Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 14 - Oscillations - Conceptual Questions - Page 401: 10

Answer

a) More resistive. b) Quickly. c) Decreased.

Work Step by Step

We know that in a damped system, the energy decays exponentially and is given by $$E=E_0e^{\frac{-t}{\tau}}$$ where $\tau$ is the time constant and is given by $$\tau=\dfrac{m}{b}$$ Now the author told us that the damping constant $b$ increases which mean that the time constant decreases. The decrease of time constant $\tau$ increases the term of $e^{-t/\tau}$ and this means that energy will be removed from the system faster. From all the above; a) The medium is more resistive since $b$ increases. b) And the oscillations damp out more quickly. c) As mentioned above, the time constant $\tau$ decreases.
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