Period of a Simple Pendulum Example Problem   Recently updated !


A simple pendulum with length L

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

formula for the period of a simple pendulum

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/s2 for gravity

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

period of a simple pendulum formula

Plug in the values for L and g

period of a simple pendulum math step 1
period of a simple pendulum math step 2

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 given the length in centimeters, you would have to convert centimeters to meters to get the correct answer.

Check out another simple pendulum example problem which uses this formula to calculate the length when the period is known. If you need to calculate the acceleration due to gravity using a pendulum, check out this example problem.

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