Let block is displaced through $x \mathrm{m}$, then weight of displaced water or upthrust (upwards)

$=-Ax\rho g$

Where, $A$ is area of a cross-section of the block and $\rho$ is density. This must be equal to force $\left(=ma\right)$ applied where $m$ is mass of the block and $a$ is acceleration.

$\therefore ma=-Ax\rho g$

or $a=-\frac{A\rho g}{m}x=-{\omega }^{2}x$

This is equation of $\mathrm{SHM}$.

The time period of oscillation,

$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{m}{A\rho g}}$

$\Rightarrow T\propto \frac{1}{\sqrt{A}}$