A spring-mass system oscillates with a frequency . If it is placed...

The frequency of a spring-mass system is given by $\nu = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$.

The frequency depends only on the spring constant $k$ and the mass $m$ of the block.

It is independent of the acceleration due to gravity or any constant external force such as the pseudo force in an accelerating elevator.

The upward acceleration of the elevator only shifts the mean position of the oscillation but does not affect the restoring force constant or the mass.

Therefore, the frequency of oscillation will remain the same.