A block of mass m is suspended through a spring of spring constant k and is in equilibrium. A sharp blow gives the block an initial downward velocity v. How far below the equilibrium position, the block comes to an instantaneous rest?

Explanation

To solve the problem of how far below the equilibrium position the block comes to an instantaneous rest after being given an initial downward velocity \( v \), we can follow these steps:

### Step 1: Understand the forces acting on the block
When the block is in equilibrium, the downward gravitational force \( mg \) is balanced by the spring force \( kx \), where \( x \) is the extension of the spring from its natural length.

### Step 2: Determine the equilibrium position
At equilibrium, we have:
\[
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