A large rectangular cube made of wood has the follow dimentions: a height, h = 2m, and an area od A = 0.25m^2. The wood that the cube is made of has a density of 800kg/m^3. The cube is then place vertically in water where it floats to rest. The density of the water is 1000kg/m^3. Then the cube is pushed down slightly (by a distance y) and released. The resulting motion is simple harmonic motion.    A) Determine the mass of the cube. B) Determine the depth,d, that the cube will float. C) If the cube is pushed further down under water by a distance, y, write an expression for the net force on the block in terms of: y,A,g,p. Where g=9.8m/s^2

A large rectangular cube made of wood has the follow dimentions: a height, h = 2m, and an area od A = 0.25m^2. The wood that the cube is made of has a density of 800kg/m^3. The cube is then place vertically in water where it floats to rest. The density of the water is 1000kg/m^3. Then the cube is pushed down slightly (by a distance y) and released. The resulting motion is simple harmonic motion. 

A) Determine the mass of the cube.

B) Determine the depth,d, that the cube will float.

C) If the cube is pushed further down under water by a distance, y, write an expression for the net force on the block in terms of: y,A,g,p. Where g=9.8m/s^2

D)Use the expression for the net forcee found in part C), and apply newton's second law (Fnet = ma) to the situation of the cube that is being pushed down slightly to derive an equation for the vertical accerlation (ay) (hint: dont forget to pick a positive direction) 

Compare your results from part D) to the equation for simple harmonic motion using this comparison, determine the value of w for this block in water and thus the oscillation frquency of the blockk floating in water.