Answer
The maximum velocity is $3.10~m/s$
The maximum acceleration is $8560~m/s^2$
Work Step by Step
We can find $\omega$:
$\omega = 2\pi~f$
$\omega = (2\pi)(440.0~Hz)$
$\omega = 880.0\pi~rad/s$
The amplitude is half the distance between the extreme positions of the motion. We can find the amplitude:
$A = \frac{2.24~mm}{2} = 1.12~mm$
We can find the maximum velocity:
$v_m = A~\omega$
$v_m = (1.12~\times 10^{-3}~m)~(880\pi~rad/s)$
$v_m = 3.10~m/s$
The maximum velocity is $3.10~m/s$
We can find the maximum acceleration:
$a_m = A~\omega^2$
$a_m = (1.12~\times 10^{-3}~m)~(880\pi~rad/s)^2$
$a_m = 8560~m/s^2$
The maximum acceleration is $8560~m/s^2$
