Question

3. A wooden cube floats on water as shown in the figure. A small force is applied from the top pushing it down by a distance xo and then released. The block is observed to bob up and down. After 100 bobs, the amplitude dies down to 10% of the initial displacement xo Let A- Area of face, h- submerged depth and x-0 at the water surface (see Fig) wood block water a) Ignoring the small damping, show that the motion is simple harmonic for some time and show that oscillation frequency 0 (g /h) 17. (b) Show that the damping time b-1/ β is 43 times longer than the oscillation time το . (64 points). Hint: Recall the Archimedes Principle that the buoyancy force is equal to the mass of the water displaced.

Please don't forget Part B.

Answer 1

So 2 2)