A small compass needle of magnetic moment ‘M’ and moment of inertial ‘I’ is free to oscillate in a magnetic field ‘B’. It is slightly disturbed from its equilibrium position and then released. Show that it executes simple harmonic motion. Hence, write the expression for its time period.

Explanation

To show that a small compass needle of magnetic moment \( M \) and moment of inertia \( I \) executes simple harmonic motion (SHM) when slightly disturbed in a magnetic field \( B \), we can follow these steps:

### Step 1: Understanding the System
When the compass needle is in equilibrium, it aligns itself with the magnetic field. If it is slightly disturbed by an angle \( \theta \), it experiences a torque due to the magnetic field.

**Hint:** Consider the forces acting on the compass needle when it is displaced from equilibrium.

### Step 2: Torque Acting on the Needle
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