$$A $4\mathrm{.}00$ kg block hangs from a spring, extending it by $16\mathrm{.}0$ cm from its unstretched position.

$($a$)$ Calculate the spring constant. $($b$)$ The block is removed, and a $0\mathrm{.}200$ kg body is hung from

the same spring. Calculate the period of oscillation of the spring with this body attached, if the

spring is stretched and then released.