# Chapter 10 - Problems - Page 403: 94

$v_m = 2.1~m/s$ $a_m = 371~m/s^2$

#### Work Step by Step

The amplitude is half the total distance that the blade moves. We can find the amplitude: $A = \frac{2.4~cm}{2} = 1.2~cm$ We can find the angular frequency: $\omega = 2\pi~f$ $\omega = (2\pi)~(28~Hz)$ $\omega = 175.9~rad/s$ We can find the maximum speed of the blade: $v_m = A~\omega$ $v_m = (0.012~m)(175.9~rad/s)$ $v_m = 2.1~m/s$ We can find the maximum acceleration of the blade: $a_m = A~\omega^2$ $a_m = (0.012~m)(175.9~rad/s)^2$ $a_m = 371~m/s^2$

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