Answer
The maximum possible amplitude is $~~3.1~cm$
Work Step by Step
The magnitude of the maximum acceleration is $~~a = A~\omega^2$
We can find the maximum possible amplitude:
$F = ma$
$mg~\mu_s = m~A~\omega^2$
$g~\mu_s = A~\omega^2$
$A = \frac{g~\mu_s}{\omega^2}$
$A = \frac{g~\mu_s}{(2\pi~f)^2}$
$A = \frac{(9.8~m/s^2)(0.50)}{[(2\pi)(2.0~Hz)]^2}$
$A = 0.031~m$
$A = 3.1~cm$
The maximum possible amplitude is $~~3.1~cm$
