Answer
(a) $m = 0.169~kg$
(b) $v_{max} = 0.565~m/s$
Work Step by Step
(a) We can find the period as:
$T = \frac{time}{oscillations}$
$T = \frac{20.0~s}{30~oscillations}$
$T = 0.667~s$
Wethencan find the mass of the ball:
$T = 2\pi~\sqrt{\frac{m}{k}}$
$m = \frac{T^2~k}{(2\pi)^2}$
$m = \frac{(0.667~s)^2(15.0~N/m)}{(2\pi)^2}$
$m = 0.169~kg$
(b) We can find the maximum speed as:
$v_{max} = A~\omega$
$v_{max} = A~\sqrt{\frac{k}{m}}$
$v_{max} = (0.0600~m)~\sqrt{\frac{15.0~N/m}{0.169~kg}}$
$v_{max} = 0.565~m/s$
