A block of mass m hangs from a vertical spring of spring constant k. If it is displaced from its equilibrium position, find the time period of oscillations.

Explanation

To find the time period of oscillations for a block of mass \( m \) hanging from a vertical spring with spring constant \( k \), we can follow these steps:

### Step 1: Understand the Forces Acting on the Block
When the block is at rest (equilibrium position), the force exerted by the spring (spring force) must balance the weight of the block. The weight of the block is given by \( mg \), where \( g \) is the acceleration due to gravity.

### Step 2: Write the Force Balance Equation
At equilibrium, the spring force \( F_s \) is equal to the weight of the block:
\[
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