Answer
$0.46s^{-1}$
Work Step by Step
The square root of k/m has dimensions of inverse time, which is correct for frequency,
$f_{1}=\sqrt \frac{k}{m_{1}}$ or, $k=m_{1}f_{1}^{2}$
Thus frequency of chair with 75-kg astronaut is
$f_{2}=f_{1}\sqrt \frac{m_{1}}{m_{2}}=(0.5)\sqrt (\frac{62+10}{75+10})=0.46s^{-1}$
