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?
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.
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 T= Tension
U= Up thrust
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...?