Answer:
mass of astronaut is M 67.362 kg
Explanation:
Given details:
spring constant k = 606 N/m
Time T = 0.848 s
The time period is
[tex]T = (2\pi)\sqrt{\frac{m}{k}}[/tex]
So the mass of the empty chair is
[tex]m = [\frac{T}{2\pi}]^2 k[/tex]
[tex]= [\frac{0.848}{2\pi}]^2*606[/tex]
= 11.038 kg
When astronaut is sitting in the chair then the time period is
[tex]T' = (2\pi)\sqrt{\frac{m'}{k}}[/tex]
[tex]m' = [\frac{T'}{2\pi}]^2k[/tex]
[tex]=[\frac{2.26}{2\pi}]^2*606[/tex]
m' = 78.40 kg
mass of astronaut is M = m' - m
= (78.40 kg) - ( 11.038 kg)
= 67.362 kg
