In Figure A$,$ block $1($mass $0\mathrm{.}50$ kg $)$ sticks to the vertical spring and oscillates vertically with a period of $0\mathrm{.}30$ s$.$ In Figure B$,$ block $2$ is glued to block $1,$ and the system now oscillates at $0\mathrm{.}40$ s $.$ Use clear, standard symbolic notation, as always.

a$)$ Determine the spring constant of the spring.

b$)$ Determine the mass of block $2.$