Straight wooden rod of mass 4.0 kg, uniform cross-section 5 cm², and constant density 700kg has a very small mass 0.6 kg attached to its one end. The rod is partially submerged in water of density 1,000kg/m³.While in equilibrium, the rod floats in a vertical position with large part of it submerged. The rod is then pushed down by distance y_maxfrom equilibrium and released resulting in its oscillation neat the surface of the water.

(Assuming no drag forces are acting in this situation) and taking g to be 9.8 m/s²

A) Use the first principles to demonstrate that such system can be treated as Simple Harmonic Oscillator. (Full solution on paper)

B) Find the rod's period of oscillations to the nearest thousandth of a second.

( Enter this value into the answer box without units).

In addition to entering your final numerical answer into the box, make sure that you write your solution neatly starting with the clear diagram and all variables on it.

Solve this problem in detail on paper. Please annotate your solution -- make short comments/ arguments for steps you are making.