A smooth block of mass m is released from rest from a height h. It slides and compresses the spring of stiffness k. Find the maximum compression of the spring .
Taking block spring a system. Now external force is doing work on system and no non-conservative force is present. The mechanincal energy should be conserved.
`DeltaK+DeltaU=0`

Explanation

To solve the problem of finding the maximum compression of the spring when a block of mass \( m \) is released from a height \( h \) and compresses a spring of stiffness \( k \), we can use the principle of conservation of mechanical energy. Here’s the step-by-step solution:

### Step 1: Identify the energies involved
When the block is released from height \( h \), it has gravitational potential energy and no kinetic energy since it starts from rest. As it falls and compresses the spring, the gravitational potential energy is converted into kinetic energy and then into spring potential energy at maximum compression.

### Step 2: Write the expression for gravitational potential energy
The gravitational potential energy (U) at height \( h \) is given by:
\[
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