Two bar magnets placed together in a vibration magnetometer take 3 seconds for 1 vibration. If one magnet is reversed, the combination takes 4 seconds for 1 vibration. Find the ratio of their magnetic moments.

Explanation

To solve the problem, we need to analyze the behavior of two bar magnets in a vibration magnetometer under two different configurations. Let's break it down step by step.

### Step 1: Understand the Initial Setup
We have two bar magnets with magnetic moments \( m_1 \) and \( m_2 \). When placed together in the same direction, the total magnetic moment \( M \) is given by:
\[ M = m_1 + m_2 \]

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