Answer
(a) The period of the motion is $0.90~s$
(b) The maximum speed is $0.56~m/s$
Work Step by Step
(a) We can find the spring constant $k$:
$kd = mg$
$k = \frac{mg}{d}$
$k = \frac{(6.8~kg)(9.80~m/s^2)}{0.20~m}$
$k = 333.2~N/m$
We can find the period of the motion:
$T = \frac{2\pi}{\omega}$
$T = 2\pi~\sqrt{\frac{m}{k}}$
$T = 2\pi~\sqrt{\frac{6.8~kg}{333.2~N/m}}$
$T = 0.90~s$
The period of the motion is $0.90~s$
(b) We can find the maximum speed:
$v_m = A~\omega$
$v_m = A~\sqrt{\frac{k}{m}}$
$v_m = (0.080~m)~\sqrt{\frac{333.2~N/m}{6.8~kg}}$
$v_m = 0.56~m/s$
The maximum speed is $0.56~m/s$
