A cylindrical piece of cork of base area A and height h floats in a liquid of density `rho_(1)`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period
`T=2pisqrt((hrho)/(rho_(1)g))`

Explanation

To solve the problem of a cylindrical piece of cork floating in a liquid and oscillating up and down, we will follow these steps:

### Step 1: Understand the Initial Condition
When the cork is floating in the liquid, the buoyant force (FB) acting on it is equal to its weight (W). This can be expressed as:
\[ FB = W \]
Where:
- \( FB = \rho_1 \cdot V_{submerged} \cdot g \)
- \( W = \rho \cdot V_{cork} \cdot g \)
...