# Simple Harmonic Motion

1. Nov 1, 2005

### Canuck156

Hi, I'm having a few problems with an assignment. Here is the question, and the progress that I've made so far. (If you can call it progress... :grumpy: )
Q) A 500g cylinder of base area a=20cm^2 and height h=30cm is floating upright in water. A 50g mass resting on top of the cylinder is suddenly removed. a) Find the resulting force and show that the resulting motion is simple harmonic. b) What are the amplitude and period of the motion?
The force exerted on the cylinder by the mass is given by f=ma=mg=0.05*9.8=0.49N. It seems logical to me that this would be equal to the initial restoring force, is this correct? I also found that the density of the cylinder is 833kg/m^3, compared to 1000kg/m^3 for water, but I don't know whether this has anything to do with the problem...
To me it seems that the next thing I need to find is the equilibrium position of the cylinder. Is this right? If so how could I do this?
Thanks a lot.

2. Nov 1, 2005

### lightgrav

At equilibrium, it will float so that
the pressure inside the cylinder at its bottom
equals the pressure outside the cylinder bottom
(that is, water P at depth of the bottom).

and yes, F = mg WAS (not IS) the force by the mass
(ma ? we have NO interest in the accelleration of m
as it was removed from on top of the cylinder!)
so the restoring Force is 0.5N (at x = .05m)

Last edited: Nov 1, 2005
3. Nov 3, 2005

### Canuck156

Ok, got it now. Thanks.