculated using the formula

where

T = period

L = length of the pendulum

g = acceleration due to gravity

### Simple Pendulum Period Example Problem

**Question:** What is the period of a simple pendulum with a length of 1 meter?

Use 9.8 m/s^{2} for gravity

Solution: Start with the period of a simple pendulum formula.

Plug in the values for L and g

T = 2π (0.32 s)

T = 2.0 s

**Answer:** The period of a simple pendulum with a length of 1 meter is 2.0 seconds.

Completing this type of problem relies on knowing the formula. The easiest way to make a mistake is mixing your units. For example, if this problem gave the length in centimeters, you would have to convert centimeters to meters to get the correct answer.