Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 15 - Oscillations - Conceptual Questions: 1

Answer

(a) The period is 2.83 s (b) The period is 1 s (c) The period is 2 s

Work Step by Step

We can write an expression for the period $T$ of a mass oscillating on a spring. $T = 2\pi~\sqrt{\frac{m}{k}} = 2~s$ (a) We can find the period $T'$ when the mass is doubled. $T' = 2\pi~\sqrt{\frac{2m}{k}}$ $T' = \sqrt{2}\times 2\pi~\sqrt{\frac{m}{k}}$ $T' = \sqrt{2}\times T$ $T' = (\sqrt{2})(2~s)$ $T' = 2.83~s$ (b) We can find the period $T'$ when the value of the spring constant is quadrupled. $T' = 2\pi~\sqrt{\frac{m}{4k}}$ $T' = \frac{1}{2}\times 2\pi~\sqrt{\frac{m}{k}}$ $T' = \frac{1}{2}\times T$ $T' = (\frac{1}{2})(2~s)$ $T' = 1~s$ (c) Since the period does not depend on the oscillation amplitude, the period of $T = 2~s$ remains the same.
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