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## Homework Statement

As in the given picture, the cylinder is drowned (not completely drowned as in partially drowned) in water. The cylinder is attached with a spring which has the spring constant of 200 N/m. The spring has attached to a unmovable point in the ceiling. The weight of the cylinder is 5 kg and the weight of the spring is inconsiderate. If the cylinder pulled slightly down then will there be a simple harmonic motion and if so what is the Period?

Important note:

The height of the cylinder is not given.

The density of the cylinder is also not given.

The density of the water is 1000 kg/m^3.

## Homework Equations

The hook's law -> F= -kx where F=force

k= the spring constant

x= is the displacement

## The Attempt at a Solution

The cylinder is moving in accelerated motion. Let's take the acceleration as a.

Applying the Newton's Law:

F=ma regarding upward motion

Where,

F=T-50+U

ma= 5a

Where T= Tension

U= Up thrust

Hence:

T-50+U=5a

-200x-50+U=5a

U=Vdg

Where V= Volume of the cylinder under water

d= Density of the cylinder

g= gravitation acceleration

This is where I am stuck. I cannot identify the volume of the cylinder under water since it is changing during the motion. What should I do next...?