College Physics (4th Edition)

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

Chapter 10 - Problems - Page 399: 43


(a) $k = 60.4~N/m$ (b) $x(t) = (12.0~cm)~cos(6.00\pi~t)$

Work Step by Step

(a) We can find the spring constant $k$: $\omega = 2\pi~f$ $\sqrt{\frac{k}{m}} = 2\pi~f$ $k = (2\pi~f)^2~m$ $k = (2\pi)^2~(3.00~Hz)^2~(0.170~kg)$ $k = 60.4~N/m$ (b) We can find the equation for the position as a function of time: $x(t) = A~cos(\omega~t)$ $x(t) = A~cos(2\pi~f~t)$ $x(t) = (12.0~cm)~cos[(2\pi)~(3.00~s)~t)]$ $x(t) = (12.0~cm)~cos(6.00\pi~t)$
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