College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 10 - Problems - Page 403: 95


$T = 2\pi~\sqrt{\frac{L}{g}}$

Work Step by Step

We can write the equation for the period of a physical pendulum: $T = 2\pi~\sqrt{\frac{I_{support}}{mgL_{cm}}}$ For a simple pendulum, $I_{support} = mL^2$ For a simple pendulum, $L_{cm} = L$ We can derive the equation for the period of a simple pendulum: $T = 2\pi~\sqrt{\frac{I_{support}}{mgL_{cm}}}$ $T = 2\pi~\sqrt{\frac{mL^2}{mgL}}$ $T = 2\pi~\sqrt{\frac{L}{g}}$
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