A horizontal spring block system of mass M executes simple haormonic motion. When the block is passing through its equilibrium position, an object of mass m is put on it and the two move together. Find the new amplitude and frequency of vibration. Given, k is the spring constant of the system.

Explanation

To solve the problem, we need to analyze the horizontal spring-block system executing simple harmonic motion (SHM) and determine the new amplitude and frequency after an additional mass is placed on it.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions:**
- The system consists of a block of mass \( M \) attached to a spring with spring constant \( k \).
- The block is executing SHM, and when it passes through the equilibrium position, it has maximum kinetic energy.

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