Question

Derive an expression for calculating time period of oscillation of floating body

Answer 1

An expression for calculating time period of oscillation of floating body is 2π√m/dAg

Consider a floating body of Base area  of A .

We apply a small force F so that the body is pushed down in the liquid, by a distance of Δx .

Let d be the density of the liquid.

Now we know the force exerted by the liquid on the body , also known  as buoyant force is equal to the weight of the liquid displaced by the body.

Weight of the liquid displaced by the body is given by ,

W = m x g = density  x Volume x g

• W = d x V x g = d x A x Y x g = ( dAg )( -y) { negative sign : in direction opposite to applied force }

• F = -ky ==> k = dAg

We know time period of oscillation for SHM is given by 2π√m/k

Therefore, time period ,

• T = 2π√m/dAg