Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 15 - Oscillations - Questions - Page 435: 10

Answer

For system 1, the spring constant is 1500 N/m and mass of the block is 500 kg and for system 2, the spring constant is 1200 N/m and mass of the block is 400 kg .

Work Step by Step

In order to maximize the amplitude of oscillations in system 2, the frequency of the system 1 should be equal to the frequency of system 2. $f_1=f_2$ or, $\frac{1}{2\pi}\sqrt {\frac{k_1}{m_1}}=\frac{1}{2\pi}\sqrt {\frac{k_2}{m_2}}$ or, $\frac{k_1}{m_1}=\frac{k_2}{m_2}$ or, $\boxed{\frac{k_1}{k_2}=\frac{m_1}{m_2}}\;............(1)$ We have to choose springs and blocks from four springs with spring constants k of 1600, 1500, 1400, and 1200 N/m, and four blocks with masses m of 800, 500, 400, and 200 kg. Among the given springs and bocks, the springs of springs constant 1500 and 1200 N/m and bocks of masses 500 and 400 kg satisfy the equation $1$. Thus, for system 1, the spring constant is 1500 N/m and mass of the block is 500 kg and for system 2, the spring constant is 1200 N/m and mass of the block is 400 kg .
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