$[5]$ Weighing astronauts. In order to study the long$-$term effects of weightlessness, astronauts in space must be weighed $($or at least "massed"$).$ One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. If the $30\mathrm{.}0$ kg chair alone oscillates with a period of $1\mathrm{.}50$ s $,$ and the period with the astronaut sitting in the chair is $2\mathrm{.}50$ s $,$ find $($a$)$ the force constant of the spring and $($b$)$ the mass of the astronaut