A rectangular block of mass m and area of cross-section A floats in...

Let block is displaced through $xm$, then weight of displaced water or upthrust (upwards)

$= - Axρg$

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.

$∴ ma = - Axρg$

or $a = - \dfrac{Aρg}{m}x = - {ω}^{2}x$

This is equation of $SHM$.

The time period of oscillation,

$T = \dfrac{2\pi}{ω} = 2\pi\sqrt{\dfrac{m}{Aρg}}$

$⇒ T ∝ \dfrac{1}{A}$