A spring is hung from the ceiling. A $0\mathrm{.}385-kg$ block is then attached to the free end of the spring. When released from rest, the block

drops $0\mathrm{.}137m$ before momentarily coming to rest, after which it moves back upward. $($a$)$ What is the spring constant of the spring? $($b$)$

Find the angular frequency of the block's vibrations.

$($I used $27\mathrm{.}54$ and $8\mathrm{.}5$ and they did not answer it correctly$)$ thx u

$($a$)$ Use the principle of conservation of energy to find the spring constant. The kinetic energy at the highest and lowest point is

zero because the mass is at rest. Thus, we only need to consider gravitational potential and elastic potential energy:

$mg{h}_i+\frac{1}{2}k{x}_i^2=mg{h}_f+\frac{1}{2}k{x}_f^2.$