Answer
The period of oscillation is $0.70~s$
Work Step by Step
We can find the value of $k$ for this system:
$kd = mg$
$k = \frac{mg}{d}$
$k = \frac{(92~kg)(9.80~m/s^2)}{0.080~m}$
$k = 11,270~N/m$
We can find the period of oscillation:
$T = \frac{2\pi}{\omega}$
$T = 2\pi~\sqrt{\frac{m}{k}}$
$T = 2\pi~\sqrt{\frac{47~kg+92~kg}{11,270~N/m}}$
$T = 0.70~s$
The period of oscillation is $0.70~s$
