A cylindrical block of wood of mass M is floating n water with its axis vertica. It is depressed a little and then released. Show that the motion of the block is simple harmonic and find its frequency.

Explanation

To solve the problem of a cylindrical block of wood floating in water, we will show that the motion of the block is simple harmonic and find its frequency. Here’s a step-by-step solution:

### Step 1: Understand the Initial Conditions
The cylindrical block of wood is floating in water with its axis vertical. The block is in equilibrium when the buoyant force equals its weight.

### Step 2: Write the Expression for Buoyant Force
The buoyant force \( F_B \) acting on the block is given by Archimedes' principle:
\[
...