Answer:
Mass of astronaut will be 119.7674 kg
Explanation:
We have given mass of the chair [tex]m_1=42.5kg[/tex]
When there is chair alone then time period of osculation [tex]T_1=1.30sec[/tex]
Now when astronaut sit on the chair then total mass [tex]m_2=m_1+mass\ of\ astronaut=42.5+mass\ of\ astronaut[/tex]
Now with astronaut time period is [tex]T_2=2.54sec[/tex]
For spring time period is given by [tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
So [tex]\frac{T_1}{T_2}=\sqrt{\frac{m_1}{m_2}}[/tex]
[tex]\frac{1.3}{2.54}=\sqrt{\frac{42.5}{42.5+mass\ of\ astronaut}}[/tex]
Squaring both side
[tex]0.2619={\frac{42.5}{42.5+mass\ of\ astronaut}}[/tex]
[tex]11.13+0.2619\times mass\ of\ astronaut=42.5[/tex]
Mass of astronaut will be 119.7674 kg
