1. The problem statement, all variables and given/known data 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. 2. Relevant equations The hook's law -> F= -kx where F=force k= the spring constant x= is the displacement 3. 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...?