How to Calculate the Period of Motion in Physics

By Ryan Menezes; Updated April 24, 2017
A pendulum's mass and arc size don't affect its period.

When an object obeys simple harmonic motion, it oscillates between two extreme positions. The period of motion measures the length of time it takes an object to complete oscillation and return to its original position. Physicists most frequently use a pendulum to illustrate simple harmonic motion, as it swings from one extreme to another. The longer the pendulum's string, the longer the period of motion.

Divide the string's length, measured in meters, by the factor measuring acceleration due to gravity, 9.81 meters per second per second. If the string measures 0.6 meters, then the equation is 0.6 / 9.81 = 0.06116.

Find the square root of this answer. In the example, the square root of 0.06116 is 0.2473.

Multiply this result by twice the constant pi, 6.2832. In the example, you would multiply 0.2473 by 6.2832 to get 1.55 seconds. This is the period of motion.

About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.