## University Physics with Modern Physics (14th Edition)

We can find the force constant $k$ of the spring. $T = 2\pi~\sqrt{\frac{m}{k}}$ $k = \frac{(2\pi)^2~m}{T^2}$ $k = \frac{(2\pi)^2~(42.5~kg)}{(1.30~s)^2}$ $k = 992.8~N/m$ We can use the period when the astronaut is sitting in the chair to find the total mass of the chair and the astronaut. $T = 2\pi~\sqrt{\frac{m}{k}}$ $m = \frac{T^2~k}{(2\pi)^2}$ $m = \frac{(2.54~s)^2(992.8~N/m)}{(2\pi)^2}$ $m = 162.2~kg$ To find the astronaut's mass $m_a$, we need to subtract the mass of the chair. $m_a = 162.2~kg-42.5~kg = 120~kg$ The astronaut's mass is 120 kg