To measure their mass while staying in zero$-$g environments, astronauts use a body$-$mass measuring device $($BMMD$).$ This consist of them grabbing a big spring, and oscillating on it in simple harmonic motion, and measuring the period. The spring constant of the BMMD is $31000$N$/$m$.$

A$)$ If the astronaut has a period of $0\mathrm{.}840$ s$,$ what is their mass?$$

B$)$ The amplitude of motion while on the BMMD is about $0\mathrm{.}0927$ m$.$ What is the astronaut$$s maximum velocity?

C$)$ What is their maximum acceleration?