A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T then:

Force applied on the body will be equal to upthrust for vertical oscillations.Let block is displaced through x m, then the weight of displaced water or upthrust (upwards)= _-AxρgWhere A is area of cross-section of the block and ρ is its density. This must be equal to force (= ma) applied, where m is mass of the block and a is acceleration.∴ ma = _ Axρgor a = -Aρgmx = -ω2xThis is the equation of simple harmonic motion.Time period of oscillationT = 2πω= 2πmAρg   ⇒T ∝1A