Answer
$v_m = 2.1~m/s$
$a_m = 371~m/s^2$
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:
$a_m = A~\omega^2$
$a_m = (0.012~m)(175.9~rad/s)^2$
$a_m = 371~m/s^2$
