When the heavy brass sphere is hung from a spring and it executes vertical vibrations with time period $T,$ time period of oscillation of spring is, $T=2\mathrm{\pi }\sqrt{\frac{\mathit{m}}{\mathit{k}}}$

Now, the sphere is immersed in a non-viscous liquid with a density $(1/10{)}^{\text{th }}$ that of brass, since the time period doesn't depend upon the volume or area of sphere, it only depends upon mass of spring therefore time period will not be affected.

When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will remain unchanged.