Answer
(a) The maximum displacement is $0.172~mm$
(b) The maximum speed is $0.13~m/s$
(c) The maximum net force is $514~N$
Work Step by Step
(a) We can find the angular frequency:
$\omega = 2\pi~f = (2\pi)(120~Hz) = 754~rad/s$
We can find the maximum displacement $A$:
$a_m = A~\omega^2$
$A = \frac{a_m}{\omega^2}$
$A = \frac{98~m/s^2}{(754~rad/s)^2}$
$A = 0.172\times 10^{-3}~m$
$A = 0.172~mm$
The maximum displacement is $0.172~mm$
(b) We can find the maximum speed $v_m$:
$v_m = A~\omega$
$v_m = (0.172\times 10^{-3}~m)(754~rad/s)$
$v_m = 0.13~m/s$
The maximum speed is $0.13~m/s$
(c) We can find the maximum net force:
$F_m = m~a_m$
$F_m = (5.24~kg)(98~m/s^2)$
$F_m = 514~N$
The maximum net force is $514~N$
