Question
What is the length of a pendulum that has a period of 0.500 s?
Question by OpenStax is licensed under CC BY 4.0
Final Answer

6.21 cm6.21\textrm{ cm}

Solution video

OpenStax College Physics, Chapter 16, Problem 22 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We are told that a simple pendulum has a period of 0.500 seconds and we are asked to find what length it must have? Well the formula for the period is 2π times the square root of its length divided by the acceleration due to gravity so we solve this for L. So we'll square both sides and we get period squared equals 4π squared times L over g and then multiply both sides by g over 4π squared. Then we get L is T squared times g divided by 4π squared. So that's 0.500 seconds squared times 9.80 meters per second squared divided by 4π squared which is 0.06206 meters which is 6.21 centimeters.

Comments

From a student email: "Hi there, I am pretty sure the answer to this question is wrong because in the solution you divided by 4 and then divided by pi^2 again. When it should just be divided by 4pi^2. I think you just hit the wrong button in the calculator"

This is a common question - it's a matter of personal preference how to enter the division into the calculator. Dividing by 4pi^2 is the same as first dividing by 4, then dividing that result by pi^2. The calculator evaluates left to right when the operators have equal precedence. For example 16 / 2 / 2 makes 4 since the calculator first evaluates 16 / 2 = 8, and then takes that result and divides by the next number 2 to get the answer 4 (8 / 2 = 4). This is the same as 16 / (2 * 2). By avoiding the brackets I've reduced the amount of button pushes by 2, which is the reason for the shortcut.
All the best,
Shaun