Answer
$f = 15.9~Hz$
$A = 2.0~cm$
Work Step by Step
We can write an expression for the maximum speed.
$v_{max} = A~\omega$
We can write an expression for the maximum acceleration.
$a_{max} = A~\omega^2$
We can divide the second equation by the first equation.
$\frac{a_{max}}{v_{max}} = \frac{A~\omega^2}{A~\omega}$
$\omega = \frac{a_{max}}{v_{max}}$
$\omega = \frac{200~m/s^2}{2.0~m/s}$
$\omega = 100~rad/s$
We can find the frequency.
$f = \frac{\omega}{2\pi}$
$f = \frac{100~rad/s}{2\pi}$
$f = 15.9~Hz$
We can find the amplitude.
$v_{max} = A~\omega$
$A = \frac{v_{max}}{\omega}$
$A = \frac{2.0~m/s}{100~rad/s}$
$A = 0.020~m = 2.0~cm$
