A block of mass m is suspended from the ceiling of a stationary standig elevator through a spring of spring constant k. Suddenly, the cable breaks and the elevator starts falling freely. Show that the bklock now executes a simple harmonic motion of amplitude `mg/k` in the elevator

Explanation

To solve the problem step by step, let's analyze the situation before and after the elevator cable breaks.

### Step 1: Analyze the initial equilibrium condition
When the elevator is stationary, the block of mass \( m \) is in equilibrium. The forces acting on the block are:
- The gravitational force acting downwards: \( F_g = mg \)
- The spring force acting upwards: \( F_s = kx \)

At equilibrium, these forces balance each other:
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