A uniform cylinder of height h, mass m and cross sectional area A is suspended vertically from a fixed point by a massless spring of force constant k, A beaker full of water is placed under the cylinder so that `1//4^(th)` of its volume is submerged in the water at equilibrium position. When the cylinder is given a small downward push and released, it starts oscillating vertically with small amplitude. Calculate the frequency of oscillation of the cylinder, Take, density of water =`rho`.

Explanation

To calculate the frequency of oscillation of the uniform cylinder suspended from a spring, we will follow these steps:

### Step 1: Understand the forces acting on the cylinder
When the cylinder is at equilibrium, the forces acting on it are:
- The spring force (upward) given by \( F_s = kx \), where \( x \) is the displacement from the equilibrium position.
- The buoyant force (upward) due to the displaced water, which can be calculated as \( F_b = V \rho g \), where \( V \) is the volume of the submerged part of the cylinder, \( \rho \) is the density of water, and \( g \) is the acceleration due to gravity.

### Step 2: Determine the volume of the submerged part of the cylinder
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